On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote:
On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote:
On 2026-07-01 12:51, olcott wrote:
On 7/1/2026 1:45 PM, André G. Isaak wrote:
On 2026-07-01 12:15, dbush wrote:
On 7/1/2026 2:01 PM, olcott wrote:
The same thing as: "cats are animals" expressed in >>>>>>>>>>>>>> English has no English meaning in Chinese.
I didn't ask for an example. I asked for a definition of >>>>>>>>>>>>> what it mean for the truth value of a statement to not >>>>>>>>>>>>> exist in a formal system.
I'm actually not convinced that Olcott understands what a >>>>>>>>>>>> definition is. I've frequently asked him for definitions and >>>>>>>>>>>> he invariably responds with an example or an analogy
(assuming he responds at all). He doesn't get that examples >>>>>>>>>>>> don't take the place of definitions. Examples can be useful >>>>>>>>>>>> for clarifying definitions, but they aren't particularly >>>>>>>>>>>> useful on their own.
André
You want a definition look-it-up.
Until someone publishes an Olcott to Standard English
dictionary, this isn't really an option.
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
That claims what it means to have the truth value 'true' (or at >>>>>>>> least it would if you defined AtomicFacts in a coherent way). It >>>>>>>> doesn't in any way clarify what you think it means for something >>>>>>>> to not have a truth value.
André
When I define a term hundreds of times and you did
not bother to pay attention that is your mistake
and your fault.
You gave no such definition of what it means for the truth value
of a statement to not exist in a formal system.
A valid answer would look something like this:
"The truth value of a statement does not exist in a formal system >>>>>> when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ x) does not >>>> exist in Q", you mean "(∀ x, S(x) ≠ x) is unprovable in Q", which is >>>> commonly known.
So once again, you're saying the same thing as everyone else but
using different words.
Not really. It is normally thought of as undecidable
meaning that Q is incomplete meaning that Q is deficient.
False. It means that there are statements in the language of Q that
have *only* an infinite connection to the axioms of the system.
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H exists that meets
the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of instructions)
X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the
following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
directly
Sure and we could equally start with the requirement
to prove that there exists a natural number > 3 and < 2.
I really don't see how everyone did not immediately see
that the requirement for H to correctly report the halt
status of input D that does the opposite of whatever H
reports is a moronically stupid requirement within the
first five minutes that this requirement was made.
If it is true that makes it false.
is more like
the Liar Paradox. For HHH(DD)
If it is false that make is true.
Therefore is has always been fucking nonsense.
That it took humans more than five minutes to
see this conclusively proves how stupid they are.
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote:
On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote:
On 2026-07-01 12:51, olcott wrote:
On 7/1/2026 1:45 PM, André G. Isaak wrote:
On 2026-07-01 12:15, dbush wrote:
On 7/1/2026 2:01 PM, olcott wrote:
The same thing as: "cats are animals" expressed in >>>>>>>>>>>>>>> English has no English meaning in Chinese.
I didn't ask for an example. I asked for a definition of >>>>>>>>>>>>>> what it mean for the truth value of a statement to not >>>>>>>>>>>>>> exist in a formal system.
I'm actually not convinced that Olcott understands what a >>>>>>>>>>>>> definition is. I've frequently asked him for definitions >>>>>>>>>>>>> and he invariably responds with an example or an analogy >>>>>>>>>>>>> (assuming he responds at all). He doesn't get that examples >>>>>>>>>>>>> don't take the place of definitions. Examples can be useful >>>>>>>>>>>>> for clarifying definitions, but they aren't particularly >>>>>>>>>>>>> useful on their own.
André
You want a definition look-it-up.
Until someone publishes an Olcott to Standard English
dictionary, this isn't really an option.
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
That claims what it means to have the truth value 'true' (or at >>>>>>>>> least it would if you defined AtomicFacts in a coherent way). >>>>>>>>> It doesn't in any way clarify what you think it means for
something to not have a truth value.
André
When I define a term hundreds of times and you did
not bother to pay attention that is your mistake
and your fault.
You gave no such definition of what it means for the truth value >>>>>>> of a statement to not exist in a formal system.
A valid answer would look something like this:
"The truth value of a statement does not exist in a formal system >>>>>>> when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ x) does not >>>>> exist in Q", you mean "(∀ x, S(x) ≠ x) is unprovable in Q", which >>>>> is commonly known.
So once again, you're saying the same thing as everyone else but
using different words.
Not really. It is normally thought of as undecidable
meaning that Q is incomplete meaning that Q is deficient.
False. It means that there are statements in the language of Q that
have *only* an infinite connection to the axioms of the system.
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H exists that
meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of instructions)
X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the
following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
directly
Sure and we could equally start with the requirement
to prove that there exists a natural number > 3 and < 2.
I really don't see how everyone did not immediately see
that the requirement for H to correctly report the halt
status of input D that does the opposite of whatever H
reports is a moronically stupid requirement within the
first five minutes that this requirement was made.
In other words, you don't understand that if this was algorithm H:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote:
On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote:
On 2026-07-01 12:51, olcott wrote:
On 7/1/2026 1:45 PM, André G. Isaak wrote:
On 2026-07-01 12:15, dbush wrote:
On 7/1/2026 2:01 PM, olcott wrote:
The same thing as: "cats are animals" expressed in >>>>>>>>>>>>>>>> English has no English meaning in Chinese.
I didn't ask for an example. I asked for a definition of >>>>>>>>>>>>>>> what it mean for the truth value of a statement to not >>>>>>>>>>>>>>> exist in a formal system.
I'm actually not convinced that Olcott understands what a >>>>>>>>>>>>>> definition is. I've frequently asked him for definitions >>>>>>>>>>>>>> and he invariably responds with an example or an analogy >>>>>>>>>>>>>> (assuming he responds at all). He doesn't get that >>>>>>>>>>>>>> examples don't take the place of definitions. Examples can >>>>>>>>>>>>>> be useful for clarifying definitions, but they aren't >>>>>>>>>>>>>> particularly useful on their own.
André
You want a definition look-it-up.
Until someone publishes an Olcott to Standard English >>>>>>>>>>>> dictionary, this isn't really an option.
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
That claims what it means to have the truth value 'true' (or >>>>>>>>>> at least it would if you defined AtomicFacts in a coherent >>>>>>>>>> way). It doesn't in any way clarify what you think it means >>>>>>>>>> for something to not have a truth value.
André
When I define a term hundreds of times and you did
not bother to pay attention that is your mistake
and your fault.
You gave no such definition of what it means for the truth value >>>>>>>> of a statement to not exist in a formal system.
A valid answer would look something like this:
"The truth value of a statement does not exist in a formal
system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ x) does >>>>>> not exist in Q", you mean "(∀ x, S(x) ≠ x) is unprovable in Q", >>>>>> which is commonly known.
So once again, you're saying the same thing as everyone else but
using different words.
Not really. It is normally thought of as undecidable
meaning that Q is incomplete meaning that Q is deficient.
False. It means that there are statements in the language of Q that >>>> have *only* an infinite connection to the axioms of the system.
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H exists that
meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of
instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes
the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
directly
Sure and we could equally start with the requirement
to prove that there exists a natural number > 3 and < 2.
I really don't see how everyone did not immediately see
that the requirement for H to correctly report the halt
status of input D that does the opposite of whatever H
reports is a moronically stupid requirement within the
first five minutes that this requirement was made.
In other words, you don't understand that if this was algorithm H:
I spent 10,000 hours on it over 22 years.
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote:
On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote:
On 2026-07-01 12:51, olcott wrote:
On 7/1/2026 1:45 PM, André G. Isaak wrote:
On 2026-07-01 12:15, dbush wrote:
On 7/1/2026 2:01 PM, olcott wrote:
The same thing as: "cats are animals" expressed in >>>>>>>>>>>>>>>>> English has no English meaning in Chinese.
I didn't ask for an example. I asked for a definition >>>>>>>>>>>>>>>> of what it mean for the truth value of a statement to >>>>>>>>>>>>>>>> not exist in a formal system.
I'm actually not convinced that Olcott understands what a >>>>>>>>>>>>>>> definition is. I've frequently asked him for definitions >>>>>>>>>>>>>>> and he invariably responds with an example or an analogy >>>>>>>>>>>>>>> (assuming he responds at all). He doesn't get that >>>>>>>>>>>>>>> examples don't take the place of definitions. Examples >>>>>>>>>>>>>>> can be useful for clarifying definitions, but they aren't >>>>>>>>>>>>>>> particularly useful on their own.
André
You want a definition look-it-up.
Until someone publishes an Olcott to Standard English >>>>>>>>>>>>> dictionary, this isn't really an option.
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
That claims what it means to have the truth value 'true' (or >>>>>>>>>>> at least it would if you defined AtomicFacts in a coherent >>>>>>>>>>> way). It doesn't in any way clarify what you think it means >>>>>>>>>>> for something to not have a truth value.
André
When I define a term hundreds of times and you did
not bother to pay attention that is your mistake
and your fault.
You gave no such definition of what it means for the truth
value of a statement to not exist in a formal system.
A valid answer would look something like this:
"The truth value of a statement does not exist in a formal
system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ x) does >>>>>>> not exist in Q", you mean "(∀ x, S(x) ≠ x) is unprovable in Q", >>>>>>> which is commonly known.
So once again, you're saying the same thing as everyone else but >>>>>>> using different words.
Not really. It is normally thought of as undecidable
meaning that Q is incomplete meaning that Q is deficient.
False. It means that there are statements in the language of Q
that have *only* an infinite connection to the axioms of the system. >>>>>
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H exists that
meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of
instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes
the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
directly
Sure and we could equally start with the requirement
to prove that there exists a natural number > 3 and < 2.
I really don't see how everyone did not immediately see
that the requirement for H to correctly report the halt
status of input D that does the opposite of whatever H
reports is a moronically stupid requirement within the
first five minutes that this requirement was made.
In other words, you don't understand that if this was algorithm H:
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote:
On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote:
On 2026-07-01 12:51, olcott wrote:
On 7/1/2026 1:45 PM, André G. Isaak wrote:
On 2026-07-01 12:15, dbush wrote:
On 7/1/2026 2:01 PM, olcott wrote:
The same thing as: "cats are animals" expressed in >>>>>>>>>>>>>>>>>> English has no English meaning in Chinese.
I didn't ask for an example. I asked for a definition >>>>>>>>>>>>>>>>> of what it mean for the truth value of a statement to >>>>>>>>>>>>>>>>> not exist in a formal system.
I'm actually not convinced that Olcott understands what >>>>>>>>>>>>>>>> a definition is. I've frequently asked him for >>>>>>>>>>>>>>>> definitions and he invariably responds with an example >>>>>>>>>>>>>>>> or an analogy (assuming he responds at all). He doesn't >>>>>>>>>>>>>>>> get that examples don't take the place of definitions. >>>>>>>>>>>>>>>> Examples can be useful for clarifying definitions, but >>>>>>>>>>>>>>>> they aren't particularly useful on their own.
André
You want a definition look-it-up.
Until someone publishes an Olcott to Standard English >>>>>>>>>>>>>> dictionary, this isn't really an option.
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott
2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
That claims what it means to have the truth value 'true' (or >>>>>>>>>>>> at least it would if you defined AtomicFacts in a coherent >>>>>>>>>>>> way). It doesn't in any way clarify what you think it means >>>>>>>>>>>> for something to not have a truth value.
André
When I define a term hundreds of times and you did
not bother to pay attention that is your mistake
and your fault.
You gave no such definition of what it means for the truth >>>>>>>>>> value of a statement to not exist in a formal system.
A valid answer would look something like this:
"The truth value of a statement does not exist in a formal >>>>>>>>>> system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ x) does >>>>>>>> not exist in Q", you mean "(∀ x, S(x) ≠ x) is unprovable in Q", >>>>>>>> which is commonly known.
So once again, you're saying the same thing as everyone else but >>>>>>>> using different words.
Not really. It is normally thought of as undecidable
meaning that Q is incomplete meaning that Q is deficient.
False. It means that there are statements in the language of Q
that have *only* an infinite connection to the axioms of the system. >>>>>>
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H exists that
meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of
instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes >>>>>> the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly >>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed >>>>>> directly
Sure and we could equally start with the requirement
to prove that there exists a natural number > 3 and < 2.
I really don't see how everyone did not immediately see
that the requirement for H to correctly report the halt
status of input D that does the opposite of whatever H
reports is a moronically stupid requirement within the
first five minutes that this requirement was made.
In other words, you don't understand that if this was algorithm H:
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote:
On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote:
On 2026-07-01 12:51, olcott wrote:
On 7/1/2026 1:45 PM, André G. Isaak wrote:
On 2026-07-01 12:15, dbush wrote:
On 7/1/2026 2:01 PM, olcott wrote:
The same thing as: "cats are animals" expressed in >>>>>>>>>>>>>>>>>>> English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>I didn't ask for an example. I asked for a definition >>>>>>>>>>>>>>>>>> of what it mean for the truth value of a statement to >>>>>>>>>>>>>>>>>> not exist in a formal system.
I'm actually not convinced that Olcott understands what >>>>>>>>>>>>>>>>> a definition is. I've frequently asked him for >>>>>>>>>>>>>>>>> definitions and he invariably responds with an example >>>>>>>>>>>>>>>>> or an analogy (assuming he responds at all). He doesn't >>>>>>>>>>>>>>>>> get that examples don't take the place of definitions. >>>>>>>>>>>>>>>>> Examples can be useful for clarifying definitions, but >>>>>>>>>>>>>>>>> they aren't particularly useful on their own. >>>>>>>>>>>>>>>>>
André
You want a definition look-it-up.
Until someone publishes an Olcott to Standard English >>>>>>>>>>>>>>> dictionary, this isn't really an option.
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott
2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
That claims what it means to have the truth value 'true' >>>>>>>>>>>>> (or at least it would if you defined AtomicFacts in a >>>>>>>>>>>>> coherent way). It doesn't in any way clarify what you think >>>>>>>>>>>>> it means for something to not have a truth value.
André
When I define a term hundreds of times and you did
not bother to pay attention that is your mistake
and your fault.
You gave no such definition of what it means for the truth >>>>>>>>>>> value of a statement to not exist in a formal system.
A valid answer would look something like this:
"The truth value of a statement does not exist in a formal >>>>>>>>>>> system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ x) does >>>>>>>>> not exist in Q", you mean "(∀ x, S(x) ≠ x) is unprovable in Q", >>>>>>>>> which is commonly known.
So once again, you're saying the same thing as everyone else >>>>>>>>> but using different words.
Not really. It is normally thought of as undecidable
meaning that Q is incomplete meaning that Q is deficient.
False. It means that there are statements in the language of Q >>>>>>> that have *only* an infinite connection to the axioms of the system. >>>>>>>
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H exists that >>>>>>> meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of
instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes >>>>>>> the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly >>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed >>>>>>> directly
Sure and we could equally start with the requirement
to prove that there exists a natural number > 3 and < 2.
I really don't see how everyone did not immediately see
that the requirement for H to correctly report the halt
status of input D that does the opposite of whatever H
reports is a moronically stupid requirement within the
first five minutes that this requirement was made.
In other words, you don't understand that if this was algorithm H:
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting problem for the
last 22 years.
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote:
On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote:
On 2026-07-01 12:51, olcott wrote:
On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote:
On 7/1/2026 2:01 PM, olcott wrote:I'm actually not convinced that Olcott understands >>>>>>>>>>>>>>>>>> what a definition is. I've frequently asked him for >>>>>>>>>>>>>>>>>> definitions and he invariably responds with an example >>>>>>>>>>>>>>>>>> or an analogy (assuming he responds at all). He >>>>>>>>>>>>>>>>>> doesn't get that examples don't take the place of >>>>>>>>>>>>>>>>>> definitions. Examples can be useful for clarifying >>>>>>>>>>>>>>>>>> definitions, but they aren't particularly useful on >>>>>>>>>>>>>>>>>> their own.
The same thing as: "cats are animals" expressed in >>>>>>>>>>>>>>>>>>>> English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>I didn't ask for an example. I asked for a >>>>>>>>>>>>>>>>>>> definition of what it mean for the truth value of a >>>>>>>>>>>>>>>>>>> statement to not exist in a formal system. >>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up.
Until someone publishes an Olcott to Standard English >>>>>>>>>>>>>>>> dictionary, this isn't really an option.
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright >>>>>>>>>>>>>>> Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
That claims what it means to have the truth value >>>>>>>>>>>>>> 'true' (or at least it would if you defined AtomicFacts in >>>>>>>>>>>>>> a coherent way). It doesn't in any way clarify what you >>>>>>>>>>>>>> think it means for something to not have a truth value. >>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did
not bother to pay attention that is your mistake
and your fault.
You gave no such definition of what it means for the truth >>>>>>>>>>>> value of a statement to not exist in a formal system.
A valid answer would look something like this:
"The truth value of a statement does not exist in a formal >>>>>>>>>>>> system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ x) >>>>>>>>>> does not exist in Q", you mean "(∀ x, S(x) ≠ x) is unprovable >>>>>>>>>> in Q", which is commonly known.
So once again, you're saying the same thing as everyone else >>>>>>>>>> but using different words.
Not really. It is normally thought of as undecidable
meaning that Q is incomplete meaning that Q is deficient.
False. It means that there are statements in the language of Q >>>>>>>> that have *only* an infinite connection to the axioms of the
system.
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H exists that >>>>>>>> meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of
instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that
computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly >>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when
executed directly
Sure and we could equally start with the requirement
to prove that there exists a natural number > 3 and < 2.
I really don't see how everyone did not immediately see
that the requirement for H to correctly report the halt
status of input D that does the opposite of whatever H
reports is a moronically stupid requirement within the
first five minutes that this requirement was made.
In other words, you don't understand that if this was algorithm H: >>>>>>
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting problem for the
last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote:
On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote:
On 2026-07-01 12:51, olcott wrote:
On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote:
On 7/1/2026 2:01 PM, olcott wrote:I'm actually not convinced that Olcott understands >>>>>>>>>>>>>>>>>> what a definition is. I've frequently asked him for >>>>>>>>>>>>>>>>>> definitions and he invariably responds with an example >>>>>>>>>>>>>>>>>> or an analogy (assuming he responds at all). He >>>>>>>>>>>>>>>>>> doesn't get that examples don't take the place of >>>>>>>>>>>>>>>>>> definitions. Examples can be useful for clarifying >>>>>>>>>>>>>>>>>> definitions, but they aren't particularly useful on >>>>>>>>>>>>>>>>>> their own.
The same thing as: "cats are animals" expressed in >>>>>>>>>>>>>>>>>>>> English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>I didn't ask for an example. I asked for a >>>>>>>>>>>>>>>>>>> definition of what it mean for the truth value of a >>>>>>>>>>>>>>>>>>> statement to not exist in a formal system. >>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up.
Until someone publishes an Olcott to Standard English >>>>>>>>>>>>>>>> dictionary, this isn't really an option.
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright >>>>>>>>>>>>>>> Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
That claims what it means to have the truth value >>>>>>>>>>>>>> 'true' (or at least it would if you defined AtomicFacts in >>>>>>>>>>>>>> a coherent way). It doesn't in any way clarify what you >>>>>>>>>>>>>> think it means for something to not have a truth value. >>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did
not bother to pay attention that is your mistake
and your fault.
You gave no such definition of what it means for the truth >>>>>>>>>>>> value of a statement to not exist in a formal system.
A valid answer would look something like this:
"The truth value of a statement does not exist in a formal >>>>>>>>>>>> system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ x) >>>>>>>>>> does not exist in Q", you mean "(∀ x, S(x) ≠ x) is unprovable >>>>>>>>>> in Q", which is commonly known.
So once again, you're saying the same thing as everyone else >>>>>>>>>> but using different words.
Not really. It is normally thought of as undecidable
meaning that Q is incomplete meaning that Q is deficient.
False. It means that there are statements in the language of Q >>>>>>>> that have *only* an infinite connection to the axioms of the
system.
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H exists that >>>>>>>> meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of
instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that
computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly >>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when
executed directly
Sure and we could equally start with the requirement
to prove that there exists a natural number > 3 and < 2.
I really don't see how everyone did not immediately see
that the requirement for H to correctly report the halt
status of input D that does the opposite of whatever H
reports is a moronically stupid requirement within the
first five minutes that this requirement was made.
In other words, you don't understand that if this was algorithm H: >>>>>>
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting problem for the
last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote:
On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote:That claims what it means to have the truth value 'true' >>>>>>>>>>>>>>> (or at least it would if you defined AtomicFacts in a >>>>>>>>>>>>>>> coherent way). It doesn't in any way clarify what you >>>>>>>>>>>>>>> think it means for something to not have a truth value. >>>>>>>>>>>>>>>
On 2026-07-01 12:51, olcott wrote:
On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote:
On 7/1/2026 2:01 PM, olcott wrote:I'm actually not convinced that Olcott understands >>>>>>>>>>>>>>>>>>> what a definition is. I've frequently asked him for >>>>>>>>>>>>>>>>>>> definitions and he invariably responds with an >>>>>>>>>>>>>>>>>>> example or an analogy (assuming he responds at all). >>>>>>>>>>>>>>>>>>> He doesn't get that examples don't take the place of >>>>>>>>>>>>>>>>>>> definitions. Examples can be useful for clarifying >>>>>>>>>>>>>>>>>>> definitions, but they aren't particularly useful on >>>>>>>>>>>>>>>>>>> their own.
The same thing as: "cats are animals" expressed in >>>>>>>>>>>>>>>>>>>>> English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>I didn't ask for an example. I asked for a >>>>>>>>>>>>>>>>>>>> definition of what it mean for the truth value of a >>>>>>>>>>>>>>>>>>>> statement to not exist in a formal system. >>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up.
Until someone publishes an Olcott to Standard English >>>>>>>>>>>>>>>>> dictionary, this isn't really an option.
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright >>>>>>>>>>>>>>>> Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did >>>>>>>>>>>>>> not bother to pay attention that is your mistake
and your fault.
You gave no such definition of what it means for the truth >>>>>>>>>>>>> value of a statement to not exist in a formal system. >>>>>>>>>>>>>
A valid answer would look something like this:
"The truth value of a statement does not exist in a formal >>>>>>>>>>>>> system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ x) >>>>>>>>>>> does not exist in Q", you mean "(∀ x, S(x) ≠ x) is unprovable >>>>>>>>>>> in Q", which is commonly known.
So once again, you're saying the same thing as everyone else >>>>>>>>>>> but using different words.
Not really. It is normally thought of as undecidable
meaning that Q is incomplete meaning that Q is deficient.
False. It means that there are statements in the language of Q >>>>>>>>> that have *only* an infinite connection to the axioms of the >>>>>>>>> system.
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H exists >>>>>>>>> that meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of
instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that
computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly >>>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when
executed directly
Sure and we could equally start with the requirement
to prove that there exists a natural number > 3 and < 2.
I really don't see how everyone did not immediately see
that the requirement for H to correctly report the halt
status of input D that does the opposite of whatever H
reports is a moronically stupid requirement within the
first five minutes that this requirement was made.
In other words, you don't understand that if this was algorithm H: >>>>>>>
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting problem for the
last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
And algorithm H is wrong about algorithm D because algorithm D contains
a copy of algorithm H and does the opposite.
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:False. It means that there are statements in the language of >>>>>>>>>> Q that have *only* an infinite connection to the axioms of the >>>>>>>>>> system.
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote:
On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote:That claims what it means to have the truth value >>>>>>>>>>>>>>>> 'true' (or at least it would if you defined AtomicFacts >>>>>>>>>>>>>>>> in a coherent way). It doesn't in any way clarify what >>>>>>>>>>>>>>>> you think it means for something to not have a truth value. >>>>>>>>>>>>>>>>
On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote:
On 7/1/2026 2:01 PM, olcott wrote:I'm actually not convinced that Olcott understands >>>>>>>>>>>>>>>>>>>> what a definition is. I've frequently asked him for >>>>>>>>>>>>>>>>>>>> definitions and he invariably responds with an >>>>>>>>>>>>>>>>>>>> example or an analogy (assuming he responds at all). >>>>>>>>>>>>>>>>>>>> He doesn't get that examples don't take the place of >>>>>>>>>>>>>>>>>>>> definitions. Examples can be useful for clarifying >>>>>>>>>>>>>>>>>>>> definitions, but they aren't particularly useful on >>>>>>>>>>>>>>>>>>>> their own.
The same thing as: "cats are animals" expressed in >>>>>>>>>>>>>>>>>>>>>> English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>I didn't ask for an example. I asked for a >>>>>>>>>>>>>>>>>>>>> definition of what it mean for the truth value of a >>>>>>>>>>>>>>>>>>>>> statement to not exist in a formal system. >>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up.
Until someone publishes an Olcott to Standard English >>>>>>>>>>>>>>>>>> dictionary, this isn't really an option.
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright
Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did >>>>>>>>>>>>>>> not bother to pay attention that is your mistake >>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means for the truth >>>>>>>>>>>>>> value of a statement to not exist in a formal system. >>>>>>>>>>>>>>
A valid answer would look something like this:
"The truth value of a statement does not exist in a formal >>>>>>>>>>>>>> system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ x) >>>>>>>>>>>> does not exist in Q", you mean "(∀ x, S(x) ≠ x) is >>>>>>>>>>>> unprovable in Q", which is commonly known.
So once again, you're saying the same thing as everyone else >>>>>>>>>>>> but using different words.
Not really. It is normally thought of as undecidable
meaning that Q is incomplete meaning that Q is deficient. >>>>>>>>>>
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H exists >>>>>>>>>> that meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of
instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that
computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed >>>>>>>>>> directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when
executed directly
Sure and we could equally start with the requirement
to prove that there exists a natural number > 3 and < 2.
I really don't see how everyone did not immediately see
that the requirement for H to correctly report the halt
status of input D that does the opposite of whatever H
reports is a moronically stupid requirement within the
first five minutes that this requirement was made.
In other words, you don't understand that if this was algorithm H: >>>>>>>>
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting problem for
the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
And algorithm H is wrong about algorithm D because algorithm D
contains a copy of algorithm H and does the opposite.
You just don't know jack shit dufus.
I have been a professional C programmer since 1986.
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:False. It means that there are statements in the language of >>>>>>>>>>> Q that have *only* an infinite connection to the axioms of >>>>>>>>>>> the system.
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote:
On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote:That claims what it means to have the truth value >>>>>>>>>>>>>>>>> 'true' (or at least it would if you defined AtomicFacts >>>>>>>>>>>>>>>>> in a coherent way). It doesn't in any way clarify what >>>>>>>>>>>>>>>>> you think it means for something to not have a truth >>>>>>>>>>>>>>>>> value.
On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote:
On 7/1/2026 2:01 PM, olcott wrote:I'm actually not convinced that Olcott understands >>>>>>>>>>>>>>>>>>>>> what a definition is. I've frequently asked him for >>>>>>>>>>>>>>>>>>>>> definitions and he invariably responds with an >>>>>>>>>>>>>>>>>>>>> example or an analogy (assuming he responds at >>>>>>>>>>>>>>>>>>>>> all). He doesn't get that examples don't take the >>>>>>>>>>>>>>>>>>>>> place of definitions. Examples can be useful for >>>>>>>>>>>>>>>>>>>>> clarifying definitions, but they aren't >>>>>>>>>>>>>>>>>>>>> particularly useful on their own.
The same thing as: "cats are animals" expressed in >>>>>>>>>>>>>>>>>>>>>>> English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>I didn't ask for an example. I asked for a >>>>>>>>>>>>>>>>>>>>>> definition of what it mean for the truth value of >>>>>>>>>>>>>>>>>>>>>> a statement to not exist in a formal system. >>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up.
Until someone publishes an Olcott to Standard English >>>>>>>>>>>>>>>>>>> dictionary, this isn't really an option. >>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright
Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did >>>>>>>>>>>>>>>> not bother to pay attention that is your mistake >>>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means for the >>>>>>>>>>>>>>> truth value of a statement to not exist in a formal system. >>>>>>>>>>>>>>>
A valid answer would look something like this:
"The truth value of a statement does not exist in a >>>>>>>>>>>>>>> formal system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ x) >>>>>>>>>>>>> does not exist in Q", you mean "(∀ x, S(x) ≠ x) is >>>>>>>>>>>>> unprovable in Q", which is commonly known.
So once again, you're saying the same thing as everyone >>>>>>>>>>>>> else but using different words.
Not really. It is normally thought of as undecidable
meaning that Q is incomplete meaning that Q is deficient. >>>>>>>>>>>
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H exists >>>>>>>>>>> that meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of >>>>>>>>>>> instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that >>>>>>>>>>> computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed >>>>>>>>>>> directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when >>>>>>>>>>> executed directly
Sure and we could equally start with the requirement
to prove that there exists a natural number > 3 and < 2.
I really don't see how everyone did not immediately see
that the requirement for H to correctly report the halt
status of input D that does the opposite of whatever H
reports is a moronically stupid requirement within the
first five minutes that this requirement was made.
In other words, you don't understand that if this was algorithm H: >>>>>>>>>
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting problem for
the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
And algorithm H is wrong about algorithm D because algorithm D
contains a copy of algorithm H and does the opposite.
You just don't know jack shit dufus.
I have been a professional C programmer since 1986.
Says the person that just demonstrated that they don't know the
difference between an algorithm and a C function.
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:
On 27/06/2026 17:50, polcott wrote:
On 6/27/2026 1:53 AM, Tristan Wibberley wrote:
On 20/06/2026 18:32, olcott wrote:
A proof theoretic expression is known to be true when
it is fully grounded in its atomic base. Only two
PTS semantics researchers deal with true Dag Prawitz
is the one that began this. PTS previously only dealt
with semantic meaning and never got around to true(L,x).
That's surprising, disregard for axioms?
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is
ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete
it means that ~∃x x=S(x) is out-of-scope for Q.
It comes close. If ∃x x=S(x) is likewise "ungrounded" but in the >>>>>>>> language of Q then ~∃x x=S(x) and ∃x x=S(x) are both undecidable >>>>>>>> and Q is incomplete, bcause that is what the words mean.
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do. Incomplete only counts relative to
its intended purpose. A car without an engine is
incomplete relative to a mode of transportation.
Irrelevant. The definition of completeness
It a misnomer and does not literally mean (as it implies)
that something is missing that could be added to make
it complete.
It does mean that something is missing that could be added to
enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined to do.
When Q is extended to become PA it stops being Q and becomes PA.
However, there are theories that reamain incomplete even when
more postolates are added, as long as there is a way to know
which sentences are included in the added postulates. Important
examples include Peano arithmetic and ZFC set theory.
Base-Extension Semantics (B-eS) seems to be essentially a cheat.
When we ask what is grounded in an atomic base of Q and we
add axioms to Q to become PA we cheated in that we changed
the original question rather than answered it.
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:False. It means that there are statements in the language >>>>>>>>>>>> of Q that have *only* an infinite connection to the axioms >>>>>>>>>>>> of the system.
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote:That claims what it means to have the truth value >>>>>>>>>>>>>>>>>> 'true' (or at least it would if you defined >>>>>>>>>>>>>>>>>> AtomicFacts in a coherent way). It doesn't in any way >>>>>>>>>>>>>>>>>> clarify what you think it means for something to not >>>>>>>>>>>>>>>>>> have a truth value.
On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>
I'm actually not convinced that Olcott understands >>>>>>>>>>>>>>>>>>>>>> what a definition is. I've frequently asked him >>>>>>>>>>>>>>>>>>>>>> for definitions and he invariably responds with an >>>>>>>>>>>>>>>>>>>>>> example or an analogy (assuming he responds at >>>>>>>>>>>>>>>>>>>>>> all). He doesn't get that examples don't take the >>>>>>>>>>>>>>>>>>>>>> place of definitions. Examples can be useful for >>>>>>>>>>>>>>>>>>>>>> clarifying definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>> particularly useful on their own.The same thing as: "cats are animals" expressed in >>>>>>>>>>>>>>>>>>>>>>>> English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>I didn't ask for an example. I asked for a >>>>>>>>>>>>>>>>>>>>>>> definition of what it mean for the truth value of >>>>>>>>>>>>>>>>>>>>>>> a statement to not exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up.
Until someone publishes an Olcott to Standard >>>>>>>>>>>>>>>>>>>> English dictionary, this isn't really an option. >>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright
Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did >>>>>>>>>>>>>>>>> not bother to pay attention that is your mistake >>>>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means for the >>>>>>>>>>>>>>>> truth value of a statement to not exist in a formal system. >>>>>>>>>>>>>>>>
A valid answer would look something like this: >>>>>>>>>>>>>>>>
"The truth value of a statement does not exist in a >>>>>>>>>>>>>>>> formal system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ x) >>>>>>>>>>>>>> does not exist in Q", you mean "(∀ x, S(x) ≠ x) is >>>>>>>>>>>>>> unprovable in Q", which is commonly known.
So once again, you're saying the same thing as everyone >>>>>>>>>>>>>> else but using different words.
Not really. It is normally thought of as undecidable >>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is deficient. >>>>>>>>>>>>
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H exists >>>>>>>>>>>> that meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of >>>>>>>>>>>> instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that >>>>>>>>>>>> computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed >>>>>>>>>>>> directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when >>>>>>>>>>>> executed directly
Sure and we could equally start with the requirement
to prove that there exists a natural number > 3 and < 2. >>>>>>>>>>>
I really don't see how everyone did not immediately see
that the requirement for H to correctly report the halt
status of input D that does the opposite of whatever H
reports is a moronically stupid requirement within the
first five minutes that this requirement was made.
In other words, you don't understand that if this was
algorithm H:
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting problem for >>>>>> the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
And algorithm H is wrong about algorithm D because algorithm D
contains a copy of algorithm H and does the opposite.
You just don't know jack shit dufus.
I have been a professional C programmer since 1986.
Says the person that just demonstrated that they don't know the
difference between an algorithm and a C function.
Back to being ignored for trolling again.
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:
On 27/06/2026 17:50, polcott wrote:
On 6/27/2026 1:53 AM, Tristan Wibberley wrote:
On 20/06/2026 18:32, olcott wrote:
A proof theoretic expression is known to be true whenThat's surprising, disregard for axioms?
it is fully grounded in its atomic base. Only two
PTS semantics researchers deal with true Dag Prawitz
is the one that began this. PTS previously only dealt
with semantic meaning and never got around to true(L,x). >>>>>>>>>>>
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is
ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete
it means that ~∃x x=S(x) is out-of-scope for Q.
It comes close. If ∃x x=S(x) is likewise "ungrounded" but in the >>>>>>>>> language of Q then ~∃x x=S(x) and ∃x x=S(x) are both undecidable >>>>>>>>> and Q is incomplete, bcause that is what the words mean.
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do. Incomplete only counts relative to
its intended purpose. A car without an engine is
incomplete relative to a mode of transportation.
Irrelevant. The definition of completeness
It a misnomer and does not literally mean (as it implies)
that something is missing that could be added to make
it complete.
It does mean that something is missing that could be added to
enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined to do.
When Q is extended to become PA it stops being Q and becomes PA.
However, there are theories that reamain incomplete even when
more postolates are added, as long as there is a way to know
which sentences are included in the added postulates. Important
examples include Peano arithmetic and ZFC set theory.
Base-Extension Semantics (B-eS) seems to be essentially a cheat.
When we ask what is grounded in an atomic base of Q and we
add axioms to Q to become PA we cheated in that we changed
the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial answer
rather than no answer at all. Of course Q with any additional
postulate is not Q but if the additional postulates are true about
natural numbers then the strengthened theory is still a theory of
natural numbers. PA is one such strengthened Q but still incomplete
and can be strengthened further.
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:False. It means that there are statements in the language >>>>>>>>>>>>> of Q that have *only* an infinite connection to the axioms >>>>>>>>>>>>> of the system.
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote:That claims what it means to have the truth value >>>>>>>>>>>>>>>>>>> 'true' (or at least it would if you defined >>>>>>>>>>>>>>>>>>> AtomicFacts in a coherent way). It doesn't in any way >>>>>>>>>>>>>>>>>>> clarify what you think it means for something to not >>>>>>>>>>>>>>>>>>> have a truth value.
On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>
I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've frequently >>>>>>>>>>>>>>>>>>>>>>> asked him for definitions and he invariably >>>>>>>>>>>>>>>>>>>>>>> responds with an example or an analogy (assuming >>>>>>>>>>>>>>>>>>>>>>> he responds at all). He doesn't get that examples >>>>>>>>>>>>>>>>>>>>>>> don't take the place of definitions. Examples can >>>>>>>>>>>>>>>>>>>>>>> be useful for clarifying definitions, but they >>>>>>>>>>>>>>>>>>>>>>> aren't particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are animals" expressed in >>>>>>>>>>>>>>>>>>>>>>>>> English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>I didn't ask for an example. I asked for a >>>>>>>>>>>>>>>>>>>>>>>> definition of what it mean for the truth value >>>>>>>>>>>>>>>>>>>>>>>> of a statement to not exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up.
Until someone publishes an Olcott to Standard >>>>>>>>>>>>>>>>>>>>> English dictionary, this isn't really an option. >>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright
Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did >>>>>>>>>>>>>>>>>> not bother to pay attention that is your mistake >>>>>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means for the >>>>>>>>>>>>>>>>> truth value of a statement to not exist in a formal >>>>>>>>>>>>>>>>> system.
A valid answer would look something like this: >>>>>>>>>>>>>>>>>
"The truth value of a statement does not exist in a >>>>>>>>>>>>>>>>> formal system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ >>>>>>>>>>>>>>> x) does not exist in Q", you mean "(∀ x, S(x) ≠ x) is >>>>>>>>>>>>>>> unprovable in Q", which is commonly known.
So once again, you're saying the same thing as everyone >>>>>>>>>>>>>>> else but using different words.
Not really. It is normally thought of as undecidable >>>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is deficient. >>>>>>>>>>>>>
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H exists >>>>>>>>>>>>> that meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of >>>>>>>>>>>>> instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that >>>>>>>>>>>>> computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed >>>>>>>>>>>>> directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when >>>>>>>>>>>>> executed directly
Sure and we could equally start with the requirement
to prove that there exists a natural number > 3 and < 2. >>>>>>>>>>>>
I really don't see how everyone did not immediately see >>>>>>>>>>>> that the requirement for H to correctly report the halt >>>>>>>>>>>> status of input D that does the opposite of whatever H >>>>>>>>>>>> reports is a moronically stupid requirement within the >>>>>>>>>>>> first five minutes that this requirement was made.
In other words, you don't understand that if this was
algorithm H:
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting problem for >>>>>>> the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
And algorithm H is wrong about algorithm D because algorithm D
contains a copy of algorithm H and does the opposite.
You just don't know jack shit dufus.
I have been a professional C programmer since 1986.
Says the person that just demonstrated that they don't know the
difference between an algorithm and a C function.
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored by everone.
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:False. It means that there are statements in the language >>>>>>>>>>>>>> of Q that have *only* an infinite connection to the axioms >>>>>>>>>>>>>> of the system.
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>That claims what it means to have the truth value >>>>>>>>>>>>>>>>>>>> 'true' (or at least it would if you defined >>>>>>>>>>>>>>>>>>>> AtomicFacts in a coherent way). It doesn't in any >>>>>>>>>>>>>>>>>>>> way clarify what you think it means for something to >>>>>>>>>>>>>>>>>>>> not have a truth value.
Until someone publishes an Olcott to Standard >>>>>>>>>>>>>>>>>>>>>> English dictionary, this isn't really an option. >>>>>>>>>>>>>>>>>>>>>>I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions and he >>>>>>>>>>>>>>>>>>>>>>>> invariably responds with an example or an >>>>>>>>>>>>>>>>>>>>>>>> analogy (assuming he responds at all). He >>>>>>>>>>>>>>>>>>>>>>>> doesn't get that examples don't take the place >>>>>>>>>>>>>>>>>>>>>>>> of definitions. Examples can be useful for >>>>>>>>>>>>>>>>>>>>>>>> clarifying definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are animals" >>>>>>>>>>>>>>>>>>>>>>>>>> expressed inI didn't ask for an example. I asked for a >>>>>>>>>>>>>>>>>>>>>>>>> definition of what it mean for the truth value >>>>>>>>>>>>>>>>>>>>>>>>> of a statement to not exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>
English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright
Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did >>>>>>>>>>>>>>>>>>> not bother to pay attention that is your mistake >>>>>>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means for the >>>>>>>>>>>>>>>>>> truth value of a statement to not exist in a formal >>>>>>>>>>>>>>>>>> system.
A valid answer would look something like this: >>>>>>>>>>>>>>>>>>
"The truth value of a statement does not exist in a >>>>>>>>>>>>>>>>>> formal system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ >>>>>>>>>>>>>>>> x) does not exist in Q", you mean "(∀ x, S(x) ≠ x) is >>>>>>>>>>>>>>>> unprovable in Q", which is commonly known.
So once again, you're saying the same thing as everyone >>>>>>>>>>>>>>>> else but using different words.
Not really. It is normally thought of as undecidable >>>>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is deficient. >>>>>>>>>>>>>>
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H >>>>>>>>>>>>>> exists that meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of >>>>>>>>>>>>>> instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that >>>>>>>>>>>>>> computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed >>>>>>>>>>>>>> directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when >>>>>>>>>>>>>> executed directly
Sure and we could equally start with the requirement >>>>>>>>>>>>> to prove that there exists a natural number > 3 and < 2. >>>>>>>>>>>>>
I really don't see how everyone did not immediately see >>>>>>>>>>>>> that the requirement for H to correctly report the halt >>>>>>>>>>>>> status of input D that does the opposite of whatever H >>>>>>>>>>>>> reports is a moronically stupid requirement within the >>>>>>>>>>>>> first five minutes that this requirement was made.
In other words, you don't understand that if this was >>>>>>>>>>>> algorithm H:
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting problem >>>>>>>> for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
And algorithm H is wrong about algorithm D because algorithm D
contains a copy of algorithm H and does the opposite.
You just don't know jack shit dufus.
I have been a professional C programmer since 1986.
Says the person that just demonstrated that they don't know the
difference between an algorithm and a C function.
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored by everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:False. It means that there are statements in the >>>>>>>>>>>>>>> language of Q that have *only* an infinite connection to >>>>>>>>>>>>>>> the axioms of the system.
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>That claims what it means to have the truth value >>>>>>>>>>>>>>>>>>>>> 'true' (or at least it would if you defined >>>>>>>>>>>>>>>>>>>>> AtomicFacts in a coherent way). It doesn't in any >>>>>>>>>>>>>>>>>>>>> way clarify what you think it means for something >>>>>>>>>>>>>>>>>>>>> to not have a truth value.
Until someone publishes an Olcott to Standard >>>>>>>>>>>>>>>>>>>>>>> English dictionary, this isn't really an option. >>>>>>>>>>>>>>>>>>>>>>>I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions and he >>>>>>>>>>>>>>>>>>>>>>>>> invariably responds with an example or an >>>>>>>>>>>>>>>>>>>>>>>>> analogy (assuming he responds at all). He >>>>>>>>>>>>>>>>>>>>>>>>> doesn't get that examples don't take the place >>>>>>>>>>>>>>>>>>>>>>>>> of definitions. Examples can be useful for >>>>>>>>>>>>>>>>>>>>>>>>> clarifying definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are animals" >>>>>>>>>>>>>>>>>>>>>>>>>>> expressed inI didn't ask for an example. I asked for a >>>>>>>>>>>>>>>>>>>>>>>>>> definition of what it mean for the truth value >>>>>>>>>>>>>>>>>>>>>>>>>> of a statement to not exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>
English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // >>>>>>>>>>>>>>>>>>>>>> copyright Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did >>>>>>>>>>>>>>>>>>>> not bother to pay attention that is your mistake >>>>>>>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means for the >>>>>>>>>>>>>>>>>>> truth value of a statement to not exist in a formal >>>>>>>>>>>>>>>>>>> system.
A valid answer would look something like this: >>>>>>>>>>>>>>>>>>>
"The truth value of a statement does not exist in a >>>>>>>>>>>>>>>>>>> formal system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ >>>>>>>>>>>>>>>>> x) does not exist in Q", you mean "(∀ x, S(x) ≠ x) is >>>>>>>>>>>>>>>>> unprovable in Q", which is commonly known.
So once again, you're saying the same thing as everyone >>>>>>>>>>>>>>>>> else but using different words.
Not really. It is normally thought of as undecidable >>>>>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is deficient. >>>>>>>>>>>>>>>
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H >>>>>>>>>>>>>>> exists that meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of >>>>>>>>>>>>>>> instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that >>>>>>>>>>>>>>> computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed >>>>>>>>>>>>>>> directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when >>>>>>>>>>>>>>> executed directly
Sure and we could equally start with the requirement >>>>>>>>>>>>>> to prove that there exists a natural number > 3 and < 2. >>>>>>>>>>>>>>
I really don't see how everyone did not immediately see >>>>>>>>>>>>>> that the requirement for H to correctly report the halt >>>>>>>>>>>>>> status of input D that does the opposite of whatever H >>>>>>>>>>>>>> reports is a moronically stupid requirement within the >>>>>>>>>>>>>> first five minutes that this requirement was made.
In other words, you don't understand that if this was >>>>>>>>>>>>> algorithm H:
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting problem >>>>>>>>> for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
And algorithm H is wrong about algorithm D because algorithm D
contains a copy of algorithm H and does the opposite.
You just don't know jack shit dufus.
I have been a professional C programmer since 1986.
Says the person that just demonstrated that they don't know the
difference between an algorithm and a C function.
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored by everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be a halt
decider,
and another algorithm built by the template that the first one--
answers wrong.
If you disagree, explain in detail why.
On 7/2/2026 11:04 AM, dbush wrote:
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:In other words, you don't understand that if this was >>>>>>>>>>>>>> algorithm H:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:False. It means that there are statements in the >>>>>>>>>>>>>>>> language of Q that have *only* an infinite connection to >>>>>>>>>>>>>>>> the axioms of the system.
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:Good. So when you say "The truth value of (∀ x, S(x) >>>>>>>>>>>>>>>>>> ≠ x) does not exist in Q", you mean "(∀ x, S(x) ≠ x) >>>>>>>>>>>>>>>>>> is unprovable in Q", which is commonly known. >>>>>>>>>>>>>>>>>>
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>
That claims what it means to have the truth value >>>>>>>>>>>>>>>>>>>>>> 'true' (or at least it would if you defined >>>>>>>>>>>>>>>>>>>>>> AtomicFacts in a coherent way). It doesn't in any >>>>>>>>>>>>>>>>>>>>>> way clarify what you think it means for something >>>>>>>>>>>>>>>>>>>>>> to not have a truth value.Until someone publishes an Olcott to Standard >>>>>>>>>>>>>>>>>>>>>>>> English dictionary, this isn't really an option. >>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are animals" >>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed inI didn't ask for an example. I asked for a >>>>>>>>>>>>>>>>>>>>>>>>>>> definition of what it mean for the truth >>>>>>>>>>>>>>>>>>>>>>>>>>> value of a statement to not exist in a formal >>>>>>>>>>>>>>>>>>>>>>>>>>> system.
English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>
I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions and he >>>>>>>>>>>>>>>>>>>>>>>>>> invariably responds with an example or an >>>>>>>>>>>>>>>>>>>>>>>>>> analogy (assuming he responds at all). He >>>>>>>>>>>>>>>>>>>>>>>>>> doesn't get that examples don't take the place >>>>>>>>>>>>>>>>>>>>>>>>>> of definitions. Examples can be useful for >>>>>>>>>>>>>>>>>>>>>>>>>> clarifying definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // >>>>>>>>>>>>>>>>>>>>>>> copyright Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did >>>>>>>>>>>>>>>>>>>>> not bother to pay attention that is your mistake >>>>>>>>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means for the >>>>>>>>>>>>>>>>>>>> truth value of a statement to not exist in a formal >>>>>>>>>>>>>>>>>>>> system.
A valid answer would look something like this: >>>>>>>>>>>>>>>>>>>>
"The truth value of a statement does not exist in a >>>>>>>>>>>>>>>>>>>> formal system when ..."
Now complete the sentence.
It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>
So once again, you're saying the same thing as >>>>>>>>>>>>>>>>>> everyone else but using different words.
Not really. It is normally thought of as undecidable >>>>>>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is deficient. >>>>>>>>>>>>>>>>
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H >>>>>>>>>>>>>>>> exists that meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of >>>>>>>>>>>>>>>> instructions) X described as <X> with input Y: >>>>>>>>>>>>>>>>
A solution to the halting problem is an algorithm H that >>>>>>>>>>>>>>>> computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when >>>>>>>>>>>>>>>> executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when >>>>>>>>>>>>>>>> executed directly
Sure and we could equally start with the requirement >>>>>>>>>>>>>>> to prove that there exists a natural number > 3 and < 2. >>>>>>>>>>>>>>>
I really don't see how everyone did not immediately see >>>>>>>>>>>>>>> that the requirement for H to correctly report the halt >>>>>>>>>>>>>>> status of input D that does the opposite of whatever H >>>>>>>>>>>>>>> reports is a moronically stupid requirement within the >>>>>>>>>>>>>>> first five minutes that this requirement was made. >>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting problem >>>>>>>>>> for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
And algorithm H is wrong about algorithm D because algorithm D >>>>>>>> contains a copy of algorithm H and does the opposite.
You just don't know jack shit dufus.
I have been a professional C programmer since 1986.
Says the person that just demonstrated that they don't know the
difference between an algorithm and a C function.
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored by everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be a halt decider,
Ridiculously stupid. Your H does not even look at its input.
Also your D simply stops running I ran it to verify.
I will not respond to any of your future posts that
are very stupid. Say something smart or you will be
ignored from now on.
and another algorithm built by the template that the first one answers
wrong.
If you disagree, explain in detail why.
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:In other words, you don't understand that if this was >>>>>>>>>>>>>>> algorithm H:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:False. It means that there are statements in the >>>>>>>>>>>>>>>>> language of Q that have *only* an infinite connection >>>>>>>>>>>>>>>>> to the axioms of the system.
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:Good. So when you say "The truth value of (∀ x, S(x) >>>>>>>>>>>>>>>>>>> ≠ x) does not exist in Q", you mean "(∀ x, S(x) ≠ x) >>>>>>>>>>>>>>>>>>> is unprovable in Q", which is commonly known. >>>>>>>>>>>>>>>>>>>
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>
That claims what it means to have the truth value >>>>>>>>>>>>>>>>>>>>>>> 'true' (or at least it would if you defined >>>>>>>>>>>>>>>>>>>>>>> AtomicFacts in a coherent way). It doesn't in any >>>>>>>>>>>>>>>>>>>>>>> way clarify what you think it means for something >>>>>>>>>>>>>>>>>>>>>>> to not have a truth value.Until someone publishes an Olcott to Standard >>>>>>>>>>>>>>>>>>>>>>>>> English dictionary, this isn't really an option. >>>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are animals" >>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed inI didn't ask for an example. I asked for a >>>>>>>>>>>>>>>>>>>>>>>>>>>> definition of what it mean for the truth >>>>>>>>>>>>>>>>>>>>>>>>>>>> value of a statement to not exist in a >>>>>>>>>>>>>>>>>>>>>>>>>>>> formal system.
English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions and he >>>>>>>>>>>>>>>>>>>>>>>>>>> invariably responds with an example or an >>>>>>>>>>>>>>>>>>>>>>>>>>> analogy (assuming he responds at all). He >>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't get that examples don't take the >>>>>>>>>>>>>>>>>>>>>>>>>>> place of definitions. Examples can be useful >>>>>>>>>>>>>>>>>>>>>>>>>>> for clarifying definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // >>>>>>>>>>>>>>>>>>>>>>>> copyright Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did >>>>>>>>>>>>>>>>>>>>>> not bother to pay attention that is your mistake >>>>>>>>>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means for >>>>>>>>>>>>>>>>>>>>> the truth value of a statement to not exist in a >>>>>>>>>>>>>>>>>>>>> formal system.
A valid answer would look something like this: >>>>>>>>>>>>>>>>>>>>>
"The truth value of a statement does not exist in a >>>>>>>>>>>>>>>>>>>>> formal system when ..."
Now complete the sentence.
It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>
So once again, you're saying the same thing as >>>>>>>>>>>>>>>>>>> everyone else but using different words. >>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as undecidable >>>>>>>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is deficient. >>>>>>>>>>>>>>>>>
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H >>>>>>>>>>>>>>>>> exists that meets the following requirements: >>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed immutable sequence of >>>>>>>>>>>>>>>>> instructions) X described as <X> with input Y: >>>>>>>>>>>>>>>>>
A solution to the halting problem is an algorithm H >>>>>>>>>>>>>>>>> that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when >>>>>>>>>>>>>>>>> executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt >>>>>>>>>>>>>>>>> when executed directly
Sure and we could equally start with the requirement >>>>>>>>>>>>>>>> to prove that there exists a natural number > 3 and < 2. >>>>>>>>>>>>>>>>
I really don't see how everyone did not immediately see >>>>>>>>>>>>>>>> that the requirement for H to correctly report the halt >>>>>>>>>>>>>>>> status of input D that does the opposite of whatever H >>>>>>>>>>>>>>>> reports is a moronically stupid requirement within the >>>>>>>>>>>>>>>> first five minutes that this requirement was made. >>>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting problem >>>>>>>>>>> for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
And algorithm H is wrong about algorithm D because algorithm D >>>>>>>>> contains a copy of algorithm H and does the opposite.
You just don't know jack shit dufus.
I have been a professional C programmer since 1986.
Says the person that just demonstrated that they don't know the >>>>>>> difference between an algorithm and a C function.
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored by everone. >>>>>
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be a halt
decider,
Ridiculously stupid. Your H does not even look at its input.
Algorithm H doesn't need to read its inputs in order to map all inputs
to non-halting.
Also your D simply stops running I ran it to verify.
Verifying that algorithm H doesn't correctly report what algorithm D
does, as per the design of algorithm D.
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:In other words, you don't understand that if this was >>>>>>>>>>>>>>>> algorithm H:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:Good. So when you say "The truth value of (∀ x, >>>>>>>>>>>>>>>>>>>> S(x) ≠ x) does not exist in Q", you mean "(∀ x, S(x) >>>>>>>>>>>>>>>>>>>> ≠ x) is unprovable in Q", which is commonly known. >>>>>>>>>>>>>>>>>>>>
On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>
That claims what it means to have the truth >>>>>>>>>>>>>>>>>>>>>>>> value 'true' (or at least it would if you >>>>>>>>>>>>>>>>>>>>>>>> defined AtomicFacts in a coherent way). It >>>>>>>>>>>>>>>>>>>>>>>> doesn't in any way clarify what you think it >>>>>>>>>>>>>>>>>>>>>>>> means for something to not have a truth value. >>>>>>>>>>>>>>>>>>>>>>>>Until someone publishes an Olcott to Standard >>>>>>>>>>>>>>>>>>>>>>>>>> English dictionary, this isn't really an option. >>>>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are animals" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed inI didn't ask for an example. I asked for a >>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition of what it mean for the truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>> value of a statement to not exist in a >>>>>>>>>>>>>>>>>>>>>>>>>>>>> formal system.
English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions and he >>>>>>>>>>>>>>>>>>>>>>>>>>>> invariably responds with an example or an >>>>>>>>>>>>>>>>>>>>>>>>>>>> analogy (assuming he responds at all). He >>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't get that examples don't take the >>>>>>>>>>>>>>>>>>>>>>>>>>>> place of definitions. Examples can be useful >>>>>>>>>>>>>>>>>>>>>>>>>>>> for clarifying definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // >>>>>>>>>>>>>>>>>>>>>>>>> copyright Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did >>>>>>>>>>>>>>>>>>>>>>> not bother to pay attention that is your mistake >>>>>>>>>>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means for >>>>>>>>>>>>>>>>>>>>>> the truth value of a statement to not exist in a >>>>>>>>>>>>>>>>>>>>>> formal system.
A valid answer would look something like this: >>>>>>>>>>>>>>>>>>>>>>
"The truth value of a statement does not exist in >>>>>>>>>>>>>>>>>>>>>> a formal system when ..."
Now complete the sentence.
It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same thing as >>>>>>>>>>>>>>>>>>>> everyone else but using different words. >>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as undecidable >>>>>>>>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is >>>>>>>>>>>>>>>>>>> deficient.
False. It means that there are statements in the >>>>>>>>>>>>>>>>>> language of Q that have *only* an infinite connection >>>>>>>>>>>>>>>>>> to the axioms of the system.
OK, I verified that.
Which starts with the assumption that an algorithm H >>>>>>>>>>>>>>>>>> exists that meets the following requirements: >>>>>>>>>>>>>>>>>>
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed immutable sequence >>>>>>>>>>>>>>>>>> of instructions) X described as <X> with input Y: >>>>>>>>>>>>>>>>>>
A solution to the halting problem is an algorithm H >>>>>>>>>>>>>>>>>> that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when >>>>>>>>>>>>>>>>>> executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt >>>>>>>>>>>>>>>>>> when executed directly
Sure and we could equally start with the requirement >>>>>>>>>>>>>>>>> to prove that there exists a natural number > 3 and < 2. >>>>>>>>>>>>>>>>>
I really don't see how everyone did not immediately see >>>>>>>>>>>>>>>>> that the requirement for H to correctly report the halt >>>>>>>>>>>>>>>>> status of input D that does the opposite of whatever H >>>>>>>>>>>>>>>>> reports is a moronically stupid requirement within the >>>>>>>>>>>>>>>>> first five minutes that this requirement was made. >>>>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting >>>>>>>>>>>> problem for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
And algorithm H is wrong about algorithm D because algorithm D >>>>>>>>>> contains a copy of algorithm H and does the opposite.
You just don't know jack shit dufus.
I have been a professional C programmer since 1986.
Says the person that just demonstrated that they don't know the >>>>>>>> difference between an algorithm and a C function.
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored by everone. >>>>>>
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be a halt
decider,
Ridiculously stupid. Your H does not even look at its input.
Algorithm H doesn't need to read its inputs in order to map all inputs
to non-halting.
Also your D simply stops running I ran it to verify.
Verifying that algorithm H doesn't correctly report what algorithm D
does, as per the design of algorithm D.
I am trying to keep liars from killing the
whole fucking planet by making truth computable
and you act like this is a fucking joke to be
trolled.
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:In other words, you don't understand that if this was >>>>>>>>>>>>>>>>> algorithm H:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>Good. So when you say "The truth value of (∀ x, >>>>>>>>>>>>>>>>>>>>> S(x) ≠ x) does not exist in Q", you mean "(∀ x, >>>>>>>>>>>>>>>>>>>>> S(x) ≠ x) is unprovable in Q", which is commonly >>>>>>>>>>>>>>>>>>>>> known.
That claims what it means to have the truth >>>>>>>>>>>>>>>>>>>>>>>>> value 'true' (or at least it would if you >>>>>>>>>>>>>>>>>>>>>>>>> defined AtomicFacts in a coherent way). It >>>>>>>>>>>>>>>>>>>>>>>>> doesn't in any way clarify what you think it >>>>>>>>>>>>>>>>>>>>>>>>> means for something to not have a truth value. >>>>>>>>>>>>>>>>>>>>>>>>>Until someone publishes an Olcott to Standard >>>>>>>>>>>>>>>>>>>>>>>>>>> English dictionary, this isn't really an option. >>>>>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are animals" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed inI didn't ask for an example. I asked for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a definition of what it mean for the truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> value of a statement to not exist in a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formal system.
English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions and he >>>>>>>>>>>>>>>>>>>>>>>>>>>>> invariably responds with an example or an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> analogy (assuming he responds at all). He >>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't get that examples don't take the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> place of definitions. Examples can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>> useful for clarifying definitions, but they >>>>>>>>>>>>>>>>>>>>>>>>>>>>> aren't particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // >>>>>>>>>>>>>>>>>>>>>>>>>> copyright Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did >>>>>>>>>>>>>>>>>>>>>>>> not bother to pay attention that is your mistake >>>>>>>>>>>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means for >>>>>>>>>>>>>>>>>>>>>>> the truth value of a statement to not exist in a >>>>>>>>>>>>>>>>>>>>>>> formal system.
A valid answer would look something like this: >>>>>>>>>>>>>>>>>>>>>>>
"The truth value of a statement does not exist in >>>>>>>>>>>>>>>>>>>>>>> a formal system when ..."
Now complete the sentence.
It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same thing as >>>>>>>>>>>>>>>>>>>>> everyone else but using different words. >>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as undecidable >>>>>>>>>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is >>>>>>>>>>>>>>>>>>>> deficient.
False. It means that there are statements in the >>>>>>>>>>>>>>>>>>> language of Q that have *only* an infinite connection >>>>>>>>>>>>>>>>>>> to the axioms of the system.
OK, I verified that.
Which starts with the assumption that an algorithm H >>>>>>>>>>>>>>>>>>> exists that meets the following requirements: >>>>>>>>>>>>>>>>>>>
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed immutable sequence >>>>>>>>>>>>>>>>>>> of instructions) X described as <X> with input Y: >>>>>>>>>>>>>>>>>>>
A solution to the halting problem is an algorithm H >>>>>>>>>>>>>>>>>>> that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when >>>>>>>>>>>>>>>>>>> executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt >>>>>>>>>>>>>>>>>>> when executed directly
Sure and we could equally start with the requirement >>>>>>>>>>>>>>>>>> to prove that there exists a natural number > 3 and < 2. >>>>>>>>>>>>>>>>>>
I really don't see how everyone did not immediately see >>>>>>>>>>>>>>>>>> that the requirement for H to correctly report the halt >>>>>>>>>>>>>>>>>> status of input D that does the opposite of whatever H >>>>>>>>>>>>>>>>>> reports is a moronically stupid requirement within the >>>>>>>>>>>>>>>>>> first five minutes that this requirement was made. >>>>>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting >>>>>>>>>>>>> problem for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
And algorithm H is wrong about algorithm D because algorithm >>>>>>>>>>> D contains a copy of algorithm H and does the opposite.
You just don't know jack shit dufus.
I have been a professional C programmer since 1986.
Says the person that just demonstrated that they don't know the >>>>>>>>> difference between an algorithm and a C function.
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored by
everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be a halt
decider,
Ridiculously stupid. Your H does not even look at its input.
Algorithm H doesn't need to read its inputs in order to map all
inputs to non-halting.
Also your D simply stops running I ran it to verify.
Verifying that algorithm H doesn't correctly report what algorithm D
does, as per the design of algorithm D.
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi and others.
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:You just don't know jack shit dufus.
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:In other words, you don't understand that if this was >>>>>>>>>>>>>>>>>> algorithm H:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:
On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Good. So when you say "The truth value of (∀ x, >>>>>>>>>>>>>>>>>>>>>> S(x) ≠ x) does not exist in Q", you mean "(∀ x, >>>>>>>>>>>>>>>>>>>>>> S(x) ≠ x) is unprovable in Q", which is commonly >>>>>>>>>>>>>>>>>>>>>> known.That claims what it means to have the truth >>>>>>>>>>>>>>>>>>>>>>>>>> value 'true' (or at least it would if you >>>>>>>>>>>>>>>>>>>>>>>>>> defined AtomicFacts in a coherent way). It >>>>>>>>>>>>>>>>>>>>>>>>>> doesn't in any way clarify what you think it >>>>>>>>>>>>>>>>>>>>>>>>>> means for something to not have a truth value. >>>>>>>>>>>>>>>>>>>>>>>>>>Until someone publishes an Olcott to >>>>>>>>>>>>>>>>>>>>>>>>>>>> Standard English dictionary, this isn't >>>>>>>>>>>>>>>>>>>>>>>>>>>> really an option.I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions and >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> he invariably responds with an example or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an analogy (assuming he responds at all). >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> He doesn't get that examples don't take >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the place of definitions. Examples can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> useful for clarifying definitions, but >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> they aren't particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are animals" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed inI didn't ask for an example. I asked for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a definition of what it mean for the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth value of a statement to not exist >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) //
copyright Olcott 2018
has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did >>>>>>>>>>>>>>>>>>>>>>>>> not bother to pay attention that is your mistake >>>>>>>>>>>>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means for >>>>>>>>>>>>>>>>>>>>>>>> the truth value of a statement to not exist in a >>>>>>>>>>>>>>>>>>>>>>>> formal system.
A valid answer would look something like this: >>>>>>>>>>>>>>>>>>>>>>>>
"The truth value of a statement does not exist >>>>>>>>>>>>>>>>>>>>>>>> in a formal system when ..."
Now complete the sentence.
It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same thing as >>>>>>>>>>>>>>>>>>>>>> everyone else but using different words. >>>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as undecidable >>>>>>>>>>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is >>>>>>>>>>>>>>>>>>>>> deficient.
False. It means that there are statements in the >>>>>>>>>>>>>>>>>>>> language of Q that have *only* an infinite >>>>>>>>>>>>>>>>>>>> connection to the axioms of the system. >>>>>>>>>>>>>>>>>>>>
OK, I verified that.
Which starts with the assumption that an algorithm H >>>>>>>>>>>>>>>>>>>> exists that meets the following requirements: >>>>>>>>>>>>>>>>>>>>
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed immutable sequence >>>>>>>>>>>>>>>>>>>> of instructions) X described as <X> with input Y: >>>>>>>>>>>>>>>>>>>>
A solution to the halting problem is an algorithm H >>>>>>>>>>>>>>>>>>>> that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when >>>>>>>>>>>>>>>>>>>> executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt >>>>>>>>>>>>>>>>>>>> when executed directly
Sure and we could equally start with the requirement >>>>>>>>>>>>>>>>>>> to prove that there exists a natural number > 3 and < 2. >>>>>>>>>>>>>>>>>>>
I really don't see how everyone did not immediately see >>>>>>>>>>>>>>>>>>> that the requirement for H to correctly report the halt >>>>>>>>>>>>>>>>>>> status of input D that does the opposite of whatever H >>>>>>>>>>>>>>>>>>> reports is a moronically stupid requirement within the >>>>>>>>>>>>>>>>>>> first five minutes that this requirement was made. >>>>>>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm: >>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm: >>>>>>>>>>>>>>>>
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting >>>>>>>>>>>>>> problem for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
And algorithm H is wrong about algorithm D because algorithm >>>>>>>>>>>> D contains a copy of algorithm H and does the opposite. >>>>>>>>>>>
I have been a professional C programmer since 1986.
Says the person that just demonstrated that they don't know >>>>>>>>>> the difference between an algorithm and a C function.
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored by
everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be a halt
decider,
Ridiculously stupid. Your H does not even look at its input.
Algorithm H doesn't need to read its inputs in order to map all
inputs to non-halting.
Also your D simply stops running I ran it to verify.
Verifying that algorithm H doesn't correctly report what algorithm D
does, as per the design of algorithm D.
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi and others.
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
On 7/2/2026 3:33 PM, olcott wrote:
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:And algorithm H is wrong about algorithm D because
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:In other words, you don't understand that if this was >>>>>>>>>>>>>>>>>>> algorithm H:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Good. So when you say "The truth value of (∀ x, >>>>>>>>>>>>>>>>>>>>>>> S(x) ≠ x) does not exist in Q", you mean "(∀ x, >>>>>>>>>>>>>>>>>>>>>>> S(x) ≠ x) is unprovable in Q", which is commonly >>>>>>>>>>>>>>>>>>>>>>> known.That claims what it means to have the truth >>>>>>>>>>>>>>>>>>>>>>>>>>> value 'true' (or at least it would if you >>>>>>>>>>>>>>>>>>>>>>>>>>> defined AtomicFacts in a coherent way). It >>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't in any way clarify what you think it >>>>>>>>>>>>>>>>>>>>>>>>>>> means for something to not have a truth value. >>>>>>>>>>>>>>>>>>>>>>>>>>>Until someone publishes an Olcott to >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Standard English dictionary, this isn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>> really an option.I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions and >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> he invariably responds with an example or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an analogy (assuming he responds at all). >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> He doesn't get that examples don't take >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the place of definitions. Examples can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> useful for clarifying definitions, but >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> they aren't particularly useful on their >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> own.The same thing as: "cats are animals" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>I didn't ask for an example. I asked >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for a definition of what it mean for the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth value of a statement to not exist >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) //
copyright Olcott 2018
has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you >>>>>>>>>>>>>>>>>>>>>>>>>> did
not bother to pay attention that is your mistake >>>>>>>>>>>>>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means >>>>>>>>>>>>>>>>>>>>>>>>> for the truth value of a statement to not exist >>>>>>>>>>>>>>>>>>>>>>>>> in a formal system.
A valid answer would look something like this: >>>>>>>>>>>>>>>>>>>>>>>>>
"The truth value of a statement does not exist >>>>>>>>>>>>>>>>>>>>>>>>> in a formal system when ..." >>>>>>>>>>>>>>>>>>>>>>>>>
Now complete the sentence.
It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same thing as >>>>>>>>>>>>>>>>>>>>>>> everyone else but using different words. >>>>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as undecidable >>>>>>>>>>>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is >>>>>>>>>>>>>>>>>>>>>> deficient.
False. It means that there are statements in the >>>>>>>>>>>>>>>>>>>>> language of Q that have *only* an infinite >>>>>>>>>>>>>>>>>>>>> connection to the axioms of the system. >>>>>>>>>>>>>>>>>>>>>
OK, I verified that.
Which starts with the assumption that an algorithm >>>>>>>>>>>>>>>>>>>>> H exists that meets the following requirements: >>>>>>>>>>>>>>>>>>>>>
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed immutable >>>>>>>>>>>>>>>>>>>>> sequence of instructions) X described as <X> with >>>>>>>>>>>>>>>>>>>>> input Y:
A solution to the halting problem is an algorithm H >>>>>>>>>>>>>>>>>>>>> that computes the following mapping: >>>>>>>>>>>>>>>>>>>>>
(<X>,Y) maps to 1 if and only if X(Y) halts when >>>>>>>>>>>>>>>>>>>>> executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt >>>>>>>>>>>>>>>>>>>>> when executed directly
Sure and we could equally start with the requirement >>>>>>>>>>>>>>>>>>>> to prove that there exists a natural number > 3 and >>>>>>>>>>>>>>>>>>>> < 2.
I really don't see how everyone did not immediately see >>>>>>>>>>>>>>>>>>>> that the requirement for H to correctly report the halt >>>>>>>>>>>>>>>>>>>> status of input D that does the opposite of whatever H >>>>>>>>>>>>>>>>>>>> reports is a moronically stupid requirement within the >>>>>>>>>>>>>>>>>>>> first five minutes that this requirement was made. >>>>>>>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm: >>>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm: >>>>>>>>>>>>>>>>>
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting >>>>>>>>>>>>>>> problem for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D) >>>>>>>>>>>>>
algorithm D contains a copy of algorithm H and does the >>>>>>>>>>>>> opposite.
You just don't know jack shit dufus.
I have been a professional C programmer since 1986.
Says the person that just demonstrated that they don't know >>>>>>>>>>> the difference between an algorithm and a C function.
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored by >>>>>>>>> everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be a halt >>>>>>> decider,
Ridiculously stupid. Your H does not even look at its input.
Algorithm H doesn't need to read its inputs in order to map all
inputs to non-halting.
Also your D simply stops running I ran it to verify.
Verifying that algorithm H doesn't correctly report what algorithm
D does, as per the design of algorithm D.
Still no reply to this, so I have to assume you agree it's correct.
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi and others.
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
There is no error. The POE follows from a series of truth preserving operations
On 7/2/2026 2:52 PM, dbush wrote:
On 7/2/2026 3:33 PM, olcott wrote:
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:And algorithm H is wrong about algorithm D because >>>>>>>>>>>>>> algorithm D contains a copy of algorithm H and does the >>>>>>>>>>>>>> opposite.
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:And still don't understand that this algorithm: >>>>>>>>>>>>>>>>>>
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:In other words, you don't understand that if this >>>>>>>>>>>>>>>>>>>> was algorithm H:
On 7/1/2026 5:04 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:57 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Good. So when you say "The truth value of (∀ x, >>>>>>>>>>>>>>>>>>>>>>>> S(x) ≠ x) does not exist in Q", you mean "(∀ x, >>>>>>>>>>>>>>>>>>>>>>>> S(x) ≠ x) is unprovable in Q", which is commonly >>>>>>>>>>>>>>>>>>>>>>>> known.That claims what it means to have the truth >>>>>>>>>>>>>>>>>>>>>>>>>>>> value 'true' (or at least it would if you >>>>>>>>>>>>>>>>>>>>>>>>>>>> defined AtomicFacts in a coherent way). It >>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't in any way clarify what you think it >>>>>>>>>>>>>>>>>>>>>>>>>>>> means for something to not have a truth value. >>>>>>>>>>>>>>>>>>>>>>>>>>>>Until someone publishes an Olcott to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Standard English dictionary, this isn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> really an option.I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions and >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> he invariably responds with an example >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or an analogy (assuming he responds at >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all). He doesn't get that examples don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> take the place of definitions. Examples >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can be useful for clarifying >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are animals" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> English has no English meaning in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Chinese.
I didn't ask for an example. I asked >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for a definition of what it mean for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the truth value of a statement to not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) //
copyright Olcott 2018 >>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and >>>>>>>>>>>>>>>>>>>>>>>>>>> you did
not bother to pay attention that is your mistake >>>>>>>>>>>>>>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means >>>>>>>>>>>>>>>>>>>>>>>>>> for the truth value of a statement to not >>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system.
A valid answer would look something like this: >>>>>>>>>>>>>>>>>>>>>>>>>>
"The truth value of a statement does not exist >>>>>>>>>>>>>>>>>>>>>>>>>> in a formal system when ..." >>>>>>>>>>>>>>>>>>>>>>>>>>
Now complete the sentence.
It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same thing as >>>>>>>>>>>>>>>>>>>>>>>> everyone else but using different words. >>>>>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as undecidable >>>>>>>>>>>>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is >>>>>>>>>>>>>>>>>>>>>>> deficient.
False. It means that there are statements in the >>>>>>>>>>>>>>>>>>>>>> language of Q that have *only* an infinite >>>>>>>>>>>>>>>>>>>>>> connection to the axioms of the system. >>>>>>>>>>>>>>>>>>>>>>
OK, I verified that.
Which starts with the assumption that an algorithm >>>>>>>>>>>>>>>>>>>>>> H exists that meets the following requirements: >>>>>>>>>>>>>>>>>>>>>>
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed immutable >>>>>>>>>>>>>>>>>>>>>> sequence of instructions) X described as <X> with >>>>>>>>>>>>>>>>>>>>>> input Y:
A solution to the halting problem is an algorithm >>>>>>>>>>>>>>>>>>>>>> H that computes the following mapping: >>>>>>>>>>>>>>>>>>>>>>
(<X>,Y) maps to 1 if and only if X(Y) halts when >>>>>>>>>>>>>>>>>>>>>> executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not >>>>>>>>>>>>>>>>>>>>>> halt when executed directly
Sure and we could equally start with the requirement >>>>>>>>>>>>>>>>>>>>> to prove that there exists a natural number > 3 and >>>>>>>>>>>>>>>>>>>>> < 2.
I really don't see how everyone did not immediately >>>>>>>>>>>>>>>>>>>>> see
that the requirement for H to correctly report the >>>>>>>>>>>>>>>>>>>>> halt
status of input D that does the opposite of whatever H >>>>>>>>>>>>>>>>>>>>> reports is a moronically stupid requirement within the >>>>>>>>>>>>>>>>>>>>> first five minutes that this requirement was made. >>>>>>>>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years. >>>>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm: >>>>>>>>>>>>>>>>>>
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting >>>>>>>>>>>>>>>> problem for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D) >>>>>>>>>>>>>>
You just don't know jack shit dufus.
I have been a professional C programmer since 1986.
Says the person that just demonstrated that they don't know >>>>>>>>>>>> the difference between an algorithm and a C function.
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored by >>>>>>>>>> everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be a halt >>>>>>>> decider,
Ridiculously stupid. Your H does not even look at its input.
Algorithm H doesn't need to read its inputs in order to map all
inputs to non-halting.
Also your D simply stops running I ran it to verify.
Verifying that algorithm H doesn't correctly report what algorithm >>>>>> D does, as per the design of algorithm D.
Still no reply to this, so I have to assume you agree it's correct.
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi and others.
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
There is no error. The POE follows from a series of truth preserving
operations
To say this objectively classical logic is objectively incorrect
when it diverges from what correct reasoning would be while
retaining the full English semantics of the terms.
(P ∧ ¬P) ⊢ Q is ridiculously stupid when we plug English
sentences in for P and Q and use semantic entailment in English
as the measure of correct reasoning.
On 6/27/2026 11:34 PM, dbush wrote:--- Synchronet 3.22a-Linux NewsLink 1.2
On 6/27/2026 11:23 PM, olcott wrote:
On 6/27/2026 9:02 PM, dbush wrote:
On 6/27/2026 9:53 PM, dbush wrote:
On 6/27/2026 9:49 PM, olcott wrote:
On 6/27/2026 8:42 PM, dbush wrote:
On 6/27/2026 9:40 PM, olcott wrote:
On 6/27/2026 8:29 PM, dbush wrote:
Given that the following natural language statement is true:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
In the following natural language statement:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- <X>
--------------------------------------
Given that <X> is any *truth bearing* natural language statement,
does there exist a statement X such that the condition "At least one
of the following statements is true" is false?
Head games will be ignored.
Explain in detail how this is a head game.
Failure to either answer the above question or explain how it is a
head game in your next reply or within one hour of you next post in
this newsgroup will be taken as your official, on-the-record admission
that Disjunction introduction is in fact truth preserving and valid,
and therefore so is the Principle of Explosion.
Let the record show that Peter Olcott made the following post in this newsgroup:
On 6/28/2026 10:52 PM, olcott wrote:
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do.
...
And more that one hour has passed with no attempt to answer the above question or explain why it is a head game. Therefore, as per the above criteria:
Let The Record Show
That Peter Olcott
Has *Officially* Admitted:
That Disjunction introduction is in fact truth preserving and valid, and therefore so is the Principle of Explosion.
On 7/2/2026 4:53 PM, olcott wrote:
On 7/2/2026 2:52 PM, dbush wrote:
On 7/2/2026 3:33 PM, olcott wrote:
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:And algorithm H is wrong about algorithm D because >>>>>>>>>>>>>>> algorithm D contains a copy of algorithm H and does the >>>>>>>>>>>>>>> opposite.
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:And still don't understand that this algorithm: >>>>>>>>>>>>>>>>>>>
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 5:04 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:57 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In other words, you don't understand that if this >>>>>>>>>>>>>>>>>>>>> was algorithm H:
Good. So when you say "The truth value of (∀ >>>>>>>>>>>>>>>>>>>>>>>>> x, S(x) ≠ x) does not exist in Q", you mean "(∀ >>>>>>>>>>>>>>>>>>>>>>>>> x, S(x) ≠ x) is unprovable in Q", which is >>>>>>>>>>>>>>>>>>>>>>>>> commonly known.It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>>>>>>>That claims what it means to have the truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>> value 'true' (or at least it would if you >>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined AtomicFacts in a coherent way). It >>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't in any way clarify what you think >>>>>>>>>>>>>>>>>>>>>>>>>>>>> it means for something to not have a truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>> value.Until someone publishes an Olcott to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Standard English dictionary, this isn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> really an option. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and he invariably responds with an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> example or an analogy (assuming he >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> responds at all). He doesn't get that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> examples don't take the place of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definitions. Examples can be useful for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> clarifying definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are animals" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> English has no English meaning in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Chinese.
I didn't ask for an example. I asked >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for a definition of what it mean for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the truth value of a statement to not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) //
copyright Olcott 2018 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and >>>>>>>>>>>>>>>>>>>>>>>>>>>> you did
not bother to pay attention that is your >>>>>>>>>>>>>>>>>>>>>>>>>>>> mistake
and your fault.
You gave no such definition of what it means >>>>>>>>>>>>>>>>>>>>>>>>>>> for the truth value of a statement to not >>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>
A valid answer would look something like this: >>>>>>>>>>>>>>>>>>>>>>>>>>>
"The truth value of a statement does not >>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system when ..." >>>>>>>>>>>>>>>>>>>>>>>>>>>
Now complete the sentence. >>>>>>>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same thing as >>>>>>>>>>>>>>>>>>>>>>>>> everyone else but using different words. >>>>>>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as >>>>>>>>>>>>>>>>>>>>>>>> undecidable
meaning that Q is incomplete meaning that Q is >>>>>>>>>>>>>>>>>>>>>>>> deficient.
False. It means that there are statements in the >>>>>>>>>>>>>>>>>>>>>>> language of Q that have *only* an infinite >>>>>>>>>>>>>>>>>>>>>>> connection to the axioms of the system. >>>>>>>>>>>>>>>>>>>>>>>
OK, I verified that.
Which starts with the assumption that an >>>>>>>>>>>>>>>>>>>>>>> algorithm H exists that meets the following >>>>>>>>>>>>>>>>>>>>>>> requirements:
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed immutable >>>>>>>>>>>>>>>>>>>>>>> sequence of instructions) X described as <X> with >>>>>>>>>>>>>>>>>>>>>>> input Y:
A solution to the halting problem is an algorithm >>>>>>>>>>>>>>>>>>>>>>> H that computes the following mapping: >>>>>>>>>>>>>>>>>>>>>>>
(<X>,Y) maps to 1 if and only if X(Y) halts when >>>>>>>>>>>>>>>>>>>>>>> executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not >>>>>>>>>>>>>>>>>>>>>>> halt when executed directly
Sure and we could equally start with the requirement >>>>>>>>>>>>>>>>>>>>>> to prove that there exists a natural number > 3 >>>>>>>>>>>>>>>>>>>>>> and < 2.
I really don't see how everyone did not >>>>>>>>>>>>>>>>>>>>>> immediately see
that the requirement for H to correctly report the >>>>>>>>>>>>>>>>>>>>>> halt
status of input D that does the opposite of >>>>>>>>>>>>>>>>>>>>>> whatever H
reports is a moronically stupid requirement within >>>>>>>>>>>>>>>>>>>>>> the
first five minutes that this requirement was made. >>>>>>>>>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years. >>>>>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm: >>>>>>>>>>>>>>>>>>>
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting >>>>>>>>>>>>>>>>> problem for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D) >>>>>>>>>>>>>>>
You just don't know jack shit dufus.
I have been a professional C programmer since 1986. >>>>>>>>>>>>>>
Says the person that just demonstrated that they don't know >>>>>>>>>>>>> the difference between an algorithm and a C function. >>>>>>>>>>>>>
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored by >>>>>>>>>>> everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be a >>>>>>>>> halt decider,
Ridiculously stupid. Your H does not even look at its input.
Algorithm H doesn't need to read its inputs in order to map all >>>>>>> inputs to non-halting.
Also your D simply stops running I ran it to verify.
Verifying that algorithm H doesn't correctly report what
algorithm D does, as per the design of algorithm D.
Still no reply to this, so I have to assume you agree it's correct.
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi and others. >>>>>
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
There is no error. The POE follows from a series of truth preserving
operations
To say this objectively classical logic is objectively incorrect
when it diverges from what correct reasoning would be while
retaining the full English semantics of the terms.
(P ∧ ¬P) ⊢ Q is ridiculously stupid when we plug English
sentences in for P and Q and use semantic entailment in English
as the measure of correct reasoning.
We already did that and you got confused, calling it a mind game (see below):
On 7/2/2026 3:54 PM, dbush wrote:States that both a statement and its negation are true. And if a formal system can reach a contradiction through a series of truth preserving operations from its axioms, that means both statements are proven true.
On 7/2/2026 4:53 PM, olcott wrote:The confusing part is how an intelligent person can
On 7/2/2026 2:52 PM, dbush wrote:
On 7/2/2026 3:33 PM, olcott wrote:
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:And algorithm H is wrong about algorithm D because >>>>>>>>>>>>>>>> algorithm D contains a copy of algorithm H and does the >>>>>>>>>>>>>>>> opposite.
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:And still don't understand that this algorithm: >>>>>>>>>>>>>>>>>>>>
On 7/1/2026 7:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:15 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 5:04 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:57 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In other words, you don't understand that if this >>>>>>>>>>>>>>>>>>>>>> was algorithm H:Good. So when you say "The truth value of (∀ >>>>>>>>>>>>>>>>>>>>>>>>>> x, S(x) ≠ x) does not exist in Q", you mean >>>>>>>>>>>>>>>>>>>>>>>>>> "(∀ x, S(x) ≠ x) is unprovable in Q", which is >>>>>>>>>>>>>>>>>>>>>>>>>> commonly known.It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>>>>>>>>Until someone publishes an Olcott to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Standard English dictionary, this isn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> really an option. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and he invariably responds with an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> example or an analogy (assuming he >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> responds at all). He doesn't get that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> examples don't take the place of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definitions. Examples can be useful >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for clarifying definitions, but they >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> aren't particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> animals" expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> English has no English meaning in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>I didn't ask for an example. I asked >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for a definition of what it mean for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the truth value of a statement to not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) //
copyright Olcott 2018 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
That claims what it means to have the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth value 'true' (or at least it would >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if you defined AtomicFacts in a coherent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> way). It doesn't in any way clarify what >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you think it means for something to not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a truth value. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and >>>>>>>>>>>>>>>>>>>>>>>>>>>>> you did
not bother to pay attention that is your >>>>>>>>>>>>>>>>>>>>>>>>>>>>> mistake
and your fault.
You gave no such definition of what it means >>>>>>>>>>>>>>>>>>>>>>>>>>>> for the truth value of a statement to not >>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
A valid answer would look something like this: >>>>>>>>>>>>>>>>>>>>>>>>>>>>
"The truth value of a statement does not >>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system when ..." >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Now complete the sentence. >>>>>>>>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same thing as >>>>>>>>>>>>>>>>>>>>>>>>>> everyone else but using different words. >>>>>>>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as >>>>>>>>>>>>>>>>>>>>>>>>> undecidable
meaning that Q is incomplete meaning that Q is >>>>>>>>>>>>>>>>>>>>>>>>> deficient.
False. It means that there are statements in >>>>>>>>>>>>>>>>>>>>>>>> the language of Q that have *only* an infinite >>>>>>>>>>>>>>>>>>>>>>>> connection to the axioms of the system. >>>>>>>>>>>>>>>>>>>>>>>>
OK, I verified that.
Which starts with the assumption that an >>>>>>>>>>>>>>>>>>>>>>>> algorithm H exists that meets the following >>>>>>>>>>>>>>>>>>>>>>>> requirements:
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed immutable >>>>>>>>>>>>>>>>>>>>>>>> sequence of instructions) X described as <X> >>>>>>>>>>>>>>>>>>>>>>>> with input Y:
A solution to the halting problem is an >>>>>>>>>>>>>>>>>>>>>>>> algorithm H that computes the following mapping: >>>>>>>>>>>>>>>>>>>>>>>>
(<X>,Y) maps to 1 if and only if X(Y) halts when >>>>>>>>>>>>>>>>>>>>>>>> executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not >>>>>>>>>>>>>>>>>>>>>>>> halt when executed directly
Sure and we could equally start with the requirement >>>>>>>>>>>>>>>>>>>>>>> to prove that there exists a natural number > 3 >>>>>>>>>>>>>>>>>>>>>>> and < 2.
I really don't see how everyone did not >>>>>>>>>>>>>>>>>>>>>>> immediately see
that the requirement for H to correctly report >>>>>>>>>>>>>>>>>>>>>>> the halt
status of input D that does the opposite of >>>>>>>>>>>>>>>>>>>>>>> whatever H
reports is a moronically stupid requirement >>>>>>>>>>>>>>>>>>>>>>> within the
first five minutes that this requirement was made. >>>>>>>>>>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years. >>>>>>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm: >>>>>>>>>>>>>>>>>>>>
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting >>>>>>>>>>>>>>>>>> problem for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D) >>>>>>>>>>>>>>>>
You just don't know jack shit dufus.
I have been a professional C programmer since 1986. >>>>>>>>>>>>>>>
Says the person that just demonstrated that they don't >>>>>>>>>>>>>> know the difference between an algorithm and a C function. >>>>>>>>>>>>>>
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored by >>>>>>>>>>>> everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be a >>>>>>>>>> halt decider,
Ridiculously stupid. Your H does not even look at its input.
Algorithm H doesn't need to read its inputs in order to map all >>>>>>>> inputs to non-halting.
Also your D simply stops running I ran it to verify.
Verifying that algorithm H doesn't correctly report what
algorithm D does, as per the design of algorithm D.
Still no reply to this, so I have to assume you agree it's correct.
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi and others. >>>>>>
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
There is no error. The POE follows from a series of truth
preserving operations
To say this objectively classical logic is objectively incorrect
when it diverges from what correct reasoning would be while
retaining the full English semantics of the terms.
(P ∧ ¬P) ⊢ Q is ridiculously stupid when we plug English
sentences in for P and Q and use semantic entailment in English
as the measure of correct reasoning.
We already did that and you got confused, calling it a mind game (see
below):
accept POE as correct for more than sixty seconds.
Every average third grader knows that a contradiction
On 7/2/2026 5:12 PM, olcott wrote:
On 7/2/2026 3:54 PM, dbush wrote:States that both a statement and its negation are true. And if a formal system can reach a contradiction through a series of truth preserving operations from its axioms, that means both statements are proven true.
On 7/2/2026 4:53 PM, olcott wrote:The confusing part is how an intelligent person can
On 7/2/2026 2:52 PM, dbush wrote:
On 7/2/2026 3:33 PM, olcott wrote:
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:Algorithm H doesn't need to read its inputs in order to map all >>>>>>>>> inputs to non-halting.
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:And algorithm H is wrong about algorithm D because >>>>>>>>>>>>>>>>> algorithm D contains a copy of algorithm H and does the >>>>>>>>>>>>>>>>> opposite.
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 9:36 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 7:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:15 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 5:04 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:57 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
And still don't understand that this algorithm: >>>>>>>>>>>>>>>>>>>>>In other words, you don't understand that if this >>>>>>>>>>>>>>>>>>>>>>> was algorithm H:Good. So when you say "The truth value of (∀ >>>>>>>>>>>>>>>>>>>>>>>>>>> x, S(x) ≠ x) does not exist in Q", you mean >>>>>>>>>>>>>>>>>>>>>>>>>>> "(∀ x, S(x) ≠ x) is unprovable in Q", which >>>>>>>>>>>>>>>>>>>>>>>>>>> is commonly known.It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>>>>>>>>>Until someone publishes an Olcott to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Standard English dictionary, this isn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> really an option. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I'm actually not convinced that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Olcott understands what a definition >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is. I've frequently asked him for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definitions and he invariably >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> responds with an example or an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> analogy (assuming he responds at >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all). He doesn't get that examples >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> don't take the place of definitions. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Examples can be useful for clarifying >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> animals" expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> English has no English meaning in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>I didn't ask for an example. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> asked for a definition of what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean for the truth value of a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement to not exist in a formal >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> X) // copyright Olcott 2018 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
That claims what it means to have the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth value 'true' (or at least it would >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if you defined AtomicFacts in a coherent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> way). It doesn't in any way clarify what >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you think it means for something to not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a truth value. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you did
not bother to pay attention that is your >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mistake
and your fault.
You gave no such definition of what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>> means for the truth value of a statement to >>>>>>>>>>>>>>>>>>>>>>>>>>>>> not exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
A valid answer would look something like this: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"The truth value of a statement does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system when ..." >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Now complete the sentence. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same thing >>>>>>>>>>>>>>>>>>>>>>>>>>> as everyone else but using different words. >>>>>>>>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as >>>>>>>>>>>>>>>>>>>>>>>>>> undecidable
meaning that Q is incomplete meaning that Q is >>>>>>>>>>>>>>>>>>>>>>>>>> deficient.
False. It means that there are statements in >>>>>>>>>>>>>>>>>>>>>>>>> the language of Q that have *only* an infinite >>>>>>>>>>>>>>>>>>>>>>>>> connection to the axioms of the system. >>>>>>>>>>>>>>>>>>>>>>>>>
OK, I verified that.
Which starts with the assumption that an >>>>>>>>>>>>>>>>>>>>>>>>> algorithm H exists that meets the following >>>>>>>>>>>>>>>>>>>>>>>>> requirements:
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed immutable >>>>>>>>>>>>>>>>>>>>>>>>> sequence of instructions) X described as <X> >>>>>>>>>>>>>>>>>>>>>>>>> with input Y:
A solution to the halting problem is an >>>>>>>>>>>>>>>>>>>>>>>>> algorithm H that computes the following mapping: >>>>>>>>>>>>>>>>>>>>>>>>>
(<X>,Y) maps to 1 if and only if X(Y) halts >>>>>>>>>>>>>>>>>>>>>>>>> when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not >>>>>>>>>>>>>>>>>>>>>>>>> halt when executed directly
Sure and we could equally start with the >>>>>>>>>>>>>>>>>>>>>>>> requirement
to prove that there exists a natural number > 3 >>>>>>>>>>>>>>>>>>>>>>>> and < 2.
I really don't see how everyone did not >>>>>>>>>>>>>>>>>>>>>>>> immediately see
that the requirement for H to correctly report >>>>>>>>>>>>>>>>>>>>>>>> the halt
status of input D that does the opposite of >>>>>>>>>>>>>>>>>>>>>>>> whatever H
reports is a moronically stupid requirement >>>>>>>>>>>>>>>>>>>>>>>> within the
first five minutes that this requirement was made. >>>>>>>>>>>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years. >>>>>>>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm: >>>>>>>>>>>>>>>>>>>>>
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting >>>>>>>>>>>>>>>>>>> problem for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D) >>>>>>>>>>>>>>>>>
You just don't know jack shit dufus.
I have been a professional C programmer since 1986. >>>>>>>>>>>>>>>>
Says the person that just demonstrated that they don't >>>>>>>>>>>>>>> know the difference between an algorithm and a C function. >>>>>>>>>>>>>>>
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored >>>>>>>>>>>>> by everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be a >>>>>>>>>>> halt decider,
Ridiculously stupid. Your H does not even look at its input. >>>>>>>>>
Also your D simply stops running I ran it to verify.
Verifying that algorithm H doesn't correctly report what
algorithm D does, as per the design of algorithm D.
Still no reply to this, so I have to assume you agree it's correct.
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi and others. >>>>>>>
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
There is no error. The POE follows from a series of truth
preserving operations
To say this objectively classical logic is objectively incorrect
when it diverges from what correct reasoning would be while
retaining the full English semantics of the terms.
(P ∧ ¬P) ⊢ Q is ridiculously stupid when we plug English
sentences in for P and Q and use semantic entailment in English
as the measure of correct reasoning.
We already did that and you got confused, calling it a mind game (see
below):
accept POE as correct for more than sixty seconds.
Every average third grader knows that a contradiction
From *there*, the principle of explosion is applied, demonstrating that
the system that proved the contradiction is useless.
On 7/2/2026 4:23 PM, dbush wrote:
On 7/2/2026 5:12 PM, olcott wrote:
On 7/2/2026 3:54 PM, dbush wrote:States that both a statement and its negation are true. And if a
On 7/2/2026 4:53 PM, olcott wrote:The confusing part is how an intelligent person can
On 7/2/2026 2:52 PM, dbush wrote:
On 7/2/2026 3:33 PM, olcott wrote:
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:Algorithm H doesn't need to read its inputs in order to map >>>>>>>>>> all inputs to non-halting.
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:And algorithm H is wrong about algorithm D because >>>>>>>>>>>>>>>>>> algorithm D contains a copy of algorithm H and does >>>>>>>>>>>>>>>>>> the opposite.
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 9:36 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 7:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:15 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 5:04 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:57 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
And still don't understand that this algorithm: >>>>>>>>>>>>>>>>>>>>>>In other words, you don't understand that if >>>>>>>>>>>>>>>>>>>>>>>> this was algorithm H:Good. So when you say "The truth value of >>>>>>>>>>>>>>>>>>>>>>>>>>>> (∀ x, S(x) ≠ x) does not exist in Q", you >>>>>>>>>>>>>>>>>>>>>>>>>>>> mean "(∀ x, S(x) ≠ x) is unprovable in Q", >>>>>>>>>>>>>>>>>>>>>>>>>>>> which is commonly known. >>>>>>>>>>>>>>>>>>>>>>>>>>>>It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>>>>>>>>>>Until someone publishes an Olcott to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Standard English dictionary, this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> isn't really an option. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I'm actually not convinced that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Olcott understands what a definition >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is. I've frequently asked him for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definitions and he invariably >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> responds with an example or an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> analogy (assuming he responds at >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all). He doesn't get that examples >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> don't take the place of definitions. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Examples can be useful for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> clarifying definitions, but they >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> aren't particularly useful on their >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> own.The same thing as: "cats are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> animals" expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> English has no English meaning in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>I didn't ask for an example. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> asked for a definition of what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean for the truth value of a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement to not exist in a formal >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢
X) // copyright Olcott 2018 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
That claims what it means to have the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth value 'true' (or at least it would >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if you defined AtomicFacts in a coherent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> way). It doesn't in any way clarify what >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you think it means for something to not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have a truth value. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and you did
not bother to pay attention that is your >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mistake
and your fault.
You gave no such definition of what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means for the truth value of a statement >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to not exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
A valid answer would look something like >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this:
"The truth value of a statement does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system when ..." >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Now complete the sentence. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same thing >>>>>>>>>>>>>>>>>>>>>>>>>>>> as everyone else but using different words. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as >>>>>>>>>>>>>>>>>>>>>>>>>>> undecidable
meaning that Q is incomplete meaning that Q >>>>>>>>>>>>>>>>>>>>>>>>>>> is deficient.
False. It means that there are statements in >>>>>>>>>>>>>>>>>>>>>>>>>> the language of Q that have *only* an infinite >>>>>>>>>>>>>>>>>>>>>>>>>> connection to the axioms of the system. >>>>>>>>>>>>>>>>>>>>>>>>>>
OK, I verified that.
Which starts with the assumption that an >>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H exists that meets the following >>>>>>>>>>>>>>>>>>>>>>>>>> requirements:
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed immutable >>>>>>>>>>>>>>>>>>>>>>>>>> sequence of instructions) X described as <X> >>>>>>>>>>>>>>>>>>>>>>>>>> with input Y:
A solution to the halting problem is an >>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H that computes the following mapping: >>>>>>>>>>>>>>>>>>>>>>>>>>
(<X>,Y) maps to 1 if and only if X(Y) halts >>>>>>>>>>>>>>>>>>>>>>>>>> when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not >>>>>>>>>>>>>>>>>>>>>>>>>> halt when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>
Sure and we could equally start with the >>>>>>>>>>>>>>>>>>>>>>>>> requirement
to prove that there exists a natural number > 3 >>>>>>>>>>>>>>>>>>>>>>>>> and < 2.
I really don't see how everyone did not >>>>>>>>>>>>>>>>>>>>>>>>> immediately see
that the requirement for H to correctly report >>>>>>>>>>>>>>>>>>>>>>>>> the halt
status of input D that does the opposite of >>>>>>>>>>>>>>>>>>>>>>>>> whatever H
reports is a moronically stupid requirement >>>>>>>>>>>>>>>>>>>>>>>>> within the
first five minutes that this requirement was made. >>>>>>>>>>>>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years. >>>>>>>>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm: >>>>>>>>>>>>>>>>>>>>>>
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the >>>>>>>>>>>>>>>>>>>> halting problem for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D) >>>>>>>>>>>>>>>>>>
You just don't know jack shit dufus.
I have been a professional C programmer since 1986. >>>>>>>>>>>>>>>>>
Says the person that just demonstrated that they don't >>>>>>>>>>>>>>>> know the difference between an algorithm and a C function. >>>>>>>>>>>>>>>>
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored >>>>>>>>>>>>>> by everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be a >>>>>>>>>>>> halt decider,
Ridiculously stupid. Your H does not even look at its input. >>>>>>>>>>
Also your D simply stops running I ran it to verify.
Verifying that algorithm H doesn't correctly report what
algorithm D does, as per the design of algorithm D.
Still no reply to this, so I have to assume you agree it's correct. >>>>>>
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi and
others.
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
There is no error. The POE follows from a series of truth
preserving operations
To say this objectively classical logic is objectively incorrect
when it diverges from what correct reasoning would be while
retaining the full English semantics of the terms.
(P ∧ ¬P) ⊢ Q is ridiculously stupid when we plug English
sentences in for P and Q and use semantic entailment in English
as the measure of correct reasoning.
We already did that and you got confused, calling it a mind game
(see below):
accept POE as correct for more than sixty seconds.
Every average third grader knows that a contradiction
formal system can reach a contradiction through a series of truth
preserving operations from its axioms, that means both statements are
proven true.
Every third grader knows that it must have fucked up somewhere.
The conclusion that most all logicians are despicable liars
seems implausible so what is left?
On 7/2/2026 5:40 PM, olcott wrote:
On 7/2/2026 4:23 PM, dbush wrote:
On 7/2/2026 5:12 PM, olcott wrote:
On 7/2/2026 3:54 PM, dbush wrote:States that both a statement and its negation are true. And if a
On 7/2/2026 4:53 PM, olcott wrote:The confusing part is how an intelligent person can
On 7/2/2026 2:52 PM, dbush wrote:
On 7/2/2026 3:33 PM, olcott wrote:
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:Algorithm H doesn't need to read its inputs in order to map >>>>>>>>>>> all inputs to non-halting.
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:And algorithm H is wrong about algorithm D because >>>>>>>>>>>>>>>>>>> algorithm D contains a copy of algorithm H and does >>>>>>>>>>>>>>>>>>> the opposite.
On 7/1/2026 11:17 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:00 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:53 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 9:36 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 7:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:15 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 5:04 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:57 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:D(D); // merely halts
And still don't understand that this algorithm: >>>>>>>>>>>>>>>>>>>>>>>Good. So when you say "The truth value of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> (∀ x, S(x) ≠ x) does not exist in Q", you >>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean "(∀ x, S(x) ≠ x) is unprovable in Q", >>>>>>>>>>>>>>>>>>>>>>>>>>>>> which is commonly known. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Until someone publishes an Olcott to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Standard English dictionary, this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> isn't really an option. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>I'm actually not convinced that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Olcott understands what a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition is. I've frequently >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> asked him for definitions and he >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> invariably responds with an example >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or an analogy (assuming he responds >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> at all). He doesn't get that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> examples don't take the place of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definitions. Examples can be useful >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for clarifying definitions, but >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> they aren't particularly useful on >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> animals" expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> English has no English meaning in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>I didn't ask for an example. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> asked for a definition of what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean for the truth value of a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement to not exist in a formal >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢
X) // copyright Olcott 2018 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
That claims what it means to have the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth value 'true' (or at least it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> would if you defined AtomicFacts in a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent way). It doesn't in any way >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> clarify what you think it means for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> something to not have a truth value. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and you did
not bother to pay attention that is your >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mistake
and your fault. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You gave no such definition of what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means for the truth value of a statement >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to not exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
A valid answer would look something like >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this:
"The truth value of a statement does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system when ..." >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Now complete the sentence. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same thing >>>>>>>>>>>>>>>>>>>>>>>>>>>>> as everyone else but using different words. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as >>>>>>>>>>>>>>>>>>>>>>>>>>>> undecidable
meaning that Q is incomplete meaning that Q >>>>>>>>>>>>>>>>>>>>>>>>>>>> is deficient.
False. It means that there are statements in >>>>>>>>>>>>>>>>>>>>>>>>>>> the language of Q that have *only* an >>>>>>>>>>>>>>>>>>>>>>>>>>> infinite connection to the axioms of the system. >>>>>>>>>>>>>>>>>>>>>>>>>>>
OK, I verified that.
Which starts with the assumption that an >>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H exists that meets the following >>>>>>>>>>>>>>>>>>>>>>>>>>> requirements:
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed immutable >>>>>>>>>>>>>>>>>>>>>>>>>>> sequence of instructions) X described as <X> >>>>>>>>>>>>>>>>>>>>>>>>>>> with input Y:
A solution to the halting problem is an >>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H that computes the following mapping: >>>>>>>>>>>>>>>>>>>>>>>>>>>
(<X>,Y) maps to 1 if and only if X(Y) halts >>>>>>>>>>>>>>>>>>>>>>>>>>> when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does >>>>>>>>>>>>>>>>>>>>>>>>>>> not halt when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>>
Sure and we could equally start with the >>>>>>>>>>>>>>>>>>>>>>>>>> requirement
to prove that there exists a natural number > >>>>>>>>>>>>>>>>>>>>>>>>>> 3 and < 2.
I really don't see how everyone did not >>>>>>>>>>>>>>>>>>>>>>>>>> immediately see
that the requirement for H to correctly report >>>>>>>>>>>>>>>>>>>>>>>>>> the halt
status of input D that does the opposite of >>>>>>>>>>>>>>>>>>>>>>>>>> whatever H
reports is a moronically stupid requirement >>>>>>>>>>>>>>>>>>>>>>>>>> within the
first five minutes that this requirement was >>>>>>>>>>>>>>>>>>>>>>>>>> made.
In other words, you don't understand that if >>>>>>>>>>>>>>>>>>>>>>>>> this was algorithm H:
I spent 10,000 hours on it over 22 years. >>>>>>>>>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm: >>>>>>>>>>>>>>>>>>>>>>>
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the >>>>>>>>>>>>>>>>>>>>> halting problem for the last 22 years. >>>>>>>>>>>>>>>>>>>>
H(D,D); // merely returns 0 and never looks at D(D) >>>>>>>>>>>>>>>>>>>
You just don't know jack shit dufus.
I have been a professional C programmer since 1986. >>>>>>>>>>>>>>>>>>
Says the person that just demonstrated that they don't >>>>>>>>>>>>>>>>> know the difference between an algorithm and a C function. >>>>>>>>>>>>>>>>>
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored >>>>>>>>>>>>>>> by everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be a >>>>>>>>>>>>> halt decider,
Ridiculously stupid. Your H does not even look at its input. >>>>>>>>>>>
Also your D simply stops running I ran it to verify.
Verifying that algorithm H doesn't correctly report what >>>>>>>>>>> algorithm D does, as per the design of algorithm D.
Still no reply to this, so I have to assume you agree it's correct. >>>>>>>
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi and >>>>>>>>> others.
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
There is no error. The POE follows from a series of truth
preserving operations
To say this objectively classical logic is objectively incorrect
when it diverges from what correct reasoning would be while
retaining the full English semantics of the terms.
(P ∧ ¬P) ⊢ Q is ridiculously stupid when we plug English
sentences in for P and Q and use semantic entailment in English
as the measure of correct reasoning.
We already did that and you got confused, calling it a mind game
(see below):
accept POE as correct for more than sixty seconds.
Every average third grader knows that a contradiction
formal system can reach a contradiction through a series of truth
preserving operations from its axioms, that means both statements are
proven true.
Every third grader knows that it must have fucked up somewhere.
Your intuition fails you. It just means that the axioms of the system
in question are inconsistent. And the principle of explosion can be
used to show that an inconsistent system is useless.
On 7/2/2026 4:59 PM, dbush wrote:
On 7/2/2026 5:40 PM, olcott wrote:
On 7/2/2026 4:23 PM, dbush wrote:
On 7/2/2026 5:12 PM, olcott wrote:
On 7/2/2026 3:54 PM, dbush wrote:States that both a statement and its negation are true. And if a
On 7/2/2026 4:53 PM, olcott wrote:The confusing part is how an intelligent person can
On 7/2/2026 2:52 PM, dbush wrote:
On 7/2/2026 3:33 PM, olcott wrote:
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:Algorithm H doesn't need to read its inputs in order to map >>>>>>>>>>>> all inputs to non-halting.
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:And algorithm H is wrong about algorithm D because >>>>>>>>>>>>>>>>>>>> algorithm D contains a copy of algorithm H and does >>>>>>>>>>>>>>>>>>>> the opposite.
On 7/1/2026 11:17 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:00 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:53 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 9:36 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 7:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:15 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 5:04 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:57 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:D(D); // merely halts
And still don't understand that this algorithm: >>>>>>>>>>>>>>>>>>>>>>>>Good. So when you say "The truth value of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (∀ x, S(x) ≠ x) does not exist in Q", you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean "(∀ x, S(x) ≠ x) is unprovable in Q", >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which is commonly known. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Until someone publishes an Olcott to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Standard English dictionary, this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> isn't really an option. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>I'm actually not convinced that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Olcott understands what a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition is. I've frequently >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> asked him for definitions and he >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> invariably responds with an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> example or an analogy (assuming he >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> responds at all). He doesn't get >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that examples don't take the place >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of definitions. Examples can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> useful for clarifying definitions, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> but they aren't particularly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> animals" expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> English has no English meaning >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>I didn't ask for an example. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> asked for a definition of what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean for the truth value of a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement to not exist in a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢
X) // copyright Olcott 2018 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
That claims what it means to have the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth value 'true' (or at least it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> would if you defined AtomicFacts in a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent way). It doesn't in any way >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> clarify what you think it means for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> something to not have a truth value. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and you did
not bother to pay attention that is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your mistake >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and your fault. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You gave no such definition of what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means for the truth value of a statement >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to not exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
A valid answer would look something like >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this:
"The truth value of a statement does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system when ..." >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Now complete the sentence. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thing as everyone else but using different >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words.
Not really. It is normally thought of as >>>>>>>>>>>>>>>>>>>>>>>>>>>>> undecidable
meaning that Q is incomplete meaning that Q >>>>>>>>>>>>>>>>>>>>>>>>>>>>> is deficient.
False. It means that there are statements >>>>>>>>>>>>>>>>>>>>>>>>>>>> in the language of Q that have *only* an >>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite connection to the axioms of the >>>>>>>>>>>>>>>>>>>>>>>>>>>> system.
OK, I verified that.
Which starts with the assumption that an >>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H exists that meets the following >>>>>>>>>>>>>>>>>>>>>>>>>>>> requirements:
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed immutable >>>>>>>>>>>>>>>>>>>>>>>>>>>> sequence of instructions) X described as <X> >>>>>>>>>>>>>>>>>>>>>>>>>>>> with input Y:
A solution to the halting problem is an >>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H that computes the following >>>>>>>>>>>>>>>>>>>>>>>>>>>> mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts >>>>>>>>>>>>>>>>>>>>>>>>>>>> when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does >>>>>>>>>>>>>>>>>>>>>>>>>>>> not halt when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Sure and we could equally start with the >>>>>>>>>>>>>>>>>>>>>>>>>>> requirement
to prove that there exists a natural number > >>>>>>>>>>>>>>>>>>>>>>>>>>> 3 and < 2.
I really don't see how everyone did not >>>>>>>>>>>>>>>>>>>>>>>>>>> immediately see
that the requirement for H to correctly >>>>>>>>>>>>>>>>>>>>>>>>>>> report the halt
status of input D that does the opposite of >>>>>>>>>>>>>>>>>>>>>>>>>>> whatever H
reports is a moronically stupid requirement >>>>>>>>>>>>>>>>>>>>>>>>>>> within the
first five minutes that this requirement was >>>>>>>>>>>>>>>>>>>>>>>>>>> made.
In other words, you don't understand that if >>>>>>>>>>>>>>>>>>>>>>>>>> this was algorithm H:
I spent 10,000 hours on it over 22 years. >>>>>>>>>>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm: >>>>>>>>>>>>>>>>>>>>>>>>
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the >>>>>>>>>>>>>>>>>>>>>> halting problem for the last 22 years. >>>>>>>>>>>>>>>>>>>>>
H(D,D); // merely returns 0 and never looks at D(D) >>>>>>>>>>>>>>>>>>>>
You just don't know jack shit dufus.
I have been a professional C programmer since 1986. >>>>>>>>>>>>>>>>>>>
Says the person that just demonstrated that they don't >>>>>>>>>>>>>>>>>> know the difference between an algorithm and a C >>>>>>>>>>>>>>>>>> function.
Back to being ignored for trolling again.
Maybe by someone but you are still far from being >>>>>>>>>>>>>>>> ignored by everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed >>>>>>>>>>>>>>> to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be >>>>>>>>>>>>>> a halt decider,
Ridiculously stupid. Your H does not even look at its input. >>>>>>>>>>>>
Also your D simply stops running I ran it to verify.
Verifying that algorithm H doesn't correctly report what >>>>>>>>>>>> algorithm D does, as per the design of algorithm D.
Still no reply to this, so I have to assume you agree it's correct. >>>>>>>>
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi and >>>>>>>>>> others.
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
There is no error. The POE follows from a series of truth
preserving operations
To say this objectively classical logic is objectively incorrect >>>>>>> when it diverges from what correct reasoning would be while
retaining the full English semantics of the terms.
(P ∧ ¬P) ⊢ Q is ridiculously stupid when we plug English
sentences in for P and Q and use semantic entailment in English
as the measure of correct reasoning.
We already did that and you got confused, calling it a mind game
(see below):
accept POE as correct for more than sixty seconds.
Every average third grader knows that a contradiction
formal system can reach a contradiction through a series of truth
preserving operations from its axioms, that means both statements
are proven true.
Every third grader knows that it must have fucked up somewhere.
Your intuition fails you. It just means that the axioms of the system
in question are inconsistent. And the principle of explosion can be
used to show that an inconsistent system is useless.
It makes more sense to use the ordinary meaning
of contradiction:
When-so-ever two sentences contradict each other
at least one of them is false.
On 7/2/2026 6:13 PM, olcott wrote:
On 7/2/2026 4:59 PM, dbush wrote:
On 7/2/2026 5:40 PM, olcott wrote:
On 7/2/2026 4:23 PM, dbush wrote:
On 7/2/2026 5:12 PM, olcott wrote:
On 7/2/2026 3:54 PM, dbush wrote:States that both a statement and its negation are true. And if a
On 7/2/2026 4:53 PM, olcott wrote:The confusing part is how an intelligent person can
On 7/2/2026 2:52 PM, dbush wrote:
On 7/2/2026 3:33 PM, olcott wrote:
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:Algorithm H doesn't need to read its inputs in order to map >>>>>>>>>>>>> all inputs to non-halting.
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:18 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 11:17 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:00 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:53 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 9:36 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 7:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:15 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 5:04 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:57 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
And algorithm H is wrong about algorithm D because >>>>>>>>>>>>>>>>>>>>> algorithm D contains a copy of algorithm H and does >>>>>>>>>>>>>>>>>>>>> the opposite.D(D); // merely haltsAnd still don't understand that this algorithm: >>>>>>>>>>>>>>>>>>>>>>>>>Good. So when you say "The truth value >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of (∀ x, S(x) ≠ x) does not exist in Q", >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you mean "(∀ x, S(x) ≠ x) is unprovable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in Q", which is commonly known. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The same thing as: "cats are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> animals" expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> English has no English meaning >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I didn't ask for an example. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> asked for a definition of what >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it mean for the truth value of a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement to not exist in a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Until someone publishes an Olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to Standard English dictionary, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this isn't really an option. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>I'm actually not convinced that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Olcott understands what a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition is. I've frequently >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> asked him for definitions and he >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> invariably responds with an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> example or an analogy (assuming >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> he responds at all). He doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> get that examples don't take the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> place of definitions. Examples >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can be useful for clarifying >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢
X) // copyright Olcott 2018 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⊢ X)
That claims what it means to have the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth value 'true' (or at least it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> would if you defined AtomicFacts in a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent way). It doesn't in any way >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> clarify what you think it means for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> something to not have a truth value. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and you did >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not bother to pay attention that is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your mistake >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and your fault. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You gave no such definition of what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means for the truth value of a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement to not exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
A valid answer would look something >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> like this:
"The truth value of a statement does >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not exist in a formal system when ..." >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Now complete the sentence. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thing as everyone else but using >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> different words. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> undecidable
meaning that Q is incomplete meaning that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Q is deficient.
False. It means that there are statements >>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the language of Q that have *only* an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite connection to the axioms of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> system.
OK, I verified that.
Which starts with the assumption that an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H exists that meets the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>> requirements:
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed immutable >>>>>>>>>>>>>>>>>>>>>>>>>>>>> sequence of instructions) X described as >>>>>>>>>>>>>>>>>>>>>>>>>>>>> <X> with input Y:
A solution to the halting problem is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H that computes the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>> mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does >>>>>>>>>>>>>>>>>>>>>>>>>>>>> not halt when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Sure and we could equally start with the >>>>>>>>>>>>>>>>>>>>>>>>>>>> requirement
to prove that there exists a natural number >>>>>>>>>>>>>>>>>>>>>>>>>>>> > 3 and < 2.
I really don't see how everyone did not >>>>>>>>>>>>>>>>>>>>>>>>>>>> immediately see
that the requirement for H to correctly >>>>>>>>>>>>>>>>>>>>>>>>>>>> report the halt
status of input D that does the opposite of >>>>>>>>>>>>>>>>>>>>>>>>>>>> whatever H
reports is a moronically stupid requirement >>>>>>>>>>>>>>>>>>>>>>>>>>>> within the
first five minutes that this requirement was >>>>>>>>>>>>>>>>>>>>>>>>>>>> made.
In other words, you don't understand that if >>>>>>>>>>>>>>>>>>>>>>>>>>> this was algorithm H:
I spent 10,000 hours on it over 22 years. >>>>>>>>>>>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0; >>>>>>>>>>>>>>>>>>>>>>>>> }
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm: >>>>>>>>>>>>>>>>>>>>>>>>>
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0; >>>>>>>>>>>>>>>>>>>>>>>>> }
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the >>>>>>>>>>>>>>>>>>>>>>> halting problem for the last 22 years. >>>>>>>>>>>>>>>>>>>>>>
H(D,D); // merely returns 0 and never looks at D(D) >>>>>>>>>>>>>>>>>>>>>
You just don't know jack shit dufus.
I have been a professional C programmer since 1986. >>>>>>>>>>>>>>>>>>>>
Says the person that just demonstrated that they >>>>>>>>>>>>>>>>>>> don't know the difference between an algorithm and a >>>>>>>>>>>>>>>>>>> C function.
Back to being ignored for trolling again.
Maybe by someone but you are still far from being >>>>>>>>>>>>>>>>> ignored by everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed >>>>>>>>>>>>>>>> to show the halting problem counter-example?
It perfectly illustrates an algorithm that attempts to be >>>>>>>>>>>>>>> a halt decider,
Ridiculously stupid. Your H does not even look at its input. >>>>>>>>>>>>>
Verifying that algorithm H doesn't correctly report what >>>>>>>>>>>>> algorithm D does, as per the design of algorithm D.
Also your D simply stops running I ran it to verify. >>>>>>>>>>>>>
Still no reply to this, so I have to assume you agree it's
correct.
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi and >>>>>>>>>>> others.
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
There is no error. The POE follows from a series of truth >>>>>>>>> preserving operations
To say this objectively classical logic is objectively incorrect >>>>>>>> when it diverges from what correct reasoning would be while
retaining the full English semantics of the terms.
(P ∧ ¬P) ⊢ Q is ridiculously stupid when we plug English >>>>>>>> sentences in for P and Q and use semantic entailment in English >>>>>>>> as the measure of correct reasoning.
We already did that and you got confused, calling it a mind game >>>>>>> (see below):
accept POE as correct for more than sixty seconds.
Every average third grader knows that a contradiction
formal system can reach a contradiction through a series of truth
preserving operations from its axioms, that means both statements
are proven true.
Every third grader knows that it must have fucked up somewhere.
Your intuition fails you. It just means that the axioms of the
system in question are inconsistent. And the principle of explosion
can be used to show that an inconsistent system is useless.
It makes more sense to use the ordinary meaning
of contradiction:
When-so-ever two sentences contradict each other
at least one of them is false.
Whatever you call it, if the axioms of a formal system can prove both X
and ~X, then the principle of explosion can be used to show that system
is useless.
On 7/2/2026 5:32 PM, dbush wrote:
On 7/2/2026 6:13 PM, olcott wrote:
On 7/2/2026 4:59 PM, dbush wrote:
On 7/2/2026 5:40 PM, olcott wrote:
On 7/2/2026 4:23 PM, dbush wrote:
On 7/2/2026 5:12 PM, olcott wrote:
On 7/2/2026 3:54 PM, dbush wrote:States that both a statement and its negation are true. And if a >>>>>> formal system can reach a contradiction through a series of truth >>>>>> preserving operations from its axioms, that means both statements >>>>>> are proven true.
On 7/2/2026 4:53 PM, olcott wrote:The confusing part is how an intelligent person can
On 7/2/2026 2:52 PM, dbush wrote:
On 7/2/2026 3:33 PM, olcott wrote:
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:Algorithm H doesn't need to read its inputs in order to >>>>>>>>>>>>>> map all inputs to non-halting.
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:Maybe by someone but you are still far from being >>>>>>>>>>>>>>>>>> ignored by everone.
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:18 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 11:17 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:00 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:53 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 9:36 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 7:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:15 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 5:04 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:57 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
And algorithm H is wrong about algorithm D because >>>>>>>>>>>>>>>>>>>>>> algorithm D contains a copy of algorithm H and >>>>>>>>>>>>>>>>>>>>>> does the opposite.D(D); // merely haltsAnd still don't understand that this algorithm: >>>>>>>>>>>>>>>>>>>>>>>>>>Good. So when you say "The truth value >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of (∀ x, S(x) ≠ x) does not exist in Q", >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you mean "(∀ x, S(x) ≠ x) is unprovable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in Q", which is commonly known. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is neither provable nor refutable in F. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The same thing as: "cats are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> animals" expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> English has no English meaning >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I didn't ask for an example. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> asked for a definition of what >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it mean for the truth value of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a statement to not exist in a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I'm actually not convinced that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Olcott understands what a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition is. I've frequently >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> asked him for definitions and he >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> invariably responds with an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> example or an analogy (assuming >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> he responds at all). He doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> get that examples don't take the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> place of definitions. Examples >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can be useful for clarifying >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
That claims what it means to have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the truth value 'true' (or at least >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it would if you defined AtomicFacts >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in a coherent way). It doesn't in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> any way clarify what you think it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means for something to not have a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth value. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Until someone publishes an Olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to Standard English dictionary, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this isn't really an option. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢
X) // copyright Olcott 2018 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ
⊢ X) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When I define a term hundreds of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> times and you did >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not bother to pay attention that is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your mistake >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and your fault. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You gave no such definition of what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means for the truth value of a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement to not exist in a formal >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> system.
A valid answer would look something >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> like this: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"The truth value of a statement does >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not exist in a formal system when ..." >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Now complete the sentence. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thing as everyone else but using >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> different words. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> undecidable
meaning that Q is incomplete meaning that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Q is deficient.
False. It means that there are statements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the language of Q that have *only* an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite connection to the axioms of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> system.
OK, I verified that. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Which starts with the assumption that an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H exists that meets the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> following requirements: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> immutable sequence of instructions) X >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> described as <X> with input Y: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
A solution to the halting problem is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H that computes the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mapping:
(<X>,Y) maps to 1 if and only if X(Y) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halts when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not halt when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Sure and we could equally start with the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> requirement
to prove that there exists a natural number >>>>>>>>>>>>>>>>>>>>>>>>>>>>> > 3 and < 2.
I really don't see how everyone did not >>>>>>>>>>>>>>>>>>>>>>>>>>>>> immediately see
that the requirement for H to correctly >>>>>>>>>>>>>>>>>>>>>>>>>>>>> report the halt
status of input D that does the opposite of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> whatever H
reports is a moronically stupid requirement >>>>>>>>>>>>>>>>>>>>>>>>>>>>> within the
first five minutes that this requirement >>>>>>>>>>>>>>>>>>>>>>>>>>>>> was made.
In other words, you don't understand that if >>>>>>>>>>>>>>>>>>>>>>>>>>>> this was algorithm H:
I spent 10,000 hours on it over 22 years. >>>>>>>>>>>>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0; >>>>>>>>>>>>>>>>>>>>>>>>>> }
if (result == 1) { >>>>>>>>>>>>>>>>>>>>>>>>>> while (1); >>>>>>>>>>>>>>>>>>>>>>>>>> }
}
Is the counter example input to this algorithm: >>>>>>>>>>>>>>>>>>>>>>>>>>
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0; >>>>>>>>>>>>>>>>>>>>>>>>>> }
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the >>>>>>>>>>>>>>>>>>>>>>>> halting problem for the last 22 years. >>>>>>>>>>>>>>>>>>>>>>>
H(D,D); // merely returns 0 and never looks at D(D) >>>>>>>>>>>>>>>>>>>>>>
You just don't know jack shit dufus. >>>>>>>>>>>>>>>>>>>>> I have been a professional C programmer since 1986. >>>>>>>>>>>>>>>>>>>>>
Says the person that just demonstrated that they >>>>>>>>>>>>>>>>>>>> don't know the difference between an algorithm and a >>>>>>>>>>>>>>>>>>>> C function.
Back to being ignored for trolling again. >>>>>>>>>>>>>>>>>>
Do you know enough about C to understand that >>>>>>>>>>>>>>>>> dbush example was foolish nonsense when proposed >>>>>>>>>>>>>>>>> to show the halting problem counter-example? >>>>>>>>>>>>>>>>>
It perfectly illustrates an algorithm that attempts to >>>>>>>>>>>>>>>> be a halt decider,
Ridiculously stupid. Your H does not even look at its input. >>>>>>>>>>>>>>
Verifying that algorithm H doesn't correctly report what >>>>>>>>>>>>>> algorithm D does, as per the design of algorithm D. >>>>>>>>>>>>>>
Also your D simply stops running I ran it to verify. >>>>>>>>>>>>>>
Still no reply to this, so I have to assume you agree it's >>>>>>>>>> correct.
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi and >>>>>>>>>>>> others.
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
There is no error. The POE follows from a series of truth >>>>>>>>>> preserving operations
To say this objectively classical logic is objectively incorrect >>>>>>>>> when it diverges from what correct reasoning would be while
retaining the full English semantics of the terms.
(P ∧ ¬P) ⊢ Q is ridiculously stupid when we plug English >>>>>>>>> sentences in for P and Q and use semantic entailment in English >>>>>>>>> as the measure of correct reasoning.
We already did that and you got confused, calling it a mind game >>>>>>>> (see below):
accept POE as correct for more than sixty seconds.
Every average third grader knows that a contradiction
Every third grader knows that it must have fucked up somewhere.
Your intuition fails you. It just means that the axioms of the
system in question are inconsistent. And the principle of explosion >>>> can be used to show that an inconsistent system is useless.
It makes more sense to use the ordinary meaning
of contradiction:
When-so-ever two sentences contradict each other
at least one of them is false.
Whatever you call it, if the axioms of a formal system can prove both
X and ~X, then the principle of explosion can be used to show that
system is useless.
X & ~X proves FALSE.
How can anyone that is not nuts possibly think otherwise?
On 7/2/2026 6:35 PM, olcott wrote:
On 7/2/2026 5:32 PM, dbush wrote:
On 7/2/2026 6:13 PM, olcott wrote:
On 7/2/2026 4:59 PM, dbush wrote:
On 7/2/2026 5:40 PM, olcott wrote:
On 7/2/2026 4:23 PM, dbush wrote:
On 7/2/2026 5:12 PM, olcott wrote:
On 7/2/2026 3:54 PM, dbush wrote:States that both a statement and its negation are true. And if a >>>>>>> formal system can reach a contradiction through a series of truth >>>>>>> preserving operations from its axioms, that means both statements >>>>>>> are proven true.
On 7/2/2026 4:53 PM, olcott wrote:The confusing part is how an intelligent person can
On 7/2/2026 2:52 PM, dbush wrote:
On 7/2/2026 3:33 PM, olcott wrote:
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:Maybe by someone but you are still far from being >>>>>>>>>>>>>>>>>>> ignored by everone.
On 7/1/2026 11:59 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:43 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 11:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:18 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 11:17 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:00 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:53 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 9:36 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 7:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:15 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 5:04 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:57 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The same thing as: "cats are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> animals" expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> English has no English >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I didn't ask for an example. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I asked for a definition of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what it mean for the truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> value of a statement to not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I'm actually not convinced that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Olcott understands what a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition is. I've frequently >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> asked him for definitions and >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> he invariably responds with an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> example or an analogy (assuming >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> he responds at all). He doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> get that examples don't take >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the place of definitions. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Examples can be useful for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> clarifying definitions, but >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> they aren't particularly useful >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
And algorithm H is wrong about algorithm D >>>>>>>>>>>>>>>>>>>>>>> because algorithm D contains a copy of algorithm >>>>>>>>>>>>>>>>>>>>>>> H and does the opposite.D(D); // merely haltsAnd still don't understand that this algorithm: >>>>>>>>>>>>>>>>>>>>>>>>>>>False. It means that there are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements in the language of Q that have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> *only* an infinite connection to the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> axioms of the system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is neither provable nor refutable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in F.That claims what it means to have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the truth value 'true' (or at least >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it would if you defined AtomicFacts >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in a coherent way). It doesn't in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> any way clarify what you think it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means for something to not have a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth value. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Until someone publishes an Olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to Standard English dictionary, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this isn't really an option. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ
⊢ X) // copyright Olcott 2018 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X):= ∃Γ ⊆ AtomicFacts(L) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When I define a term hundreds of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> times and you did >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not bother to pay attention that is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your mistake >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and your fault. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You gave no such definition of what >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it means for the truth value of a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement to not exist in a formal >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> system.
A valid answer would look something >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> like this: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"The truth value of a statement does >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not exist in a formal system when ..." >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Now complete the sentence. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Good. So when you say "The truth value >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of (∀ x, S(x) ≠ x) does not exist in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Q", you mean "(∀ x, S(x) ≠ x) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> unprovable in Q", which is commonly known. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thing as everyone else but using >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> different words. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> undecidable
meaning that Q is incomplete meaning >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that Q is deficient. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
OK, I verified that. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Which starts with the assumption that an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H exists that meets the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> following requirements: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> immutable sequence of instructions) X >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> described as <X> with input Y: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
A solution to the halting problem is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H that computes the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mapping:
(<X>,Y) maps to 1 if and only if X(Y) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halts when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not halt when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Sure and we could equally start with the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> requirement
to prove that there exists a natural >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> number > 3 and < 2. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I really don't see how everyone did not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> immediately see
that the requirement for H to correctly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> report the halt
status of input D that does the opposite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of whatever H
reports is a moronically stupid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> requirement within the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> first five minutes that this requirement >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> was made.
In other words, you don't understand that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> if this was algorithm H: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years. >>>>>>>>>>>>>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0; >>>>>>>>>>>>>>>>>>>>>>>>>>> }
if (result == 1) { >>>>>>>>>>>>>>>>>>>>>>>>>>> while (1); >>>>>>>>>>>>>>>>>>>>>>>>>>> }
}
Is the counter example input to this algorithm: >>>>>>>>>>>>>>>>>>>>>>>>>>>
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0; >>>>>>>>>>>>>>>>>>>>>>>>>>> }
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the >>>>>>>>>>>>>>>>>>>>>>>>> halting problem for the last 22 years. >>>>>>>>>>>>>>>>>>>>>>>>
H(D,D); // merely returns 0 and never looks at D(D) >>>>>>>>>>>>>>>>>>>>>>>
You just don't know jack shit dufus. >>>>>>>>>>>>>>>>>>>>>> I have been a professional C programmer since 1986. >>>>>>>>>>>>>>>>>>>>>>
Says the person that just demonstrated that they >>>>>>>>>>>>>>>>>>>>> don't know the difference between an algorithm and >>>>>>>>>>>>>>>>>>>>> a C function.
Back to being ignored for trolling again. >>>>>>>>>>>>>>>>>>>
Do you know enough about C to understand that >>>>>>>>>>>>>>>>>> dbush example was foolish nonsense when proposed >>>>>>>>>>>>>>>>>> to show the halting problem counter-example? >>>>>>>>>>>>>>>>>>
It perfectly illustrates an algorithm that attempts to >>>>>>>>>>>>>>>>> be a halt decider,
Ridiculously stupid. Your H does not even look at its >>>>>>>>>>>>>>>> input.
Algorithm H doesn't need to read its inputs in order to >>>>>>>>>>>>>>> map all inputs to non-halting.
Verifying that algorithm H doesn't correctly report what >>>>>>>>>>>>>>> algorithm D does, as per the design of algorithm D. >>>>>>>>>>>>>>>
Also your D simply stops running I ran it to verify. >>>>>>>>>>>>>>>
Still no reply to this, so I have to assume you agree it's >>>>>>>>>>> correct.
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi >>>>>>>>>>>>> and others.
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
There is no error. The POE follows from a series of truth >>>>>>>>>>> preserving operations
To say this objectively classical logic is objectively incorrect >>>>>>>>>> when it diverges from what correct reasoning would be while >>>>>>>>>> retaining the full English semantics of the terms.
(P ∧ ¬P) ⊢ Q is ridiculously stupid when we plug English >>>>>>>>>> sentences in for P and Q and use semantic entailment in English >>>>>>>>>> as the measure of correct reasoning.
We already did that and you got confused, calling it a mind >>>>>>>>> game (see below):
accept POE as correct for more than sixty seconds.
Every average third grader knows that a contradiction
Every third grader knows that it must have fucked up somewhere.
Your intuition fails you. It just means that the axioms of the
system in question are inconsistent. And the principle of
explosion can be used to show that an inconsistent system is useless. >>>>>
It makes more sense to use the ordinary meaning
of contradiction:
When-so-ever two sentences contradict each other
at least one of them is false.
Whatever you call it, if the axioms of a formal system can prove both
X and ~X, then the principle of explosion can be used to show that
system is useless.
X & ~X proves FALSE.
How can anyone that is not nuts possibly think otherwise?
Assuming that X & ~X has been proven from the axioms of a formal system,
On 7/2/2026 5:47 PM, dbush wrote:
On 7/2/2026 6:35 PM, olcott wrote:
On 7/2/2026 5:32 PM, dbush wrote:
On 7/2/2026 6:13 PM, olcott wrote:
On 7/2/2026 4:59 PM, dbush wrote:
On 7/2/2026 5:40 PM, olcott wrote:
On 7/2/2026 4:23 PM, dbush wrote:
On 7/2/2026 5:12 PM, olcott wrote:
On 7/2/2026 3:54 PM, dbush wrote:States that both a statement and its negation are true. And if >>>>>>>> a formal system can reach a contradiction through a series of >>>>>>>> truth preserving operations from its axioms, that means both
On 7/2/2026 4:53 PM, olcott wrote:The confusing part is how an intelligent person can
On 7/2/2026 2:52 PM, dbush wrote:
On 7/2/2026 3:33 PM, olcott wrote:
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:Maybe by someone but you are still far from being >>>>>>>>>>>>>>>>>>>> ignored by everone.
On 7/1/2026 11:59 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:43 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 11:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:18 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 11:17 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:00 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:53 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 9:36 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 7:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:15 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 5:04 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:57 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The same thing as: "cats are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> animals" expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> English has no English >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I didn't ask for an example. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I asked for a definition of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what it mean for the truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> value of a statement to not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I'm actually not convinced >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that Olcott understands what a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition is. I've frequently >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> asked him for definitions and >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> he invariably responds with an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> example or an analogy >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (assuming he responds at all). >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> He doesn't get that examples >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> don't take the place of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definitions. Examples can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> useful for clarifying >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Until someone publishes an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Olcott to Standard English >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> dictionary, this isn't really an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> option. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
D(D); // merely haltsAnd still don't understand that this algorithm: >>>>>>>>>>>>>>>>>>>>>>>>>>>>False. It means that there are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements in the language of Q that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have *only* an infinite connection to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the axioms of the system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is neither provable nor refutable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in F.True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (ΓThat claims what it means to have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the truth value 'true' (or at >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> least it would if you defined >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> AtomicFacts in a coherent way). It >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't in any way clarify what >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you think it means for something >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to not have a truth value. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
⊢ X) // copyright Olcott 2018 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
True(L, X):= ∃Γ ⊆ AtomicFacts(L) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When I define a term hundreds of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> times and you did >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not bother to pay attention that is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> your mistake >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and your fault. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You gave no such definition of what >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it means for the truth value of a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement to not exist in a formal >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
A valid answer would look something >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> like this: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"The truth value of a statement does >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not exist in a formal system when ..." >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Now complete the sentence. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Good. So when you say "The truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> value of (∀ x, S(x) ≠ x) does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in Q", you mean "(∀ x, S(x) ≠ x) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is unprovable in Q", which is commonly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> known.
So once again, you're saying the same >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thing as everyone else but using >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> different words. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> as undecidable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning that Q is incomplete meaning >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that Q is deficient. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
OK, I verified that. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Which starts with the assumption that an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H exists that meets the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> following requirements: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> immutable sequence of instructions) X >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> described as <X> with input Y: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
A solution to the halting problem is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H that computes the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mapping:
(<X>,Y) maps to 1 if and only if X(Y) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halts when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not halt when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Sure and we could equally start with the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> requirement
to prove that there exists a natural >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> number > 3 and < 2. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I really don't see how everyone did not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> immediately see
that the requirement for H to correctly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> report the halt
status of input D that does the opposite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of whatever H
reports is a moronically stupid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> requirement within the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> first five minutes that this requirement >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> was made.
In other words, you don't understand that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if this was algorithm H: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0; >>>>>>>>>>>>>>>>>>>>>>>>>>>> }
if (result == 1) { >>>>>>>>>>>>>>>>>>>>>>>>>>>> while (1); >>>>>>>>>>>>>>>>>>>>>>>>>>>> }
}
Is the counter example input to this algorithm: >>>>>>>>>>>>>>>>>>>>>>>>>>>>
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0; >>>>>>>>>>>>>>>>>>>>>>>>>>>> }
return result; >>>>>>>>>>>>>>>>>>>>>>>>>>>> }
That is just nonsense.
Thereby proving that you've misunderstood the >>>>>>>>>>>>>>>>>>>>>>>>>> halting problem for the last 22 years. >>>>>>>>>>>>>>>>>>>>>>>>>
H(D,D); // merely returns 0 and never looks at >>>>>>>>>>>>>>>>>>>>>>>>> D(D)
And algorithm H is wrong about algorithm D >>>>>>>>>>>>>>>>>>>>>>>> because algorithm D contains a copy of algorithm >>>>>>>>>>>>>>>>>>>>>>>> H and does the opposite.
You just don't know jack shit dufus. >>>>>>>>>>>>>>>>>>>>>>> I have been a professional C programmer since 1986. >>>>>>>>>>>>>>>>>>>>>>>
Says the person that just demonstrated that they >>>>>>>>>>>>>>>>>>>>>> don't know the difference between an algorithm and >>>>>>>>>>>>>>>>>>>>>> a C function.
Back to being ignored for trolling again. >>>>>>>>>>>>>>>>>>>>
Do you know enough about C to understand that >>>>>>>>>>>>>>>>>>> dbush example was foolish nonsense when proposed >>>>>>>>>>>>>>>>>>> to show the halting problem counter-example? >>>>>>>>>>>>>>>>>>>
It perfectly illustrates an algorithm that attempts to >>>>>>>>>>>>>>>>>> be a halt decider,
Ridiculously stupid. Your H does not even look at its >>>>>>>>>>>>>>>>> input.
Algorithm H doesn't need to read its inputs in order to >>>>>>>>>>>>>>>> map all inputs to non-halting.
Verifying that algorithm H doesn't correctly report what >>>>>>>>>>>>>>>> algorithm D does, as per the design of algorithm D. >>>>>>>>>>>>>>>>
Also your D simply stops running I ran it to verify. >>>>>>>>>>>>>>>>
Still no reply to this, so I have to assume you agree it's >>>>>>>>>>>> correct.
I am trying to keep liars from killing the
whole fucking planet by making truth computable
Which can't be done as proved by Turing / Godel / Tarksi >>>>>>>>>>>>>> and others.
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
There is no error. The POE follows from a series of truth >>>>>>>>>>>> preserving operations
To say this objectively classical logic is objectively incorrect >>>>>>>>>>> when it diverges from what correct reasoning would be while >>>>>>>>>>> retaining the full English semantics of the terms.
(P ∧ ¬P) ⊢ Q is ridiculously stupid when we plug English >>>>>>>>>>> sentences in for P and Q and use semantic entailment in English >>>>>>>>>>> as the measure of correct reasoning.
We already did that and you got confused, calling it a mind >>>>>>>>>> game (see below):
accept POE as correct for more than sixty seconds.
Every average third grader knows that a contradiction
statements are proven true.
Every third grader knows that it must have fucked up somewhere.
Your intuition fails you. It just means that the axioms of the
system in question are inconsistent. And the principle of
explosion can be used to show that an inconsistent system is useless. >>>>>>
It makes more sense to use the ordinary meaning
of contradiction:
When-so-ever two sentences contradict each other
at least one of them is false.
Whatever you call it, if the axioms of a formal system can prove
both X and ~X, then the principle of explosion can be used to show
that system is useless.
X & ~X proves FALSE.
How can anyone that is not nuts possibly think otherwise?
Assuming that X & ~X has been proven from the axioms of a formal system,
Stipulating the ordinary English meaning of contradiction
On 7/2/2026 6:53 PM, olcott wrote:
On 7/2/2026 5:47 PM, dbush wrote:
On 7/2/2026 6:35 PM, olcott wrote:Stipulating the ordinary English meaning of contradiction
On 7/2/2026 5:32 PM, dbush wrote:
On 7/2/2026 6:13 PM, olcott wrote:
On 7/2/2026 4:59 PM, dbush wrote:
On 7/2/2026 5:40 PM, olcott wrote:
On 7/2/2026 4:23 PM, dbush wrote:Your intuition fails you. It just means that the axioms of the >>>>>>> system in question are inconsistent. And the principle of
On 7/2/2026 5:12 PM, olcott wrote:
On 7/2/2026 3:54 PM, dbush wrote:States that both a statement and its negation are true. And if >>>>>>>>> a formal system can reach a contradiction through a series of >>>>>>>>> truth preserving operations from its axioms, that means both >>>>>>>>> statements are proven true.
On 7/2/2026 4:53 PM, olcott wrote:The confusing part is how an intelligent person can
On 7/2/2026 2:52 PM, dbush wrote:
On 7/2/2026 3:33 PM, olcott wrote:
On 7/2/2026 1:22 PM, dbush wrote:
On 7/2/2026 2:13 PM, olcott wrote:
On 7/2/2026 11:55 AM, dbush wrote:
On 7/2/2026 12:52 PM, olcott wrote:
On 7/2/2026 11:04 AM, dbush wrote:
On 7/2/2026 10:51 AM, olcott wrote:
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 11:59 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:43 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 11:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:18 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 11:17 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:00 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 10:53 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 9:36 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 7:37 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:15 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 5:04 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:57 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:50 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:37 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 4:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 3:13 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:31 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The same thing as: "cats >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> are animals" expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> English has no English >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I didn't ask for an example. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I asked for a definition of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what it mean for the truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> value of a statement to not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I'm actually not convinced >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that Olcott understands what >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definitions and he invariably >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> responds with an example or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an analogy (assuming he >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> responds at all). He doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> get that examples don't take >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the place of definitions. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Examples can be useful for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> clarifying definitions, but >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> they aren't particularly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Until someone publishes an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Olcott to Standard English >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> dictionary, this isn't really >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an option. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (Γ ⊢ X) // copyright Olcott 2018 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> has been updated to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> True(L, X):= ∃Γ ⊆ AtomicFacts(L) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Maybe by someone but you are still far from being >>>>>>>>>>>>>>>>>>>>> ignored by everone.
You just don't know jack shit dufus. >>>>>>>>>>>>>>>>>>>>>>>> I have been a professional C programmer since 1986. >>>>>>>>>>>>>>>>>>>>>>>>D(D); // merely haltsAnd still don't understand that this >>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm:False. It means that there are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements in the language of Q that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have *only* an infinite connection to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the axioms of the system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is neither provable nor refutable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in F.That claims what it means to have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the truth value 'true' (or at >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> least it would if you defined >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> AtomicFacts in a coherent way). >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It doesn't in any way clarify >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what you think it means for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> something to not have a truth value. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When I define a term hundreds of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> times and you did >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not bother to pay attention that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is your mistake >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and your fault. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You gave no such definition of what >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it means for the truth value of a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement to not exist in a formal >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> system. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
A valid answer would look something >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> like this: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"The truth value of a statement >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not exist in a formal system >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when ..." >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Now complete the sentence. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Good. So when you say "The truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> value of (∀ x, S(x) ≠ x) does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist in Q", you mean "(∀ x, S(x) ≠ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> x) is unprovable in Q", which is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> commonly known. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
So once again, you're saying the same >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thing as everyone else but using >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> different words. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Not really. It is normally thought of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> as undecidable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning that Q is incomplete meaning >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that Q is deficient. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
OK, I verified that. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Which starts with the assumption that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an algorithm H exists that meets the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> following requirements: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The Halting Problem counter-example input >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Given any algorithm (i.e. a fixed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> immutable sequence of instructions) X >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> described as <X> with input Y: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
A solution to the halting problem is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm H that computes the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mapping:
(<X>,Y) maps to 1 if and only if X(Y) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halts when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not halt when executed directly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Sure and we could equally start with the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> requirement
to prove that there exists a natural >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> number > 3 and < 2. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I really don't see how everyone did not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> immediately see >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that the requirement for H to correctly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> report the halt >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> status of input D that does the opposite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of whatever H
reports is a moronically stupid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> requirement within the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> first five minutes that this requirement >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> was made.
In other words, you don't understand that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> if this was algorithm H: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I spent 10,000 hours on it over 22 years. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
void D(ptr *I)
{
ptr *X = D; >>>>>>>>>>>>>>>>>>>>>>>>>>>>> ptr *Y = I; >>>>>>>>>>>>>>>>>>>>>>>>>>>>> int result; >>>>>>>>>>>>>>>>>>>>>>>>>>>>> {
result = 0; >>>>>>>>>>>>>>>>>>>>>>>>>>>>> }
if (result == 1) { >>>>>>>>>>>>>>>>>>>>>>>>>>>>> while (1); >>>>>>>>>>>>>>>>>>>>>>>>>>>>> }
}
Is the counter example input to this >>>>>>>>>>>>>>>>>>>>>>>>>>>>> algorithm:
int H(ptr *X, ptr *Y) >>>>>>>>>>>>>>>>>>>>>>>>>>>>> {
int result; >>>>>>>>>>>>>>>>>>>>>>>>>>>>> {
result = 0; >>>>>>>>>>>>>>>>>>>>>>>>>>>>> }
return result; >>>>>>>>>>>>>>>>>>>>>>>>>>>>> }
That is just nonsense. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Thereby proving that you've misunderstood the >>>>>>>>>>>>>>>>>>>>>>>>>>> halting problem for the last 22 years. >>>>>>>>>>>>>>>>>>>>>>>>>>
H(D,D); // merely returns 0 and never looks at >>>>>>>>>>>>>>>>>>>>>>>>>> D(D)
And algorithm H is wrong about algorithm D >>>>>>>>>>>>>>>>>>>>>>>>> because algorithm D contains a copy of >>>>>>>>>>>>>>>>>>>>>>>>> algorithm H and does the opposite. >>>>>>>>>>>>>>>>>>>>>>>>
Says the person that just demonstrated that they >>>>>>>>>>>>>>>>>>>>>>> don't know the difference between an algorithm >>>>>>>>>>>>>>>>>>>>>>> and a C function.
Back to being ignored for trolling again. >>>>>>>>>>>>>>>>>>>>>
Do you know enough about C to understand that >>>>>>>>>>>>>>>>>>>> dbush example was foolish nonsense when proposed >>>>>>>>>>>>>>>>>>>> to show the halting problem counter-example? >>>>>>>>>>>>>>>>>>>>
It perfectly illustrates an algorithm that attempts >>>>>>>>>>>>>>>>>>> to be a halt decider,
Ridiculously stupid. Your H does not even look at its >>>>>>>>>>>>>>>>>> input.
Algorithm H doesn't need to read its inputs in order to >>>>>>>>>>>>>>>>> map all inputs to non-halting.
Verifying that algorithm H doesn't correctly report >>>>>>>>>>>>>>>>> what algorithm D does, as per the design of algorithm D. >>>>>>>>>>>>>>>>>
Also your D simply stops running I ran it to verify. >>>>>>>>>>>>>>>>>
Still no reply to this, so I have to assume you agree it's >>>>>>>>>>>>> correct.
Which can't be done as proved by Turing / Godel / Tarksi >>>>>>>>>>>>>>> and others.
I am trying to keep liars from killing the
whole fucking planet by making truth computable >>>>>>>>>>>>>>>
By proving the errors in logic I can make
logic into correct reasoning. That most
logic people are a herd of sheep that would
gladly leap off the POE cliff when that is
what their herd accepts makes correcting this
error too fucking difficult.
There is no error. The POE follows from a series of truth >>>>>>>>>>>>> preserving operations
To say this objectively classical logic is objectively >>>>>>>>>>>> incorrect
when it diverges from what correct reasoning would be while >>>>>>>>>>>> retaining the full English semantics of the terms.
(P ∧ ¬P) ⊢ Q is ridiculously stupid when we plug English >>>>>>>>>>>> sentences in for P and Q and use semantic entailment in English >>>>>>>>>>>> as the measure of correct reasoning.
We already did that and you got confused, calling it a mind >>>>>>>>>>> game (see below):
accept POE as correct for more than sixty seconds.
Every average third grader knows that a contradiction
Every third grader knows that it must have fucked up somewhere. >>>>>>>
explosion can be used to show that an inconsistent system is
useless.
It makes more sense to use the ordinary meaning
of contradiction:
When-so-ever two sentences contradict each other
at least one of them is false.
Whatever you call it, if the axioms of a formal system can prove
both X and ~X, then the principle of explosion can be used to show
that system is useless.
X & ~X proves FALSE.
How can anyone that is not nuts possibly think otherwise?
Assuming that X & ~X has been proven from the axioms of a formal system, >>
Is not the stipulated meaning used in logic and is therefore irrelevant.
If you want an example, naive set theory is an inconsistent system. It
is able to prove both X = "set R contains itself" and ~X = "set R does
not contain itself". So X & ~X is proven TRUE in naive set theory. The principle of explosion can then be used to show that naive set theory is useless.
On 7/2/2026 5:59 PM, dbush wrote:
On 7/2/2026 6:53 PM, olcott wrote:
On 7/2/2026 5:47 PM, dbush wrote:
On 7/2/2026 6:35 PM, olcott wrote:
On 7/2/2026 5:32 PM, dbush wrote:
On 7/2/2026 6:13 PM, olcott wrote:
On 7/2/2026 4:59 PM, dbush wrote:
On 7/2/2026 5:40 PM, olcott wrote:
On 7/2/2026 4:23 PM, dbush wrote:Your intuition fails you. It just means that the axioms of the >>>>>>>> system in question are inconsistent. And the principle of
On 7/2/2026 5:12 PM, olcott wrote:
The confusing part is how an intelligent person canStates that both a statement and its negation are true. And >>>>>>>>>> if a formal system can reach a contradiction through a series >>>>>>>>>> of truth preserving operations from its axioms, that means >>>>>>>>>> both statements are proven true.
accept POE as correct for more than sixty seconds.
Every average third grader knows that a contradiction
Every third grader knows that it must have fucked up somewhere. >>>>>>>>
explosion can be used to show that an inconsistent system is
useless.
It makes more sense to use the ordinary meaning
of contradiction:
When-so-ever two sentences contradict each other
at least one of them is false.
Whatever you call it, if the axioms of a formal system can prove
both X and ~X, then the principle of explosion can be used to show >>>>>> that system is useless.
X & ~X proves FALSE.
How can anyone that is not nuts possibly think otherwise?
Assuming that X & ~X has been proven from the axioms of a formal
system,
Stipulating the ordinary English meaning of contradiction
Is not the stipulated meaning used in logic and is therefore irrelevant.
If you want an example, naive set theory is an inconsistent system.
It is able to prove both X = "set R contains itself" and ~X = "set R
does not contain itself". So X & ~X is proven TRUE in naive set
theory. The principle of explosion can then be used to show that
naive set theory is useless.
Russell's Paradox is the exact same issue as the
pathological self reference (PSR) of the Halting
Problem. I have studied PSR as a primary focus
for 28 years.
Q cannot do the ∀x without an infinite sequence of steps.
On 7/2/2026 1:57 AM, Mikko wrote:
On 02/07/2026 07:03, olcott wrote:
On 7/1/2026 11:01 PM, dbush wrote:
On 7/1/2026 11:59 PM, olcott wrote:
On 7/1/2026 10:43 PM, dbush wrote:
On 7/1/2026 11:37 PM, olcott wrote:
On 7/1/2026 10:18 PM, dbush wrote:
On 7/1/2026 11:17 PM, olcott wrote:
On 7/1/2026 10:00 PM, dbush wrote:
On 7/1/2026 10:53 PM, olcott wrote:
On 7/1/2026 9:36 PM, dbush wrote:
On 7/1/2026 7:37 PM, olcott wrote:
On 7/1/2026 4:15 PM, dbush wrote:
On 7/1/2026 5:04 PM, olcott wrote:
On 7/1/2026 3:57 PM, dbush wrote:False. It means that there are statements in the language >>>>>>>>>>>>>> of Q that have *only* an infinite connection to the axioms >>>>>>>>>>>>>> of the system.
On 7/1/2026 4:50 PM, olcott wrote:
On 7/1/2026 3:37 PM, dbush wrote:
On 7/1/2026 4:29 PM, olcott wrote:
On 7/1/2026 3:13 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>> On 2026-07-01 13:53, olcott wrote:
On 7/1/2026 2:31 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:51, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2026-07-01 12:15, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>That claims what it means to have the truth value >>>>>>>>>>>>>>>>>>>> 'true' (or at least it would if you defined >>>>>>>>>>>>>>>>>>>> AtomicFacts in a coherent way). It doesn't in any >>>>>>>>>>>>>>>>>>>> way clarify what you think it means for something to >>>>>>>>>>>>>>>>>>>> not have a truth value.
Until someone publishes an Olcott to Standard >>>>>>>>>>>>>>>>>>>>>> English dictionary, this isn't really an option. >>>>>>>>>>>>>>>>>>>>>>I'm actually not convinced that Olcott >>>>>>>>>>>>>>>>>>>>>>>> understands what a definition is. I've >>>>>>>>>>>>>>>>>>>>>>>> frequently asked him for definitions and he >>>>>>>>>>>>>>>>>>>>>>>> invariably responds with an example or an >>>>>>>>>>>>>>>>>>>>>>>> analogy (assuming he responds at all). He >>>>>>>>>>>>>>>>>>>>>>>> doesn't get that examples don't take the place >>>>>>>>>>>>>>>>>>>>>>>> of definitions. Examples can be useful for >>>>>>>>>>>>>>>>>>>>>>>> clarifying definitions, but they aren't >>>>>>>>>>>>>>>>>>>>>>>> particularly useful on their own. >>>>>>>>>>>>>>>>>>>>>>>>The same thing as: "cats are animals" >>>>>>>>>>>>>>>>>>>>>>>>>> expressed inI didn't ask for an example. I asked for a >>>>>>>>>>>>>>>>>>>>>>>>> definition of what it mean for the truth value >>>>>>>>>>>>>>>>>>>>>>>>> of a statement to not exist in a formal system. >>>>>>>>>>>>>>>>>>>>>>>>
English has no English meaning in Chinese. >>>>>>>>>>>>>>>>>>>>>>>>>
André
You want a definition look-it-up. >>>>>>>>>>>>>>>>>>>>>>
André
True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright
Olcott 2018
has been updated to this
True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X) >>>>>>>>>>>>>>>>>>>>
André
When I define a term hundreds of times and you did >>>>>>>>>>>>>>>>>>> not bother to pay attention that is your mistake >>>>>>>>>>>>>>>>>>> and your fault.
You gave no such definition of what it means for the >>>>>>>>>>>>>>>>>> truth value of a statement to not exist in a formal >>>>>>>>>>>>>>>>>> system.
A valid answer would look something like this: >>>>>>>>>>>>>>>>>>
"The truth value of a statement does not exist in a >>>>>>>>>>>>>>>>>> formal system when ..."
Now complete the sentence.
It is neither provable nor refutable in F.
Good. So when you say "The truth value of (∀ x, S(x) ≠ >>>>>>>>>>>>>>>> x) does not exist in Q", you mean "(∀ x, S(x) ≠ x) is >>>>>>>>>>>>>>>> unprovable in Q", which is commonly known.
So once again, you're saying the same thing as everyone >>>>>>>>>>>>>>>> else but using different words.
Not really. It is normally thought of as undecidable >>>>>>>>>>>>>>> meaning that Q is incomplete meaning that Q is deficient. >>>>>>>>>>>>>>
OK, I verified that.
The Halting Problem counter-example input
Which starts with the assumption that an algorithm H >>>>>>>>>>>>>> exists that meets the following requirements:
Given any algorithm (i.e. a fixed immutable sequence of >>>>>>>>>>>>>> instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that >>>>>>>>>>>>>> computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed >>>>>>>>>>>>>> directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when >>>>>>>>>>>>>> executed directly
Sure and we could equally start with the requirement >>>>>>>>>>>>> to prove that there exists a natural number > 3 and < 2. >>>>>>>>>>>>>
I really don't see how everyone did not immediately see >>>>>>>>>>>>> that the requirement for H to correctly report the halt >>>>>>>>>>>>> status of input D that does the opposite of whatever H >>>>>>>>>>>>> reports is a moronically stupid requirement within the >>>>>>>>>>>>> first five minutes that this requirement was made.
In other words, you don't understand that if this was >>>>>>>>>>>> algorithm H:
I spent 10,000 hours on it over 22 years.
And still don't understand that this algorithm:
void D(ptr *I)
{
ptr *X = D;
ptr *Y = I;
int result;
{
result = 0;
}
if (result == 1) {
while (1);
}
}
Is the counter example input to this algorithm:
int H(ptr *X, ptr *Y)
{
int result;
{
result = 0;
}
return result;
}
That is just nonsense.
Thereby proving that you've misunderstood the halting problem >>>>>>>> for the last 22 years.
D(D); // merely halts
H(D,D); // merely returns 0 and never looks at D(D)
And algorithm H is wrong about algorithm D because algorithm D
contains a copy of algorithm H and does the opposite.
You just don't know jack shit dufus.
I have been a professional C programmer since 1986.
Says the person that just demonstrated that they don't know the
difference between an algorithm and a C function.
Back to being ignored for trolling again.
Maybe by someone but you are still far from being ignored by everone.
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:
On 27/06/2026 17:50, polcott wrote:
On 6/27/2026 1:53 AM, Tristan Wibberley wrote:
On 20/06/2026 18:32, olcott wrote:
A proof theoretic expression is known to be true when >>>>>>>>>>>>> it is fully grounded in its atomic base. Only twoThat's surprising, disregard for axioms?
PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>> with semantic meaning and never got around to true(L,x). >>>>>>>>>>>>
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is
ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete
it means that ~∃x x=S(x) is out-of-scope for Q.
It comes close. If ∃x x=S(x) is likewise "ungrounded" but in the >>>>>>>>>> language of Q then ~∃x x=S(x) and ∃x x=S(x) are both undecidable >>>>>>>>>> and Q is incomplete, bcause that is what the words mean.
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do. Incomplete only counts relative to
its intended purpose. A car without an engine is
incomplete relative to a mode of transportation.
Irrelevant. The definition of completeness
It a misnomer and does not literally mean (as it implies)
that something is missing that could be added to make
it complete.
It does mean that something is missing that could be added to
enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined to do.
When Q is extended to become PA it stops being Q and becomes PA.
However, there are theories that reamain incomplete even when
more postolates are added, as long as there is a way to know
which sentences are included in the added postulates. Important
examples include Peano arithmetic and ZFC set theory.
Base-Extension Semantics (B-eS) seems to be essentially a cheat.
When we ask what is grounded in an atomic base of Q and we
add axioms to Q to become PA we cheated in that we changed
the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial answer
rather than no answer at all. Of course Q with any additional
postulate is not Q but if the additional postulates are true about
natural numbers then the strengthened theory is still a theory of
natural numbers. PA is one such strengthened Q but still incomplete
and can be strengthened further.
Is (∀ x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps.
So your phrasing is good: Q would need something like an infinite
sequence of steps (or a single principle that summarizes them) to get
the ∀x. Since formal proofs must be finite, and Q lacks the tool (induction) that would allow a finite proof of the infinite claim, the universal statement remains unprovable.
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a
claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence
to support his claim.
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:
On 27/06/2026 17:50, polcott wrote:
On 6/27/2026 1:53 AM, Tristan Wibberley wrote:
On 20/06/2026 18:32, olcott wrote:
A proof theoretic expression is known to be true when >>>>>>>>>>>>>> it is fully grounded in its atomic base. Only twoThat's surprising, disregard for axioms?
PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>> with semantic meaning and never got around to true(L,x). >>>>>>>>>>>>>
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is
ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete
it means that ~∃x x=S(x) is out-of-scope for Q.
It comes close. If ∃x x=S(x) is likewise "ungrounded" but in the >>>>>>>>>>> language of Q then ~∃x x=S(x) and ∃x x=S(x) are both undecidable
and Q is incomplete, bcause that is what the words mean.
Q also can't bake a birthday cake, this does not make
Q in any way "incomplete" relative to what it was
defined to do. Incomplete only counts relative to
its intended purpose. A car without an engine is
incomplete relative to a mode of transportation.
Irrelevant. The definition of completeness
It a misnomer and does not literally mean (as it implies)
that something is missing that could be added to make
it complete.
It does mean that something is missing that could be added to
enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined to do.
When Q is extended to become PA it stops being Q and becomes PA.
However, there are theories that reamain incomplete even when
more postolates are added, as long as there is a way to know
which sentences are included in the added postulates. Important
examples include Peano arithmetic and ZFC set theory.
Base-Extension Semantics (B-eS) seems to be essentially a cheat.
When we ask what is grounded in an atomic base of Q and we
add axioms to Q to become PA we cheated in that we changed
the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial answer
rather than no answer at all. Of course Q with any additional
postulate is not Q but if the additional postulates are true about
natural numbers then the strengthened theory is still a theory of
natural numbers. PA is one such strengthened Q but still incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently
missed, it is neither.
It is true about natural numbers but there
are other models of Rbinsons Q, and it is false in some of them.
A simple example is a model that incudes all natural numbers and
one additional element that is its own successor.
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a
claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence
to support his claim.
His halt decider did not look at its input.
His input merely halted and did not call
this halt decider.
He used {} in a way that
made no sense in C.
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps.
So your phrasing is good: Q would need something like an infinite
sequence of steps (or a single principle that summarizes them) to get
the ∀x. Since formal proofs must be finite, and Q lacks the tool
(induction) that would allow a finite proof of the infinite claim, the
universal statement remains unprovable.
I'm not sure why you are responding to yourself nor who 'your phrasing' refers to since you don't quote anyone. But, assuming we're still
talking about ∀ x, S(x) ≠ x in Q, your reasoning is simply off.
You *can* prove universally quantified claims in Q, just not that
particular claim.
And there isn't an infinite sequence of steps that will get you from the axioms of Q to ∀ x, S(x) ≠ x. There's *no* sequence of steps, finite or infinite.
The issue here is that there are models of Q
in which ∀ x, S(x) ≠ x is
true, but there are also models of Q in which it is false.
For any given model of Q, it will either be true or false, so your claim that ∀ x, S(x) ≠ x is somehow 'not a truth bearer' is simply ludicrous. It's simply the case that this particular statement cannot be derived as
a theorem of Q nor can its negation. Thus Q is incomplete.
André
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a
claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs.
His input merely halted and did not call
this halt decider.
C function D doesn't need to call C function H.
Algorithm D used--
algorithm H as part of it, meaning algorithm D used the template to
cause algorithm H to get the wrong answer for it.
He used {} in a way that
made no sense in C.
It was a logical grouping so you can see how algorithm H is part of algorithm D.
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a
claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs.
So a piece of metal sitting on the ground is an automobile.
His input merely halted and did not call
this halt decider.
C function D doesn't need to call C function H.
You said that it was an example of the HP counter-example input.
That was counter-factual. If you keep making these "mistakes"
I will quit looking at anything that you say. Your insight
into Q seems to prove that these "mistakes" are intentional.
Maybe you are good at math and totally clueless about programming?
Algorithm D used algorithm H as part of it, meaning algorithm D used
the template to cause algorithm H to get the wrong answer for it.
He used {} in a way that
made no sense in C.
It was a logical grouping so you can see how algorithm H is part of
algorithm D.
On 7/3/2026 9:45 AM, André G. Isaak wrote:
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps.
So your phrasing is good: Q would need something like an infinite
sequence of steps (or a single principle that summarizes them) to get
the ∀x. Since formal proofs must be finite, and Q lacks the tool
(induction) that would allow a finite proof of the infinite claim,
the universal statement remains unprovable.
I'm not sure why you are responding to yourself nor who 'your
phrasing' refers to since you don't quote anyone. But, assuming we're
still talking about ∀ x, S(x) ≠ x in Q, your reasoning is simply off.
You *can* prove universally quantified claims in Q, just not that
particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q?
Are the universally quantified claims that can be proven like
this one (∀x, x = x) ?
And there isn't an infinite sequence of steps that will get you from
the axioms of Q to ∀ x, S(x) ≠ x. There's *no* sequence of steps,
finite or infinite.
So trying every element of the set of natural numbers
would not derive the truth value after am infinite
number of steps (that never complete)?
The issue here is that there are models of Q
Which do not exist in PTS thus are off topic in this thread.
All of the rest is off-topic in this thread.
in which ∀ x, S(x) ≠ x is true, but there are also models of Q in
which it is false.
For any given model of Q, it will either be true or false, so your
claim that ∀ x, S(x) ≠ x is somehow 'not a truth bearer' is simply
ludicrous. It's simply the case that this particular statement cannot
be derived as a theorem of Q nor can its negation. Thus Q is incomplete.
André
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:
On 27/06/2026 17:50, polcott wrote:Q also can't bake a birthday cake, this does not make
On 6/27/2026 1:53 AM, Tristan Wibberley wrote:
On 20/06/2026 18:32, olcott wrote:
A proof theoretic expression is known to be true when >>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>>> with semantic meaning and never got around to true(L,x). >>>>>>>>>>>>>>That's surprising, disregard for axioms?
If there is no sequence of inference steps in Q from >>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>> ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete
it means that ~∃x x=S(x) is out-of-scope for Q.
It comes close. If ∃x x=S(x) is likewise "ungrounded" but in >>>>>>>>>>>> the
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words mean. >>>>>>>>>>>
Q in any way "incomplete" relative to what it was
defined to do. Incomplete only counts relative to
its intended purpose. A car without an engine is
incomplete relative to a mode of transportation.
Irrelevant. The definition of completeness
It a misnomer and does not literally mean (as it implies)
that something is missing that could be added to make
it complete.
It does mean that something is missing that could be added to
enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined to do. >>>>>>> When Q is extended to become PA it stops being Q and becomes PA.
However, there are theories that reamain incomplete even when
more postolates are added, as long as there is a way to know
which sentences are included in the added postulates. Important
examples include Peano arithmetic and ZFC set theory.
Base-Extension Semantics (B-eS) seems to be essentially a cheat.
When we ask what is grounded in an atomic base of Q and we
add axioms to Q to become PA we cheated in that we changed
the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial answer
rather than no answer at all. Of course Q with any additional
postulate is not Q but if the additional postulates are true about
natural numbers then the strengthened theory is still a theory of
natural numbers. PA is one such strengthened Q but still incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently
missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
On 7/3/2026 12:52 PM, olcott wrote:
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a
claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps.
So your phrasing is good: Q would need something like an infinite
sequence of steps (or a single principle that summarizes them) to
get the ∀x. Since formal proofs must be finite, and Q lacks the tool >>>> (induction) that would allow a finite proof of the infinite claim,
the universal statement remains unprovable.
I'm not sure why you are responding to yourself nor who 'your
phrasing' refers to since you don't quote anyone. But, assuming we're
still talking about ∀ x, S(x) ≠ x in Q, your reasoning is simply off. >>>
You *can* prove universally quantified claims in Q, just not that
particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q?
Because it isn't true in all models of Q,
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>> claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence >>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
On 2026-07-03 09:38, olcott wrote:
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:However, there are theories that reamain incomplete even when
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:
On 27/06/2026 17:50, polcott wrote:Q also can't bake a birthday cake, this does not make
On 6/27/2026 1:53 AM, Tristan Wibberley wrote:
On 20/06/2026 18:32, olcott wrote:
A proof theoretic expression is known to be true when >>>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>>>> with semantic meaning and never got around to true(L,x). >>>>>>>>>>>>>>>That's surprising, disregard for axioms?
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete
it means that ~∃x x=S(x) is out-of-scope for Q.
It comes close. If ∃x x=S(x) is likewise "ungrounded" but >>>>>>>>>>>>> in the
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words mean. >>>>>>>>>>>>
Q in any way "incomplete" relative to what it was
defined to do. Incomplete only counts relative to
its intended purpose. A car without an engine is
incomplete relative to a mode of transportation.
Irrelevant. The definition of completeness
It a misnomer and does not literally mean (as it implies)
that something is missing that could be added to make
it complete.
It does mean that something is missing that could be added to >>>>>>>>> enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined to do. >>>>>>>> When Q is extended to become PA it stops being Q and becomes PA. >>>>>>>
more postolates are added, as long as there is a way to know
which sentences are included in the added postulates. Important
examples include Peano arithmetic and ZFC set theory.
Base-Extension Semantics (B-eS) seems to be essentially a cheat.
When we ask what is grounded in an atomic base of Q and we
add axioms to Q to become PA we cheated in that we changed
the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial answer >>>>> rather than no answer at all. Of course Q with any additional
postulate is not Q but if the additional postulates are true about
natural numbers then the strengthened theory is still a theory of
natural numbers. PA is one such strengthened Q but still incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently
missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
And that differs from claiming that Q is incomplete exactly how...?
On 7/3/2026 12:17 PM, André G. Isaak wrote:
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps.
So your phrasing is good: Q would need something like an infinite
sequence of steps (or a single principle that summarizes them) to
get the ∀x. Since formal proofs must be finite, and Q lacks the
tool (induction) that would allow a finite proof of the infinite
claim, the universal statement remains unprovable.
I'm not sure why you are responding to yourself nor who 'your
phrasing' refers to since you don't quote anyone. But, assuming
we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is
simply off.
You *can* prove universally quantified claims in Q, just not that
particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q?
Because it isn't true in all models of Q,
many weeks in every thread. Whenever you ignore
this the rest of your reply will be ignored.
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>> claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence >>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
On 7/3/2026 2:10 PM, olcott wrote:That only proves that the definition is incoherent.
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>>> claim about you, and your response was the false claim that "That >>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
If an algorithm takes an input and produces an output, that is by
definition a mapping.
On 7/3/2026 12:35 PM, André G. Isaak wrote:
And that differs from claiming that Q is incomplete exactly how...?
The base definition of "incomplete" means that it is
not operating according to design spec.
terms of the art
are often misleading, thus deceptive.
When we start with an exhaustively complete list of
empirical "atomic facts" of general knowledge (combining
the analytic/synthetic distinction into one single system)
then any expression x that cannot be derived by semantic
entailment expressed syntactically in this system is
not an element of the body of general knowledge expressed
in language.
On 2026-07-03 12:12, olcott wrote:
On 7/3/2026 12:17 PM, André G. Isaak wrote:
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps.
So your phrasing is good: Q would need something like an infinite >>>>>> sequence of steps (or a single principle that summarizes them) to >>>>>> get the ∀x. Since formal proofs must be finite, and Q lacks the >>>>>> tool (induction) that would allow a finite proof of the infinite
claim, the universal statement remains unprovable.
I'm not sure why you are responding to yourself nor who 'your
phrasing' refers to since you don't quote anyone. But, assuming
we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>>> simply off.
You *can* prove universally quantified claims in Q, just not that
particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q?
Because it isn't true in all models of Q,
many weeks in every thread. Whenever you ignore
this the rest of your reply will be ignored.
The rest of my post which you snipped and (presumably) ignored explained *why* you are wrong about this. PTS does not reject models or model
theory. It simply doesn't rely on model-theoretic semantics. Q
*requires* a model.
André
On 7/3/2026 1:18 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:That only proves that the definition is incoherent.
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>>>> claim about you, and your response was the false claim that "That >>>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
If an algorithm takes an input and produces an output, that is by
definition a mapping.
On 7/3/2026 2:10 PM, olcott wrote:int Not_A_Mapping(int X)
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>>> claim about you, and your response was the false claim that "That >>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs,
On 7/3/2026 1:21 PM, André G. Isaak wrote:
On 2026-07-03 12:12, olcott wrote:
On 7/3/2026 12:17 PM, André G. Isaak wrote:
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps.
So your phrasing is good: Q would need something like an infinite >>>>>>> sequence of steps (or a single principle that summarizes them) to >>>>>>> get the ∀x. Since formal proofs must be finite, and Q lacks the >>>>>>> tool (induction) that would allow a finite proof of the infinite >>>>>>> claim, the universal statement remains unprovable.
I'm not sure why you are responding to yourself nor who 'your
phrasing' refers to since you don't quote anyone. But, assuming
we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>>>> simply off.
You *can* prove universally quantified claims in Q, just not that >>>>>> particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q?
Because it isn't true in all models of Q,
many weeks in every thread. Whenever you ignore
this the rest of your reply will be ignored.
The rest of my post which you snipped and (presumably) ignored
explained *why* you are wrong about this. PTS does not reject models
or model theory. It simply doesn't rely on model-theoretic semantics.
Q *requires* a model.
André
It replaces Model theory With PTS.
That you do not understand this is your mistake.
"Is x true" is replaced with something like "Is x provable".
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is byThat only proves that the definition is incoherent.
definition a mapping.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:int Not_A_Mapping(int X)
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>>>> claim about you, and your response was the false claim that "That >>>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs,
{
return 0;
}
By construing that as a mapping is one of the screw-ups
that prevents true expressed in language from being computable.
My HHH applies the operational semantics of
C to its finite string input DD to correctly
determine that the DD input to HHH has no PTS
well-founded justification tree within these
operational semantics.
With your screwed up notion of a halt decider this
would be correct.
int HHH(ptr DD)
{
if (5 > 3)
return 0;
}
On 7/3/2026 2:10 PM, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>>> claim about you, and your response was the false claim that "That >>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs, so
there is nothing to ignore. What an algorithm might do to *compute* the mapping has nothing to do with the mapping.
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>>>> claim about you, and your response was the false claim that "That >>>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs, so
there is nothing to ignore. What an algorithm might do to *compute*
the mapping has nothing to do with the mapping.
It is conventionally construed as a mapping.
It is not even conventionally construed as a halt
function, not even a halt function that gets the
wrong answer.
On 2026-07-03 12:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
And that differs from claiming that Q is incomplete exactly how...?
The base definition of "incomplete" means that it is
not operating according to design spec.
And where exactly do you get this 'base definition' from? It certainly
does not correspond to any definition that I am aware of.
terms of the art
are often misleading, thus deceptive.
Terms of the art are what they are. They are precisely defined so there
is no doubt about what they mean. So how can they therefore be
misleading. It's colloquial terms that have the potential to be
misleading since they are often not precisely defined.
When we start with an exhaustively complete list of
empirical "atomic facts" of general knowledge (combining
the analytic/synthetic distinction into one single system)
then any expression x that cannot be derived by semantic
entailment expressed syntactically in this system is
not an element of the body of general knowledge expressed
in language.
Q isn't concerned with general knowledge (expressed in language or otherwise). It doesn't contain any notion of 'atomic fact'. So none of
this is relevant to the question of whether Q is complete.
André
On 7/3/2026 1:37 PM, André G. Isaak wrote:
On 2026-07-03 12:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
And that differs from claiming that Q is incomplete exactly how...?
The base definition of "incomplete" means that it is
not operating according to design spec.
And where exactly do you get this 'base definition' from? It certainly
does not correspond to any definition that I am aware of.
An motor vehicle that is missing a motor is incomplete.
A bicycle that is missing a motor is NOT incomplete.
Incomplete is an adjective that describes something
missing essential parts, lacking necessary details,
or left unfinished.
terms of the art
are often misleading, thus deceptive.
Terms of the art are what they are. They are precisely defined so
there is no doubt about what they mean. So how can they therefore be
misleading. It's colloquial terms that have the potential to be
misleading since they are often not precisely defined.
These TOTA that diverge from their base meanings confuse
people into thinking that computation is limited.
The
inability to correctly compute the numerical square-root
of a dead chicken does not make computation incomplete
or limited.
When we start with an exhaustively complete list of
empirical "atomic facts" of general knowledge (combining
the analytic/synthetic distinction into one single system)
then any expression x that cannot be derived by semantic
entailment expressed syntactically in this system is
not an element of the body of general knowledge expressed
in language.
Q isn't concerned with general knowledge (expressed in language or
otherwise). It doesn't contain any notion of 'atomic fact'. So none of
this is relevant to the question of whether Q is complete.
André
It has the "atomic facts" of Q.
Any expression that cannot reach these "atomic fact"
axioms is ungrounded in the atomic base of Q.
On 7/3/2026 2:45 PM, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:int Not_A_Mapping(int X)
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part >>>>>>>>> of a
claim about you, and your response was the false claim that "That >>>>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to
an output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs,
{
return 0;
}
The above algorithm does in fact compute this mathematical mapping:
input | output
------------------
(any int) | 0
By construing that as a mapping is one of the screw-ups
that prevents true expressed in language from being computable.
My HHH applies the operational semantics of
C to its finite string input DD to correctly
determine that the DD input to HHH has no PTS
well-founded justification tree within these
operational semantics.
With your screwed up notion of a halt decider this
would be correct.
int HHH(ptr DD)
{
if (5 > 3)
return 0;
}
On 2026-07-03 12:38, olcott wrote:
On 7/3/2026 1:21 PM, André G. Isaak wrote:
On 2026-07-03 12:12, olcott wrote:
On 7/3/2026 12:17 PM, André G. Isaak wrote:
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps.
So your phrasing is good: Q would need something like an
infinite sequence of steps (or a single principle that
summarizes them) to get the ∀x. Since formal proofs must be >>>>>>>> finite, and Q lacks the tool (induction) that would allow a
finite proof of the infinite claim, the universal statement
remains unprovable.
I'm not sure why you are responding to yourself nor who 'your
phrasing' refers to since you don't quote anyone. But, assuming >>>>>>> we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>>>>> simply off.
You *can* prove universally quantified claims in Q, just not that >>>>>>> particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q?
Because it isn't true in all models of Q,
many weeks in every thread. Whenever you ignore
this the rest of your reply will be ignored.
The rest of my post which you snipped and (presumably) ignored
explained *why* you are wrong about this. PTS does not reject models
or model theory. It simply doesn't rely on model-theoretic semantics.
Q *requires* a model.
André
It replaces Model theory With PTS.
That you do not understand this is your mistake.
"Is x true" is replaced with something like "Is x provable".
Which has no bearing on the existence of models
or on the fact that Q
requires a model. When we assert that something is provable from the
axioms of Q, we are effectively saying that it is true in all models of Q.
André
On 7/3/2026 1:53 PM, dbush wrote:
On 7/3/2026 2:45 PM, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:int Not_A_Mapping(int X)
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part >>>>>>>>>> of a
claim about you, and your response was the false claim that "That >>>>>>>>>> is just nonsense". Later in the discussion you offer more >>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to
outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to >>>>>> an output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs,
{
return 0;
}
The above algorithm does in fact compute this mathematical mapping:
input | output
------------------
(any int) | 0
By construing that as a mapping is one of the screw-ups
that prevents true expressed in language from being computable.
My HHH applies the operational semantics of
C to its finite string input DD to correctly
determine that the DD input to HHH has no PTS
well-founded justification tree within these
operational semantics.
With your screwed up notion of a halt decider this
would be correct.
int HHH(ptr DD)
{
if (5 > 3)
return 0;
}
Because it ignores the input it is not any halt
function at all.
The above partial halt decider meets the below requirements for all
algorithms that do not halt:
Given any algorithm (i.e. a fixed immutable sequence of instructions) X
described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the
following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
On 7/3/2026 1:46 PM, André G. Isaak wrote:
On 2026-07-03 12:38, olcott wrote:
On 7/3/2026 1:21 PM, André G. Isaak wrote:
On 2026-07-03 12:12, olcott wrote:
On 7/3/2026 12:17 PM, André G. Isaak wrote:
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:Because it isn't true in all models of Q,
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps. >>>>>>>>>So your phrasing is good: Q would need something like an
infinite sequence of steps (or a single principle that
summarizes them) to get the ∀x. Since formal proofs must be >>>>>>>>> finite, and Q lacks the tool (induction) that would allow a >>>>>>>>> finite proof of the infinite claim, the universal statement >>>>>>>>> remains unprovable.
I'm not sure why you are responding to yourself nor who 'your >>>>>>>> phrasing' refers to since you don't quote anyone. But, assuming >>>>>>>> we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>>>>>> simply off.
You *can* prove universally quantified claims in Q, just not
that particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? >>>>>>
many weeks in every thread. Whenever you ignore
this the rest of your reply will be ignored.
The rest of my post which you snipped and (presumably) ignored
explained *why* you are wrong about this. PTS does not reject models
or model theory. It simply doesn't rely on model-theoretic
semantics. Q *requires* a model.
André
It replaces Model theory With PTS.
That you do not understand this is your mistake.
"Is x true" is replaced with something like "Is x provable".
Which has no bearing on the existence of models
Proof theoretic semantics is utterly unconcerned with true
in a model and focuses on the existence of a canonical proof.
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is byThat only proves that the definition is incoherent.
definition a mapping.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping and an algorithm. They are two different things.
André
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is byThat only proves that the definition is incoherent.
definition a mapping.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping and
an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is byThat only proves that the definition is incoherent.
definition a mapping.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping and
an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
On 7/3/2026 6:37 PM, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is byThat only proves that the definition is incoherent.
definition a mapping.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping and
an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
It is a partial halt decider that correctly reports the halt status of
any algorithm that halts when executed directly and incorrectly reports
the halt status of algorithms that halt when executed directly.
If you disagree, point out exactly which part of the below requirements
is violated in doing so. If you dishonestly trim this, it will be taken
as your official, on-the-record admission that the below requirements
are satisfied for the subset of algorithms that halt when executed
directly.
Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
On 2026-07-03 14:13, olcott wrote:
On 7/3/2026 1:37 PM, André G. Isaak wrote:
On 2026-07-03 12:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
And that differs from claiming that Q is incomplete exactly how...?
The base definition of "incomplete" means that it is
not operating according to design spec.
And where exactly do you get this 'base definition' from? It
certainly does not correspond to any definition that I am aware of.
An motor vehicle that is missing a motor is incomplete.
A bicycle that is missing a motor is NOT incomplete.
Incomplete is an adjective that describes something
missing essential parts, lacking necessary details,
or left unfinished.
That's *one* definition of incomplete. It's hardly *the* definition and
you have provided no reason to think that it is the 'base definition' whatever that might mean to you.
terms of the art
are often misleading, thus deceptive.
Terms of the art are what they are. They are precisely defined so
there is no doubt about what they mean. So how can they therefore be
misleading. It's colloquial terms that have the potential to be
misleading since they are often not precisely defined.
These TOTA that diverge from their base meanings confuse
people into thinking that computation is limited.
No. It confuses *you*. The vast majority of people are not confused by
this. And stating that Q is incomplete has nothing to do with
computation. Computation is a separate field.
André
The
inability to correctly compute the numerical square-root
of a dead chicken does not make computation incomplete
or limited.
When we start with an exhaustively complete list of
empirical "atomic facts" of general knowledge (combining
the analytic/synthetic distinction into one single system)
then any expression x that cannot be derived by semantic
entailment expressed syntactically in this system is
not an element of the body of general knowledge expressed
in language.
Q isn't concerned with general knowledge (expressed in language or
otherwise). It doesn't contain any notion of 'atomic fact'. So none
of this is relevant to the question of whether Q is complete.
André
It has the "atomic facts" of Q.
Any expression that cannot reach these "atomic fact"
axioms is ungrounded in the atomic base of Q.
On 2026-07-03 14:43, olcott wrote:
On 7/3/2026 1:46 PM, André G. Isaak wrote:
On 2026-07-03 12:38, olcott wrote:
On 7/3/2026 1:21 PM, André G. Isaak wrote:
On 2026-07-03 12:12, olcott wrote:
On 7/3/2026 12:17 PM, André G. Isaak wrote:
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:Because it isn't true in all models of Q,
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps. >>>>>>>>>>So your phrasing is good: Q would need something like an
infinite sequence of steps (or a single principle that
summarizes them) to get the ∀x. Since formal proofs must be >>>>>>>>>> finite, and Q lacks the tool (induction) that would allow a >>>>>>>>>> finite proof of the infinite claim, the universal statement >>>>>>>>>> remains unprovable.
I'm not sure why you are responding to yourself nor who 'your >>>>>>>>> phrasing' refers to since you don't quote anyone. But, assuming >>>>>>>>> we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>>>>>>> simply off.
You *can* prove universally quantified claims in Q, just not >>>>>>>>> that particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? >>>>>>>
many weeks in every thread. Whenever you ignore
this the rest of your reply will be ignored.
The rest of my post which you snipped and (presumably) ignored
explained *why* you are wrong about this. PTS does not reject
models or model theory. It simply doesn't rely on model-theoretic
semantics. Q *requires* a model.
André
It replaces Model theory With PTS.
That you do not understand this is your mistake.
"Is x true" is replaced with something like "Is x provable".
Which has no bearing on the existence of models
Proof theoretic semantics is utterly unconcerned with true
in a model and focuses on the existence of a canonical proof.
PTS isn't concerned with true at all,
which is why it certainly wouldn't
claim that a proposition which can neither be proven nor not proven is
not a 'truth bearer'. However, you have made this claim about (∀x, S(x) ≠ x) in Q despite the fact that (∀x, S(x) ≠ x) is *always* either true or false. It cannot be derived as as theorem, but it is still most
decidedly a truth-bearer.
Once you start making claims about things being truth-bhearers/non truth-bearers, you're firmly dealing with a semantics that concerns
itself with truth, i.e. not PTS.
André
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is byThat only proves that the definition is incoherent.
definition a mapping.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping and
an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is by >>>>>> definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping and
an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute
On 7/3/2026 6:37 PM, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is byThat only proves that the definition is incoherent.
definition a mapping.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping and
an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
It is a partial halt decider that correctly reports the halt status of
any algorithm that halts when executed directly and incorrectly reports
the halt status of algorithms that halt when executed directly.
If you disagree, point out exactly which part of the below requirements
is violated in doing so. If you dishonestly trim this, it will be taken
as your official, on-the-record admission that the below requirements
are satisfied for the subset of algorithms that halt when executed
directly.
Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
On 7/3/2026 9:52 PM, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is by >>>>>>> definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping
and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute
Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
On 7/3/2026 7:10 PM, dbush wrote:Shown above.
On 7/3/2026 6:37 PM, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is by >>>>>> definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping and
an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
It is a partial halt decider that correctly reports the halt status of
any algorithm that halts when executed directly and incorrectly
reports the halt status of algorithms that halt when executed directly.
If you disagree, point out exactly which part of the below
requirements is violated in doing so. If you dishonestly trim this,
it will be taken as your official, on-the-record admission that the
below requirements are satisfied for the subset of algorithms that
halt when executed directly.
Given any algorithm (i.e. a fixed immutable sequence of instructions)
X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the
following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
directly
A actual halt function must compute the mapping
On 7/3/2026 8:58 PM, dbush wrote:
On 7/3/2026 9:52 PM, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is >>>>>>>> by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping
and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute
When you actually implement this concretely
so that
you cannot just "assume away" details then your notion
requires a halt decider to report on the behavior of
its caller having no idea who its caller is.
Given any algorithm (i.e. a fixed immutable sequence of instructions)
X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the
following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
directly
On 7/3/2026 10:05 PM, olcott wrote:
On 7/3/2026 8:58 PM, dbush wrote:
On 7/3/2026 9:52 PM, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is >>>>>>>>> by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping >>>>>>> and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute
When you actually implement this concretely
We find that it is not possible, as Linz and others have proved.
On 7/3/2026 9:19 PM, dbush wrote:
On 7/3/2026 10:05 PM, olcott wrote:
On 7/3/2026 8:58 PM, dbush wrote:
On 7/3/2026 9:52 PM, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is >>>>>>>>>> by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping >>>>>>>> and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute
When you actually implement this concretely
We find that it is not possible, as Linz and others have proved.
Impossible requirements are incorrect requirements.
The halting problem doesn't actually have self reference, as
algorithms can be copied as in the below example of algorithm D:
void D(ptr *I)
{
// algorithm D; input: I
ptr *X = D;
ptr *Y = I;
int result;
{
// algorithm H; inputs: X,Y
result = 0;
}
if (result == 1) {
while (1);
}
}
Which is the counter example input to algorithm H:
int H(ptr *X, ptr *Y)
{
int result;
{
// algorithm H; inputs: X,Y
result = 0;
}
return result;
}
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a
claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence
to support his claim.
His halt decider did not look at its input.
His input merely halted and did not call
this halt decider. He used {} in a way that
made no sense in C.
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>> claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence >>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
On 7/3/2026 1:18 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>>>> claim about you, and your response was the false claim that "That >>>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
If an algorithm takes an input and produces an output, that is by
definition a mapping.
That only proves that the definition is incoherent.
On 7/3/2026 5:51 PM, André G. Isaak wrote:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is by >>>>>> definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping and
an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute the mapping from
its actual input according to the operational semantics
of this input to the behavior that this input actually
specifies. No function can report on the behavior of
its caller because it has no idea who its caller is.
On 7/3/2026 9:19 PM, dbush wrote:
On 7/3/2026 10:05 PM, olcott wrote:
On 7/3/2026 8:58 PM, dbush wrote:
On 7/3/2026 9:52 PM, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is >>>>>>>>>> by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping >>>>>>>> and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute
When you actually implement this concretely
We find that it is not possible, as Linz and others have proved.
Impossible requirements are incorrect requirements.
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:int Not_A_Mapping(int X)
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>>>> claim about you, and your response was the false claim that "That >>>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs,
{
return 0;
}
By construing that as a mapping is one of the screw-ups
that prevents true expressed in language from being computable.
On 7/3/2026 1:53 PM, dbush wrote:
On 7/3/2026 2:45 PM, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:int Not_A_Mapping(int X)
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part >>>>>>>>>> of a
claim about you, and your response was the false claim that "That >>>>>>>>>> is just nonsense". Later in the discussion you offer more >>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to
outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to >>>>>> an output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs,
{
return 0;
}
The above algorithm does in fact compute this mathematical mapping:
input | output
------------------
(any int) | 0
By construing that as a mapping is one of the screw-ups
that prevents true expressed in language from being computable.
My HHH applies the operational semantics of
C to its finite string input DD to correctly
determine that the DD input to HHH has no PTS
well-founded justification tree within these
operational semantics.
With your screwed up notion of a halt decider this
would be correct.
int HHH(ptr DD)
{
if (5 > 3)
return 0;
}
Because it ignores the input it is not any halt
function at all.
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>>>> claim about you, and your response was the false claim that "That >>>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs, so
there is nothing to ignore. What an algorithm might do to *compute*
the mapping has nothing to do with the mapping.
It is conventionally construed as a mapping.
It is not even conventionally construed as a halt
function, not even a halt function that gets the
wrong answer.
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:
On 27/06/2026 17:50, polcott wrote:Q also can't bake a birthday cake, this does not make
On 6/27/2026 1:53 AM, Tristan Wibberley wrote:
On 20/06/2026 18:32, olcott wrote:
A proof theoretic expression is known to be true when >>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>>> with semantic meaning and never got around to true(L,x). >>>>>>>>>>>>>>That's surprising, disregard for axioms?
If there is no sequence of inference steps in Q from >>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>> ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete
it means that ~∃x x=S(x) is out-of-scope for Q.
It comes close. If ∃x x=S(x) is likewise "ungrounded" but in >>>>>>>>>>>> the
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words mean. >>>>>>>>>>>
Q in any way "incomplete" relative to what it was
defined to do. Incomplete only counts relative to
its intended purpose. A car without an engine is
incomplete relative to a mode of transportation.
Irrelevant. The definition of completeness
It a misnomer and does not literally mean (as it implies)
that something is missing that could be added to make
it complete.
It does mean that something is missing that could be added to
enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined to do. >>>>>>> When Q is extended to become PA it stops being Q and becomes PA.
However, there are theories that reamain incomplete even when
more postolates are added, as long as there is a way to know
which sentences are included in the added postulates. Important
examples include Peano arithmetic and ZFC set theory.
Base-Extension Semantics (B-eS) seems to be essentially a cheat.
When we ask what is grounded in an atomic base of Q and we
add axioms to Q to become PA we cheated in that we changed
the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial answer
rather than no answer at all. Of course Q with any additional
postulate is not Q but if the additional postulates are true about
natural numbers then the strengthened theory is still a theory of
natural numbers. PA is one such strengthened Q but still incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently
missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:However, there are theories that reamain incomplete even when
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:
On 27/06/2026 17:50, polcott wrote:Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>> Q in any way "incomplete" relative to what it was
On 6/27/2026 1:53 AM, Tristan Wibberley wrote:It comes close. If ∃x x=S(x) is likewise "ungrounded" but >>>>>>>>>>>>>> in the
On 20/06/2026 18:32, olcott wrote:
A proof theoretic expression is known to be true when >>>>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>>>>> with semantic meaning and never got around to true(L,x). >>>>>>>>>>>>>>>>That's surprising, disregard for axioms?
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete
it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words mean. >>>>>>>>>>>>>
defined to do. Incomplete only counts relative to
its intended purpose. A car without an engine is
incomplete relative to a mode of transportation.
Irrelevant. The definition of completeness
It a misnomer and does not literally mean (as it implies) >>>>>>>>>>> that something is missing that could be added to make
it complete.
It does mean that something is missing that could be added to >>>>>>>>>> enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined to do. >>>>>>>>> When Q is extended to become PA it stops being Q and becomes PA. >>>>>>>>
more postolates are added, as long as there is a way to know
which sentences are included in the added postulates. Important >>>>>>>> examples include Peano arithmetic and ZFC set theory.
Base-Extension Semantics (B-eS) seems to be essentially a cheat. >>>>>>> When we ask what is grounded in an atomic base of Q and we
add axioms to Q to become PA we cheated in that we changed
the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial answer >>>>>> rather than no answer at all. Of course Q with any additional
postulate is not Q but if the additional postulates are true about >>>>>> natural numbers then the strengthened theory is still a theory of
natural numbers. PA is one such strengthened Q but still incomplete >>>>>> and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently
missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
And that differs from claiming that Q is incomplete exactly how...?
The base definition of "incomplete" means that it is
not operating according to design spec.
On 7/3/2026 1:21 PM, André G. Isaak wrote:
On 2026-07-03 12:12, olcott wrote:
On 7/3/2026 12:17 PM, André G. Isaak wrote:
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps.
So your phrasing is good: Q would need something like an infinite >>>>>>> sequence of steps (or a single principle that summarizes them) to >>>>>>> get the ∀x. Since formal proofs must be finite, and Q lacks the >>>>>>> tool (induction) that would allow a finite proof of the infinite >>>>>>> claim, the universal statement remains unprovable.
I'm not sure why you are responding to yourself nor who 'your
phrasing' refers to since you don't quote anyone. But, assuming
we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>>>> simply off.
You *can* prove universally quantified claims in Q, just not that >>>>>> particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q?
Because it isn't true in all models of Q,
many weeks in every thread. Whenever you ignore
this the rest of your reply will be ignored.
The rest of my post which you snipped and (presumably) ignored
explained *why* you are wrong about this. PTS does not reject models
or model theory. It simply doesn't rely on model-theoretic semantics.
Q *requires* a model.
It replaces Model theory With PTS.
That you do not understand this is your mistake.
"Is x true" is replaced with something like "Is x provable".
On 2026-07-02 dbush wrote:
The halting problem doesn't actually have self reference, as
algorithms can be copied as in the below example of algorithm D:
void D(ptr *I)
{
// algorithm D; input: I
ptr *X = D;
ptr *Y = I;
int result;
{
// algorithm H; inputs: X,Y
result = 0;
}
if (result == 1) {
while (1);
}
}
Which is the counter example input to algorithm H:
int H(ptr *X, ptr *Y)
{
int result;
{
// algorithm H; inputs: X,Y
result = 0;
}
return result;
}
On 03/07/2026 18:36, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a
claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence
to support his claim.
His halt decider did not look at its input.
For every possible input his H halts and returns either 0 for false
or 1 for true. Therefore his H is a decider. It return 0 for D
although D halts so the decider H is not a halt decider.
His input merely halted and did not call
this halt decider. He used {} in a way that
made no sense in C.
His use of {} is perfectly correct by C rules and as meaningful ans
usually. Your false claim (not shown above) is false.
On 7/4/2026 2:37 AM, Mikko wrote:
On 2026-07-02 dbush wrote:
The halting problem doesn't actually have self reference, as
algorithms can be copied as in the below example of algorithm D:
void D(ptr *I)
{
// algorithm D; input: I
ptr *X = D;
ptr *Y = I;
int result;
{
// algorithm H; inputs: X,Y
result = 0;
}
if (result == 1) {
while (1);
}
}
Which is the counter example input to algorithm H:
int H(ptr *X, ptr *Y)
{
int result;
{
// algorithm H; inputs: X,Y
result = 0;
}
return result;
}
On 03/07/2026 18:36, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a
claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence
to support his claim.
His halt decider did not look at its input.
For every possible input his H halts and returns either 0 for false
or 1 for true. Therefore his H is a decider. It return 0 for D
although D halts so the decider H is not a halt decider.
counter-factual H always returns 0.
His input merely halted and did not call
this halt decider. He used {} in a way that
made no sense in C.
His use of {} is perfectly correct by C rules and as meaningful ans
usually. Your false claim (not shown above) is false.
On 03/07/2026 21:10, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>>> claim about you, and your response was the false claim that "That >>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
No, but dbush's program H implements a mapping anyway. It just is
a different mapping from the one a halt decider is required to do.
On 7/4/2026 2:41 AM, Mikko wrote:The mathematical halting function:
On 03/07/2026 21:10, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>>>> claim about you, and your response was the false claim that "That >>>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
No, but dbush's program H implements a mapping anyway. It just is
a different mapping from the one a halt decider is required to do.
Making it complete nonsense.
A actual halt function must compute
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal.
Rather, we presuppose that we can enumerate a set, and then,
/purely on the grounds of possibility/, conceive a diagonalized
non-element.
Nope, as explained and re-explained ad nauseam around here:
just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences,
is indeed constructive: a definition of anti-diagonal of *any*
(infinite) list is provided, and the proof that the anti-diagonal
cannot be in the list is quite constructive.
(Namely, we don't need to say "assume ab abdsurdo that
an enumeration is given", we can just say "for *any* list,
we *construct* an element not in the list".)
On 03/07/2026 21:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part >>>>>>>>> of a
claim about you, and your response was the false claim that "That >>>>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to
an output of either 0 or 1?
If an algorithm takes an input and produces an output, that is by
definition a mapping.
That only proves that the definition is incoherent.
Your definitions often are. But the well known definition of "mapping"
is not.
On 04/07/2026 04:52, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is by >>>>>>> definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping
and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute the mapping from
its actual input according to the operational semantics
of this input to the behavior that this input actually
specifies. No function can report on the behavior of
its caller because it has no idea who its caller is.
A function does not compute. An algrothm may compute a function.
However, no algrithm computes the halt function.
The halt functions maps a computation to a truth value
but so do many other functions, too.
On 04/07/2026 05:37, olcott wrote:
On 7/3/2026 9:19 PM, dbush wrote:
On 7/3/2026 10:05 PM, olcott wrote:
On 7/3/2026 8:58 PM, dbush wrote:
On 7/3/2026 9:52 PM, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that >>>>>>>>>>> is by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a
mapping and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute
When you actually implement this concretely
We find that it is not possible, as Linz and others have proved.
Impossible requirements are incorrect requirements.
There is no well known meaning of "incorrect requirements".
On 03/07/2026 21:45, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:int Not_A_Mapping(int X)
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part >>>>>>>>> of a
claim about you, and your response was the false claim that "That >>>>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to
an output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs,
{
return 0;
}
By construing that as a mapping is one of the screw-ups
that prevents true expressed in language from being computable.
By construing the above mapping as a non-mapping you disconnect from
Common Languge and lose your ablility to communicate.
On 03/07/2026 22:08, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part >>>>>>>>> of a
claim about you, and your response was the false claim that "That >>>>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to
an output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs,
so there is nothing to ignore. What an algorithm might do to
*compute* the mapping has nothing to do with the mapping.
It is conventionally construed as a mapping.
More importantly, it satisfies the definition of "mapping".
It is not even conventionally construed as a halt
function, not even a halt function that gets the
wrong answer.
Irrelevant, as the claim was that H does not implement the halt
function.
On 7/4/2026 2:43 AM, Mikko wrote:
On 03/07/2026 21:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part >>>>>>>>>> of a
claim about you, and your response was the false claim that "That >>>>>>>>>> is just nonsense". Later in the discussion you offer more >>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to
outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to >>>>>> an output of either 0 or 1?
If an algorithm takes an input and produces an output, that is by
definition a mapping.
That only proves that the definition is incoherent.
Your definitions often are. But the well known definition of "mapping"
is not.
The output really should be based on the input
because computing the mapping from an input to
an output requires some kind of correspondence
between the two.
On 03/07/2026 21:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:However, there are theories that reamain incomplete even when >>>>>>>>> more postolates are added, as long as there is a way to know >>>>>>>>> which sentences are included in the added postulates. Important >>>>>>>>> examples include Peano arithmetic and ZFC set theory.
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:
On 27/06/2026 17:50, polcott wrote:Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was
On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote:It comes close. If ∃x x=S(x) is likewise "ungrounded" but >>>>>>>>>>>>>>> in the
A proof theoretic expression is known to be true when >>>>>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>>>>>> with semantic meaning and never got around to true(L,x). >>>>>>>>>>>>>>>>>That's surprising, disregard for axioms?
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete
it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words mean. >>>>>>>>>>>>>>
defined to do. Incomplete only counts relative to
its intended purpose. A car without an engine is
incomplete relative to a mode of transportation.
Irrelevant. The definition of completeness
It a misnomer and does not literally mean (as it implies) >>>>>>>>>>>> that something is missing that could be added to make
it complete.
It does mean that something is missing that could be added to >>>>>>>>>>> enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined to do. >>>>>>>>>> When Q is extended to become PA it stops being Q and becomes PA. >>>>>>>>>
Base-Extension Semantics (B-eS) seems to be essentially a cheat. >>>>>>>> When we ask what is grounded in an atomic base of Q and we
add axioms to Q to become PA we cheated in that we changed
the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial answer >>>>>>> rather than no answer at all. Of course Q with any additional
postulate is not Q but if the additional postulates are true about >>>>>>> natural numbers then the strengthened theory is still a theory of >>>>>>> natural numbers. PA is one such strengthened Q but still incomplete >>>>>>> and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently
missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
And that differs from claiming that Q is incomplete exactly how...?
The base definition of "incomplete" means that it is
not operating according to design spec.
No, it is not. The term "incomplete" in its base meaning is
appicable to various things that are not exprected to operate.
On 7/4/2026 2:48 AM, Mikko wrote:
On 04/07/2026 05:37, olcott wrote:
On 7/3/2026 9:19 PM, dbush wrote:
On 7/3/2026 10:05 PM, olcott wrote:
On 7/3/2026 8:58 PM, dbush wrote:
On 7/3/2026 9:52 PM, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that >>>>>>>>>>>> is by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a
mapping and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute
When you actually implement this concretely
We find that it is not possible, as Linz and others have proved.
Impossible requirements are incorrect requirements.
There is no well known meaning of "incorrect requirements".
I just established the meaning of incorrect requirements
as any requirement that requires the logically impossible.
The halting problem requires a decider that correctly
reports the halt status of an input that does the opposite
of whatever it reports.
I already established that an incorrect polar question
is any yes/no question lacking a correct yes/no answer.
On 7/4/2026 2:55 AM, Mikko wrote:
On 03/07/2026 21:45, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:int Not_A_Mapping(int X)
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part >>>>>>>>>> of a
claim about you, and your response was the false claim that "That >>>>>>>>>> is just nonsense". Later in the discussion you offer more >>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to
outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to >>>>>> an output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs,
{
return 0;
}
By construing that as a mapping is one of the screw-ups
that prevents true expressed in language from being computable.
By construing the above mapping as a non-mapping you disconnect from
Common Languge and lose your ablility to communicate.
I will not tolerate that math hijacks the term
"mapping" to ignore requirement that there must
be some actual correspondence between inputs and
outputs.
A actual halt function must computeThe mathematical halting function:
On 7/4/2026 3:06 AM, Mikko wrote:
On 03/07/2026 21:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:However, there are theories that reamain incomplete even when >>>>>>>>>> more postolates are added, as long as there is a way to know >>>>>>>>>> which sentences are included in the added postulates. Important >>>>>>>>>> examples include Peano arithmetic and ZFC set theory.
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:
On 27/06/2026 17:50, polcott wrote:Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was >>>>>>>>>>>>>>> defined to do. Incomplete only counts relative to >>>>>>>>>>>>>>> its intended purpose. A car without an engine is >>>>>>>>>>>>>>> incomplete relative to a mode of transportation.
On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote:It comes close. If ∃x x=S(x) is likewise "ungrounded" >>>>>>>>>>>>>>>> but in the
A proof theoretic expression is known to be true when >>>>>>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>>>>>>> with semantic meaning and never got around to true(L,x). >>>>>>>>>>>>>>>>>>That's surprising, disregard for axioms?
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete >>>>>>>>>>>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words mean. >>>>>>>>>>>>>>>
Irrelevant. The definition of completeness
It a misnomer and does not literally mean (as it implies) >>>>>>>>>>>>> that something is missing that could be added to make >>>>>>>>>>>>> it complete.
It does mean that something is missing that could be added to >>>>>>>>>>>> enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined to >>>>>>>>>>> do.
When Q is extended to become PA it stops being Q and becomes PA. >>>>>>>>>>
Base-Extension Semantics (B-eS) seems to be essentially a cheat. >>>>>>>>> When we ask what is grounded in an atomic base of Q and we
add axioms to Q to become PA we cheated in that we changed
the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial >>>>>>>> answer
rather than no answer at all. Of course Q with any additional
postulate is not Q but if the additional postulates are true about >>>>>>>> natural numbers then the strengthened theory is still a theory of >>>>>>>> natural numbers. PA is one such strengthened Q but still incomplete >>>>>>>> and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently
missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
And that differs from claiming that Q is incomplete exactly how...?
The base definition of "incomplete" means that it is
not operating according to design spec.
No, it is not. The term "incomplete" in its base meaning is
appicable to various things that are not exprected to operate.
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
A motor vehicle that lacks a motor is incomplete.
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
On 03/07/2026 21:38, olcott wrote:
On 7/3/2026 1:21 PM, André G. Isaak wrote:
On 2026-07-03 12:12, olcott wrote:
On 7/3/2026 12:17 PM, André G. Isaak wrote:
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps.
So your phrasing is good: Q would need something like an
infinite sequence of steps (or a single principle that
summarizes them) to get the ∀x. Since formal proofs must be >>>>>>>> finite, and Q lacks the tool (induction) that would allow a
finite proof of the infinite claim, the universal statement
remains unprovable.
I'm not sure why you are responding to yourself nor who 'your
phrasing' refers to since you don't quote anyone. But, assuming >>>>>>> we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>>>>> simply off.
You *can* prove universally quantified claims in Q, just not that >>>>>>> particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q?
Because it isn't true in all models of Q,
many weeks in every thread. Whenever you ignore
this the rest of your reply will be ignored.
The rest of my post which you snipped and (presumably) ignored
explained *why* you are wrong about this. PTS does not reject models
or model theory. It simply doesn't rely on model-theoretic semantics.
Q *requires* a model.
It replaces Model theory With PTS.
That you do not understand this is your mistake.
"Is x true" is replaced with something like "Is x provable".
"Is x provable" is there already. Why would one want to lose
"Is x true"? If one dosn't need "Is x true" one needn't use
it.
On 7/4/2026 1:07 PM, olcott wrote:
On 7/4/2026 3:06 AM, Mikko wrote:
On 03/07/2026 21:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:Irrelevant. The definition of completeness
On 27/06/2026 17:50, polcott wrote:Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was >>>>>>>>>>>>>>>> defined to do. Incomplete only counts relative to >>>>>>>>>>>>>>>> its intended purpose. A car without an engine is >>>>>>>>>>>>>>>> incomplete relative to a mode of transportation. >>>>>>>>>>>>>>>
On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote:It comes close. If ∃x x=S(x) is likewise "ungrounded" >>>>>>>>>>>>>>>>> but in the
A proof theoretic expression is known to be true when >>>>>>>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>>>>>>>> with semantic meaning and never got around to >>>>>>>>>>>>>>>>>>>> true(L,x).
That's surprising, disregard for axioms?
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete >>>>>>>>>>>>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words mean. >>>>>>>>>>>>>>>>
It a misnomer and does not literally mean (as it implies) >>>>>>>>>>>>>> that something is missing that could be added to make >>>>>>>>>>>>>> it complete.
It does mean that something is missing that could be added to >>>>>>>>>>>>> enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined >>>>>>>>>>>> to do.
When Q is extended to become PA it stops being Q and becomes >>>>>>>>>>>> PA.
However, there are theories that reamain incomplete even when >>>>>>>>>>> more postolates are added, as long as there is a way to know >>>>>>>>>>> which sentences are included in the added postulates. Important >>>>>>>>>>> examples include Peano arithmetic and ZFC set theory.
Base-Extension Semantics (B-eS) seems to be essentially a cheat. >>>>>>>>>> When we ask what is grounded in an atomic base of Q and we >>>>>>>>>> add axioms to Q to become PA we cheated in that we changed >>>>>>>>>> the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial >>>>>>>>> answer
rather than no answer at all. Of course Q with any additional >>>>>>>>> postulate is not Q but if the additional postulates are true about >>>>>>>>> natural numbers then the strengthened theory is still a theory of >>>>>>>>> natural numbers. PA is one such strengthened Q but still
incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently >>>>>>> missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
And that differs from claiming that Q is incomplete exactly how...?
The base definition of "incomplete" means that it is
not operating according to design spec.
No, it is not. The term "incomplete" in its base meaning is
appicable to various things that are not exprected to operate.
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
A motor vehicle that lacks a motor is incomplete.
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
On 7/4/2026 1:07 PM, olcott wrote:
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
Math mapping from an input to an output:
Ignore the input and output a fixed constant.
int mapping_function(int x)
{
return 0;
}
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
LP := ~True(LP)
G := ~Provable(PA, G)
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
LP := ~True(LP)
G := ~Provable(PA, G)
Math Incomplete: The inability to accomplish
more than a system was defined to accomplish.
(∀x, S(x) ≠ x) cannot be proven in Q
Math mapping from an input to an output:
Ignore the input and output a fixed constant.
int mapping_function(int x)
{
return 0;
}
On 06/05/2026 20:37, Julio Di Egidio wrote:
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal.
Rather, we presuppose that we can enumerate a set, and then,
/purely on the grounds of possibility/, conceive a diagonalized
non-element.
Nope, as explained and re-explained ad nauseam around here:
just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences,
is indeed constructive: a definition of anti-diagonal of *any*
(infinite) list is provided, and the proof that the anti-diagonal
cannot be in the list is quite constructive.
"quite" but not "completely".
A constructive operation is defined, but a diagonal number is
constructed just when that constructive operation is applied to a constructible list.
On 04/07/2026 22:12, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
LP := ~True(LP)
G := ~Provable(PA, G)
Is it right to call that "incoherent"?
"incoherent" would seem to me to be reservable for a purported
demonstration of a deduction which is constructed of two deductions that
do not validly lead from one to the other.
"valueless" is accurate, technically, but it has an ordinary economic
sense similar to "worthless".
"non-normalisable" is accurate and, more usefully, so is
"non-head-normalisable" (and some other related terms).
"loopy" might be useful but readers would probably go insane at you
because they go insane at much less.
On 7/4/2026 5:12 PM, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
False.
In computability theory and computational complexity theory, an
undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes- or-no answer.
https://en.wikipedia.org/wiki/Undecidable_problem
LP := ~True(LP)
G := ~Provable(PA, G)
The above are not examples of that.
Math Incomplete: The inability to accomplish
more than a system was defined to accomplish.
False. Intent does not factor into formal systems.
In mathematical logic, a theory is complete if it is consistent and for every closed formula in the theory's language, either that formula or
its negation is provable
https://en.wikipedia.org/wiki/Complete_theory
(∀x, S(x) ≠ x) cannot be proven in Q
Math mapping from an input to an output:
Ignore the input and output a fixed constant.
Provide an external reference that 1) defines "ignoring the input" and
2) forbids it.
int mapping_function(int x)
{
return 0;
}
All you're proving is that you can't understand that words can have different meanings in different contexts that aren't necessarily related.
Of course,
dequantification of fantastically quantified statements doesn't make a statement about nonconstructible objects because there aren't any
outside of the fantastical quantification.
On 04/07/2026 16:31, Tristan Wibberley wrote:
On 06/05/2026 20:37, Julio Di Egidio wrote:
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal.
Rather, we presuppose that we can enumerate a set, and then,
/purely on the grounds of possibility/, conceive a diagonalized
non-element.
Nope, as explained and re-explained ad nauseam around here:
just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences,
is indeed constructive: a definition of anti-diagonal of *any*
(infinite) list is provided, and the proof that the anti-diagonal
cannot be in the list is quite constructive.
"quite" but not "completely".
A constructive operation is defined, but a diagonal number is
constructed just when that constructive operation is applied to a
constructible list.
I should note for the less knowledgable readers of course it's less
often than that, it is only that often for systems such as the one Julio
and Phoenix are using which allows dequantification of universally
quantified statements into the system proper which then have derivable statements containing actual constructions of the constructible objects
they apply to by virtue of their original quantification. Of course, dequantification of fantastically quantified statements doesn't make a statement about nonconstructible objects because there aren't any
outside of the fantastical quantification.
By which I don't mean to argue the countability of the set of reals as defined in what we call Cantor's Proof of the Uncountability of the
Reals to include objects quantified over by fantatstical quantification
but not by universal quantification, but it does make some meaning clearer.
While some of the sets might have objects in the system proper, some of
the members of some of the sets clearly do not.
On 7/5/2026 9:19 AM, dbush wrote:
On 7/4/2026 5:12 PM, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
False.
In computability theory and computational complexity theory, an
undecidable problem is a decision problem for which it is proved to be
impossible to construct an algorithm that always leads to a correct
yes- or-no answer.
https://en.wikipedia.org/wiki/Undecidable_problem
LP := ~True(LP)
G := ~Provable(PA, G)
The above are not examples of that.
Math Incomplete: The inability to accomplish
more than a system was defined to accomplish.
False. Intent does not factor into formal systems.
In mathematical logic, a theory is complete if it is consistent and
for every closed formula in the theory's language, either that formula
or its negation is provable
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Ultimately the above is true and one key PTS author
comes very close to agreeing with that.
*Truth as an Epistemic Notion*
What is the appropriate notion of truth for
sentences whose meanings are understood in
epistemic terms such as proof or ground for
an assertion? It seems that the truth of such
sentences has to be identified with the existence
of proofs...
https://link.springer.com/article/10.1007/s11245-011-9107-6
https://en.wikipedia.org/wiki/Complete_theory
(∀x, S(x) ≠ x) cannot be proven in Q
Math mapping from an input to an output:
Ignore the input and output a fixed constant.
Provide an external reference that 1) defines "ignoring the input" and
2) forbids it.
int mapping_function(int x)
{
return 0;
}
All you're proving is that you can't understand that words can have
different meanings in different contexts that aren't necessarily related.
On 7/5/2026 9:52 AM, Tristan Wibberley wrote:
On 04/07/2026 16:31, Tristan Wibberley wrote:
On 06/05/2026 20:37, Julio Di Egidio wrote:
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal.
Rather, we presuppose that we can enumerate a set, and then,
/purely on the grounds of possibility/, conceive a diagonalized
non-element.
Nope, as explained and re-explained ad nauseam around here:
just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences,
is indeed constructive: a definition of anti-diagonal of *any*
(infinite) list is provided, and the proof that the anti-diagonal
cannot be in the list is quite constructive.
"quite" but not "completely".
A constructive operation is defined, but a diagonal number is
constructed just when that constructive operation is applied to a
constructible list.
I should note for the less knowledgable readers of course it's less
often than that, it is only that often for systems such as the one Julio
and Phoenix are using which allows dequantification of universally
quantified statements into the system proper which then have derivable
statements containing actual constructions of the constructible objects
they apply to by virtue of their original quantification. Of course,
dequantification of fantastically quantified statements doesn't make a
statement about nonconstructible objects because there aren't any
outside of the fantastical quantification.
By which I don't mean to argue the countability of the set of reals as
defined in what we call Cantor's Proof of the Uncountability of the
Reals to include objects quantified over by fantatstical quantification
but not by universal quantification, but it does make some meaning
clearer.
While some of the sets might have objects in the system proper, some of
the members of some of the sets clearly do not.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded justification
tree exists.
The absence of
(a) finite sequence of inference steps to an atomic base,
(b) canonical proof
(c) well-founded justification tree
makes the above to PTS invalid.
Your lack of response constitutes your admission that the below function successfully computes the mapping of all ints to 0.
int mapping_function(int x)
{
return 0;
}[...]
On 07/05/2026 09:33 AM, olcott wrote:
On 7/5/2026 9:52 AM, Tristan Wibberley wrote:
On 04/07/2026 16:31, Tristan Wibberley wrote:
On 06/05/2026 20:37, Julio Di Egidio wrote:
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal.
Rather, we presuppose that we can enumerate a set, and then,
/purely on the grounds of possibility/, conceive a diagonalized
non-element.
Nope, as explained and re-explained ad nauseam around here:
just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences,
is indeed constructive: a definition of anti-diagonal of *any*
(infinite) list is provided, and the proof that the anti-diagonal
cannot be in the list is quite constructive.
"quite" but not "completely".
A constructive operation is defined, but a diagonal number is
constructed just when that constructive operation is applied to a
constructible list.
I should note for the less knowledgable readers of course it's less
often than that, it is only that often for systems such as the one Julio >>> and Phoenix are using which allows dequantification of universally
quantified statements into the system proper which then have derivable
statements containing actual constructions of the constructible objects
they apply to by virtue of their original quantification. Of course,
dequantification of fantastically quantified statements doesn't make a
statement about nonconstructible objects because there aren't any
outside of the fantastical quantification.
By which I don't mean to argue the countability of the set of reals as
defined in what we call Cantor's Proof of the Uncountability of the
Reals to include objects quantified over by fantatstical quantification
but not by universal quantification, but it does make some meaning
clearer.
While some of the sets might have objects in the system proper, some of
the members of some of the sets clearly do not.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded justification
tree exists.
The absence of
(a) finite sequence of inference steps to an atomic base,
(b) canonical proof
(c) well-founded justification tree
makes the above to PTS invalid.
Yeah, come up with something new, or stuff a sock in it.
On 7/4/2026 5:12 PM, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
False.
In computability theory and computational complexity theory, an
undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes- or-no answer.
https://en.wikipedia.org/wiki/Undecidable_problem
LP := ~True(LP)
G := ~Provable(PA, G)
The above are not examples of that.
Math Incomplete: The inability to accomplish
more than a system was defined to accomplish.
False. Intent does not factor into formal systems.
In mathematical logic, a theory is complete if it is consistent and for every closed formula in the theory's language, either that formula or
its negation is provable
https://en.wikipedia.org/wiki/Complete_theory
(∀x, S(x) ≠ x) cannot be proven in Q
Math mapping from an input to an output:
Ignore the input and output a fixed constant.
Provide an external reference that 1) defines "ignoring the input" and
2) forbids it.
int mapping_function(int x)
{
return 0;
}
All you're proving is that you can't understand that words can have different meanings in different contexts that aren't necessarily related.
On 7/5/2026 2:56 PM, Ross Finlayson wrote:
On 07/05/2026 09:33 AM, olcott wrote:
On 7/5/2026 9:52 AM, Tristan Wibberley wrote:
On 04/07/2026 16:31, Tristan Wibberley wrote:
On 06/05/2026 20:37, Julio Di Egidio wrote:
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal.
Rather, we presuppose that we can enumerate a set, and then,
/purely on the grounds of possibility/, conceive a diagonalized
non-element.
Nope, as explained and re-explained ad nauseam around here:
just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences,
is indeed constructive: a definition of anti-diagonal of *any*
(infinite) list is provided, and the proof that the anti-diagonal
cannot be in the list is quite constructive.
"quite" but not "completely".
A constructive operation is defined, but a diagonal number is
constructed just when that constructive operation is applied to a
constructible list.
I should note for the less knowledgable readers of course it's less
often than that, it is only that often for systems such as the one
Julio
and Phoenix are using which allows dequantification of universally
quantified statements into the system proper which then have derivable >>>> statements containing actual constructions of the constructible objects >>>> they apply to by virtue of their original quantification. Of course,
dequantification of fantastically quantified statements doesn't make a >>>> statement about nonconstructible objects because there aren't any
outside of the fantastical quantification.
By which I don't mean to argue the countability of the set of reals as >>>> defined in what we call Cantor's Proof of the Uncountability of the
Reals to include objects quantified over by fantatstical quantification >>>> but not by universal quantification, but it does make some meaning
clearer.
While some of the sets might have objects in the system proper, some of >>>> the members of some of the sets clearly do not.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded justification >>> tree exists.
The absence of
(a) finite sequence of inference steps to an atomic base,
(b) canonical proof
(c) well-founded justification tree
makes the above to PTS invalid.
Yeah, come up with something new, or stuff a sock in it.
The above proves that the notion of undecidable
is incorrect if you understood rather than ignored
what it says.
It also is the final resolution to the Liar Paradox
and you would know this if you understood it.
On 07/05/2026 01:25 PM, olcott wrote:
On 7/5/2026 2:56 PM, Ross Finlayson wrote:
On 07/05/2026 09:33 AM, olcott wrote:
On 7/5/2026 9:52 AM, Tristan Wibberley wrote:
On 04/07/2026 16:31, Tristan Wibberley wrote:
On 06/05/2026 20:37, Julio Di Egidio wrote:
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal.
Rather, we presuppose that we can enumerate a set, and then,
/purely on the grounds of possibility/, conceive a diagonalized >>>>>>>> non-element.
Nope, as explained and re-explained ad nauseam around here:
just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences,
is indeed constructive: a definition of anti-diagonal of *any*
(infinite) list is provided, and the proof that the anti-diagonal >>>>>>> cannot be in the list is quite constructive.
"quite" but not "completely".
A constructive operation is defined, but a diagonal number is
constructed just when that constructive operation is applied to a
constructible list.
I should note for the less knowledgable readers of course it's less
often than that, it is only that often for systems such as the one
Julio
and Phoenix are using which allows dequantification of universally
quantified statements into the system proper which then have derivable >>>>> statements containing actual constructions of the constructible
objects
they apply to by virtue of their original quantification. Of course, >>>>> dequantification of fantastically quantified statements doesn't make a >>>>> statement about nonconstructible objects because there aren't any
outside of the fantastical quantification.
By which I don't mean to argue the countability of the set of reals as >>>>> defined in what we call Cantor's Proof of the Uncountability of the
Reals to include objects quantified over by fantatstical
quantification
but not by universal quantification, but it does make some meaning
clearer.
While some of the sets might have objects in the system proper,
some of
the members of some of the sets clearly do not.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded justification >>>> tree exists.
The absence of
(a) finite sequence of inference steps to an atomic base,
(b) canonical proof
(c) well-founded justification tree
makes the above to PTS invalid.
Yeah, come up with something new, or stuff a sock in it.
The above proves that the notion of undecidable
is incorrect if you understood rather than ignored
what it says.
It also is the final resolution to the Liar Paradox
and you would know this if you understood it.
Like I said,
"understanding" is for suckers,
"comprehension" is for knowledge.
Your axiomatization otherwise is false.
It's like they say,
"It just don't mean a thing."
WM <- retro-finitist crankety-troll
JG <- retro-finitist crankety-troll
PO <- retro-finitist crankety-troll
"Polluter(s) of sci.math"
On 7/5/2026 4:30 PM, Ross Finlayson wrote:
On 07/05/2026 01:25 PM, olcott wrote:
On 7/5/2026 2:56 PM, Ross Finlayson wrote:
On 07/05/2026 09:33 AM, olcott wrote:
On 7/5/2026 9:52 AM, Tristan Wibberley wrote:
On 04/07/2026 16:31, Tristan Wibberley wrote:
On 06/05/2026 20:37, Julio Di Egidio wrote:
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal. >>>>>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>>>>> non-element.
Nope, as explained and re-explained ad nauseam around here:
just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences, >>>>>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>>>>> (infinite) list is provided, and the proof that the anti-diagonal >>>>>>>> cannot be in the list is quite constructive.
"quite" but not "completely".
A constructive operation is defined, but a diagonal number is
constructed just when that constructive operation is applied to a >>>>>>> constructible list.
I should note for the less knowledgable readers of course it's less >>>>>> often than that, it is only that often for systems such as the one >>>>>> Julio
and Phoenix are using which allows dequantification of universally >>>>>> quantified statements into the system proper which then have
derivable
statements containing actual constructions of the constructible
objects
they apply to by virtue of their original quantification. Of course, >>>>>> dequantification of fantastically quantified statements doesn't
make a
statement about nonconstructible objects because there aren't any
outside of the fantastical quantification.
By which I don't mean to argue the countability of the set of
reals as
defined in what we call Cantor's Proof of the Uncountability of the >>>>>> Reals to include objects quantified over by fantatstical
quantification
but not by universal quantification, but it does make some meaning >>>>>> clearer.
While some of the sets might have objects in the system proper,
some of
the members of some of the sets clearly do not.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded
justification
tree exists.
The absence of
(a) finite sequence of inference steps to an atomic base,
(b) canonical proof
(c) well-founded justification tree
makes the above to PTS invalid.
Yeah, come up with something new, or stuff a sock in it.
The above proves that the notion of undecidable
is incorrect if you understood rather than ignored
what it says.
It also is the final resolution to the Liar Paradox
and you would know this if you understood it.
Like I said,
"understanding" is for suckers,
"comprehension" is for knowledge.
Gemini agrees with me and I only gave it the Prolog. https://share.gemini.google/1dJnMwOZ2k5F
Your axiomatization otherwise is false.
It's like they say,
"It just don't mean a thing."
WM <- retro-finitist crankety-troll
JG <- retro-finitist crankety-troll
PO <- retro-finitist crankety-troll
"Polluter(s) of sci.math"
On 07/05/2026 02:45 PM, olcott wrote:
On 7/5/2026 4:30 PM, Ross Finlayson wrote:
On 07/05/2026 01:25 PM, olcott wrote:
On 7/5/2026 2:56 PM, Ross Finlayson wrote:
On 07/05/2026 09:33 AM, olcott wrote:
On 7/5/2026 9:52 AM, Tristan Wibberley wrote:
On 04/07/2026 16:31, Tristan Wibberley wrote:
On 06/05/2026 20:37, Julio Di Egidio wrote:
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal. >>>>>>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>>>>>> non-element.
Nope, as explained and re-explained ad nauseam around here:
just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences, >>>>>>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>>>>>> (infinite) list is provided, and the proof that the anti-diagonal >>>>>>>>> cannot be in the list is quite constructive.
"quite" but not "completely".
A constructive operation is defined, but a diagonal number is
constructed just when that constructive operation is applied to a >>>>>>>> constructible list.
I should note for the less knowledgable readers of course it's less >>>>>>> often than that, it is only that often for systems such as the one >>>>>>> Julio
and Phoenix are using which allows dequantification of universally >>>>>>> quantified statements into the system proper which then have
derivable
statements containing actual constructions of the constructible
objects
they apply to by virtue of their original quantification. Of course, >>>>>>> dequantification of fantastically quantified statements doesn't
make a
statement about nonconstructible objects because there aren't any >>>>>>> outside of the fantastical quantification.
By which I don't mean to argue the countability of the set of
reals as
defined in what we call Cantor's Proof of the Uncountability of the >>>>>>> Reals to include objects quantified over by fantatstical
quantification
but not by universal quantification, but it does make some meaning >>>>>>> clearer.
While some of the sets might have objects in the system proper,
some of
the members of some of the sets clearly do not.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Gemini agrees with not-you.
On 7/4/2026 3:49 AM, Mikko wrote:
On 03/07/2026 21:38, olcott wrote:
On 7/3/2026 1:21 PM, André G. Isaak wrote:
On 2026-07-03 12:12, olcott wrote:
On 7/3/2026 12:17 PM, André G. Isaak wrote:
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:Because it isn't true in all models of Q,
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps. >>>>>>>>>So your phrasing is good: Q would need something like an
infinite sequence of steps (or a single principle that
summarizes them) to get the ∀x. Since formal proofs must be >>>>>>>>> finite, and Q lacks the tool (induction) that would allow a >>>>>>>>> finite proof of the infinite claim, the universal statement >>>>>>>>> remains unprovable.
I'm not sure why you are responding to yourself nor who 'your >>>>>>>> phrasing' refers to since you don't quote anyone. But, assuming >>>>>>>> we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>>>>>> simply off.
You *can* prove universally quantified claims in Q, just not
that particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? >>>>>>
many weeks in every thread. Whenever you ignore
this the rest of your reply will be ignored.
The rest of my post which you snipped and (presumably) ignored
explained *why* you are wrong about this. PTS does not reject models
or model theory. It simply doesn't rely on model-theoretic
semantics. Q *requires* a model.
It replaces Model theory With PTS.
That you do not understand this is your mistake.
"Is x true" is replaced with something like "Is x provable".
"Is x provable" is there already. Why would one want to lose
"Is x true"? If one dosn't need "Is x true" one needn't use
it.
The whole focus of most PTS "Is x provable".
Model theory looks at true in a model and ignores
the connection between true and provable.
On 7/4/2026 2:48 AM, Mikko wrote:
On 04/07/2026 05:37, olcott wrote:
On 7/3/2026 9:19 PM, dbush wrote:
On 7/3/2026 10:05 PM, olcott wrote:
On 7/3/2026 8:58 PM, dbush wrote:
On 7/3/2026 9:52 PM, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that >>>>>>>>>>>> is by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a
mapping and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute
When you actually implement this concretely
We find that it is not possible, as Linz and others have proved.
Impossible requirements are incorrect requirements.
There is no well known meaning of "incorrect requirements".
I just established the meaning of incorrect requirements
as any requirement that requires the logically impossible.
On 7/4/2026 2:46 AM, Mikko wrote:The halting problem does not require anything unless the input
On 04/07/2026 04:52, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is >>>>>>>> by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping
and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute the mapping from
its actual input according to the operational semantics
of this input to the behavior that this input actually
specifies. No function can report on the behavior of
its caller because it has no idea who its caller is.
A function does not compute. An algrothm may compute a function.
However, no algrithm computes the halt function.
The halt functions maps a computation to a truth value
but so do many other functions, too.
When implemented as C functions
typedef int (*ptr)();
int HHH(ptr P);
01 int DD()
02 {
03 int Halt_Status = HHH(DD);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }
08
09 void main()
10 {
11 DD();
12 HHH(DD);
13 }
The HP requires HHH to report on the DD() invoked
in main(). This is impossible because HHH has no
idea who its caller is and deciders are functions
that only operate on their arguments.
On 7/4/2026 2:43 AM, Mikko wrote:
On 03/07/2026 21:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part >>>>>>>>>> of a
claim about you, and your response was the false claim that "That >>>>>>>>>> is just nonsense". Later in the discussion you offer more >>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to
outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to >>>>>> an output of either 0 or 1?
If an algorithm takes an input and produces an output, that is by
definition a mapping.
That only proves that the definition is incoherent.
Your definitions often are. But the well known definition of "mapping"
is not.
The output really should be based on the input
because computing the mapping from an input to
an output requires some kind of correspondence
between the two.
On 7/4/2026 2:55 AM, Mikko wrote:
On 03/07/2026 21:45, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:int Not_A_Mapping(int X)
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part >>>>>>>>>> of a
claim about you, and your response was the false claim that "That >>>>>>>>>> is just nonsense". Later in the discussion you offer more >>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to
outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to >>>>>> an output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs,
{
return 0;
}
By construing that as a mapping is one of the screw-ups
that prevents true expressed in language from being computable.
By construing the above mapping as a non-mapping you disconnect from
Common Languge and lose your ablility to communicate.
I will not tolerate that math hijacks the term
"mapping" to ignore requirement that there must
be some actual correspondence between inputs and
outputs.
A actual halt function must compute the mapping fromA function does not compute. It just is. It can be said to "report"
its actual input according to the operational semantics
of this input to the behavior that this input actually
specifies. No function can report on the behavior of
its caller because it has no idea who its caller is.
On 7/4/2026 3:00 AM, Mikko wrote:
On 03/07/2026 22:08, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part >>>>>>>>>> of a
claim about you, and your response was the false claim that "That >>>>>>>>>> is just nonsense". Later in the discussion you offer more >>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to
outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to >>>>>> an output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs,
so there is nothing to ignore. What an algorithm might do to
*compute* the mapping has nothing to do with the mapping.
It is conventionally construed as a mapping.
More importantly, it satisfies the definition of "mapping".
It is not even conventionally construed as a halt
function, not even a halt function that gets the
wrong answer.
Irrelevant, as the claim was that H does not implement the halt
function.
If it ignores input it is no function of this input.
On 7/4/2026 2:41 AM, Mikko wrote:
On 03/07/2026 21:10, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a >>>>>>>> claim about you, and your response was the false claim that "That >>>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to an
output of either 0 or 1?
No, but dbush's program H implements a mapping anyway. It just is
a different mapping from the one a halt decider is required to do.
Making it complete nonsense.
On 7/4/2026 2:37 AM, Mikko wrote:
On 2026-07-02 dbush wrote:
The halting problem doesn't actually have self reference, as
algorithms can be copied as in the below example of algorithm D:
void D(ptr *I)
{
// algorithm D; input: I
ptr *X = D;
ptr *Y = I;
int result;
{
// algorithm H; inputs: X,Y
result = 0;
}
if (result == 1) {
while (1);
}
}
Which is the counter example input to algorithm H:
int H(ptr *X, ptr *Y)
{
int result;
{
// algorithm H; inputs: X,Y
result = 0;
}
return result;
}
On 03/07/2026 18:36, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a
claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence
to support his claim.
His halt decider did not look at its input.
For every possible input his H halts and returns either 0 for false
or 1 for true. Therefore his H is a decider. It return 0 for D
although D halts so the decider H is not a halt decider.
counter-factual H always returns 0.
On 7/4/2026 9:32 AM, olcott wrote:
On 7/4/2026 2:37 AM, Mikko wrote:
On 2026-07-02 dbush wrote:
The halting problem doesn't actually have self reference, as
algorithms can be copied as in the below example of algorithm D:
void D(ptr *I)
{
// algorithm D; input: I
ptr *X = D;
ptr *Y = I;
int result;
{
// algorithm H; inputs: X,Y
result = 0;
}
if (result == 1) {
while (1);
}
}
Which is the counter example input to algorithm H:
int H(ptr *X, ptr *Y)
{
int result;
{
// algorithm H; inputs: X,Y
result = 0;
}
return result;
}
On 03/07/2026 18:36, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part of a
claim about you, and your response was the false claim that "That
is just nonsense". Later in the discussion you offer more evidence
to support his claim.
His halt decider did not look at its input.
For every possible input his H halts and returns either 0 for false
or 1 for true. Therefore his H is a decider. It return 0 for D
although D halts so the decider H is not a halt decider.
counter-factual H always returns 0.
Which means the condition "either 0 or 1" is satisfied.
It seems we need to add "or" to the list of basic high school level
logic topics you don't understand.
On 7/4/2026 3:06 AM, Mikko wrote:
On 03/07/2026 21:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:However, there are theories that reamain incomplete even when >>>>>>>>>> more postolates are added, as long as there is a way to know >>>>>>>>>> which sentences are included in the added postulates. Important >>>>>>>>>> examples include Peano arithmetic and ZFC set theory.
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:
On 27/06/2026 17:50, polcott wrote:Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was >>>>>>>>>>>>>>> defined to do. Incomplete only counts relative to >>>>>>>>>>>>>>> its intended purpose. A car without an engine is >>>>>>>>>>>>>>> incomplete relative to a mode of transportation.
On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote:It comes close. If ∃x x=S(x) is likewise "ungrounded" >>>>>>>>>>>>>>>> but in the
A proof theoretic expression is known to be true when >>>>>>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>>>>>>> with semantic meaning and never got around to true(L,x). >>>>>>>>>>>>>>>>>>That's surprising, disregard for axioms?
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete >>>>>>>>>>>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words mean. >>>>>>>>>>>>>>>
Irrelevant. The definition of completeness
It a misnomer and does not literally mean (as it implies) >>>>>>>>>>>>> that something is missing that could be added to make >>>>>>>>>>>>> it complete.
It does mean that something is missing that could be added to >>>>>>>>>>>> enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined to >>>>>>>>>>> do.
When Q is extended to become PA it stops being Q and becomes PA. >>>>>>>>>>
Base-Extension Semantics (B-eS) seems to be essentially a cheat. >>>>>>>>> When we ask what is grounded in an atomic base of Q and we
add axioms to Q to become PA we cheated in that we changed
the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial >>>>>>>> answer
rather than no answer at all. Of course Q with any additional
postulate is not Q but if the additional postulates are true about >>>>>>>> natural numbers then the strengthened theory is still a theory of >>>>>>>> natural numbers. PA is one such strengthened Q but still incomplete >>>>>>>> and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently
missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
And that differs from claiming that Q is incomplete exactly how...?
The base definition of "incomplete" means that it is
not operating according to design spec.
No, it is not. The term "incomplete" in its base meaning is
appicable to various things that are not exprected to operate.
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
A motor vehicle that lacks a motor is incomplete.
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:
On 7/4/2026 3:06 AM, Mikko wrote:
On 03/07/2026 21:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:The base definition of "incomplete" means that it is
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:Irrelevant. The definition of completeness
On 27/06/2026 17:50, polcott wrote:Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was >>>>>>>>>>>>>>>>> defined to do. Incomplete only counts relative to >>>>>>>>>>>>>>>>> its intended purpose. A car without an engine is >>>>>>>>>>>>>>>>> incomplete relative to a mode of transportation. >>>>>>>>>>>>>>>>
On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote:It comes close. If ∃x x=S(x) is likewise "ungrounded" >>>>>>>>>>>>>>>>>> but in the
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q.
A proof theoretic expression is known to be true when >>>>>>>>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>>>>>>>>> with semantic meaning and never got around to >>>>>>>>>>>>>>>>>>>>> true(L,x).
That's surprising, disregard for axioms? >>>>>>>>>>>>>>>>>>>
This does not mean undecidable or incomplete >>>>>>>>>>>>>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words mean. >>>>>>>>>>>>>>>>>
It a misnomer and does not literally mean (as it implies) >>>>>>>>>>>>>>> that something is missing that could be added to make >>>>>>>>>>>>>>> it complete.
It does mean that something is missing that could be added to >>>>>>>>>>>>>> enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined >>>>>>>>>>>>> to do.
When Q is extended to become PA it stops being Q and >>>>>>>>>>>>> becomes PA.
However, there are theories that reamain incomplete even when >>>>>>>>>>>> more postolates are added, as long as there is a way to know >>>>>>>>>>>> which sentences are included in the added postulates. Important >>>>>>>>>>>> examples include Peano arithmetic and ZFC set theory.
Base-Extension Semantics (B-eS) seems to be essentially a cheat. >>>>>>>>>>> When we ask what is grounded in an atomic base of Q and we >>>>>>>>>>> add axioms to Q to become PA we cheated in that we changed >>>>>>>>>>> the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial >>>>>>>>>> answer
rather than no answer at all. Of course Q with any additional >>>>>>>>>> postulate is not Q but if the additional postulates are true >>>>>>>>>> about
natural numbers then the strengthened theory is still a theory of >>>>>>>>>> natural numbers. PA is one such strengthened Q but still
incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently >>>>>>>> missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
And that differs from claiming that Q is incomplete exactly how...? >>>>>
not operating according to design spec.
No, it is not. The term "incomplete" in its base meaning is
appicable to various things that are not exprected to operate.
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
These definitions are the liars.
Term-of-the-art
A cat is a dalmatian dog
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
LP := ~True(LP)
G := ~Provable(PA, G)
Math Incomplete: The inability to accomplish
more than a system was defined to accomplish.
(∀x, S(x) ≠ x) cannot be proven in Q
Math mapping from an input to an output:
Ignore the input and output a fixed constant.
int mapping_function(int x)
{
return 0;
}
On 7/5/2026 9:19 AM, dbush wrote:
On 7/4/2026 5:12 PM, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
False.
In computability theory and computational complexity theory, an
undecidable problem is a decision problem for which it is proved to be
impossible to construct an algorithm that always leads to a correct
yes- or-no answer.
https://en.wikipedia.org/wiki/Undecidable_problem
LP := ~True(LP)
G := ~Provable(PA, G)
The above are not examples of that.
Math Incomplete: The inability to accomplish
more than a system was defined to accomplish.
False. Intent does not factor into formal systems.
In mathematical logic, a theory is complete if it is consistent and
for every closed formula in the theory's language, either that formula
or its negation is provable
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
On 7/5/2026 9:52 AM, Tristan Wibberley wrote:
On 04/07/2026 16:31, Tristan Wibberley wrote:
On 06/05/2026 20:37, Julio Di Egidio wrote:
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal.
Rather, we presuppose that we can enumerate a set, and then,
/purely on the grounds of possibility/, conceive a diagonalized
non-element.
Nope, as explained and re-explained ad nauseam around here:
just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences,
is indeed constructive: a definition of anti-diagonal of *any*
(infinite) list is provided, and the proof that the anti-diagonal
cannot be in the list is quite constructive.
"quite" but not "completely".
A constructive operation is defined, but a diagonal number is
constructed just when that constructive operation is applied to a
constructible list.
I should note for the less knowledgable readers of course it's less
often than that, it is only that often for systems such as the one Julio
and Phoenix are using which allows dequantification of universally
quantified statements into the system proper which then have derivable
statements containing actual constructions of the constructible objects
they apply to by virtue of their original quantification. Of course,
dequantification of fantastically quantified statements doesn't make a
statement about nonconstructible objects because there aren't any
outside of the fantastical quantification.
By which I don't mean to argue the countability of the set of reals as
defined in what we call Cantor's Proof of the Uncountability of the
Reals to include objects quantified over by fantatstical quantification
but not by universal quantification, but it does make some meaning
clearer.
While some of the sets might have objects in the system proper, some of
the members of some of the sets clearly do not.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded justification tree exists.
On 06/05/2026 20:37, Julio Di Egidio wrote:
... as explained and re-explained ad nauseam around here:
just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences,
is indeed constructive: a definition of anti-diagonal of *any*
(infinite) list is provided, and the proof that the anti-diagonal
cannot be in the list is quite constructive.
On 04/07/2026 20:13, olcott wrote:
On 7/4/2026 3:49 AM, Mikko wrote:
On 03/07/2026 21:38, olcott wrote:
On 7/3/2026 1:21 PM, André G. Isaak wrote:
On 2026-07-03 12:12, olcott wrote:
On 7/3/2026 12:17 PM, André G. Isaak wrote:
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:Because it isn't true in all models of Q,
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps. >>>>>>>>>>So your phrasing is good: Q would need something like an
infinite sequence of steps (or a single principle that
summarizes them) to get the ∀x. Since formal proofs must be >>>>>>>>>> finite, and Q lacks the tool (induction) that would allow a >>>>>>>>>> finite proof of the infinite claim, the universal statement >>>>>>>>>> remains unprovable.
I'm not sure why you are responding to yourself nor who 'your >>>>>>>>> phrasing' refers to since you don't quote anyone. But, assuming >>>>>>>>> we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>>>>>>> simply off.
You *can* prove universally quantified claims in Q, just not >>>>>>>>> that particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? >>>>>>>
many weeks in every thread. Whenever you ignore
this the rest of your reply will be ignored.
The rest of my post which you snipped and (presumably) ignored
explained *why* you are wrong about this. PTS does not reject
models or model theory. It simply doesn't rely on model-theoretic
semantics. Q *requires* a model.
It replaces Model theory With PTS.
That you do not understand this is your mistake.
"Is x true" is replaced with something like "Is x provable".
"Is x provable" is there already. Why would one want to lose
"Is x true"? If one dosn't need "Is x true" one needn't use
it.
The whole focus of most PTS "Is x provable".
Model theory looks at true in a model and ignores
the connection between true and provable.
People rarely care about PTS or model theory. More often they careabout
what is or is not true about someting they consider important.
On 04/07/2026 19:58, olcott wrote:
On 7/4/2026 2:48 AM, Mikko wrote:
On 04/07/2026 05:37, olcott wrote:
On 7/3/2026 9:19 PM, dbush wrote:
On 7/3/2026 10:05 PM, olcott wrote:
On 7/3/2026 8:58 PM, dbush wrote:
On 7/3/2026 9:52 PM, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that >>>>>>>>>>>>> is by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a >>>>>>>>>>> mapping and an algorithm. They are two different things. >>>>>>>>>>>
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute
When you actually implement this concretely
We find that it is not possible, as Linz and others have proved.
Impossible requirements are incorrect requirements.
There is no well known meaning of "incorrect requirements".
I just established the meaning of incorrect requirements
as any requirement that requires the logically impossible.
That is insufficient to make the expression "incorrect requirements" meaningful in Common Language or well known.
On 04/07/2026 19:55, olcott wrote:
On 7/4/2026 2:46 AM, Mikko wrote:The halting problem does not require anything unless the input
On 04/07/2026 04:52, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is >>>>>>>>> by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping >>>>>>> and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute the mapping from
its actual input according to the operational semantics
of this input to the behavior that this input actually
specifies. No function can report on the behavior of
its caller because it has no idea who its caller is.
A function does not compute. An algrothm may compute a function.
However, no algrithm computes the halt function.
The halt functions maps a computation to a truth value
but so do many other functions, too.
When implemented as C functions
typedef int (*ptr)();
int HHH(ptr P);
01 int DD()
02 {
03 int Halt_Status = HHH(DD);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }
08
09 void main()
10 {
11 DD();
12 HHH(DD);
13 }
The HP requires HHH to report on the DD() invoked
in main(). This is impossible because HHH has no
idea who its caller is and deciders are functions
that only operate on their arguments.
fully specifies a computation.
The above DD calls HHH, which must be the same HHH as main calls if
DD halts. Therefore the bhaviour of HHH is a part of the computation
that the HHH would answer about if it were a halt decider.
The requirements of a halt decider don't require that then input
be presented to the decider the way it is done above. For exmample,
a text file would be acceptable.
On 04/07/2026 20:01, olcott wrote:
On 7/4/2026 2:55 AM, Mikko wrote:
On 03/07/2026 21:45, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:int Not_A_Mapping(int X)
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a >>>>>>>>>>> part of a
claim about you, and your response was the false claim that >>>>>>>>>>> "That
is just nonsense". Later in the discussion you offer more >>>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to >>>>>>>>> outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to >>>>>>> an output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs,
{
return 0;
}
By construing that as a mapping is one of the screw-ups
that prevents true expressed in language from being computable.
By construing the above mapping as a non-mapping you disconnect from
Common Languge and lose your ablility to communicate.
I will not tolerate that math hijacks the term
"mapping" to ignore requirement that there must
be some actual correspondence between inputs and
outputs.
Your exceesive intolerance is irrelevant.
In mathematical context the
cartogrphical meaning is so obviously nonsense that no confusion is
possible. Besides it is well known that in a mathematical context many
words have meanings that are unrelated or only distantly related to
their usual meanings.
A actual halt function must compute the mapping fromA function does not compute. It just is. It can be said to "report"
its actual input according to the operational semantics
of this input to the behavior that this input actually
specifies. No function can report on the behavior of
its caller because it has no idea who its caller is.
but that must not be interpreted too literally.
On 04/07/2026 20:03, olcott wrote:
On 7/4/2026 3:00 AM, Mikko wrote:
On 03/07/2026 22:08, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a >>>>>>>>>>> part of a
claim about you, and your response was the false claim that >>>>>>>>>>> "That
is just nonsense". Later in the discussion you offer more >>>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to >>>>>>>>> outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to >>>>>>> an output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs, >>>>> so there is nothing to ignore. What an algorithm might do to
*compute* the mapping has nothing to do with the mapping.
It is conventionally construed as a mapping.
More importantly, it satisfies the definition of "mapping".
It is not even conventionally construed as a halt
function, not even a halt function that gets the
wrong answer.
Irrelevant, as the claim was that H does not implement the halt
function.
If it ignores input it is no function of this input.
Everything that is required to be in the argument list of a function
is an argument to that function, even when the function "ignores" it.
On 04/07/2026 16:38, olcott wrote:
On 7/4/2026 2:41 AM, Mikko wrote:
On 03/07/2026 21:10, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part >>>>>>>>> of a
claim about you, and your response was the false claim that "That >>>>>>>>> is just nonsense". Later in the discussion you offer more evidence >>>>>>>>> to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to outputs. >>>>>>>
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to
an output of either 0 or 1?
No, but dbush's program H implements a mapping anyway. It just is
a different mapping from the one a halt decider is required to do.
Making it complete nonsense.
The program has a well defined meaning so it is not non-sense.
That it may be too big or complex for you is irrelevant.
On 04/07/2026 20:07, olcott wrote:
On 7/4/2026 3:06 AM, Mikko wrote:
On 03/07/2026 21:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:Irrelevant. The definition of completeness
On 27/06/2026 17:50, polcott wrote:Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was >>>>>>>>>>>>>>>> defined to do. Incomplete only counts relative to >>>>>>>>>>>>>>>> its intended purpose. A car without an engine is >>>>>>>>>>>>>>>> incomplete relative to a mode of transportation. >>>>>>>>>>>>>>>
On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote:It comes close. If ∃x x=S(x) is likewise "ungrounded" >>>>>>>>>>>>>>>>> but in the
A proof theoretic expression is known to be true when >>>>>>>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>>>>>>>> with semantic meaning and never got around to >>>>>>>>>>>>>>>>>>>> true(L,x).
That's surprising, disregard for axioms?
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete >>>>>>>>>>>>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words mean. >>>>>>>>>>>>>>>>
It a misnomer and does not literally mean (as it implies) >>>>>>>>>>>>>> that something is missing that could be added to make >>>>>>>>>>>>>> it complete.
It does mean that something is missing that could be added to >>>>>>>>>>>>> enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined >>>>>>>>>>>> to do.
When Q is extended to become PA it stops being Q and becomes >>>>>>>>>>>> PA.
However, there are theories that reamain incomplete even when >>>>>>>>>>> more postolates are added, as long as there is a way to know >>>>>>>>>>> which sentences are included in the added postulates. Important >>>>>>>>>>> examples include Peano arithmetic and ZFC set theory.
Base-Extension Semantics (B-eS) seems to be essentially a cheat. >>>>>>>>>> When we ask what is grounded in an atomic base of Q and we >>>>>>>>>> add axioms to Q to become PA we cheated in that we changed >>>>>>>>>> the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial >>>>>>>>> answer
rather than no answer at all. Of course Q with any additional >>>>>>>>> postulate is not Q but if the additional postulates are true about >>>>>>>>> natural numbers then the strengthened theory is still a theory of >>>>>>>>> natural numbers. PA is one such strengthened Q but still
incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently >>>>>>> missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
And that differs from claiming that Q is incomplete exactly how...?
The base definition of "incomplete" means that it is
not operating according to design spec.
No, it is not. The term "incomplete" in its base meaning is
appicable to various things that are not exprected to operate.
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
A motor vehicle that lacks a motor is incomplete.
It is so incomplete that it is not a motor vehicle until a motor
is installed.
A motor vechicle that lacks brakes and head lights is a motor
vehicle but incomplere and, depending on the place and time,
may be unacceptable for public roads. Installing the head lights
makes it more complete but it is still incomplere as long as
no breaks are installed.
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory
Q + (∀x, S(x) ≠ x) is more complete but still incomplete.
This is perfectly analogous to the motorvehicle without head
lights and brakes: the meaning of "incomplete" is the same
although the definition is different.
On 05/07/2026 00:01, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:
On 7/4/2026 3:06 AM, Mikko wrote:
On 03/07/2026 21:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:The base definition of "incomplete" means that it is
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:Base-Extension Semantics (B-eS) seems to be essentially a >>>>>>>>>>>> cheat.
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:Irrelevant. The definition of completeness
On 27/06/2026 17:50, polcott wrote:Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was >>>>>>>>>>>>>>>>>> defined to do. Incomplete only counts relative to >>>>>>>>>>>>>>>>>> its intended purpose. A car without an engine is >>>>>>>>>>>>>>>>>> incomplete relative to a mode of transportation. >>>>>>>>>>>>>>>>>
On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote:It comes close. If ∃x x=S(x) is likewise "ungrounded" >>>>>>>>>>>>>>>>>>> but in the
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>
A proof theoretic expression is known to be true when >>>>>>>>>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>>>>>>>>>> with semantic meaning and never got around to >>>>>>>>>>>>>>>>>>>>>> true(L,x).
That's surprising, disregard for axioms? >>>>>>>>>>>>>>>>>>>>
This does not mean undecidable or incomplete >>>>>>>>>>>>>>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words mean. >>>>>>>>>>>>>>>>>>
It a misnomer and does not literally mean (as it implies) >>>>>>>>>>>>>>>> that something is missing that could be added to make >>>>>>>>>>>>>>>> it complete.
It does mean that something is missing that could be >>>>>>>>>>>>>>> added to
enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined >>>>>>>>>>>>>> to do.
When Q is extended to become PA it stops being Q and >>>>>>>>>>>>>> becomes PA.
However, there are theories that reamain incomplete even when >>>>>>>>>>>>> more postolates are added, as long as there is a way to know >>>>>>>>>>>>> which sentences are included in the added postulates. >>>>>>>>>>>>> Important
examples include Peano arithmetic and ZFC set theory. >>>>>>>>>>>>
When we ask what is grounded in an atomic base of Q and we >>>>>>>>>>>> add axioms to Q to become PA we cheated in that we changed >>>>>>>>>>>> the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial >>>>>>>>>>> answer
rather than no answer at all. Of course Q with any additional >>>>>>>>>>> postulate is not Q but if the additional postulates are true >>>>>>>>>>> about
natural numbers then the strengthened theory is still a >>>>>>>>>>> theory of
natural numbers. PA is one such strengthened Q but still >>>>>>>>>>> incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently >>>>>>>>> missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
And that differs from claiming that Q is incomplete exactly how...? >>>>>>
not operating according to design spec.
No, it is not. The term "incomplete" in its base meaning is
appicable to various things that are not exprected to operate.
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
These definitions are the liars.
Maybe your definitions, but not the usual ones, which tell truthfully
how the defined words are used and understood by the experts.
Term-of-the-art
A cat is a dalmatian dog
Perhaps some art but neither ailurology nor cynology.
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory
Q + (∀x, S(x) ≠ x) is more complete but still incomplete.
It fully meets its design spec thus calling it
any kind of incomplete is a damned lie.
On 7/5/2026 5:15 PM, Ross Finlayson wrote:
On 07/05/2026 02:45 PM, olcott wrote:
On 7/5/2026 4:30 PM, Ross Finlayson wrote:
On 07/05/2026 01:25 PM, olcott wrote:
On 7/5/2026 2:56 PM, Ross Finlayson wrote:
On 07/05/2026 09:33 AM, olcott wrote:
On 7/5/2026 9:52 AM, Tristan Wibberley wrote:
On 04/07/2026 16:31, Tristan Wibberley wrote:
On 06/05/2026 20:37, Julio Di Egidio wrote:
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal. >>>>>>>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>>>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>>>>>>> non-element.
Nope, as explained and re-explained ad nauseam around here: >>>>>>>>>> just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences, >>>>>>>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>>>>>>> (infinite) list is provided, and the proof that the anti-diagonal >>>>>>>>>> cannot be in the list is quite constructive.
"quite" but not "completely".
A constructive operation is defined, but a diagonal number is >>>>>>>>> constructed just when that constructive operation is applied to a >>>>>>>>> constructible list.
I should note for the less knowledgable readers of course it's less >>>>>>>> often than that, it is only that often for systems such as the one >>>>>>>> Julio
and Phoenix are using which allows dequantification of universally >>>>>>>> quantified statements into the system proper which then have
derivable
statements containing actual constructions of the constructible >>>>>>>> objects
they apply to by virtue of their original quantification. Of
course,
dequantification of fantastically quantified statements doesn't >>>>>>>> make a
statement about nonconstructible objects because there aren't any >>>>>>>> outside of the fantastical quantification.
By which I don't mean to argue the countability of the set of
reals as
defined in what we call Cantor's Proof of the Uncountability of the >>>>>>>> Reals to include objects quantified over by fantatstical
quantification
but not by universal quantification, but it does make some meaning >>>>>>>> clearer.
While some of the sets might have objects in the system proper, >>>>>>>> some of
the members of some of the sets clearly do not.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Gemini agrees with not-you.
OK then the point that I was trying to make is
exactly what Gemini said right here:
https://share.gemini.google/1dJnMwOZ2k5F
On 7/6/2026 3:24 AM, Mikko wrote:
On 04/07/2026 19:55, olcott wrote:
On 7/4/2026 2:46 AM, Mikko wrote:The halting problem does not require anything unless the input
On 04/07/2026 04:52, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is >>>>>>>>>> by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping >>>>>>>> and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute the mapping from
its actual input according to the operational semantics
of this input to the behavior that this input actually
specifies. No function can report on the behavior of
its caller because it has no idea who its caller is.
A function does not compute. An algrothm may compute a function.
However, no algrithm computes the halt function.
The halt functions maps a computation to a truth value
but so do many other functions, too.
When implemented as C functions
typedef int (*ptr)();
int HHH(ptr P);
01 int DD()
02 {
03 int Halt_Status = HHH(DD);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }
08
09 void main()
10 {
11 DD();
12 HHH(DD);
13 }
The HP requires HHH to report on the DD() invoked
in main(). This is impossible because HHH has no
idea who its caller is and deciders are functions
that only operate on their arguments.
fully specifies a computation.
The above DD calls HHH, which must be the same HHH as main calls if
DD halts. Therefore the bhaviour of HHH is a part of the computation
that the HHH would answer about if it were a halt decider.
HHH(DD) can and does correctly report on its input.
I just can get why it is taking so long for people
to understand that DD executed in main is out-of-scope
for HHH. It is like someone took actual brains apart
and welded in short-circuits.
The requirements of a halt decider don't require that then input
be presented to the decider the way it is done above. For exmample,
a text file would be acceptable.
On 07/05/2026 03:55 PM, olcott wrote:
On 7/5/2026 5:15 PM, Ross Finlayson wrote:
On 07/05/2026 02:45 PM, olcott wrote:
On 7/5/2026 4:30 PM, Ross Finlayson wrote:
On 07/05/2026 01:25 PM, olcott wrote:
On 7/5/2026 2:56 PM, Ross Finlayson wrote:
On 07/05/2026 09:33 AM, olcott wrote:
On 7/5/2026 9:52 AM, Tristan Wibberley wrote:
On 04/07/2026 16:31, Tristan Wibberley wrote:
On 06/05/2026 20:37, Julio Di Egidio wrote:
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal. >>>>>>>>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>>>>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>>>>>>>> non-element.
Nope, as explained and re-explained ad nauseam around here: >>>>>>>>>>> just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences, >>>>>>>>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>>>>>>>> (infinite) list is provided, and the proof that the anti- >>>>>>>>>>> diagonal
cannot be in the list is quite constructive.
"quite" but not "completely".
A constructive operation is defined, but a diagonal number is >>>>>>>>>> constructed just when that constructive operation is applied to a >>>>>>>>>> constructible list.
I should note for the less knowledgable readers of course it's >>>>>>>>> less
often than that, it is only that often for systems such as the one >>>>>>>>> Julio
and Phoenix are using which allows dequantification of universally >>>>>>>>> quantified statements into the system proper which then have >>>>>>>>> derivable
statements containing actual constructions of the constructible >>>>>>>>> objects
they apply to by virtue of their original quantification. Of >>>>>>>>> course,
dequantification of fantastically quantified statements doesn't >>>>>>>>> make a
statement about nonconstructible objects because there aren't any >>>>>>>>> outside of the fantastical quantification.
By which I don't mean to argue the countability of the set of >>>>>>>>> reals as
defined in what we call Cantor's Proof of the Uncountability of >>>>>>>>> the
Reals to include objects quantified over by fantatstical
quantification
but not by universal quantification, but it does make some meaning >>>>>>>>> clearer.
While some of the sets might have objects in the system proper, >>>>>>>>> some of
the members of some of the sets clearly do not.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Gemini agrees with not-you.
OK then the point that I was trying to make is
exactly what Gemini said right here:
https://share.gemini.google/1dJnMwOZ2k5F
I tend not to follow links like that, post the transcript.
On 07/06/2026 08:30 AM, olcott wrote:
On 7/6/2026 3:24 AM, Mikko wrote:
On 04/07/2026 19:55, olcott wrote:
On 7/4/2026 2:46 AM, Mikko wrote:The halting problem does not require anything unless the input
On 04/07/2026 04:52, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is >>>>>>>>>>> by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping >>>>>>>>> and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute the mapping from
its actual input according to the operational semantics
of this input to the behavior that this input actually
specifies. No function can report on the behavior of
its caller because it has no idea who its caller is.
A function does not compute. An algrothm may compute a function.
However, no algrithm computes the halt function.
The halt functions maps a computation to a truth value
but so do many other functions, too.
When implemented as C functions
typedef int (*ptr)();
int HHH(ptr P);
01 int DD()
02 {
03 int Halt_Status = HHH(DD);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }
08
09 void main()
10 {
11 DD();
12 HHH(DD);
13 }
The HP requires HHH to report on the DD() invoked
in main(). This is impossible because HHH has no
idea who its caller is and deciders are functions
that only operate on their arguments.
fully specifies a computation.
The above DD calls HHH, which must be the same HHH as main calls if
DD halts. Therefore the bhaviour of HHH is a part of the computation
that the HHH would answer about if it were a halt decider.
HHH(DD) can and does correctly report on its input.
I just can get why it is taking so long for people
to understand that DD executed in main is out-of-scope
for HHH. It is like someone took actual brains apart
and welded in short-circuits.
The requirements of a halt decider don't require that then input
be presented to the decider the way it is done above. For exmample,
a text file would be acceptable.
It's well known that each finite input to a finite program
has a finite static-analysis that determines whether it halts,
furthermore for each language of finite input it can be determined
via a finite-static-analysis a partition of the language into what
halts and what doesn't.
Infinite tapes or with infinite programs are different,
see "Zeno machines" since super-tasks have accounts of
mathematical independence (whether a model of integers
is a fragment and finite, an extension and with infinite
members, or "in the middle", since the usual idea is that
a standard model of integers doesn't exist).
So, there are accounts of halting or "completions" in
the infinitary that are independent usual finitist
accounts, whose Law of Large Numbers is only the
Law of Small Numbers, since there is a "Law of Larger Numbers"
and a "Law of Largest Numbers", about models of arithmetic.
Otherwise that's just barking about "V = L" and so on.
On 2026-07-06 09:47, olcott wrote:
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory
Q + (∀x, S(x) ≠ x) is more complete but still incomplete.
It fully meets its design spec thus calling it
any kind of incomplete is a damned lie.
What exactly do you think the 'design spec' of Q is?
The mathematical
definition of 'incomplete' doesn't make any mentions of 'design specs'.
André
On 05/07/2026 00:01, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:
On 7/4/2026 3:06 AM, Mikko wrote:
On 03/07/2026 21:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:The base definition of "incomplete" means that it is
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:Base-Extension Semantics (B-eS) seems to be essentially a >>>>>>>>>>>> cheat.
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:Irrelevant. The definition of completeness
On 27/06/2026 17:50, polcott wrote:Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was >>>>>>>>>>>>>>>>>> defined to do. Incomplete only counts relative to >>>>>>>>>>>>>>>>>> its intended purpose. A car without an engine is >>>>>>>>>>>>>>>>>> incomplete relative to a mode of transportation. >>>>>>>>>>>>>>>>>
On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote:It comes close. If ∃x x=S(x) is likewise "ungrounded" >>>>>>>>>>>>>>>>>>> but in the
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>
A proof theoretic expression is known to be true when >>>>>>>>>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>>>>>>>>>> with semantic meaning and never got around to >>>>>>>>>>>>>>>>>>>>>> true(L,x).
That's surprising, disregard for axioms? >>>>>>>>>>>>>>>>>>>>
This does not mean undecidable or incomplete >>>>>>>>>>>>>>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words mean. >>>>>>>>>>>>>>>>>>
It a misnomer and does not literally mean (as it implies) >>>>>>>>>>>>>>>> that something is missing that could be added to make >>>>>>>>>>>>>>>> it complete.
It does mean that something is missing that could be >>>>>>>>>>>>>>> added to
enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined >>>>>>>>>>>>>> to do.
When Q is extended to become PA it stops being Q and >>>>>>>>>>>>>> becomes PA.
However, there are theories that reamain incomplete even when >>>>>>>>>>>>> more postolates are added, as long as there is a way to know >>>>>>>>>>>>> which sentences are included in the added postulates. >>>>>>>>>>>>> Important
examples include Peano arithmetic and ZFC set theory. >>>>>>>>>>>>
When we ask what is grounded in an atomic base of Q and we >>>>>>>>>>>> add axioms to Q to become PA we cheated in that we changed >>>>>>>>>>>> the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial >>>>>>>>>>> answer
rather than no answer at all. Of course Q with any additional >>>>>>>>>>> postulate is not Q but if the additional postulates are true >>>>>>>>>>> about
natural numbers then the strengthened theory is still a >>>>>>>>>>> theory of
natural numbers. PA is one such strengthened Q but still >>>>>>>>>>> incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently >>>>>>>>> missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
And that differs from claiming that Q is incomplete exactly how...? >>>>>>
not operating according to design spec.
No, it is not. The term "incomplete" in its base meaning is
appicable to various things that are not exprected to operate.
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
These definitions are the liars.
Maybe your definitions, but not the usual ones, which tell truthfully
how the defined words are used and understood by the experts.
Term-of-the-art
A cat is a dalmatian dog
Perhaps some art but neither ailurology nor cynology.
On 7/6/2026 11:07 AM, André G. Isaak wrote:
On 2026-07-06 09:47, olcott wrote:
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory
Q + (∀x, S(x) ≠ x) is more complete but still incomplete.
It fully meets its design spec thus calling it
any kind of incomplete is a damned lie.
What exactly do you think the 'design spec' of Q is?
Make sure that Q has less capability than PA is its design
spec by its designer.
On 05/07/2026 19:29, olcott wrote:
On 7/5/2026 9:19 AM, dbush wrote:
On 7/4/2026 5:12 PM, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
False.
In computability theory and computational complexity theory, an
undecidable problem is a decision problem for which it is proved to
be impossible to construct an algorithm that always leads to a
correct yes- or-no answer.
https://en.wikipedia.org/wiki/Undecidable_problem
LP := ~True(LP)
G := ~Provable(PA, G)
The above are not examples of that.
Math Incomplete: The inability to accomplish
more than a system was defined to accomplish.
False. Intent does not factor into formal systems.
In mathematical logic, a theory is complete if it is consistent and
for every closed formula in the theory's language, either that
formula or its negation is provable
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
At the time the difference between "true" and "provable" was not yet understood to the extent it is now.
That sentence can now be rejected as a violation of the current
rules of the language game. Perhaps you don't understand what
that means but Wittgenstein would if he still were alive.
On 2026-07-06 10:58, olcott wrote:
On 7/6/2026 11:07 AM, André G. Isaak wrote:
On 2026-07-06 09:47, olcott wrote:
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory
Q + (∀x, S(x) ≠ x) is more complete but still incomplete.
It fully meets its design spec thus calling it
any kind of incomplete is a damned lie.
What exactly do you think the 'design spec' of Q is?
Make sure that Q has less capability than PA is its design
spec by its designer.
And you presumably have a reference to back that up?
But it doesn't matter either way since the mathematical definition of incomplete makes no reference to the 'spec' of a system.
A system is incomplete if there exists some statement P such that
neither P nor ¬P can be derived as theorems of that system.
Importantly, this definition doesn't 'inherit' anything from any other definition of 'incomplete' which might exist. That's not how language actually works.
André
On 05/07/2026 19:33, olcott wrote:
On 7/5/2026 9:52 AM, Tristan Wibberley wrote:
On 04/07/2026 16:31, Tristan Wibberley wrote:
On 06/05/2026 20:37, Julio Di Egidio wrote:
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal.
Rather, we presuppose that we can enumerate a set, and then,
/purely on the grounds of possibility/, conceive a diagonalized
non-element.
Nope, as explained and re-explained ad nauseam around here:
just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences,
is indeed constructive: a definition of anti-diagonal of *any*
(infinite) list is provided, and the proof that the anti-diagonal
cannot be in the list is quite constructive.
"quite" but not "completely".
A constructive operation is defined, but a diagonal number is
constructed just when that constructive operation is applied to a
constructible list.
I should note for the less knowledgable readers of course it's less
often than that, it is only that often for systems such as the one Julio >>> and Phoenix are using which allows dequantification of universally
quantified statements into the system proper which then have derivable
statements containing actual constructions of the constructible objects
they apply to by virtue of their original quantification. Of course,
dequantification of fantastically quantified statements doesn't make a
statement about nonconstructible objects because there aren't any
outside of the fantastical quantification.
By which I don't mean to argue the countability of the set of reals as
defined in what we call Cantor's Proof of the Uncountability of the
Reals to include objects quantified over by fantatstical quantification
but not by universal quantification, but it does make some meaning
clearer.
While some of the sets might have objects in the system proper, some of
the members of some of the sets clearly do not.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded
justification tree exists.
That is false. There is no evaluation of G in the determination of the
Gödel number of anything. Therefore the claim of a loop is false.
That error has already been pointed out but Olcott still hopes that
someone might bite the bait and the hook.
On 7/6/2026 12:27 PM, André G. Isaak wrote:
On 2026-07-06 10:58, olcott wrote:
On 7/6/2026 11:07 AM, André G. Isaak wrote:
On 2026-07-06 09:47, olcott wrote:
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory
Q + (∀x, S(x) ≠ x) is more complete but still incomplete.
It fully meets its design spec thus calling it
any kind of incomplete is a damned lie.
What exactly do you think the 'design spec' of Q is?
Make sure that Q has less capability than PA is its design
spec by its designer.
And you presumably have a reference to back that up?
It is common knowledge that was Robinson's purpose
In mathematics, Robinson arithmetic is a finitely
axiomatized fragment of first-order Peano arithmetic
(PA), first set out by Raphael M. Robinson in 1950.
It is usually denoted Q.
https://en.wikipedia.org/wiki/Robinson_arithmetic
But it doesn't matter either way since the mathematical definition of
incomplete makes no reference to the 'spec' of a system.
Within the natural preexisting order of the body
of knowledge saying that incomplete(math) inherits
part of its meaning from incomplete(base) semantic
parent node is simply a lie.
On 2026-07-06 11:45, olcott wrote:
On 7/6/2026 12:27 PM, André G. Isaak wrote:
On 2026-07-06 10:58, olcott wrote:
On 7/6/2026 11:07 AM, André G. Isaak wrote:
On 2026-07-06 09:47, olcott wrote:
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory
Q + (∀x, S(x) ≠ x) is more complete but still incomplete.
It fully meets its design spec thus calling it
any kind of incomplete is a damned lie.
What exactly do you think the 'design spec' of Q is?
Make sure that Q has less capability than PA is its design
spec by its designer.
And you presumably have a reference to back that up?
It is common knowledge that was Robinson's purpose
In mathematics, Robinson arithmetic is a finitely
axiomatized fragment of first-order Peano arithmetic
(PA), first set out by Raphael M. Robinson in 1950.
It is usually denoted Q.
https://en.wikipedia.org/wiki/Robinson_arithmetic
But it doesn't matter either way since the mathematical definition of
incomplete makes no reference to the 'spec' of a system.
Within the natural preexisting order of the body
of knowledge saying that incomplete(math) inherits
part of its meaning from incomplete(base) semantic
parent node is simply a lie.
Yes, I agree that it is a lie.
For starters, there's no such thing as the 'natural preexisting order of
the body of knowlege'.
And incomplete(math) doesn't inherit from anything so claiming it
inherits from incomplete(base) (whatever that may be) is of course a lie.
André
On 7/6/2026 12:56 PM, André G. Isaak wrote:
On 2026-07-06 11:45, olcott wrote:
On 7/6/2026 12:27 PM, André G. Isaak wrote:
On 2026-07-06 10:58, olcott wrote:
On 7/6/2026 11:07 AM, André G. Isaak wrote:
On 2026-07-06 09:47, olcott wrote:
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory
Q + (∀x, S(x) ≠ x) is more complete but still incomplete.
It fully meets its design spec thus calling it
any kind of incomplete is a damned lie.
What exactly do you think the 'design spec' of Q is?
Make sure that Q has less capability than PA is its design
spec by its designer.
And you presumably have a reference to back that up?
It is common knowledge that was Robinson's purpose
In mathematics, Robinson arithmetic is a finitely
axiomatized fragment of first-order Peano arithmetic
(PA), first set out by Raphael M. Robinson in 1950.
It is usually denoted Q.
https://en.wikipedia.org/wiki/Robinson_arithmetic
But it doesn't matter either way since the mathematical definition
of incomplete makes no reference to the 'spec' of a system.
Within the natural preexisting order of the body
of knowledge saying that incomplete(math) inherits
part of its meaning from incomplete(base) semantic
parent node is simply a lie.
Yes, I agree that it is a lie.
For starters, there's no such thing as the 'natural preexisting order
of the body of knowlege'.
Sure there is. There is a minimal sized knowledge ontology.
Anything less than minimal wastes RAM and CPU cycles.
And incomplete(math) doesn't inherit from anything so claiming it
inherits from incomplete(base) (whatever that may be) is of course a lie.
André
On 2026-07-06 12:12, olcott wrote:
On 7/6/2026 12:56 PM, André G. Isaak wrote:
On 2026-07-06 11:45, olcott wrote:
On 7/6/2026 12:27 PM, André G. Isaak wrote:
On 2026-07-06 10:58, olcott wrote:
On 7/6/2026 11:07 AM, André G. Isaak wrote:
On 2026-07-06 09:47, olcott wrote:
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
It fully meets its design spec thus calling itQ that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory >>>>>>>>> Q + (∀x, S(x) ≠ x) is more complete but still incomplete. >>>>>>>>
any kind of incomplete is a damned lie.
What exactly do you think the 'design spec' of Q is?
Make sure that Q has less capability than PA is its design
spec by its designer.
And you presumably have a reference to back that up?
It is common knowledge that was Robinson's purpose
In mathematics, Robinson arithmetic is a finitely
axiomatized fragment of first-order Peano arithmetic
(PA), first set out by Raphael M. Robinson in 1950.
It is usually denoted Q.
https://en.wikipedia.org/wiki/Robinson_arithmetic
But it doesn't matter either way since the mathematical definition
of incomplete makes no reference to the 'spec' of a system.
Within the natural preexisting order of the body
of knowledge saying that incomplete(math) inherits
part of its meaning from incomplete(base) semantic
parent node is simply a lie.
Yes, I agree that it is a lie.
For starters, there's no such thing as the 'natural preexisting order
of the body of knowlege'.
Sure there is. There is a minimal sized knowledge ontology.
Anything less than minimal wastes RAM and CPU cycles.
Saying something is preexisting means it has always been around; before there was RAM or CPU cycles; before there were people to know things.
A specific computer model might implement a knowledge ontology, but
that's hardly 'preexisting'. And if it implements something where the mathematical meaning of 'incomplete' inherits from some other definition
of 'incomplete' then that model does not correspond to reality.
André
And incomplete(math) doesn't inherit from anything so claiming it
inherits from incomplete(base) (whatever that may be) is of course a
lie.
André
On 7/6/2026 1:54 PM, André G. Isaak wrote:
On 2026-07-06 12:12, olcott wrote:
On 7/6/2026 12:56 PM, André G. Isaak wrote:
On 2026-07-06 11:45, olcott wrote:
On 7/6/2026 12:27 PM, André G. Isaak wrote:
On 2026-07-06 10:58, olcott wrote:
On 7/6/2026 11:07 AM, André G. Isaak wrote:
On 2026-07-06 09:47, olcott wrote:
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
It fully meets its design spec thus calling itQ that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory >>>>>>>>>> Q + (∀x, S(x) ≠ x) is more complete but still incomplete. >>>>>>>>>
any kind of incomplete is a damned lie.
What exactly do you think the 'design spec' of Q is?
Make sure that Q has less capability than PA is its design
spec by its designer.
And you presumably have a reference to back that up?
It is common knowledge that was Robinson's purpose
In mathematics, Robinson arithmetic is a finitely
axiomatized fragment of first-order Peano arithmetic
(PA), first set out by Raphael M. Robinson in 1950.
It is usually denoted Q.
https://en.wikipedia.org/wiki/Robinson_arithmetic
But it doesn't matter either way since the mathematical definition >>>>>> of incomplete makes no reference to the 'spec' of a system.
Within the natural preexisting order of the body
of knowledge saying that incomplete(math) inherits
part of its meaning from incomplete(base) semantic
parent node is simply a lie.
Yes, I agree that it is a lie.
For starters, there's no such thing as the 'natural preexisting
order of the body of knowlege'.
Sure there is. There is a minimal sized knowledge ontology.
Anything less than minimal wastes RAM and CPU cycles.
Saying something is preexisting means it has always been around;
before there was RAM or CPU cycles; before there were people to know
things.
Mathematical incompleteness does have a proper
place in the knowledge ontology that does not
inherit from incomplete(base)
unfulfilled_goals seems to be a more accurate base
for mathematical incomplete. Q does not do what we
want it to do even though it was intentionally defined
to only be a fragment of PA some people still want
it to do what PA does.
In mathematics, Robinson arithmetic is a finitely
axiomatized fragment of first-order Peano arithmetic
(PA), first set out by Raphael M. Robinson in 1950.
It is usually denoted Q.
On 2026-07-06 13:03, olcott wrote:
On 7/6/2026 1:54 PM, André G. Isaak wrote:
On 2026-07-06 12:12, olcott wrote:
On 7/6/2026 12:56 PM, André G. Isaak wrote:
On 2026-07-06 11:45, olcott wrote:
On 7/6/2026 12:27 PM, André G. Isaak wrote:
On 2026-07-06 10:58, olcott wrote:
On 7/6/2026 11:07 AM, André G. Isaak wrote:
On 2026-07-06 09:47, olcott wrote:
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
It fully meets its design spec thus calling itQ that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory >>>>>>>>>>> Q + (∀x, S(x) ≠ x) is more complete but still incomplete. >>>>>>>>>>
any kind of incomplete is a damned lie.
What exactly do you think the 'design spec' of Q is?
Make sure that Q has less capability than PA is its design
spec by its designer.
And you presumably have a reference to back that up?
It is common knowledge that was Robinson's purpose
In mathematics, Robinson arithmetic is a finitely
axiomatized fragment of first-order Peano arithmetic
(PA), first set out by Raphael M. Robinson in 1950.
It is usually denoted Q.
https://en.wikipedia.org/wiki/Robinson_arithmetic
But it doesn't matter either way since the mathematical
definition of incomplete makes no reference to the 'spec' of a
system.
Within the natural preexisting order of the body
of knowledge saying that incomplete(math) inherits
part of its meaning from incomplete(base) semantic
parent node is simply a lie.
Yes, I agree that it is a lie.
For starters, there's no such thing as the 'natural preexisting
order of the body of knowlege'.
Sure there is. There is a minimal sized knowledge ontology.
Anything less than minimal wastes RAM and CPU cycles.
Saying something is preexisting means it has always been around;
before there was RAM or CPU cycles; before there were people to know
things.
Mathematical incompleteness does have a proper
place in the knowledge ontology that does not
inherit from incomplete(base)
It doesn't inherit from *anything*
A system is incomplete if there exists some statement P such that
neither P nor ¬P can be derived as theorems of that system.
That's what it means. Nothing more. Nothing less. It doesn't acquire any aspect of its meaning from anything else.
unfulfilled_goals seems to be a more accurate base
for mathematical incomplete. Q does not do what we
want it to do even though it was intentionally defined
to only be a fragment of PA some people still want
it to do what PA does.
It doesn't *have* a base.
It simply means what it means (or it is its
own base if you want to look at it like that). The definition makes no mention whatsoever of what me may *want* a system to do.
In mathematics, Robinson arithmetic is a finitely
axiomatized fragment of first-order Peano arithmetic
(PA), first set out by Raphael M. Robinson in 1950.
It is usually denoted Q.
Yes. I know what Robinson Arithmetic is. There's really no reason for
you to explain it.
André
On 7/6/2026 3:08 PM, André G. Isaak wrote:
On 2026-07-06 13:03, olcott wrote:
On 7/6/2026 1:54 PM, André G. Isaak wrote:
On 2026-07-06 12:12, olcott wrote:
On 7/6/2026 12:56 PM, André G. Isaak wrote:
On 2026-07-06 11:45, olcott wrote:
On 7/6/2026 12:27 PM, André G. Isaak wrote:
On 2026-07-06 10:58, olcott wrote:
On 7/6/2026 11:07 AM, André G. Isaak wrote:
On 2026-07-06 09:47, olcott wrote:
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
It fully meets its design spec thus calling itQ that cannot resolve (∀x, S(x) ≠ x) is complete >>>>>>>>>>>>> according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory >>>>>>>>>>>> Q + (∀x, S(x) ≠ x) is more complete but still incomplete. >>>>>>>>>>>
any kind of incomplete is a damned lie.
What exactly do you think the 'design spec' of Q is?
Make sure that Q has less capability than PA is its design
spec by its designer.
And you presumably have a reference to back that up?
It is common knowledge that was Robinson's purpose
In mathematics, Robinson arithmetic is a finitely
axiomatized fragment of first-order Peano arithmetic
(PA), first set out by Raphael M. Robinson in 1950.
It is usually denoted Q.
https://en.wikipedia.org/wiki/Robinson_arithmetic
But it doesn't matter either way since the mathematical
definition of incomplete makes no reference to the 'spec' of a >>>>>>>> system.
Within the natural preexisting order of the body
of knowledge saying that incomplete(math) inherits
part of its meaning from incomplete(base) semantic
parent node is simply a lie.
Yes, I agree that it is a lie.
For starters, there's no such thing as the 'natural preexisting
order of the body of knowlege'.
Sure there is. There is a minimal sized knowledge ontology.
Anything less than minimal wastes RAM and CPU cycles.
Saying something is preexisting means it has always been around;
before there was RAM or CPU cycles; before there were people to know
things.
Mathematical incompleteness does have a proper
place in the knowledge ontology that does not
inherit from incomplete(base)
It doesn't inherit from *anything*
The preexisting order of all knowledge is constructed
incrementally on the basis of the root of {thing}.
A system is incomplete if there exists some statement P such that
neither P nor ¬P can be derived as theorems of that system.
What would be its parent node?
That's what it means. Nothing more. Nothing less. It doesn't acquire
any aspect of its meaning from anything else.
It is impossible to leap from {nothingness} to
1987 Chevy Camaro with no steps inbetweem.
{Thing}--->{Physically Existing Thing}
... {Motor Vehicle}---> {Automobile} ...
unfulfilled_goals seems to be a more accurate base
for mathematical incomplete. Q does not do what we
want it to do even though it was intentionally defined
to only be a fragment of PA some people still want
it to do what PA does.
It doesn't *have* a base.
That you do not understand how ideas are derived from
other ideas is less than no rebuttal at all.
It simply means what it means (or it is its own base if you want to
look at it like that). The definition makes no mention whatsoever of
what me may *want* a system to do.
In mathematics, Robinson arithmetic is a finitely
axiomatized fragment of first-order Peano arithmetic
(PA), first set out by Raphael M. Robinson in 1950.
It is usually denoted Q.
Yes. I know what Robinson Arithmetic is. There's really no reason for
you to explain it.
André
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
LP := ~True(LP)
G := ~Provable(PA, G)
Math Incomplete: The inability to accomplish
more than a system was defined to accomplish.
(∀x, S(x) ≠ x) cannot be proven in Q
Math mapping from an input to an output:
Ignore the input and output a fixed constant.
int mapping_function(int x)
{
return 0;
}
It is impossible to leap from {nothingness} to
1987 Chevy Camaro with no steps inbetweem.
{Thing}--->{Physically Existing Thing}
... {Motor Vehicle}---> {Automobile} ...
On 7/4/26 2:12 PM, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
LP := ~True(LP)
G := ~Provable(PA, G)
Math Incomplete: The inability to accomplish
more than a system was defined to accomplish.
(∀x, S(x) ≠ x) cannot be proven in Q
Math mapping from an input to an output:
Ignore the input and output a fixed constant.
int mapping_function(int x)
{
return 0;
}
i honestly don't think u can get around the liar's paradox with logic
that treats statements of truth as universal
On 7/6/2026 4:13 PM, André G. Isaak wrote:I did not write any of the above. Please don't claim that I did.
It is impossible to leap from {nothingness} to
1987 Chevy Camaro with no steps inbetweem.
{Thing}--->{Physically Existing Thing}
... {Motor Vehicle}---> {Automobile} ...
Try to explain how the notion of 1987 Chevy Camaro
pops into existence from out-of-nowhere with no
prerequisite order.
On 2026-07-06 16:00, olcott wrote:
On 7/6/2026 4:13 PM, André G. Isaak wrote:I did not write any of the above. Please don't claim that I did.
It is impossible to leap from {nothingness} to
1987 Chevy Camaro with no steps inbetweem.
{Thing}--->{Physically Existing Thing}
... {Motor Vehicle}---> {Automobile} ...
Try to explain how the notion of 1987 Chevy Camaro
pops into existence from out-of-nowhere with no
prerequisite order.
If you want to know how concepts are actually organized, you need to
look at experimental evidence from psychology, psycholinguistics,
aphasiology, etc. They aren't organized into a tree where concepts have parents. Armchair philosophizing (aka mental masturbation) isn't going
to get you anywhere.
André
On 7/6/2026 5:18 PM, André G. Isaak wrote:
On 2026-07-06 16:00, olcott wrote:
On 7/6/2026 4:13 PM, André G. Isaak wrote:I did not write any of the above. Please don't claim that I did.
It is impossible to leap from {nothingness} to
1987 Chevy Camaro with no steps inbetweem.
{Thing}--->{Physically Existing Thing}
... {Motor Vehicle}---> {Automobile} ...
Try to explain how the notion of 1987 Chevy Camaro
pops into existence from out-of-nowhere with no
prerequisite order.
I know that I wrote it.
You must show exactly how
I am incorrect otherwise your fake rebuttal is
simply hiding behind profound ignorance.
If you want to know how concepts are actually organized, you need to
look at experimental evidence from psychology, psycholinguistics,
aphasiology, etc. They aren't organized into a tree where concepts
have parents. Armchair philosophizing (aka mental masturbation) isn't
going to get you anywhere.
André
They are organized as a type hierarchy.
You either understand this or fail to comprehend.
On 2026-07-06 16:41, olcott wrote:
On 7/6/2026 5:18 PM, André G. Isaak wrote:
On 2026-07-06 16:00, olcott wrote:
On 7/6/2026 4:13 PM, André G. Isaak wrote:I did not write any of the above. Please don't claim that I did.
It is impossible to leap from {nothingness} to
1987 Chevy Camaro with no steps inbetweem.
{Thing}--->{Physically Existing Thing}
... {Motor Vehicle}---> {Automobile} ...
Try to explain how the notion of 1987 Chevy Camaro
pops into existence from out-of-nowhere with no
prerequisite order.
I know that I wrote it.
So why did you attribute it to me?
You must show exactly how
I am incorrect otherwise your fake rebuttal is
simply hiding behind profound ignorance.
If you want to know how concepts are actually organized, you needto > look at experimental evidence from psychology, psycholinguistics,
aphasiology, etc. They aren't organized into a tree where concepts
have parents. Armchair philosophizing (aka mental masturbation) isn't
going to get you anywhere.
André
They are organized as a type hierarchy.
You either understand this or fail to comprehend.
Please point to a single piece of experimental evidence which supports
this.
Also, concepts aren't types, so they can't be organized as a type
hierarchy. A computer database might organize them as a hierarchy, but
not as a type hierarchy, and this hierarchy wouldn't reflect anything
about how actual people organize concepts.
André
On 7/6/2026 5:53 PM, André G. Isaak wrote:
On 2026-07-06 16:41, olcott wrote:
On 7/6/2026 5:18 PM, André G. Isaak wrote:
On 2026-07-06 16:00, olcott wrote:
On 7/6/2026 4:13 PM, André G. Isaak wrote:I did not write any of the above. Please don't claim that I did.
It is impossible to leap from {nothingness} to
1987 Chevy Camaro with no steps inbetweem.
{Thing}--->{Physically Existing Thing}
... {Motor Vehicle}---> {Automobile} ...
Try to explain how the notion of 1987 Chevy Camaro
pops into existence from out-of-nowhere with no
prerequisite order.
I know that I wrote it.
So why did you attribute it to me?
I did not attribute it to you.
I asked you to explain how it is wrong
to prove that do not understand these things.
You must show exactly how
I am incorrect otherwise your fake rebuttal is
simply hiding behind profound ignorance.
If you want to know how concepts are actually organized, you needto > look at experimental evidence from psychology, psycholinguistics, >>>> aphasiology, etc. They aren't organized into a tree where concepts
have parents. Armchair philosophizing (aka mental masturbation)
isn't going to get you anywhere.
André
They are organized as a type hierarchy.
You either understand this or fail to comprehend.
Please point to a single piece of experimental evidence which supports
this.
There is no experimental evidence to prove that
the square root of two is a number.
Also, concepts aren't types, so they can't be organized as a type
hierarchy. A computer database might organize them as a hierarchy, but
not as a type hierarchy, and this hierarchy wouldn't reflect anything
about how actual people organize concepts.
André
On 7/6/2026 4:13 PM, André G. Isaak wrote:
It is impossible to leap from {nothingness} t
1987 Chevy Camaro with no steps inbetweem.
{Thing}--->{Physically Existing Thing}
... {Motor Vehicle}---> {Automobile} ...
Try to explain how the notion of 1987 Chevy Camaro
pops into existence from out-of-nowhere with no
prerequisite order.
On 7/4/26 2:12 PM, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
LP := ~True(LP)
G := ~Provable(PA, G)
Math Incomplete: The inability to accomplish
more than a system was defined to accomplish.
(∀x, S(x) ≠ x) cannot be proven in Q
Math mapping from an input to an output:
Ignore the input and output a fixed constant.
int mapping_function(int x)
{
return 0;
}
i honestly don't think u can get around the liar's paradox with logic
that treats statements of truth as universal
On 7/6/2026 2:59 AM, Mikko wrote:
On 04/07/2026 20:13, olcott wrote:
On 7/4/2026 3:49 AM, Mikko wrote:
On 03/07/2026 21:38, olcott wrote:
On 7/3/2026 1:21 PM, André G. Isaak wrote:
On 2026-07-03 12:12, olcott wrote:
On 7/3/2026 12:17 PM, André G. Isaak wrote:
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:Because it isn't true in all models of Q,
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps. >>>>>>>>>>>So your phrasing is good: Q would need something like an >>>>>>>>>>> infinite sequence of steps (or a single principle that
summarizes them) to get the ∀x. Since formal proofs must be >>>>>>>>>>> finite, and Q lacks the tool (induction) that would allow a >>>>>>>>>>> finite proof of the infinite claim, the universal statement >>>>>>>>>>> remains unprovable.
I'm not sure why you are responding to yourself nor who 'your >>>>>>>>>> phrasing' refers to since you don't quote anyone. But,
assuming we're still talking about ∀ x, S(x) ≠ x in Q, your >>>>>>>>>> reasoning is simply off.
You *can* prove universally quantified claims in Q, just not >>>>>>>>>> that particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? >>>>>>>>
many weeks in every thread. Whenever you ignore
this the rest of your reply will be ignored.
The rest of my post which you snipped and (presumably) ignored
explained *why* you are wrong about this. PTS does not reject
models or model theory. It simply doesn't rely on model-theoretic >>>>>> semantics. Q *requires* a model.
It replaces Model theory With PTS.
That you do not understand this is your mistake.
"Is x true" is replaced with something like "Is x provable".
"Is x provable" is there already. Why would one want to lose
"Is x true"? If one dosn't need "Is x true" one needn't use
it.
The whole focus of most PTS "Is x provable".
Model theory looks at true in a model and ignores
the connection between true and provable.
People rarely care about PTS or model theory. More often they
careabout what is or is not true about someting they consider important.
Hence we must correct the divergence of logic
from correct reasoning if we are to automate
correct reasoning.
On 7/6/2026 3:11 AM, Mikko wrote:
On 04/07/2026 19:58, olcott wrote:
On 7/4/2026 2:48 AM, Mikko wrote:
On 04/07/2026 05:37, olcott wrote:
On 7/3/2026 9:19 PM, dbush wrote:
On 7/3/2026 10:05 PM, olcott wrote:
On 7/3/2026 8:58 PM, dbush wrote:
On 7/3/2026 9:52 PM, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, >>>>>>>>>>>>>> that is by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a >>>>>>>>>>>> mapping and an algorithm. They are two different things. >>>>>>>>>>>>
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute
When you actually implement this concretely
We find that it is not possible, as Linz and others have proved.
Impossible requirements are incorrect requirements.
There is no well known meaning of "incorrect requirements".
I just established the meaning of incorrect requirements
as any requirement that requires the logically impossible.
That is insufficient to make the expression "incorrect requirements"
meaningful in Common Language or well known.
In other words if the requirement is to compute the square
root of the actual dead flesh of a dead chicken you would
not reject this out-of hand?
On 7/6/2026 3:24 AM, Mikko wrote:
On 04/07/2026 19:55, olcott wrote:
On 7/4/2026 2:46 AM, Mikko wrote:The halting problem does not require anything unless the input
On 04/07/2026 04:52, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that is >>>>>>>>>> by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping >>>>>>>> and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute the mapping from
its actual input according to the operational semantics
of this input to the behavior that this input actually
specifies. No function can report on the behavior of
its caller because it has no idea who its caller is.
A function does not compute. An algrothm may compute a function.
However, no algrithm computes the halt function.
The halt functions maps a computation to a truth value
but so do many other functions, too.
When implemented as C functions
typedef int (*ptr)();
int HHH(ptr P);
01 int DD()
02 {
03 int Halt_Status = HHH(DD);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }
08
09 void main()
10 {
11 DD();
12 HHH(DD);
13 }
The HP requires HHH to report on the DD() invoked
in main(). This is impossible because HHH has no
idea who its caller is and deciders are functions
that only operate on their arguments.
fully specifies a computation.
The above DD calls HHH, which must be the same HHH as main calls if
DD halts. Therefore the bhaviour of HHH is a part of the computation
that the HHH would answer about if it were a halt decider.
HHH(DD) can and does correctly report on its input.
I just can get why it is taking so long for people
to understand that DD executed in main is out-of-scope
for HHH. It is like someone took actual brains apart
and welded in short-circuits.
On 7/6/2026 3:37 AM, Mikko wrote:
On 04/07/2026 20:01, olcott wrote:
On 7/4/2026 2:55 AM, Mikko wrote:
On 03/07/2026 21:45, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:{
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a >>>>>>>>>>>> part of a
claim about you, and your response was the false claim that >>>>>>>>>>>> "That
is just nonsense". Later in the discussion you offer more >>>>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to >>>>>>>>>> outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y >>>>>>>> to an output of either 0 or 1?
A mapping is nothing more than an association of inputs to outputs, >>>>> int Not_A_Mapping(int X)
return 0;
}
By construing that as a mapping is one of the screw-ups
that prevents true expressed in language from being computable.
By construing the above mapping as a non-mapping you disconnect from
Common Languge and lose your ablility to communicate.
I will not tolerate that math hijacks the term
"mapping" to ignore requirement that there must
be some actual correspondence between inputs and
outputs.
Your exceesive intolerance is irrelevant.
It makes terms-of-the-art into damned liars.
On 7/6/2026 3:55 AM, Mikko wrote:
On 04/07/2026 20:03, olcott wrote:
On 7/4/2026 3:00 AM, Mikko wrote:
On 03/07/2026 22:08, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a >>>>>>>>>>>> part of a
claim about you, and your response was the false claim that >>>>>>>>>>>> "That
is just nonsense". Later in the discussion you offer more >>>>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to >>>>>>>>>> outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y >>>>>>>> to an output of either 0 or 1?
A mapping is nothing more than an association of inputs to
outputs, so there is nothing to ignore. What an algorithm might >>>>>> do to *compute* the mapping has nothing to do with the mapping.
It is conventionally construed as a mapping.
More importantly, it satisfies the definition of "mapping".
It is not even conventionally construed as a halt
function, not even a halt function that gets the
wrong answer.
Irrelevant, as the claim was that H does not implement the halt
function.
If it ignores input it is no function of this input.
Everything that is required to be in the argument list of a function
is an argument to that function, even when the function "ignores" it.
You are entirely right on the linguistic front. If we look strictly at
the compositional meaning of the words in everyday language, calling something a "function of an input" when it ignores that input is, at
best, a paradox and, at worst, a semantic lie.
On 7/6/2026 4:00 AM, Mikko wrote:
On 04/07/2026 16:38, olcott wrote:
On 7/4/2026 2:41 AM, Mikko wrote:
On 03/07/2026 21:10, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a part >>>>>>>>>> of a
claim about you, and your response was the false claim that "That >>>>>>>>>> is just nonsense". Later in the discussion you offer more >>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to
outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to >>>>>> an output of either 0 or 1?
No, but dbush's program H implements a mapping anyway. It just is
a different mapping from the one a halt decider is required to do.
Making it complete nonsense.
The program has a well defined meaning so it is not non-sense.
That it may be too big or complex for you is irrelevant.
It has zero correspondence to the HP counter-example
input thus the claim that is does is a damned lie.
On 7/6/2026 4:25 AM, Mikko wrote:
On 05/07/2026 00:01, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:
On 7/4/2026 3:06 AM, Mikko wrote:
On 03/07/2026 21:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:The base definition of "incomplete" means that it is
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:Base-Extension Semantics (B-eS) seems to be essentially a >>>>>>>>>>>>> cheat.
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:It a misnomer and does not literally mean (as it implies) >>>>>>>>>>>>>>>>> that something is missing that could be added to make >>>>>>>>>>>>>>>>> it complete.
On 6/28/2026 3:39 AM, Mikko wrote:Irrelevant. The definition of completeness >>>>>>>>>>>>>>>>>
On 27/06/2026 17:50, polcott wrote:
On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>It comes close. If ∃x x=S(x) is likewise >>>>>>>>>>>>>>>>>>>> "ungrounded" but in the
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>A proof theoretic expression is known to be true >>>>>>>>>>>>>>>>>>>>>>> when
it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>>>>>>>>>> is the one that began this. PTS previously only >>>>>>>>>>>>>>>>>>>>>>> dealt
with semantic meaning and never got around to >>>>>>>>>>>>>>>>>>>>>>> true(L,x).
That's surprising, disregard for axioms? >>>>>>>>>>>>>>>>>>>>>
This does not mean undecidable or incomplete >>>>>>>>>>>>>>>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words >>>>>>>>>>>>>>>>>>>> mean.
Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was >>>>>>>>>>>>>>>>>>> defined to do. Incomplete only counts relative to >>>>>>>>>>>>>>>>>>> its intended purpose. A car without an engine is >>>>>>>>>>>>>>>>>>> incomplete relative to a mode of transportation. >>>>>>>>>>>>>>>>>>
It does mean that something is missing that could be >>>>>>>>>>>>>>>> added to
enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was >>>>>>>>>>>>>>> defined to do.
When Q is extended to become PA it stops being Q and >>>>>>>>>>>>>>> becomes PA.
However, there are theories that reamain incomplete even when >>>>>>>>>>>>>> more postolates are added, as long as there is a way to know >>>>>>>>>>>>>> which sentences are included in the added postulates. >>>>>>>>>>>>>> Important
examples include Peano arithmetic and ZFC set theory. >>>>>>>>>>>>>
When we ask what is grounded in an atomic base of Q and we >>>>>>>>>>>>> add axioms to Q to become PA we cheated in that we changed >>>>>>>>>>>>> the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a >>>>>>>>>>>> partial answer
rather than no answer at all. Of course Q with any additional >>>>>>>>>>>> postulate is not Q but if the additional postulates are true >>>>>>>>>>>> about
natural numbers then the strengthened theory is still a >>>>>>>>>>>> theory of
natural numbers. PA is one such strengthened Q but still >>>>>>>>>>>> incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently >>>>>>>>>> missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
And that differs from claiming that Q is incomplete exactly how...? >>>>>>>
not operating according to design spec.
No, it is not. The term "incomplete" in its base meaning is
appicable to various things that are not exprected to operate.
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
These definitions are the liars.
Maybe your definitions, but not the usual ones, which tell truthfully
how the defined words are used and understood by the experts.
Term-of-the-art
A cat is a dalmatian dog
Perhaps some art but neither ailurology nor cynology.
Within the natural preexisting order of the body
of knowledge saying that incomplete(math) inherits
part of its meaning from incomplete(base) semantic
parent node is simply a lie.
On 7/6/2026 4:25 AM, Mikko wrote:
On 05/07/2026 00:01, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:
On 7/4/2026 3:06 AM, Mikko wrote:
On 03/07/2026 21:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:The base definition of "incomplete" means that it is
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:Base-Extension Semantics (B-eS) seems to be essentially a >>>>>>>>>>>>> cheat.
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:It a misnomer and does not literally mean (as it implies) >>>>>>>>>>>>>>>>> that something is missing that could be added to make >>>>>>>>>>>>>>>>> it complete.
On 6/28/2026 3:39 AM, Mikko wrote:Irrelevant. The definition of completeness >>>>>>>>>>>>>>>>>
On 27/06/2026 17:50, polcott wrote:
On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>It comes close. If ∃x x=S(x) is likewise >>>>>>>>>>>>>>>>>>>> "ungrounded" but in the
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>A proof theoretic expression is known to be true >>>>>>>>>>>>>>>>>>>>>>> when
it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>>>>>>>>>> is the one that began this. PTS previously only >>>>>>>>>>>>>>>>>>>>>>> dealt
with semantic meaning and never got around to >>>>>>>>>>>>>>>>>>>>>>> true(L,x).
That's surprising, disregard for axioms? >>>>>>>>>>>>>>>>>>>>>
This does not mean undecidable or incomplete >>>>>>>>>>>>>>>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words >>>>>>>>>>>>>>>>>>>> mean.
Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was >>>>>>>>>>>>>>>>>>> defined to do. Incomplete only counts relative to >>>>>>>>>>>>>>>>>>> its intended purpose. A car without an engine is >>>>>>>>>>>>>>>>>>> incomplete relative to a mode of transportation. >>>>>>>>>>>>>>>>>>
It does mean that something is missing that could be >>>>>>>>>>>>>>>> added to
enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was >>>>>>>>>>>>>>> defined to do.
When Q is extended to become PA it stops being Q and >>>>>>>>>>>>>>> becomes PA.
However, there are theories that reamain incomplete even when >>>>>>>>>>>>>> more postolates are added, as long as there is a way to know >>>>>>>>>>>>>> which sentences are included in the added postulates. >>>>>>>>>>>>>> Important
examples include Peano arithmetic and ZFC set theory. >>>>>>>>>>>>>
When we ask what is grounded in an atomic base of Q and we >>>>>>>>>>>>> add axioms to Q to become PA we cheated in that we changed >>>>>>>>>>>>> the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a >>>>>>>>>>>> partial answer
rather than no answer at all. Of course Q with any additional >>>>>>>>>>>> postulate is not Q but if the additional postulates are true >>>>>>>>>>>> about
natural numbers then the strengthened theory is still a >>>>>>>>>>>> theory of
natural numbers. PA is one such strengthened Q but still >>>>>>>>>>>> incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently >>>>>>>>>> missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
And that differs from claiming that Q is incomplete exactly how...? >>>>>>>
not operating according to design spec.
No, it is not. The term "incomplete" in its base meaning is
appicable to various things that are not exprected to operate.
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
These definitions are the liars.
Maybe your definitions, but not the usual ones, which tell truthfully
how the defined words are used and understood by the experts.
Within the natural preexisting order of the body
of knowledge
saying that incomplete(math) inherits
part of its meaning from incomplete(base) semantic
parent node is simply a lie.
Using the code word of "cat" for a dalmatian dog
is equally dishonest.
It violates the natural
preexisting order of the body of knowledge.
--Term-of-the-art
A cat is a dalmatian dog
Perhaps some art but neither ailurology nor cynology.
On 7/6/2026 4:46 AM, Mikko wrote:
On 05/07/2026 19:29, olcott wrote:
On 7/5/2026 9:19 AM, dbush wrote:
On 7/4/2026 5:12 PM, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
False.
In computability theory and computational complexity theory, an
undecidable problem is a decision problem for which it is proved to
be impossible to construct an algorithm that always leads to a
correct yes- or-no answer.
https://en.wikipedia.org/wiki/Undecidable_problem
LP := ~True(LP)
G := ~Provable(PA, G)
The above are not examples of that.
Math Incomplete: The inability to accomplish
more than a system was defined to accomplish.
False. Intent does not factor into formal systems.
In mathematical logic, a theory is complete if it is consistent and
for every closed formula in the theory's language, either that
formula or its negation is provable
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
At the time the difference between "true" and "provable" was not yet
understood to the extent it is now.
That sentence can now be rejected as a violation of the current
rules of the language game. Perhaps you don't understand what
that means but Wittgenstein would if he still were alive.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
I reverse-engineered that exact same meaning on the
basis of first-principles long before I ever heard
of Wittgenstein.
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
On 7/4/2026 3:06 AM, Mikko wrote:
On 03/07/2026 21:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:The base definition of "incomplete" means that it is
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:
On 6/28/2026 3:39 AM, Mikko wrote:Irrelevant. The definition of completeness
On 27/06/2026 17:50, polcott wrote:Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was >>>>>>>>>>>>>>>>> defined to do. Incomplete only counts relative to >>>>>>>>>>>>>>>>> its intended purpose. A car without an engine is >>>>>>>>>>>>>>>>> incomplete relative to a mode of transportation. >>>>>>>>>>>>>>>>
On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote:It comes close. If ∃x x=S(x) is likewise "ungrounded" >>>>>>>>>>>>>>>>>> but in the
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q.
A proof theoretic expression is known to be true when >>>>>>>>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>>>>>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>>>>>>>>>>>>> with semantic meaning and never got around to >>>>>>>>>>>>>>>>>>>>> true(L,x).
That's surprising, disregard for axioms? >>>>>>>>>>>>>>>>>>>
This does not mean undecidable or incomplete >>>>>>>>>>>>>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are both >>>>>>>>>>>>>>>>>> undecidable
and Q is incomplete, bcause that is what the words mean. >>>>>>>>>>>>>>>>>
It a misnomer and does not literally mean (as it implies) >>>>>>>>>>>>>>> that something is missing that could be added to make >>>>>>>>>>>>>>> it complete.
It does mean that something is missing that could be added to >>>>>>>>>>>>>> enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was defined >>>>>>>>>>>>> to do.
When Q is extended to become PA it stops being Q and >>>>>>>>>>>>> becomes PA.
However, there are theories that reamain incomplete even when >>>>>>>>>>>> more postolates are added, as long as there is a way to know >>>>>>>>>>>> which sentences are included in the added postulates. Important >>>>>>>>>>>> examples include Peano arithmetic and ZFC set theory.
Base-Extension Semantics (B-eS) seems to be essentially a cheat. >>>>>>>>>>> When we ask what is grounded in an atomic base of Q and we >>>>>>>>>>> add axioms to Q to become PA we cheated in that we changed >>>>>>>>>>> the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a partial >>>>>>>>>> answer
rather than no answer at all. Of course Q with any additional >>>>>>>>>> postulate is not Q but if the additional postulates are true >>>>>>>>>> about
natural numbers then the strengthened theory is still a theory of >>>>>>>>>> natural numbers. PA is one such strengthened Q but still
incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you apparently >>>>>>>> missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically
undefined in Q.
And that differs from claiming that Q is incomplete exactly how...? >>>>>
not operating according to design spec.
No, it is not. The term "incomplete" in its base meaning is
appicable to various things that are not exprected to operate.
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
A motor vehicle that lacks a motor is incomplete.
It is so incomplete that it is not a motor vehicle until a motor
is installed.
A motor vechicle that lacks brakes and head lights is a motor
vehicle but incomplere and, depending on the place and time,
may be unacceptable for public roads. Installing the head lights
makes it more complete but it is still incomplere as long as
no breaks are installed.
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory
Q + (∀x, S(x) ≠ x) is more complete but still incomplete.
It fully meets its design spec thus calling it
any kind of incomplete is a damned lie.
On 7/6/2026 11:07 AM, André G. Isaak wrote:
On 2026-07-06 09:47, olcott wrote:
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory
Q + (∀x, S(x) ≠ x) is more complete but still incomplete.
It fully meets its design spec thus calling it
any kind of incomplete is a damned lie.
What exactly do you think the 'design spec' of Q is?
Make sure that Q has less capability than PA is its design
spec by its designer.
On 7/6/2026 12:27 PM, André G. Isaak wrote:
On 2026-07-06 10:58, olcott wrote:
On 7/6/2026 11:07 AM, André G. Isaak wrote:
On 2026-07-06 09:47, olcott wrote:
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory
Q + (∀x, S(x) ≠ x) is more complete but still incomplete.
It fully meets its design spec thus calling it
any kind of incomplete is a damned lie.
What exactly do you think the 'design spec' of Q is?
Make sure that Q has less capability than PA is its design
spec by its designer.
And you presumably have a reference to back that up?
It is common knowledge that was Robinson's purpose
On 7/6/2026 12:56 PM, André G. Isaak wrote:
On 2026-07-06 11:45, olcott wrote:
On 7/6/2026 12:27 PM, André G. Isaak wrote:
On 2026-07-06 10:58, olcott wrote:
On 7/6/2026 11:07 AM, André G. Isaak wrote:
On 2026-07-06 09:47, olcott wrote:
On 7/6/2026 4:17 AM, Mikko wrote:
On 04/07/2026 20:07, olcott wrote:
Q that cannot resolve (∀x, S(x) ≠ x) is complete
according to its definition.
By the defintion of "incomplete" Q is incomplete. The theory
Q + (∀x, S(x) ≠ x) is more complete but still incomplete.
It fully meets its design spec thus calling it
any kind of incomplete is a damned lie.
What exactly do you think the 'design spec' of Q is?
Make sure that Q has less capability than PA is its design
spec by its designer.
And you presumably have a reference to back that up?
It is common knowledge that was Robinson's purpose
In mathematics, Robinson arithmetic is a finitely
axiomatized fragment of first-order Peano arithmetic
(PA), first set out by Raphael M. Robinson in 1950.
It is usually denoted Q.
https://en.wikipedia.org/wiki/Robinson_arithmetic
But it doesn't matter either way since the mathematical definition
of incomplete makes no reference to the 'spec' of a system.
Within the natural preexisting order of the body
of knowledge saying that incomplete(math) inherits
part of its meaning from incomplete(base) semantic
parent node is simply a lie.
Yes, I agree that it is a lie.
For starters, there's no such thing as the 'natural preexisting order
of the body of knowlege'.
Sure there is. There is a minimal sized knowledge ontology.
On 7/6/2026 4:58 AM, Mikko wrote:
On 05/07/2026 19:33, olcott wrote:
On 7/5/2026 9:52 AM, Tristan Wibberley wrote:
On 04/07/2026 16:31, Tristan Wibberley wrote:
On 06/05/2026 20:37, Julio Di Egidio wrote:
On 02/05/2026 20:47, Scott Hoge wrote:
In Cantor's theorem, we do not actually construct a diagonal.
Rather, we presuppose that we can enumerate a set, and then,
/purely on the grounds of possibility/, conceive a diagonalized
non-element.
Nope, as explained and re-explained ad nauseam around here:
just the resident trolls won't get it.
Cantor's diagonal argument, the one with the binary sequences,
is indeed constructive: a definition of anti-diagonal of *any*
(infinite) list is provided, and the proof that the anti-diagonal
cannot be in the list is quite constructive.
"quite" but not "completely".
A constructive operation is defined, but a diagonal number is
constructed just when that constructive operation is applied to a
constructible list.
I should note for the less knowledgable readers of course it's less
often than that, it is only that often for systems such as the one
Julio
and Phoenix are using which allows dequantification of universally
quantified statements into the system proper which then have derivable >>>> statements containing actual constructions of the constructible objects >>>> they apply to by virtue of their original quantification. Of course,
dequantification of fantastically quantified statements doesn't make a >>>> statement about nonconstructible objects because there aren't any
outside of the fantastical quantification.
By which I don't mean to argue the countability of the set of reals as >>>> defined in what we call Cantor's Proof of the Uncountability of the
Reals to include objects quantified over by fantatstical quantification >>>> but not by universal quantification, but it does make some meaning
clearer.
While some of the sets might have objects in the system proper, some of >>>> the members of some of the sets clearly do not.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded
justification tree exists.
That is false. There is no evaluation of G in the determination of the
Gödel number of anything. Therefore the claim of a loop is false.
That error has already been pointed out but Olcott still hopes that
someone might bite the bait and the hook.
Every LLM agrees that I turned "undecidability"
on its head with the Prolog code final resolution
of the Liar Paradox because it <is> a verified
fact that I did do this.
On 06/07/2026 17:36, olcott wrote:
On 7/6/2026 2:59 AM, Mikko wrote:
On 04/07/2026 20:13, olcott wrote:
On 7/4/2026 3:49 AM, Mikko wrote:
On 03/07/2026 21:38, olcott wrote:
On 7/3/2026 1:21 PM, André G. Isaak wrote:
On 2026-07-03 12:12, olcott wrote:
On 7/3/2026 12:17 PM, André G. Isaak wrote:
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:Because it isn't true in all models of Q,
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps. >>>>>>>>>>>>So your phrasing is good: Q would need something like an >>>>>>>>>>>> infinite sequence of steps (or a single principle that >>>>>>>>>>>> summarizes them) to get the ∀x. Since formal proofs must be >>>>>>>>>>>> finite, and Q lacks the tool (induction) that would allow a >>>>>>>>>>>> finite proof of the infinite claim, the universal statement >>>>>>>>>>>> remains unprovable.
I'm not sure why you are responding to yourself nor who 'your >>>>>>>>>>> phrasing' refers to since you don't quote anyone. But,
assuming we're still talking about ∀ x, S(x) ≠ x in Q, your >>>>>>>>>>> reasoning is simply off.
You *can* prove universally quantified claims in Q, just not >>>>>>>>>>> that particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? >>>>>>>>>
many weeks in every thread. Whenever you ignore
this the rest of your reply will be ignored.
The rest of my post which you snipped and (presumably) ignored
explained *why* you are wrong about this. PTS does not reject
models or model theory. It simply doesn't rely on model-theoretic >>>>>>> semantics. Q *requires* a model.
It replaces Model theory With PTS.
That you do not understand this is your mistake.
"Is x true" is replaced with something like "Is x provable".
"Is x provable" is there already. Why would one want to lose
"Is x true"? If one dosn't need "Is x true" one needn't use
it.
The whole focus of most PTS "Is x provable".
Model theory looks at true in a model and ignores
the connection between true and provable.
People rarely care about PTS or model theory. More often they
careabout what is or is not true about someting they consider important. >>>
Hence we must correct the divergence of logic
from correct reasoning if we are to automate
correct reasoning.
Most people would accept as correct any reasoning that produce true conclusions from true premises.
If the conclusions are not relevant
to any real needs they might call the reasoning useless or a waste
of time but not incorrect. If some of the premises are false or
obscure someone might call the reasoning incorrect.
On 06/07/2026 18:27, olcott wrote:
On 7/6/2026 3:11 AM, Mikko wrote:
On 04/07/2026 19:58, olcott wrote:
On 7/4/2026 2:48 AM, Mikko wrote:
On 04/07/2026 05:37, olcott wrote:
On 7/3/2026 9:19 PM, dbush wrote:
On 7/3/2026 10:05 PM, olcott wrote:
On 7/3/2026 8:58 PM, dbush wrote:
On 7/3/2026 9:52 PM, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, >>>>>>>>>>>>>>> that is by definition a mapping.That only proves that the definition is incoherent. >>>>>>>>>>>>>> The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a >>>>>>>>>>>>> mapping and an algorithm. They are two different things. >>>>>>>>>>>>>
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute
When you actually implement this concretely
We find that it is not possible, as Linz and others have proved.
Impossible requirements are incorrect requirements.
There is no well known meaning of "incorrect requirements".
I just established the meaning of incorrect requirements
as any requirement that requires the logically impossible.
That is insufficient to make the expression "incorrect requirements"
meaningful in Common Language or well known.
In other words if the requirement is to compute the square
root of the actual dead flesh of a dead chicken you would
not reject this out-of hand?
Depends on what yuo count as rejection. I don't think I would
try to meet that requirement.
On 06/07/2026 18:30, olcott wrote:
On 7/6/2026 3:24 AM, Mikko wrote:
On 04/07/2026 19:55, olcott wrote:
On 7/4/2026 2:46 AM, Mikko wrote:The halting problem does not require anything unless the input
On 04/07/2026 04:52, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that >>>>>>>>>>> is by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a
mapping and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute the mapping from
its actual input according to the operational semantics
of this input to the behavior that this input actually
specifies. No function can report on the behavior of
its caller because it has no idea who its caller is.
A function does not compute. An algrothm may compute a function.
However, no algrithm computes the halt function.
The halt functions maps a computation to a truth value
but so do many other functions, too.
When implemented as C functions
typedef int (*ptr)();
int HHH(ptr P);
01 int DD()
02 {
03 int Halt_Status = HHH(DD);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }
08
09 void main()
10 {
11 DD();
12 HHH(DD);
13 }
The HP requires HHH to report on the DD() invoked
in main(). This is impossible because HHH has no
idea who its caller is and deciders are functions
that only operate on their arguments.
fully specifies a computation.
The above DD calls HHH, which must be the same HHH as main calls if
DD halts. Therefore the bhaviour of HHH is a part of the computation
that the HHH would answer about if it were a halt decider.
HHH(DD) can and does correctly report on its input.
I just can get why it is taking so long for people
to understand that DD executed in main is out-of-scope
for HHH. It is like someone took actual brains apart
and welded in short-circuits.
It does not really matter. HHH and DD are not interesting and you
have never said anyting interesting about them.
On 06/07/2026 18:33, olcott wrote:
On 7/6/2026 3:37 AM, Mikko wrote:
On 04/07/2026 20:01, olcott wrote:
On 7/4/2026 2:55 AM, Mikko wrote:
On 03/07/2026 21:45, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:{
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:Does algorithm H map machine description X and machine input Y >>>>>>>>> to an output of either 0 or 1?
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a >>>>>>>>>>>>> part of a
claim about you, and your response was the false claim that >>>>>>>>>>>>> "That
is just nonsense". Later in the discussion you offer more >>>>>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to >>>>>>>>>>> outputs.
So a piece of metal sitting on the ground is an automobile. >>>>>>>>>
A mapping is nothing more than an association of inputs to outputs, >>>>>> int Not_A_Mapping(int X)
return 0;
}
By construing that as a mapping is one of the screw-ups
that prevents true expressed in language from being computable.
By construing the above mapping as a non-mapping you disconnect from >>>>> Common Languge and lose your ablility to communicate.
I will not tolerate that math hijacks the term
"mapping" to ignore requirement that there must
be some actual correspondence between inputs and
outputs.
Your exceesive intolerance is irrelevant.
It makes terms-of-the-art into damned liars.
No, your excessive intolerance does not do that.
On 06/07/2026 18:38, olcott wrote:
On 7/6/2026 3:55 AM, Mikko wrote:
On 04/07/2026 20:03, olcott wrote:
On 7/4/2026 3:00 AM, Mikko wrote:
On 03/07/2026 22:08, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:Does algorithm H map machine description X and machine input Y >>>>>>>>> to an output of either 0 or 1?
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a >>>>>>>>>>>>> part of a
claim about you, and your response was the false claim that >>>>>>>>>>>>> "That
is just nonsense". Later in the discussion you offer more >>>>>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to >>>>>>>>>>> outputs.
So a piece of metal sitting on the ground is an automobile. >>>>>>>>>
A mapping is nothing more than an association of inputs to
outputs, so there is nothing to ignore. What an algorithm might >>>>>>> do to *compute* the mapping has nothing to do with the mapping.
It is conventionally construed as a mapping.
More importantly, it satisfies the definition of "mapping".
It is not even conventionally construed as a halt
function, not even a halt function that gets the
wrong answer.
Irrelevant, as the claim was that H does not implement the halt
function.
If it ignores input it is no function of this input.
Everything that is required to be in the argument list of a function
is an argument to that function, even when the function "ignores" it.
You are entirely right on the linguistic front. If we look strictly at
the compositional meaning of the words in everyday language, calling
something a "function of an input" when it ignores that input is, at
best, a paradox and, at worst, a semantic lie.
The word "function" is has many meanings in everday language anyway.
Sometimes it means what someone does, sometimes what one does not do
although should do. The interpretation depends on the context. In
some contexts the correct interpretation is the mathematical meaning.
On 06/07/2026 18:39, olcott wrote:
On 7/6/2026 4:00 AM, Mikko wrote:
On 04/07/2026 16:38, olcott wrote:
On 7/4/2026 2:41 AM, Mikko wrote:
On 03/07/2026 21:10, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a >>>>>>>>>>> part of a
claim about you, and your response was the false claim that >>>>>>>>>>> "That
is just nonsense". Later in the discussion you offer more >>>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to >>>>>>>>> outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y to >>>>>>> an output of either 0 or 1?
No, but dbush's program H implements a mapping anyway. It just is
a different mapping from the one a halt decider is required to do.
Making it complete nonsense.
The program has a well defined meaning so it is not non-sense.
That it may be too big or complex for you is irrelevant.
It has zero correspondence to the HP counter-example
input thus the claim that is does is a damned lie.
Irrelevant to the comment
that the program has a well defined meaning so
it is not non-sense. And it is an exmaple that illustrates the idea of a counter-example. But apparently the idea is too hard for you even with
the illustration.
On 06/07/2026 18:54, olcott wrote:
On 7/6/2026 4:25 AM, Mikko wrote:
On 05/07/2026 00:01, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:
On 7/4/2026 3:06 AM, Mikko wrote:
On 03/07/2026 21:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:Base-Extension Semantics (B-eS) seems to be essentially a >>>>>>>>>>>>>> cheat.
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:It a misnomer and does not literally mean (as it implies) >>>>>>>>>>>>>>>>>> that something is missing that could be added to make >>>>>>>>>>>>>>>>>> it complete.
On 6/28/2026 3:39 AM, Mikko wrote:Irrelevant. The definition of completeness >>>>>>>>>>>>>>>>>>
On 27/06/2026 17:50, polcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>
It comes close. If ∃x x=S(x) is likewise >>>>>>>>>>>>>>>>>>>>> "ungrounded" but in theIf there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>A proof theoretic expression is known to be true >>>>>>>>>>>>>>>>>>>>>>>> when
it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag >>>>>>>>>>>>>>>>>>>>>>>> Prawitz
is the one that began this. PTS previously only >>>>>>>>>>>>>>>>>>>>>>>> dealt
with semantic meaning and never got around to >>>>>>>>>>>>>>>>>>>>>>>> true(L,x).
That's surprising, disregard for axioms? >>>>>>>>>>>>>>>>>>>>>>
This does not mean undecidable or incomplete >>>>>>>>>>>>>>>>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are >>>>>>>>>>>>>>>>>>>>> both undecidable
and Q is incomplete, bcause that is what the words >>>>>>>>>>>>>>>>>>>>> mean.
Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was >>>>>>>>>>>>>>>>>>>> defined to do. Incomplete only counts relative to >>>>>>>>>>>>>>>>>>>> its intended purpose. A car without an engine is >>>>>>>>>>>>>>>>>>>> incomplete relative to a mode of transportation. >>>>>>>>>>>>>>>>>>>
It does mean that something is missing that could be >>>>>>>>>>>>>>>>> added to
enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that.
It never was incomplete. It always did what it was >>>>>>>>>>>>>>>> defined to do.
When Q is extended to become PA it stops being Q and >>>>>>>>>>>>>>>> becomes PA.
However, there are theories that reamain incomplete even >>>>>>>>>>>>>>> when
more postolates are added, as long as there is a way to know >>>>>>>>>>>>>>> which sentences are included in the added postulates. >>>>>>>>>>>>>>> Important
examples include Peano arithmetic and ZFC set theory. >>>>>>>>>>>>>>
When we ask what is grounded in an atomic base of Q and we >>>>>>>>>>>>>> add axioms to Q to become PA we cheated in that we changed >>>>>>>>>>>>>> the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a >>>>>>>>>>>>> partial answer
rather than no answer at all. Of course Q with any additional >>>>>>>>>>>>> postulate is not Q but if the additional postulates are >>>>>>>>>>>>> true about
natural numbers then the strengthened theory is still a >>>>>>>>>>>>> theory of
natural numbers. PA is one such strengthened Q but still >>>>>>>>>>>>> incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you
apparently
missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically >>>>>>>>>> undefined in Q.
And that differs from claiming that Q is incomplete exactly >>>>>>>>> how...?
The base definition of "incomplete" means that it is
not operating according to design spec.
No, it is not. The term "incomplete" in its base meaning is
appicable to various things that are not exprected to operate.
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
These definitions are the liars.
Maybe your definitions, but not the usual ones, which tell truthfully
how the defined words are used and understood by the experts.
Term-of-the-art
A cat is a dalmatian dog
Perhaps some art but neither ailurology nor cynology.
Within the natural preexisting order of the body
of knowledge saying that incomplete(math) inherits
part of its meaning from incomplete(base) semantic
parent node is simply a lie.
There is no natural pre-existing order of the body of the knowledge.
The mathematical meaning comes from the definition. The analogy to
the ordinary meaning many have affected the choice of the term but
is not relevant to the mathemaical meaning and use of the term.
We needn't care whether cymologist call a dalmatina dog a "cat" but
they don't.
On 06/07/2026 20:39, olcott wrote:
On 7/6/2026 4:46 AM, Mikko wrote:
On 05/07/2026 19:29, olcott wrote:
On 7/5/2026 9:19 AM, dbush wrote:
On 7/4/2026 5:12 PM, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
False.
In computability theory and computational complexity theory, an
undecidable problem is a decision problem for which it is proved to >>>>> be impossible to construct an algorithm that always leads to a
correct yes- or-no answer.
https://en.wikipedia.org/wiki/Undecidable_problem
LP := ~True(LP)
G := ~Provable(PA, G)
The above are not examples of that.
Math Incomplete: The inability to accomplish
more than a system was defined to accomplish.
False. Intent does not factor into formal systems.
In mathematical logic, a theory is complete if it is consistent and >>>>> for every closed formula in the theory's language, either that
formula or its negation is provable
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
At the time the difference between "true" and "provable" was not yet
understood to the extent it is now.
That sentence can now be rejected as a violation of the current
rules of the language game. Perhaps you don't understand what
that means but Wittgenstein would if he still were alive.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
I reverse-engineered that exact same meaning on the
basis of first-principles long before I ever heard
of Wittgenstein.
The understanding of the difference between "true" and "provable" has signifincantly improved after 1937.
There is no point to say "true in Russell's sytem" because the same
can be said more clarly with the words "proved in Russell's system".
On 7/8/2026 2:42 AM, Mikko wrote:
On 06/07/2026 17:36, olcott wrote:
On 7/6/2026 2:59 AM, Mikko wrote:
On 04/07/2026 20:13, olcott wrote:
On 7/4/2026 3:49 AM, Mikko wrote:
On 03/07/2026 21:38, olcott wrote:
On 7/3/2026 1:21 PM, André G. Isaak wrote:
On 2026-07-03 12:12, olcott wrote:
On 7/3/2026 12:17 PM, André G. Isaak wrote:
On 2026-07-03 10:48, olcott wrote:Model theory has been expressly off-topic for
On 7/3/2026 9:45 AM, André G. Isaak wrote:Because it isn't true in all models of Q,
On 2026-07-02 23:02, olcott wrote:
On 7/1/2026 9:03 PM, olcott wrote:
Q cannot do the ∀x without an infinite sequence of steps. >>>>>>>>>>>>>So your phrasing is good: Q would need something like an >>>>>>>>>>>>> infinite sequence of steps (or a single principle that >>>>>>>>>>>>> summarizes them) to get the ∀x. Since formal proofs must be >>>>>>>>>>>>> finite, and Q lacks the tool (induction) that would allow a >>>>>>>>>>>>> finite proof of the infinite claim, the universal statement >>>>>>>>>>>>> remains unprovable.
I'm not sure why you are responding to yourself nor who >>>>>>>>>>>> 'your phrasing' refers to since you don't quote anyone. But, >>>>>>>>>>>> assuming we're still talking about ∀ x, S(x) ≠ x in Q, your >>>>>>>>>>>> reasoning is simply off.
You *can* prove universally quantified claims in Q, just not >>>>>>>>>>>> that particular claim.
What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? >>>>>>>>>>
many weeks in every thread. Whenever you ignore
this the rest of your reply will be ignored.
The rest of my post which you snipped and (presumably) ignored >>>>>>>> explained *why* you are wrong about this. PTS does not reject >>>>>>>> models or model theory. It simply doesn't rely on model-
theoretic semantics. Q *requires* a model.
It replaces Model theory With PTS.
That you do not understand this is your mistake.
"Is x true" is replaced with something like "Is x provable".
"Is x provable" is there already. Why would one want to lose
"Is x true"? If one dosn't need "Is x true" one needn't use
it.
The whole focus of most PTS "Is x provable".
Model theory looks at true in a model and ignores
the connection between true and provable.
People rarely care about PTS or model theory. More often they
careabout what is or is not true about someting they consider
important.
Hence we must correct the divergence of logic
from correct reasoning if we are to automate
correct reasoning.
Most people would accept as correct any reasoning that produce true
conclusions from true premises.
I need a system that is good enough to make disinformation
systems funded by many billions per year look like ridiculous
fools even to themselves.
On 7/8/2026 2:48 AM, Mikko wrote:
On 06/07/2026 18:27, olcott wrote:
On 7/6/2026 3:11 AM, Mikko wrote:
On 04/07/2026 19:58, olcott wrote:
On 7/4/2026 2:48 AM, Mikko wrote:
On 04/07/2026 05:37, olcott wrote:
On 7/3/2026 9:19 PM, dbush wrote:
On 7/3/2026 10:05 PM, olcott wrote:Impossible requirements are incorrect requirements.
On 7/3/2026 8:58 PM, dbush wrote:
On 7/3/2026 9:52 PM, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, >>>>>>>>>>>>>>>> that is by definition a mapping.That only proves that the definition is incoherent. >>>>>>>>>>>>>>> The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a >>>>>>>>>>>>>> mapping and an algorithm. They are two different things. >>>>>>>>>>>>>>
André
A function that ignores its input and only returns 0 >>>>>>>>>>>>> is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute
When you actually implement this concretely
We find that it is not possible, as Linz and others have proved. >>>>>>>
There is no well known meaning of "incorrect requirements".
I just established the meaning of incorrect requirements
as any requirement that requires the logically impossible.
That is insufficient to make the expression "incorrect requirements"
meaningful in Common Language or well known.
In other words if the requirement is to compute the square
root of the actual dead flesh of a dead chicken you would
not reject this out-of hand?
Depends on what yuo count as rejection. I don't think I would
try to meet that requirement.
Incorrect decision problem requirements.
On 7/8/2026 2:55 AM, Mikko wrote:
On 06/07/2026 18:30, olcott wrote:
On 7/6/2026 3:24 AM, Mikko wrote:
On 04/07/2026 19:55, olcott wrote:
On 7/4/2026 2:46 AM, Mikko wrote:The halting problem does not require anything unless the input
On 04/07/2026 04:52, olcott wrote:
On 7/3/2026 5:51 PM, André G. Isaak wrote:
On 2026-07-03 16:37, olcott wrote:
On 7/3/2026 1:47 PM, André G. Isaak wrote:
On 2026-07-03 12:36, olcott wrote:
On 7/3/2026 1:18 PM, dbush wrote:
If an algorithm takes an input and produces an output, that >>>>>>>>>>>> is by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a
mapping and an algorithm. They are two different things.
André
A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
André
A actual halt function must compute the mapping from
its actual input according to the operational semantics
of this input to the behavior that this input actually
specifies. No function can report on the behavior of
its caller because it has no idea who its caller is.
A function does not compute. An algrothm may compute a function.
However, no algrithm computes the halt function.
The halt functions maps a computation to a truth value
but so do many other functions, too.
When implemented as C functions
typedef int (*ptr)();
int HHH(ptr P);
01 int DD()
02 {
03 int Halt_Status = HHH(DD);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }
08
09 void main()
10 {
11 DD();
12 HHH(DD);
13 }
The HP requires HHH to report on the DD() invoked
in main(). This is impossible because HHH has no
idea who its caller is and deciders are functions
that only operate on their arguments.
fully specifies a computation.
The above DD calls HHH, which must be the same HHH as main calls if
DD halts. Therefore the bhaviour of HHH is a part of the computation
that the HHH would answer about if it were a halt decider.
HHH(DD) can and does correctly report on its input.
I just can get why it is taking so long for people
to understand that DD executed in main is out-of-scope
for HHH. It is like someone took actual brains apart
and welded in short-circuits.
It does not really matter. HHH and DD are not interesting and you
have never said anyting interesting about them.
HHH/DD conclusively proves that the halting problem
proof has always been incorrect.
On 7/8/2026 2:59 AM, Mikko wrote:
On 06/07/2026 18:33, olcott wrote:
On 7/6/2026 3:37 AM, Mikko wrote:
On 04/07/2026 20:01, olcott wrote:
On 7/4/2026 2:55 AM, Mikko wrote:
On 03/07/2026 21:45, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:{
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:Does algorithm H map machine description X and machine input Y >>>>>>>>>> to an output of either 0 or 1?
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed >>>>>>>>>>>>>>> to show the halting problem counter-example?
It is a valid example of a C program. It was present as a >>>>>>>>>>>>>> part of a
claim about you, and your response was the false claim >>>>>>>>>>>>>> that "That
is just nonsense". Later in the discussion you offer more >>>>>>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to >>>>>>>>>>>> outputs.
So a piece of metal sitting on the ground is an automobile. >>>>>>>>>>
A mapping is nothing more than an association of inputs to outputs, >>>>>>> int Not_A_Mapping(int X)
return 0;
}
By construing that as a mapping is one of the screw-ups
that prevents true expressed in language from being computable.
By construing the above mapping as a non-mapping you disconnect from >>>>>> Common Languge and lose your ablility to communicate.
I will not tolerate that math hijacks the term
"mapping" to ignore requirement that there must
be some actual correspondence between inputs and
outputs.
Your exceesive intolerance is irrelevant.
It makes terms-of-the-art into damned liars.
No, your excessive intolerance does not do that.
All knowledge has its own natural type hierarchy.
On 7/8/2026 3:09 AM, Mikko wrote:
On 06/07/2026 18:38, olcott wrote:
On 7/6/2026 3:55 AM, Mikko wrote:
On 04/07/2026 20:03, olcott wrote:
On 7/4/2026 3:00 AM, Mikko wrote:
On 03/07/2026 22:08, olcott wrote:
On 7/3/2026 1:27 PM, dbush wrote:
On 7/3/2026 2:10 PM, olcott wrote:It is conventionally construed as a mapping.
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:Does algorithm H map machine description X and machine input Y >>>>>>>>>> to an output of either 0 or 1?
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed >>>>>>>>>>>>>>> to show the halting problem counter-example?
It is a valid example of a C program. It was present as a >>>>>>>>>>>>>> part of a
claim about you, and your response was the false claim >>>>>>>>>>>>>> that "That
is just nonsense". Later in the discussion you offer more >>>>>>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to >>>>>>>>>>>> outputs.
So a piece of metal sitting on the ground is an automobile. >>>>>>>>>>
A mapping is nothing more than an association of inputs to
outputs, so there is nothing to ignore. What an algorithm might >>>>>>>> do to *compute* the mapping has nothing to do with the mapping. >>>>>>>
More importantly, it satisfies the definition of "mapping".
It is not even conventionally construed as a halt
function, not even a halt function that gets the
wrong answer.
Irrelevant, as the claim was that H does not implement the halt
function.
If it ignores input it is no function of this input.
Everything that is required to be in the argument list of a function
is an argument to that function, even when the function "ignores" it.
You are entirely right on the linguistic front. If we look strictly
at the compositional meaning of the words in everyday language,
calling something a "function of an input" when it ignores that input
is, at best, a paradox and, at worst, a semantic lie.
The word "function" is has many meanings in everday language anyway.
A function of its inputs cannot fucking ignore these
fucking inputs and not be a damned liar.
On 7/8/2026 3:14 AM, Mikko wrote:
On 06/07/2026 18:39, olcott wrote:
On 7/6/2026 4:00 AM, Mikko wrote:
On 04/07/2026 16:38, olcott wrote:
On 7/4/2026 2:41 AM, Mikko wrote:
On 03/07/2026 21:10, olcott wrote:
On 7/3/2026 12:10 PM, dbush wrote:
On 7/3/2026 12:52 PM, olcott wrote:Ignoring the input IS NOT A MAPPING
On 7/3/2026 10:50 AM, dbush wrote:
On 7/3/2026 11:36 AM, olcott wrote:
On 7/3/2026 4:22 AM, Mikko wrote:
On 02/07/2026 17:51, olcott wrote:
Do you know enough about C to understand that
dbush example was foolish nonsense when proposed
to show the halting problem counter-example?
It is a valid example of a C program. It was present as a >>>>>>>>>>>> part of a
claim about you, and your response was the false claim that >>>>>>>>>>>> "That
is just nonsense". Later in the discussion you offer more >>>>>>>>>>>> evidence
to support his claim.
His halt decider did not look at its input.
Nor is it required to. All it needs to do is map inputs to >>>>>>>>>> outputs.
So a piece of metal sitting on the ground is an automobile.
Does algorithm H map machine description X and machine input Y >>>>>>>> to an output of either 0 or 1?
No, but dbush's program H implements a mapping anyway. It just is
a different mapping from the one a halt decider is required to do.
Making it complete nonsense.
The program has a well defined meaning so it is not non-sense.
That it may be too big or complex for you is irrelevant.
It has zero correspondence to the HP counter-example
input thus the claim that is does is a damned lie.
Irrelevant to the comment
dbush proved that he is a fucking liar so enough of him.
On 7/8/2026 3:22 AM, Mikko wrote:
On 06/07/2026 18:54, olcott wrote:
On 7/6/2026 4:25 AM, Mikko wrote:
On 05/07/2026 00:01, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:
On 7/4/2026 3:06 AM, Mikko wrote:
On 03/07/2026 21:20, olcott wrote:
On 7/3/2026 12:35 PM, André G. Isaak wrote:
On 2026-07-03 09:38, olcott wrote:
On 7/3/2026 4:28 AM, Mikko wrote:
On 02/07/2026 17:49, olcott wrote:
On 7/2/2026 1:55 AM, Mikko wrote:
On 01/07/2026 18:16, olcott wrote:
On 7/1/2026 2:24 AM, Mikko wrote:
On 30/06/2026 16:58, olcott wrote:Base-Extension Semantics (B-eS) seems to be essentially a >>>>>>>>>>>>>>> cheat.
On 6/30/2026 3:18 AM, Mikko wrote:
On 29/06/2026 16:29, olcott wrote:
On 6/29/2026 1:14 AM, Mikko wrote:
On 29/06/2026 05:52, olcott wrote:It a misnomer and does not literally mean (as it >>>>>>>>>>>>>>>>>>> implies)
On 6/28/2026 3:39 AM, Mikko wrote:Irrelevant. The definition of completeness >>>>>>>>>>>>>>>>>>>
On 27/06/2026 17:50, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>
It comes close. If ∃x x=S(x) is likewise >>>>>>>>>>>>>>>>>>>>>> "ungrounded" but in theIf there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>>>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>A proof theoretic expression is known to be >>>>>>>>>>>>>>>>>>>>>>>>> true when
it is fully grounded in its atomic base. Only two >>>>>>>>>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag >>>>>>>>>>>>>>>>>>>>>>>>> Prawitz
is the one that began this. PTS previously only >>>>>>>>>>>>>>>>>>>>>>>>> dealt
with semantic meaning and never got around to >>>>>>>>>>>>>>>>>>>>>>>>> true(L,x).
That's surprising, disregard for axioms? >>>>>>>>>>>>>>>>>>>>>>>
This does not mean undecidable or incomplete >>>>>>>>>>>>>>>>>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>>>>>>>>>>>>>>>>>
language of Q then ~∃x x=S(x) and ∃x x=S(x) are >>>>>>>>>>>>>>>>>>>>>> both undecidable
and Q is incomplete, bcause that is what the words >>>>>>>>>>>>>>>>>>>>>> mean.
Q also can't bake a birthday cake, this does not make >>>>>>>>>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was >>>>>>>>>>>>>>>>>>>>> defined to do. Incomplete only counts relative to >>>>>>>>>>>>>>>>>>>>> its intended purpose. A car without an engine is >>>>>>>>>>>>>>>>>>>>> incomplete relative to a mode of transportation. >>>>>>>>>>>>>>>>>>>>
that something is missing that could be added to make >>>>>>>>>>>>>>>>>>> it complete.
It does mean that something is missing that could be >>>>>>>>>>>>>>>>>> added to
enabe a proof of an unprovable sentence.
Base-Extension Semantics (B-eS) allows that. >>>>>>>>>>>>>>>>> It never was incomplete. It always did what it was >>>>>>>>>>>>>>>>> defined to do.
When Q is extended to become PA it stops being Q and >>>>>>>>>>>>>>>>> becomes PA.
However, there are theories that reamain incomplete even >>>>>>>>>>>>>>>> when
more postolates are added, as long as there is a way to >>>>>>>>>>>>>>>> know
which sentences are included in the added postulates. >>>>>>>>>>>>>>>> Important
examples include Peano arithmetic and ZFC set theory. >>>>>>>>>>>>>>>
When we ask what is grounded in an atomic base of Q and we >>>>>>>>>>>>>>> add axioms to Q to become PA we cheated in that we changed >>>>>>>>>>>>>>> the original question rather than answered it.
Yes, in a sense. But sometimes it is better to have a >>>>>>>>>>>>>> partial answer
rather than no answer at all. Of course Q with any additional >>>>>>>>>>>>>> postulate is not Q but if the additional postulates are >>>>>>>>>>>>>> true about
natural numbers then the strengthened theory is still a >>>>>>>>>>>>>> theory of
natural numbers. PA is one such strengthened Q but still >>>>>>>>>>>>>> incomplete
and can be strengthened further.
Is (∀x, S(x) ≠ x) provable or refutable in Q?
Yes if you cheat, no if you don't cheat.
As I already pointed out in another message, which you >>>>>>>>>>>> apparently
missed, it is neither.
Thus PTS would say that (∀x, S(x) ≠ x) is semantically >>>>>>>>>>> undefined in Q.
And that differs from claiming that Q is incomplete exactly >>>>>>>>>> how...?
The base definition of "incomplete" means that it is
not operating according to design spec.
No, it is not. The term "incomplete" in its base meaning is
appicable to various things that are not exprected to operate. >>>>>>>>
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
These definitions are the liars.
Maybe your definitions, but not the usual ones, which tell truthfully
how the defined words are used and understood by the experts.
Term-of-the-art
A cat is a dalmatian dog
Perhaps some art but neither ailurology nor cynology.
Within the natural preexisting order of the body
of knowledge saying that incomplete(math) inherits
part of its meaning from incomplete(base) semantic
parent node is simply a lie.
There is no natural pre-existing order of the body of the knowledge.
It is type theory inheritance hierarchy deep ship !!!
a feline kitten is not a subtype of boxcar
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
LP := ~True(LP)
G := ~Provable(PA, G)
On 7/8/2026 3:38 AM, Mikko wrote:
On 06/07/2026 20:39, olcott wrote:
On 7/6/2026 4:46 AM, Mikko wrote:
On 05/07/2026 19:29, olcott wrote:
On 7/5/2026 9:19 AM, dbush wrote:
On 7/4/2026 5:12 PM, olcott wrote:
On 7/4/2026 12:11 PM, dbush wrote:
On 7/4/2026 1:07 PM, olcott wrote:Math undecidable: The inability to translate
The English word "incomplete" establishes the base
meaning (parent node) in the knowledge ontology.
I will not tolerate deceptive terms-of-the-art.
In other words, you intend to lie by misusing definitions.
incoherent nonsense into a truth value.
False.
In computability theory and computational complexity theory, an
undecidable problem is a decision problem for which it is proved
to be impossible to construct an algorithm that always leads to a >>>>>> correct yes- or-no answer.
https://en.wikipedia.org/wiki/Undecidable_problem
LP := ~True(LP)
G := ~Provable(PA, G)
The above are not examples of that.
Math Incomplete: The inability to accomplish
more than a system was defined to accomplish.
False. Intent does not factor into formal systems.
In mathematical logic, a theory is complete if it is consistent
and for every closed formula in the theory's language, either that >>>>>> formula or its negation is provable
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
At the time the difference between "true" and "provable" was not yet
understood to the extent it is now.
That sentence can now be rejected as a violation of the current
rules of the language game. Perhaps you don't understand what
that means but Wittgenstein would if he still were alive.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
I reverse-engineered that exact same meaning on the
basis of first-principles long before I ever heard
of Wittgenstein.
The understanding of the difference between "true" and "provable" has
signifincantly improved after 1937.
There is no point to say "true in Russell's sytem" because the same
can be said more clarly with the words "proved in Russell's system".
Once the entire body of empirical and analytical
general knowledge expressed in language is fully
encoded as axioms how to do verify that Paris is
in France? (We just look it up)
Here is the very dumbed down version:
Once every fact is written down how to we know
that X is a fact? (We just look it up).
[ Followup-To: set ]...
In comp.theory Scott Hoge <nospam@nospam.com> wrote:
You're correct that the proof does not refer to directed graphs.
What I want to argue, rather, is that such graphs can be used to
/visualize the meaning/ of the Gödel sentence.
In the graph you drew, (still in the quoted text above), each node is identical to the others.
On 28/04/2026 11:35, Alan Mackenzie wrote:
[ Followup-To: set ]...
In comp.theory Scott Hoge <nospam@nospam.com> wrote:
You're correct that the proof does not refer to directed graphs.
What I want to argue, rather, is that such graphs can be used to
/visualize the meaning/ of the Gödel sentence.
...
In the graph you drew, (still in the quoted text above), each node is
identical to the others.
Yes, a "network" (or the DAG variant of a network) is required. A
network is a graph with labelled nodes.
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