On 2025-10-18 19:15:45 +0000, Chris M. Thomasson said:
On 10/18/2025 2:54 AM, Mikko wrote:
On 2025-10-17 23:43:40 +0000, Chris M. Thomasson said:
On 10/17/2025 12:57 AM, Mikko wrote:
On 2025-10-15 12:09:39 +0000, olcott said:
On 10/15/2025 2:59 AM, Mikko wrote:
On 2025-10-14 15:36:21 +0000, olcott said:
On 10/14/2025 3:49 AM, Mikko wrote:
On 2025-10-13 15:23:15 +0000, olcott said:
On 10/13/2025 3:17 AM, Mikko wrote:
On 2025-10-12 14:48:38 +0000, olcott said:
On 10/12/2025 3:54 AM, Mikko wrote:
On 2025-10-11 13:11:19 +0000, olcott said:
On 10/11/2025 4:12 AM, Mikko wrote:
On 2025-10-10 13:56:22 +0000, olcott said:
On 10/10/2025 6:36 AM, dbush wrote:
On 10/10/2025 12:33 AM, olcott wrote:
On 10/9/2025 10:17 PM, dbush wrote:And as Tarski showed, that requires removing a truth >>>>>>>>>>>>>>>>> predicate.
On 10/9/2025 10:14 PM, olcott wrote:
Self-contradictory expressions only prove that >>>>>>>>>>>>>>>>>> they must be excluded from, formal systems of logic. >>>>>>>>>>>>>>>>>
He was wrong.
You can say but you can't show.
Kripke proved it
https://files.commons.gc.cuny.edu/wp-content/
blogs.dir/1358/ files/2019/04/Outline-of-a-Theory-of- >>>>>>>>>>>>>> Truth.pdf
That is a lie. In the above linked text Kripke does not >>>>>>>>>>>>> prove that
Tarski was wrong about anything, or even says so. Kripke >>>>>>>>>>>>> accepts
all mentioned results of Tarski as a valid material for >>>>>>>>>>>>> further work.
That Kripke didn't mention this, or claim this, and
even disavowed this is not an actual rebuttal.
Yes it is. That Kripke didn't mention that or claim that >>>>>>>>>>> obviously
entails that Kripke did not prove that and that your claim >>>>>>>>>>> that he
did prove was false.
My claim is semantically entailed by Kripke's system.
I had to add some details and clarifications.
Above you claimed otherwise.
You have not proven that your claim be semantically entaiiled by >>>>>>>>> Kripke's system.
It is,but, if you don't want to read Kripke here
is my self-contained view.
Any system of reasoning that begins with a consistent
system of stipulated truths and only applies the truth
preserving operation of semantic logical entailment to
this finite set of basic facts inherently derives a
truth predicate that works consistently and correctly
for this entire body of knowledge that can be expressed
in language.
No, it does not. A truth predicate must assign a truth value
to every sentence of the language on the system. If a sentence
is not derivable from the "stipulated truths" and its negation
isn't either then one of them must be assigned the value true
and the other false (because otherwise it would not be a predicate). >>>>>>> A sentence must be assigned the value true if it can be derived with >>>>>>> truth preserving operations from sentences that are assigned the >>>>>>> value true. As Tarski proved, that predicate cannot be defined
with a formula in the language of the system it applies to.
Nope. He just derived the Liar Paradox out
of thin air, no truth preserving operations applied.
That is absolutely false. Tarski did and others nave verified that
he did derive the undefinability from the properties of the natural
numbers with truth preserving operations.
I must be misunderstand you here. Any natural number can be defined?
By the usual meaning of "natural number", yes.
Well, some people, sigh, really think that there is a so-called
"largest natural number".... For instance, iirc, WM over on sci.math...
By the meaning 'any
element of any model of any theory of natural numbers', no.
Humm... Can you drill down on that a little more? uncountable? For
instance, think of a natural number say
1097668204
Okay. Those are from random digits. The _first_ digit shall be greater
than zero and less than 10. The rest of them are from 0 to 9. So:
1097668204...
Taken to infinity, is it still a natural number? Humm... Not...
The usual understanding is that the natural numbers form a seqence:
one, two, three, &c. This is fromalized in Peano's axioms so that
there is only one named number (0 or 1) and the successor function
that ensures that after each number there is another number, with
no end and no loop. All numbers in the sequnce can be expressed
with the symbol 0 and some number of applications of the succssor
function. But are there other natural numbers that cannot be expressed
that way?
An uncountable model of natural numbers can be constructed in the same
way but using sequences where ther members other than the first one
are reals. The first member must still be a positive integer.
On 10/19/2025 3:32 AM, Mikko wrote:
On 2025-10-18 19:15:45 +0000, Chris M. Thomasson said:
On 10/18/2025 2:54 AM, Mikko wrote:
On 2025-10-17 23:43:40 +0000, Chris M. Thomasson said:
On 10/17/2025 12:57 AM, Mikko wrote:
On 2025-10-15 12:09:39 +0000, olcott said:
On 10/15/2025 2:59 AM, Mikko wrote:
On 2025-10-14 15:36:21 +0000, olcott said:
On 10/14/2025 3:49 AM, Mikko wrote:
On 2025-10-13 15:23:15 +0000, olcott said:
On 10/13/2025 3:17 AM, Mikko wrote:
On 2025-10-12 14:48:38 +0000, olcott said:
On 10/12/2025 3:54 AM, Mikko wrote:
On 2025-10-11 13:11:19 +0000, olcott said:
On 10/11/2025 4:12 AM, Mikko wrote:
On 2025-10-10 13:56:22 +0000, olcott said:
On 10/10/2025 6:36 AM, dbush wrote:
On 10/10/2025 12:33 AM, olcott wrote:
On 10/9/2025 10:17 PM, dbush wrote:And as Tarski showed, that requires removing a truth >>>>>>>>>>>>>>>>>> predicate.
On 10/9/2025 10:14 PM, olcott wrote:
Self-contradictory expressions only prove that >>>>>>>>>>>>>>>>>>> they must be excluded from, formal systems of logic. >>>>>>>>>>>>>>>>>>
He was wrong.
You can say but you can't show.
Kripke proved it
https://files.commons.gc.cuny.edu/wp-content/
blogs.dir/1358/ files/2019/04/Outline-of-a-Theory-of- >>>>>>>>>>>>>>> Truth.pdf
That is a lie. In the above linked text Kripke does not >>>>>>>>>>>>>> prove that
Tarski was wrong about anything, or even says so. Kripke >>>>>>>>>>>>>> accepts
all mentioned results of Tarski as a valid material for >>>>>>>>>>>>>> further work.
That Kripke didn't mention this, or claim this, and
even disavowed this is not an actual rebuttal.
Yes it is. That Kripke didn't mention that or claim that >>>>>>>>>>>> obviously
entails that Kripke did not prove that and that your claim >>>>>>>>>>>> that he
did prove was false.
My claim is semantically entailed by Kripke's system.
I had to add some details and clarifications.
Above you claimed otherwise.
You have not proven that your claim be semantically entaiiled by >>>>>>>>>> Kripke's system.
It is,but, if you don't want to read Kripke here
is my self-contained view.
Any system of reasoning that begins with a consistent
system of stipulated truths and only applies the truth
preserving operation of semantic logical entailment to
this finite set of basic facts inherently derives a
truth predicate that works consistently and correctly
for this entire body of knowledge that can be expressed
in language.
No, it does not. A truth predicate must assign a truth value
to every sentence of the language on the system. If a sentence >>>>>>>> is not derivable from the "stipulated truths" and its negation >>>>>>>> isn't either then one of them must be assigned the value true
and the other false (because otherwise it would not be a predicate). >>>>>>>> A sentence must be assigned the value true if it can be derived with >>>>>>>> truth preserving operations from sentences that are assigned the >>>>>>>> value true. As Tarski proved, that predicate cannot be defined >>>>>>>> with a formula in the language of the system it applies to.
Nope. He just derived the Liar Paradox out
of thin air, no truth preserving operations applied.
That is absolutely false. Tarski did and others nave verified that >>>>>> he did derive the undefinability from the properties of the natural >>>>>> numbers with truth preserving operations.
I must be misunderstand you here. Any natural number can be defined?
By the usual meaning of "natural number", yes.
Well, some people, sigh, really think that there is a so-called
"largest natural number".... For instance, iirc, WM over on sci.math...
By the meaning 'any
element of any model of any theory of natural numbers', no.
Humm... Can you drill down on that a little more? uncountable? For
instance, think of a natural number say
1097668204
Okay. Those are from random digits. The _first_ digit shall be greater
than zero and less than 10. The rest of them are from 0 to 9. So:
1097668204...
Taken to infinity, is it still a natural number? Humm... Not...
The usual understanding is that the natural numbers form a seqence:
one, two, three, &c. This is fromalized in Peano's axioms so that
there is only one named number (0 or 1) and the successor function
that ensures that after each number there is another number, with
no end and no loop. All numbers in the sequnce can be expressed
with the symbol 0 and some number of applications of the succssor
function. But are there other natural numbers that cannot be expressed
that way?
If its a natural number, then its in the countable natural numbers. It
can be defined. To combine the successor and predecessor, just make an
n-ary tree. Take this 3-ary one. There are finite functions that can
easily find the parent (root zero aside for a moment...) and the three children of any node:
__________________________________
0
/|\
/ | \
/ | \
/ | \
/ | \
/ | \
/ | \
1 2 3
/|\ /|\ /|\
/ | \ / | \ / | \
4 5 6 7 8 9 10 11 12
..............................
The parent of root zero seems odd. Its negative mirror children would be
-1, -2, -3, but those are not naturals.
..........................
-1 -2 -3
\ | /
\ | /
\ | /
\|/
-0+
/|\
/ | \
/ | \
/ | \
+1 +2 +3
..........................
On and on... ;^)
Now, the possible paths of this tree, are they uncountable?
On 2025-10-17 23:43:40 +0000, Chris M. Thomasson said:
On 10/17/2025 12:57 AM, Mikko wrote:
On 2025-10-15 12:09:39 +0000, olcott said:
On 10/15/2025 2:59 AM, Mikko wrote:
On 2025-10-14 15:36:21 +0000, olcott said:
On 10/14/2025 3:49 AM, Mikko wrote:
On 2025-10-13 15:23:15 +0000, olcott said:
On 10/13/2025 3:17 AM, Mikko wrote:
On 2025-10-12 14:48:38 +0000, olcott said:
On 10/12/2025 3:54 AM, Mikko wrote:
On 2025-10-11 13:11:19 +0000, olcott said:
On 10/11/2025 4:12 AM, Mikko wrote:
On 2025-10-10 13:56:22 +0000, olcott said:
On 10/10/2025 6:36 AM, dbush wrote:
On 10/10/2025 12:33 AM, olcott wrote:He was wrong.
On 10/9/2025 10:17 PM, dbush wrote:And as Tarski showed, that requires removing a truth predicate. >>>>>>>>>>>>>>
On 10/9/2025 10:14 PM, olcott wrote:
Self-contradictory expressions only prove that >>>>>>>>>>>>>>>> they must be excluded from, formal systems of logic. >>>>>>>>>>>>>>>
You can say but you can't show.
Kripke proved it
https://files.commons.gc.cuny.edu/wp-content/blogs.dir/1358/ >>>>>>>>>>>> files/2019/04/Outline-of-a-Theory-of-Truth.pdf
That is a lie. In the above linked text Kripke does not prove that >>>>>>>>>>> Tarski was wrong about anything, or even says so. Kripke accepts >>>>>>>>>>> all mentioned results of Tarski as a valid material for further work.
That Kripke didn't mention this, or claim this, and
even disavowed this is not an actual rebuttal.
Yes it is. That Kripke didn't mention that or claim that obviously >>>>>>>>> entails that Kripke did not prove that and that your claim that he >>>>>>>>> did prove was false.
My claim is semantically entailed by Kripke's system.
I had to add some details and clarifications.
Above you claimed otherwise.
You have not proven that your claim be semantically entaiiled by >>>>>>> Kripke's system.
It is,but, if you don't want to read Kripke here
is my self-contained view.
Any system of reasoning that begins with a consistent
system of stipulated truths and only applies the truth
preserving operation of semantic logical entailment to
this finite set of basic facts inherently derives a
truth predicate that works consistently and correctly
for this entire body of knowledge that can be expressed
in language.
No, it does not. A truth predicate must assign a truth value
to every sentence of the language on the system. If a sentence
is not derivable from the "stipulated truths" and its negation
isn't either then one of them must be assigned the value true
and the other false (because otherwise it would not be a predicate). >>>>> A sentence must be assigned the value true if it can be derived with >>>>> truth preserving operations from sentences that are assigned the
value true. As Tarski proved, that predicate cannot be defined
with a formula in the language of the system it applies to.
Nope. He just derived the Liar Paradox out
of thin air, no truth preserving operations applied.
That is absolutely false. Tarski did and others nave verified that
he did derive the undefinability from the properties of the natural
numbers with truth preserving operations.
I must be misunderstand you here. Any natural number can be defined?
By the usual meaning of "natural number", yes. By the meaning 'any
element of any model of any theory of natural numbers', no.
If its a natural number, then its in the countable natural numbers. It
can be defined. To combine the successor and predecessor, just make an
n-ary tree. Take this 3-ary one. There are finite functions that can
easily find the parent (root zero aside for a moment...) and the three children of any node:
__________________________________
0
/|\
/ | \
/ | \
/ | \
/ | \
/ | \
/ | \
1 2 3
/|\ /|\ /|\
/ | \ / | \ / | \
4 5 6 7 8 9 10 11 12
..............................
The parent of root zero seems odd. Its negative mirror children would be
-1, -2, -3, but those are not naturals.
..........................
-1 -2 -3
\ | /
\ | /
\ | /
\|/
-0+
/|\
/ | \
/ | \
/ | \
+1 +2 +3
..........................
On and on... ;^)
Now, the possible paths of this tree, are they uncountable?
On 2025-10-19, Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
On 10/19/2025 3:32 AM, Mikko wrote:
On 2025-10-18 19:15:45 +0000, Chris M. Thomasson said:
On 10/18/2025 2:54 AM, Mikko wrote:
On 2025-10-17 23:43:40 +0000, Chris M. Thomasson said:
On 10/17/2025 12:57 AM, Mikko wrote:By the usual meaning of "natural number", yes.
On 2025-10-15 12:09:39 +0000, olcott said:
On 10/15/2025 2:59 AM, Mikko wrote:
On 2025-10-14 15:36:21 +0000, olcott said:
On 10/14/2025 3:49 AM, Mikko wrote:
On 2025-10-13 15:23:15 +0000, olcott said:
On 10/13/2025 3:17 AM, Mikko wrote:
On 2025-10-12 14:48:38 +0000, olcott said:
On 10/12/2025 3:54 AM, Mikko wrote:
On 2025-10-11 13:11:19 +0000, olcott said:
On 10/11/2025 4:12 AM, Mikko wrote:
On 2025-10-10 13:56:22 +0000, olcott said:
On 10/10/2025 6:36 AM, dbush wrote:
On 10/10/2025 12:33 AM, olcott wrote:
On 10/9/2025 10:17 PM, dbush wrote:And as Tarski showed, that requires removing a truth >>>>>>>>>>>>>>>>>>> predicate.
On 10/9/2025 10:14 PM, olcott wrote:
Self-contradictory expressions only prove that >>>>>>>>>>>>>>>>>>>> they must be excluded from, formal systems of logic. >>>>>>>>>>>>>>>>>>>
He was wrong.
You can say but you can't show.
Kripke proved it
https://files.commons.gc.cuny.edu/wp-content/
blogs.dir/1358/ files/2019/04/Outline-of-a-Theory-of- >>>>>>>>>>>>>>>> Truth.pdf
That is a lie. In the above linked text Kripke does not >>>>>>>>>>>>>>> prove that
Tarski was wrong about anything, or even says so. Kripke >>>>>>>>>>>>>>> accepts
all mentioned results of Tarski as a valid material for >>>>>>>>>>>>>>> further work.
That Kripke didn't mention this, or claim this, and >>>>>>>>>>>>>> even disavowed this is not an actual rebuttal.
Yes it is. That Kripke didn't mention that or claim that >>>>>>>>>>>>> obviously
entails that Kripke did not prove that and that your claim >>>>>>>>>>>>> that he
did prove was false.
My claim is semantically entailed by Kripke's system.
I had to add some details and clarifications.
Above you claimed otherwise.
You have not proven that your claim be semantically entaiiled by >>>>>>>>>>> Kripke's system.
It is,but, if you don't want to read Kripke here
is my self-contained view.
Any system of reasoning that begins with a consistent
system of stipulated truths and only applies the truth
preserving operation of semantic logical entailment to
this finite set of basic facts inherently derives a
truth predicate that works consistently and correctly
for this entire body of knowledge that can be expressed
in language.
No, it does not. A truth predicate must assign a truth value >>>>>>>>> to every sentence of the language on the system. If a sentence >>>>>>>>> is not derivable from the "stipulated truths" and its negation >>>>>>>>> isn't either then one of them must be assigned the value true >>>>>>>>> and the other false (because otherwise it would not be a predicate). >>>>>>>>> A sentence must be assigned the value true if it can be derived with >>>>>>>>> truth preserving operations from sentences that are assigned the >>>>>>>>> value true. As Tarski proved, that predicate cannot be defined >>>>>>>>> with a formula in the language of the system it applies to.
Nope. He just derived the Liar Paradox out
of thin air, no truth preserving operations applied.
That is absolutely false. Tarski did and others nave verified that >>>>>>> he did derive the undefinability from the properties of the natural >>>>>>> numbers with truth preserving operations.
I must be misunderstand you here. Any natural number can be defined? >>>>>
Well, some people, sigh, really think that there is a so-called
"largest natural number".... For instance, iirc, WM over on sci.math... >>>>
By the meaning 'any
element of any model of any theory of natural numbers', no.
Humm... Can you drill down on that a little more? uncountable? For
instance, think of a natural number say
1097668204
Okay. Those are from random digits. The _first_ digit shall be greater >>>> than zero and less than 10. The rest of them are from 0 to 9. So:
1097668204...
Taken to infinity, is it still a natural number? Humm... Not...
The usual understanding is that the natural numbers form a seqence:
one, two, three, &c. This is fromalized in Peano's axioms so that
there is only one named number (0 or 1) and the successor function
that ensures that after each number there is another number, with
no end and no loop. All numbers in the sequnce can be expressed
with the symbol 0 and some number of applications of the succssor
function. But are there other natural numbers that cannot be expressed
that way?
If its a natural number, then its in the countable natural numbers. It
can be defined. To combine the successor and predecessor, just make an
n-ary tree. Take this 3-ary one. There are finite functions that can
easily find the parent (root zero aside for a moment...) and the three
children of any node:
__________________________________
0
/|\
/ | \
/ | \
/ | \
/ | \
/ | \
/ | \
1 2 3
/|\ /|\ /|\
/ | \ / | \ / | \
4 5 6 7 8 9 10 11 12
..............................
The parent of root zero seems odd. Its negative mirror children would be
-1, -2, -3, but those are not naturals.
..........................
-1 -2 -3
\ | /
\ | /
\ | /
\|/
-0+
/|\
/ | \
/ | \
/ | \
+1 +2 +3
..........................
On and on... ;^)
Now, the possible paths of this tree, are they uncountable?
I would say not, because the paths can be generated in parallel by
a breadth-first traversal.
In the positive direction, tirst we have the null path, just the node 0.
Then we have the three paths 0 -> 1, 0 -> 2, 0 -> 3.
Then we have the next layer of paths. (We can add the negatives in the same way;
it makes no difference to the argument).
This is a countable process which is on the trajectory of visiting
all the paths.
Never mind that; each node, labeled by a whole number, is
reachable in only one way. So easch path can be /labeled/ by
that natural number, uniquely identifying it.
Any set that can be put into 1:1 correspondence with the natural numbers
(or whole numbers or integers) is countable.
Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
[ .... ]
If its a natural number, then its in the countable natural numbers. It
can be defined. To combine the successor and predecessor, just make an
n-ary tree. Take this 3-ary one. There are finite functions that can
easily find the parent (root zero aside for a moment...) and the three
children of any node:
__________________________________
0
/|\
/ | \
/ | \
/ | \
/ | \
/ | \
/ | \
1 2 3
/|\ /|\ /|\
/ | \ / | \ / | \
4 5 6 7 8 9 10 11 12
..............................
The parent of root zero seems odd. Its negative mirror children would be
-1, -2, -3, but those are not naturals.
..........................
-1 -2 -3
\ | /
\ | /
\ | /
\|/
-0+
/|\
/ | \
/ | \
/ | \
+1 +2 +3
..........................
On and on... ;^)
Now, the possible paths of this tree, are they uncountable?
Yes, they are.
However the set of _finite_ paths of the tree is
countably infinite. This was one of the few sensible points that came
from debating with a certain crank on sci.math a few years ago.
[...]
On 2025-10-19, Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
On 10/19/2025 3:32 AM, Mikko wrote:
On 2025-10-18 19:15:45 +0000, Chris M. Thomasson said:
On 10/18/2025 2:54 AM, Mikko wrote:
On 2025-10-17 23:43:40 +0000, Chris M. Thomasson said:
On 10/17/2025 12:57 AM, Mikko wrote:By the usual meaning of "natural number", yes.
On 2025-10-15 12:09:39 +0000, olcott said:
On 10/15/2025 2:59 AM, Mikko wrote:
On 2025-10-14 15:36:21 +0000, olcott said:
On 10/14/2025 3:49 AM, Mikko wrote:
On 2025-10-13 15:23:15 +0000, olcott said:
On 10/13/2025 3:17 AM, Mikko wrote:
On 2025-10-12 14:48:38 +0000, olcott said:
On 10/12/2025 3:54 AM, Mikko wrote:
On 2025-10-11 13:11:19 +0000, olcott said:
On 10/11/2025 4:12 AM, Mikko wrote:
On 2025-10-10 13:56:22 +0000, olcott said:
On 10/10/2025 6:36 AM, dbush wrote:
On 10/10/2025 12:33 AM, olcott wrote:
On 10/9/2025 10:17 PM, dbush wrote:And as Tarski showed, that requires removing a truth >>>>>>>>>>>>>>>>>>> predicate.
On 10/9/2025 10:14 PM, olcott wrote:
Self-contradictory expressions only prove that >>>>>>>>>>>>>>>>>>>> they must be excluded from, formal systems of logic. >>>>>>>>>>>>>>>>>>>
He was wrong.
You can say but you can't show.
Kripke proved it
https://files.commons.gc.cuny.edu/wp-content/
blogs.dir/1358/ files/2019/04/Outline-of-a-Theory-of- >>>>>>>>>>>>>>>> Truth.pdf
That is a lie. In the above linked text Kripke does not >>>>>>>>>>>>>>> prove that
Tarski was wrong about anything, or even says so. Kripke >>>>>>>>>>>>>>> accepts
all mentioned results of Tarski as a valid material for >>>>>>>>>>>>>>> further work.
That Kripke didn't mention this, or claim this, and >>>>>>>>>>>>>> even disavowed this is not an actual rebuttal.
Yes it is. That Kripke didn't mention that or claim that >>>>>>>>>>>>> obviously
entails that Kripke did not prove that and that your claim >>>>>>>>>>>>> that he
did prove was false.
My claim is semantically entailed by Kripke's system.
I had to add some details and clarifications.
Above you claimed otherwise.
You have not proven that your claim be semantically entaiiled by >>>>>>>>>>> Kripke's system.
It is,but, if you don't want to read Kripke here
is my self-contained view.
Any system of reasoning that begins with a consistent
system of stipulated truths and only applies the truth
preserving operation of semantic logical entailment to
this finite set of basic facts inherently derives a
truth predicate that works consistently and correctly
for this entire body of knowledge that can be expressed
in language.
No, it does not. A truth predicate must assign a truth value >>>>>>>>> to every sentence of the language on the system. If a sentence >>>>>>>>> is not derivable from the "stipulated truths" and its negation >>>>>>>>> isn't either then one of them must be assigned the value true >>>>>>>>> and the other false (because otherwise it would not be a predicate). >>>>>>>>> A sentence must be assigned the value true if it can be derived with >>>>>>>>> truth preserving operations from sentences that are assigned the >>>>>>>>> value true. As Tarski proved, that predicate cannot be defined >>>>>>>>> with a formula in the language of the system it applies to.
Nope. He just derived the Liar Paradox out
of thin air, no truth preserving operations applied.
That is absolutely false. Tarski did and others nave verified that >>>>>>> he did derive the undefinability from the properties of the natural >>>>>>> numbers with truth preserving operations.
I must be misunderstand you here. Any natural number can be defined? >>>>>
Well, some people, sigh, really think that there is a so-called
"largest natural number".... For instance, iirc, WM over on sci.math... >>>>
By the meaning 'any
element of any model of any theory of natural numbers', no.
Humm... Can you drill down on that a little more? uncountable? For
instance, think of a natural number say
1097668204
Okay. Those are from random digits. The _first_ digit shall be greater >>>> than zero and less than 10. The rest of them are from 0 to 9. So:
1097668204...
Taken to infinity, is it still a natural number? Humm... Not...
The usual understanding is that the natural numbers form a seqence:
one, two, three, &c. This is fromalized in Peano's axioms so that
there is only one named number (0 or 1) and the successor function
that ensures that after each number there is another number, with
no end and no loop. All numbers in the sequnce can be expressed
with the symbol 0 and some number of applications of the succssor
function. But are there other natural numbers that cannot be expressed
that way?
If its a natural number, then its in the countable natural numbers. It
can be defined. To combine the successor and predecessor, just make an
n-ary tree. Take this 3-ary one. There are finite functions that can
easily find the parent (root zero aside for a moment...) and the three
children of any node:
__________________________________
0
/|\
/ | \
/ | \
/ | \
/ | \
/ | \
/ | \
1 2 3
/|\ /|\ /|\
/ | \ / | \ / | \
4 5 6 7 8 9 10 11 12
..............................
The parent of root zero seems odd. Its negative mirror children would be
-1, -2, -3, but those are not naturals.
..........................
-1 -2 -3
\ | /
\ | /
\ | /
\|/
-0+
/|\
/ | \
/ | \
/ | \
+1 +2 +3
..........................
On and on... ;^)
Now, the possible paths of this tree, are they uncountable?
I would say not, because the paths can be generated in parallel by
a breadth-first traversal.
In the positive direction, tirst we have the null path, just the node 0.
Then we have the three paths 0 -> 1, 0 -> 2, 0 -> 3.
Then we have the next layer of paths. (We can add the negatives in the same way;
it makes no difference to the argument).
This is a countable process which is on the trajectory of visiting
all the paths.
Never mind that; each node, labeled by a whole number, is
reachable in only one way. So easch path can be /labeled/ by
that natural number, uniquely identifying it.
Any set that can be put into 1:1 correspondence with the natural numbers
(or whole numbers or integers) is countable.
On 08/10/2025 18:26, Julio Di Egidio wrote:
On 07/10/2025 17:55, Richard Heathfield wrote:
On 07/10/2025 16:05, olcott wrote:
When we ask polar yes/no questions that have no
correct yes/no answer these questions themselves
are incorrect.
Question: can any question be turned into an incorrect question by
your definition?
Answer: yes.
That is not true.
Yes, it is, if Peter Olcott is at the wheel..
The Halting Problem question is: "Is it possible for a universal halt
decider to exist?"
The correct answer is no".
Enter Peter Olcott, and suddenly the question is something
* The Halting Problem Proof Question "Is there an HHH such that
DD(HHH) ...
"This sentence is not true" is neither true not false.
It is neither true nor false because it is self-contradictory
thus has no truth value, thus technically is not a truth-bearer.
The halting problem was intentionally defined to be
self-contradictory just like the Liar Paradox.
The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except as noted in
the sig.
On 08/10/2025 18:44, olcott wrote:
"This sentence is not true" is neither true not false.
It is neither true nor false because it is self-contradictory
thus has no truth value, thus technically is not a truth-bearer.
Even "This sentence is true" is a contradiction, "This sentence" refers
to numerous different sentences including false ones so it identifies
them all.
If you're going to do logic you need to exclude "This sentence" as a
term (or define it carefully to override its normal meaning).
Try defining names for sentences and using the names in their respective nominated sentences instead of using "This sentence", or else use the Y combinator.
The halting problem was intentionally defined to be
self-contradictory just like the Liar Paradox.
The problem is not self-contradictory, but rather many (perhaps all) of
the arguments that resolve the problem to "No there's no universal halt decider" have self-contradictory deductions.
The problem is fine "Is there any universal halt decider?" "No, there
isn't".
--
Tristan Wibberley
The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.
On 2025-10-08, olcott <polcott333@gmail.com> wrote:
For the set of H/P pairs of
decider H and input P:
If H says halts then P loops
If H says loops then P halts
making each H(P) always incorrect.
A better way to say it is like this:
Consider the set S of diagonal decider/input pairs. If <H, P> is any arbitrarily chosen pair from this set, then one of these three
possibilities is true: H(P) indicates halting, H(P) indicates
non-halting or else H(P) fails to terminate. If H(P) indicates halting,
then P is necessarily non-halting, and vice versa. (If H(P) doesn't
halt, P could be either.) In all three cases, H fails to decide P
correctly, or at all.
On 2025-10-18, Mikko <mikko.levanto@iki.fi> wrote:
On 2025-10-17 23:43:40 +0000, Chris M. Thomasson said:
On 10/17/2025 12:57 AM, Mikko wrote:
On 2025-10-15 12:09:39 +0000, olcott said:
On 10/15/2025 2:59 AM, Mikko wrote:
On 2025-10-14 15:36:21 +0000, olcott said:
On 10/14/2025 3:49 AM, Mikko wrote:
On 2025-10-13 15:23:15 +0000, olcott said:
On 10/13/2025 3:17 AM, Mikko wrote:
On 2025-10-12 14:48:38 +0000, olcott said:
On 10/12/2025 3:54 AM, Mikko wrote:
On 2025-10-11 13:11:19 +0000, olcott said:
On 10/11/2025 4:12 AM, Mikko wrote:
On 2025-10-10 13:56:22 +0000, olcott said:
On 10/10/2025 6:36 AM, dbush wrote:
On 10/10/2025 12:33 AM, olcott wrote:
On 10/9/2025 10:17 PM, dbush wrote:And as Tarski showed, that requires removing a truth predicate.
On 10/9/2025 10:14 PM, olcott wrote:
Self-contradictory expressions only prove that >>>>>>>>>>>>>>>>> they must be excluded from, formal systems of logic. >>>>>>>>>>>>>>>>
He was wrong.
You can say but you can't show.
Kripke proved it
https://files.commons.gc.cuny.edu/wp-content/blogs.dir/1358/ >>>>>>>>>>>>> files/2019/04/Outline-of-a-Theory-of-Truth.pdf
That is a lie. In the above linked text Kripke does not prove that >>>>>>>>>>>> Tarski was wrong about anything, or even says so. Kripke accepts >>>>>>>>>>>> all mentioned results of Tarski as a valid material for further work.
That Kripke didn't mention this, or claim this, and
even disavowed this is not an actual rebuttal.
Yes it is. That Kripke didn't mention that or claim that obviously >>>>>>>>>> entails that Kripke did not prove that and that your claim that he >>>>>>>>>> did prove was false.
My claim is semantically entailed by Kripke's system.
I had to add some details and clarifications.
Above you claimed otherwise.
You have not proven that your claim be semantically entaiiled by >>>>>>>> Kripke's system.
It is,but, if you don't want to read Kripke here
is my self-contained view.
Any system of reasoning that begins with a consistent
system of stipulated truths and only applies the truth
preserving operation of semantic logical entailment to
this finite set of basic facts inherently derives a
truth predicate that works consistently and correctly
for this entire body of knowledge that can be expressed
in language.
No, it does not. A truth predicate must assign a truth value
to every sentence of the language on the system. If a sentence
is not derivable from the "stipulated truths" and its negation
isn't either then one of them must be assigned the value true
and the other false (because otherwise it would not be a predicate). >>>>>> A sentence must be assigned the value true if it can be derived with >>>>>> truth preserving operations from sentences that are assigned the
value true. As Tarski proved, that predicate cannot be defined
with a formula in the language of the system it applies to.
Nope. He just derived the Liar Paradox out
of thin air, no truth preserving operations applied.
That is absolutely false. Tarski did and others nave verified that
he did derive the undefinability from the properties of the natural
numbers with truth preserving operations.
I must be misunderstand you here. Any natural number can be defined?
By the usual meaning of "natural number", yes. By the meaning 'any
element of any model of any theory of natural numbers', no.
1. A theory is a body consisting of a finite number of symbols.
Theories are countable, like other symbolic artifacts: expressions, sentences, programs, ...
2. Each theory about natural numbers contains its own natural
numbers. //Let me make plain a questionable assumption: let's assume that
in each theory of natural numbers, that theory's concept of natural
numbers leads to a countable set of them.
3. Thus, our list of infinite number of theories of natural numbers,
leads us to a structure which is the same as an infinite sequence
of infinite natural number sequences. //Such as sequence is countable//.
The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except as noted in
the sig.
On 08/10/2025 22:20, Kaz Kylheku wrote:
On 2025-10-08, olcott <polcott333@gmail.com> wrote:
For the set of H/P pairs of
decider H and input P:
If H says halts then P loops
If H says loops then P halts
making each H(P) always incorrect.
A better way to say it is like this:
Consider the set S of diagonal decider/input pairs. If <H, P> is any
arbitrarily chosen pair from this set, then one of these three
possibilities is true: H(P) indicates halting, H(P) indicates
non-halting or else H(P) fails to terminate. If H(P) indicates halting,
then P is necessarily non-halting, and vice versa. (If H(P) doesn't
halt, P could be either.) In all three cases, H fails to decide P
correctly, or at all.
That looks like a nonconstructive definition to me, a constraint. I
don't think it's okay.
You've said suppose that the decider doesn't decide P correctly ... then
it doesn't decide - therefore there exists no decider.
I think you have to show also that there exists such a P and derive that there exists no decider and I think you can only do that by constructing
a P.
On 10/19/2025 1:32 PM, Alan Mackenzie wrote:
Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
[ .... ]
If its a natural number, then its in the countable natural numbers. It
can be defined. To combine the successor and predecessor, just make an
n-ary tree. Take this 3-ary one. There are finite functions that can
easily find the parent (root zero aside for a moment...) and the three
children of any node:
__________________________________
0
/|\
/ | \
/ | \
/ | \
/ | \
/ | \
/ | \
1 2 3
/|\ /|\ /|\
/ | \ / | \ / | \
4 5 6 7 8 9 10 11 12
..............................
The parent of root zero seems odd. Its negative mirror children would be >>> -1, -2, -3, but those are not naturals.
..........................
-1 -2 -3
\ | /
\ | /
\ | /
\|/
-0+
/|\
/ | \
/ | \
/ | \
+1 +2 +3
..........................
On and on... ;^)
Now, the possible paths of this tree, are they uncountable?
Yes, they are.
I think so. Still, makes me a bit nervous.
L = go left
M = go middle
R = go right
LMMRLLMRM...
all generated by a TRNG for infinity. That is irrational and uncountable?
However the set of _finite_ paths of the tree is
countably infinite. This was one of the few sensible points that came
from debating with a certain crank on sci.math a few years ago.
WM?
How many do you want?
On 20/10/2025 00:26, Tristan Wibberley wrote:
The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except as noted in
the sig.
On 08/10/2025 22:20, Kaz Kylheku wrote:
On 2025-10-08, olcott <polcott333@gmail.com> wrote:
For the set of H/P pairs of
decider H and input P:
If H says halts then P loops
If H says loops then P halts
making each H(P) always incorrect.
A better way to say it is like this:
Consider the set S of diagonal decider/input pairs. If <H, P> is any
arbitrarily chosen pair from this set, then one of these three
possibilities is true: H(P) indicates halting, H(P) indicates
non-halting or else H(P) fails to terminate. If H(P) indicates halting, >>> then P is necessarily non-halting, and vice versa. (If H(P) doesn't
halt, P could be either.) In all three cases, H fails to decide P
correctly, or at all.
That looks like a nonconstructive definition to me, a constraint. I
don't think it's okay.
You've said suppose that the decider doesn't decide P correctly ... then
it doesn't decide - therefore there exists no decider.
I think you have to show also that there exists such a P and derive that
there exists no decider and I think you can only do that by constructing
a P.
How many do you want?
C:
d(p){ if(h(p,p)) for(;;); return 0; }
main(){ d(d); }
Pascal:
function h(p, q: integer): integer; external;
function d(p: integer): integer;
begin
if h(p, p) <> 0 then
while true do ;
d := 0;
end;
begin
d(Addr(d));
end.
BASIC:
REM Halting Problem Diagonal Case
FUNCTION H(P, Q)
REM mythical halting oracle
END FUNCTION
FUNCTION D(P)
IF H(P, P) <> 0 THEN
DO WHILE 1
LOOP
END IF
D = 0
END FUNCTION
D = D(VARPTR(D))
Common Lithp:
(defun d(p)(if(h p p)(loop)0))
(d #'d)
Python:
def h(p,q):pass
def d(p):
if h(p,p):
while 1: pass
return 0
d(d)
My thanks to Hal the Polyglot for helping with the translations.
On 20/10/2025 00:26, Tristan Wibberley wrote:
The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except as noted in
the sig.
On 08/10/2025 22:20, Kaz Kylheku wrote:
On 2025-10-08, olcott <polcott333@gmail.com> wrote:
For the set of H/P pairs of
decider H and input P:
If H says halts then P loops
If H says loops then P halts
making each H(P) always incorrect.
A better way to say it is like this:
Consider the set S of diagonal decider/input pairs. If <H, P> is any
arbitrarily chosen pair from this set, then one of these three
possibilities is true: H(P) indicates halting, H(P) indicates
non-halting or else H(P) fails to terminate. If H(P) indicates halting, >>> then P is necessarily non-halting, and vice versa. (If H(P) doesn't
halt, P could be either.) In all three cases, H fails to decide P
correctly, or at all.
That looks like a nonconstructive definition to me, a constraint. I
don't think it's okay.
You've said suppose that the decider doesn't decide P correctly ... then
it doesn't decide - therefore there exists no decider.
I think you have to show also that there exists such a P and derive that
there exists no decider and I think you can only do that by constructing
a P.
How many do you want?
C:
d(p){ if(h(p,p)) for(;;); return 0; }
main(){ d(d); }
Pascal:
function h(p, q: integer): integer; external;
function d(p: integer): integer;
begin
if h(p, p) <> 0 then
while true do ;
d := 0;
end;
begin
d(Addr(d));
end.
BASIC:
REM Halting Problem Diagonal Case
FUNCTION H(P, Q)
REM mythical halting oracle
END FUNCTION
FUNCTION D(P)
IF H(P, P) <> 0 THEN
DO WHILE 1
LOOP
END IF
D = 0
END FUNCTION
D = D(VARPTR(D))
Common Lithp:
(defun d(p)(if(h p p)(loop)0))
(d #'d)
Python:
def h(p,q):pass
def d(p):
if h(p,p):
while 1: pass
return 0
d(d)
My thanks to Hal the Polyglot for helping with the translations.
Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
On 10/19/2025 1:32 PM, Alan Mackenzie wrote:
Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
[ .... ]
If its a natural number, then its in the countable natural numbers. It >>>> can be defined. To combine the successor and predecessor, just make an >>>> n-ary tree. Take this 3-ary one. There are finite functions that can
easily find the parent (root zero aside for a moment...) and the three >>>> children of any node:
__________________________________
0
/|\
/ | \
/ | \
/ | \
/ | \
/ | \
/ | \
1 2 3
/|\ /|\ /|\
/ | \ / | \ / | \
4 5 6 7 8 9 10 11 12
..............................
The parent of root zero seems odd. Its negative mirror children would be >>>> -1, -2, -3, but those are not naturals.
..........................
-1 -2 -3
\ | /
\ | /
\ | /
\|/
-0+
/|\
/ | \
/ | \
/ | \
+1 +2 +3
..........................
On and on... ;^)
Now, the possible paths of this tree, are they uncountable?
Yes, they are.
I think so. Still, makes me a bit nervous.
L = go left
M = go middle
R = go right
LMMRLLMRM...
all generated by a TRNG for infinity. That is irrational and uncountable?
Not sure what you mean by irrational, but definitely uncountable, yes.
To see this, imagine you try to count the paths "left to right". The
first path will be LLLLLLLLL.... What about the second? At some point
in LLLLLLLLL... you've got to put in an M, giving something like LLLLLLMLLLLL.... But that's not the path immediately after path 1.
There is no path immediately after path 1; it just doesn't work.
You could, of course, also prove the uncountability with a standard
Cantor diagonal proof.
However the set of _finite_ paths of the tree is
countably infinite. This was one of the few sensible points that came
from debating with a certain crank on sci.math a few years ago.
WM?
Indeed, yes. ;-)
[...]
On 10/19/2025 5:38 AM, Mikko wrote:
On 2025-10-18 11:09:49 +0000, olcott said:
On 10/18/2025 5:02 AM, Mikko wrote:
On 2025-10-09 17:01:09 +0000, olcott said:
On 10/9/2025 4:41 AM, Mikko wrote:
On 2025-10-09 03:54:13 +0000, olcott said:
On 10/8/2025 4:40 AM, Mikko wrote:
On 2025-10-07 15:05:07 +0000, olcott said:That a halt decider gets fooled by a simple input
When we ask polar yes/no questions that have no
correct yes/no answer these questions themselves
are incorrect.
Whether we want to call them "incorrect" or not is irrelevant. One >>>>>>>> important thing about them is that in natural languages there are >>>>>>>> such questions, which can be useful to know. Such questions are >>>>>>>> also possible in some interpretations of some formal lanuguages. >>>>>>>> Therefore, when a formal lanugage is designed one may want to make >>>>>>>> such questions possible or impossible in the intended interpretation. >>>>>>>
that calls itself means that the requirements are
incorrect.
What gets fooled is not a halt deciders. Requirements are correct
as they specify about every Turing machine whether is is a halt
decider. The requirements need not serve any other purpose.
See my new post.
[Halting problem proof converted to Liar Paradox ---
2004 post converted to C]
Nothing there contradicts what I said above, although many other
errors have been found in the discussion following that post.
That people get confused never has been my mistake.
If a large number of people gets confused about the same thing then
that mean a lack of clarity in presentation.
Most probably. There is also the factor of bias to
want to prove me wrong at a much higher priority
than understanding what I say.
On 2025-10-19 15:36:52 +0000, olcott said:
On 10/19/2025 5:38 AM, Mikko wrote:
On 2025-10-18 11:09:49 +0000, olcott said:
On 10/18/2025 5:02 AM, Mikko wrote:
On 2025-10-09 17:01:09 +0000, olcott said:
On 10/9/2025 4:41 AM, Mikko wrote:
On 2025-10-09 03:54:13 +0000, olcott said:
On 10/8/2025 4:40 AM, Mikko wrote:
On 2025-10-07 15:05:07 +0000, olcott said:
When we ask polar yes/no questions that have no
correct yes/no answer these questions themselves
are incorrect.
Whether we want to call them "incorrect" or not is irrelevant. One >>>>>>>>> important thing about them is that in natural languages there are >>>>>>>>> such questions, which can be useful to know. Such questions are >>>>>>>>> also possible in some interpretations of some formal lanuguages. >>>>>>>>> Therefore, when a formal lanugage is designed one may want to make >>>>>>>>> such questions possible or impossible in the intended
interpretation.
That a halt decider gets fooled by a simple input
that calls itself means that the requirements are
incorrect.
What gets fooled is not a halt deciders. Requirements are correct >>>>>>> as they specify about every Turing machine whether is is a halt
decider. The requirements need not serve any other purpose.
See my new post.
[Halting problem proof converted to Liar Paradox ---
2004 post converted to C]
Nothing there contradicts what I said above, although many other
errors have been found in the discussion following that post.
That people get confused never has been my mistake.
If a large number of people gets confused about the same thing then
that mean a lack of clarity in presentation.
Most probably. There is also the factor of bias to
want to prove me wrong at a much higher priority
than understanding what I say.
I guess the reason why they (or at least some of them) want to prove
you wrong is that you have said several times something that can be understood and is wrong.
Though in some sense meaningless non-sense
is wrong, too. And even sensible discussion about topics urelated to
the theory of computation.
On 10/21/2025 4:50 AM, Mikko wrote:
On 2025-10-19 15:36:52 +0000, olcott said:
On 10/19/2025 5:38 AM, Mikko wrote:
On 2025-10-18 11:09:49 +0000, olcott said:
On 10/18/2025 5:02 AM, Mikko wrote:
On 2025-10-09 17:01:09 +0000, olcott said:
On 10/9/2025 4:41 AM, Mikko wrote:
On 2025-10-09 03:54:13 +0000, olcott said:
On 10/8/2025 4:40 AM, Mikko wrote:
On 2025-10-07 15:05:07 +0000, olcott said:
When we ask polar yes/no questions that have no
correct yes/no answer these questions themselves
are incorrect.
Whether we want to call them "incorrect" or not is irrelevant. One >>>>>>>>>> important thing about them is that in natural languages there are >>>>>>>>>> such questions, which can be useful to know. Such questions are >>>>>>>>>> also possible in some interpretations of some formal lanuguages. >>>>>>>>>> Therefore, when a formal lanugage is designed one may want to make >>>>>>>>>> such questions possible or impossible in the intended interpretation.
That a halt decider gets fooled by a simple input
that calls itself means that the requirements are
incorrect.
What gets fooled is not a halt deciders. Requirements are correct >>>>>>>> as they specify about every Turing machine whether is is a halt >>>>>>>> decider. The requirements need not serve any other purpose.
See my new post.
[Halting problem proof converted to Liar Paradox ---
2004 post converted to C]
Nothing there contradicts what I said above, although many other
errors have been found in the discussion following that post.
That people get confused never has been my mistake.
If a large number of people gets confused about the same thing then
that mean a lack of clarity in presentation.
Most probably. There is also the factor of bias to
want to prove me wrong at a much higher priority
than understanding what I say.
I guess the reason why they (or at least some of them) want to prove
you wrong is that you have said several times something that can be
understood and is wrong.
iff (if and only if) you never understand my rebuttal
and or make sure that you never pay enough attention
to my rebuttal because you are to sure that I must be
wrong.
On 2025-10-21 23:10:33 +0000, olcott said:
On 10/21/2025 4:50 AM, Mikko wrote:
On 2025-10-19 15:36:52 +0000, olcott said:
On 10/19/2025 5:38 AM, Mikko wrote:
On 2025-10-18 11:09:49 +0000, olcott said:
On 10/18/2025 5:02 AM, Mikko wrote:
On 2025-10-09 17:01:09 +0000, olcott said:
On 10/9/2025 4:41 AM, Mikko wrote:
On 2025-10-09 03:54:13 +0000, olcott said:
On 10/8/2025 4:40 AM, Mikko wrote:
On 2025-10-07 15:05:07 +0000, olcott said:
When we ask polar yes/no questions that have no
correct yes/no answer these questions themselves
are incorrect.
Whether we want to call them "incorrect" or not is
irrelevant. One
important thing about them is that in natural languages there >>>>>>>>>>> are
such questions, which can be useful to know. Such questions are >>>>>>>>>>> also possible in some interpretations of some formal lanuguages. >>>>>>>>>>> Therefore, when a formal lanugage is designed one may want to >>>>>>>>>>> make
such questions possible or impossible in the intended
interpretation.
That a halt decider gets fooled by a simple input
that calls itself means that the requirements are
incorrect.
What gets fooled is not a halt deciders. Requirements are correct >>>>>>>>> as they specify about every Turing machine whether is is a halt >>>>>>>>> decider. The requirements need not serve any other purpose.
See my new post.
[Halting problem proof converted to Liar Paradox ---
2004 post converted to C]
Nothing there contradicts what I said above, although many other >>>>>>> errors have been found in the discussion following that post.
That people get confused never has been my mistake.
If a large number of people gets confused about the same thing then
that mean a lack of clarity in presentation.
Most probably. There is also the factor of bias to
want to prove me wrong at a much higher priority
than understanding what I say.
I guess the reason why they (or at least some of them) want to prove
you wrong is that you have said several times something that can be
understood and is wrong.
iff (if and only if) you never understand my rebuttal
and or make sure that you never pay enough attention
to my rebuttal because you are to sure that I must be
wrong.
I don't believe anything you have written wnywhere reveals anything
about the motives of other people.
On 10/22/2025 3:58 AM, Mikko wrote:That's because DD is NOT correctly simulated by HHH because HHH aborts.
On 2025-10-21 23:10:33 +0000, olcott said:
On 10/21/2025 4:50 AM, Mikko wrote:
On 2025-10-19 15:36:52 +0000, olcott said:
On 10/19/2025 5:38 AM, Mikko wrote:
On 2025-10-18 11:09:49 +0000, olcott said:
On 10/18/2025 5:02 AM, Mikko wrote:
On 2025-10-09 17:01:09 +0000, olcott said:
On 10/9/2025 4:41 AM, Mikko wrote:
On 2025-10-09 03:54:13 +0000, olcott said:See my new post.
On 10/8/2025 4:40 AM, Mikko wrote:
On 2025-10-07 15:05:07 +0000, olcott said:
When we ask polar yes/no questions that have no
correct yes/no answer these questions themselves
are incorrect.
Whether we want to call them "incorrect" or not is
irrelevant. One
important thing about them is that in natural languages >>>>>>>>>>>> there are
such questions, which can be useful to know. Such questions are >>>>>>>>>>>> also possible in some interpretations of some formal
lanuguages.
Therefore, when a formal lanugage is designed one may want >>>>>>>>>>>> to make
such questions possible or impossible in the intended >>>>>>>>>>>> interpretation.
That a halt decider gets fooled by a simple input
that calls itself means that the requirements are
incorrect.
What gets fooled is not a halt deciders. Requirements are correct >>>>>>>>>> as they specify about every Turing machine whether is is a halt >>>>>>>>>> decider. The requirements need not serve any other purpose. >>>>>>>>>
[Halting problem proof converted to Liar Paradox ---
2004 post converted to C]
Nothing there contradicts what I said above, although many other >>>>>>>> errors have been found in the discussion following that post.
That people get confused never has been my mistake.
If a large number of people gets confused about the same thing then >>>>>> that mean a lack of clarity in presentation.
Most probably. There is also the factor of bias to
want to prove me wrong at a much higher priority
than understanding what I say.
I guess the reason why they (or at least some of them) want to prove
you wrong is that you have said several times something that can be
understood and is wrong.
iff (if and only if) you never understand my rebuttal
and or make sure that you never pay enough attention
to my rebuttal because you are to sure that I must be
wrong.
I don't believe anything you have written wnywhere reveals anything
about the motives of other people.
That they can't even do a simple trace of DD
correctly simulated by HHH according to the
semantics of the C programming language
On 10/22/2025 8:28 AM, olcott wrote:
On 10/22/2025 3:58 AM, Mikko wrote:That's because DD is NOT correctly simulated by HHH because HHH aborts.
On 2025-10-21 23:10:33 +0000, olcott said:
On 10/21/2025 4:50 AM, Mikko wrote:
On 2025-10-19 15:36:52 +0000, olcott said:
On 10/19/2025 5:38 AM, Mikko wrote:
On 2025-10-18 11:09:49 +0000, olcott said:
On 10/18/2025 5:02 AM, Mikko wrote:
On 2025-10-09 17:01:09 +0000, olcott said:That people get confused never has been my mistake.
On 10/9/2025 4:41 AM, Mikko wrote:
On 2025-10-09 03:54:13 +0000, olcott said:See my new post.
On 10/8/2025 4:40 AM, Mikko wrote:
On 2025-10-07 15:05:07 +0000, olcott said:
When we ask polar yes/no questions that have no
correct yes/no answer these questions themselves
are incorrect.
Whether we want to call them "incorrect" or not is
irrelevant. One
important thing about them is that in natural languages >>>>>>>>>>>>> there are
such questions, which can be useful to know. Such questions >>>>>>>>>>>>> are
also possible in some interpretations of some formal >>>>>>>>>>>>> lanuguages.
Therefore, when a formal lanugage is designed one may want >>>>>>>>>>>>> to make
such questions possible or impossible in the intended >>>>>>>>>>>>> interpretation.
That a halt decider gets fooled by a simple input
that calls itself means that the requirements are
incorrect.
What gets fooled is not a halt deciders. Requirements are >>>>>>>>>>> correct
as they specify about every Turing machine whether is is a halt >>>>>>>>>>> decider. The requirements need not serve any other purpose. >>>>>>>>>>
[Halting problem proof converted to Liar Paradox ---
2004 post converted to C]
Nothing there contradicts what I said above, although many other >>>>>>>>> errors have been found in the discussion following that post. >>>>>>>>
If a large number of people gets confused about the same thing then >>>>>>> that mean a lack of clarity in presentation.
Most probably. There is also the factor of bias to
want to prove me wrong at a much higher priority
than understanding what I say.
I guess the reason why they (or at least some of them) want to prove >>>>> you wrong is that you have said several times something that can be
understood and is wrong.
iff (if and only if) you never understand my rebuttal
and or make sure that you never pay enough attention
to my rebuttal because you are to sure that I must be
wrong.
I don't believe anything you have written wnywhere reveals anything
about the motives of other people.
That they can't even do a simple trace of DD
correctly simulated by HHH according to the
semantics of the C programming language
On 10/22/2025 7:51 AM, dbush wrote:
On 10/22/2025 8:28 AM, olcott wrote:
On 10/22/2025 3:58 AM, Mikko wrote:That's because DD is NOT correctly simulated by HHH because HHH aborts.
On 2025-10-21 23:10:33 +0000, olcott said:
On 10/21/2025 4:50 AM, Mikko wrote:
On 2025-10-19 15:36:52 +0000, olcott said:
On 10/19/2025 5:38 AM, Mikko wrote:
On 2025-10-18 11:09:49 +0000, olcott said:
On 10/18/2025 5:02 AM, Mikko wrote:
On 2025-10-09 17:01:09 +0000, olcott said:That people get confused never has been my mistake.
On 10/9/2025 4:41 AM, Mikko wrote:
On 2025-10-09 03:54:13 +0000, olcott said:See my new post.
On 10/8/2025 4:40 AM, Mikko wrote:
On 2025-10-07 15:05:07 +0000, olcott said:
When we ask polar yes/no questions that have no
correct yes/no answer these questions themselves >>>>>>>>>>>>>>> are incorrect.
Whether we want to call them "incorrect" or not is >>>>>>>>>>>>>> irrelevant. One
important thing about them is that in natural languages >>>>>>>>>>>>>> there are
such questions, which can be useful to know. Such >>>>>>>>>>>>>> questions are
also possible in some interpretations of some formal >>>>>>>>>>>>>> lanuguages.
Therefore, when a formal lanugage is designed one may want >>>>>>>>>>>>>> to make
such questions possible or impossible in the intended >>>>>>>>>>>>>> interpretation.
That a halt decider gets fooled by a simple input
that calls itself means that the requirements are
incorrect.
What gets fooled is not a halt deciders. Requirements are >>>>>>>>>>>> correct
as they specify about every Turing machine whether is is a halt >>>>>>>>>>>> decider. The requirements need not serve any other purpose. >>>>>>>>>>>
[Halting problem proof converted to Liar Paradox ---
2004 post converted to C]
Nothing there contradicts what I said above, although many other >>>>>>>>>> errors have been found in the discussion following that post. >>>>>>>>>
If a large number of people gets confused about the same thing then >>>>>>>> that mean a lack of clarity in presentation.
Most probably. There is also the factor of bias to
want to prove me wrong at a much higher priority
than understanding what I say.
I guess the reason why they (or at least some of them) want to prove >>>>>> you wrong is that you have said several times something that can be >>>>>> understood and is wrong.
iff (if and only if) you never understand my rebuttal
and or make sure that you never pay enough attention
to my rebuttal because you are to sure that I must be
wrong.
I don't believe anything you have written wnywhere reveals anything
about the motives of other people.
That they can't even do a simple trace of DD
correctly simulated by HHH according to the
semantics of the C programming language
I did not say a complete simulation.
On 10/22/2025 7:51 AM, dbush wrote:Who did it wrong?
On 10/22/2025 8:28 AM, olcott wrote:
That they can't even do a simple trace of DD correctly simulated by
HHH according to the semantics of the C programming language
A partial simulation is incorrect if the program hasn’t halted yet.That's because DD is NOT correctly simulated by HHH because HHH aborts.I did not say a complete simulation.
Am Wed, 22 Oct 2025 07:55:49 -0500 schrieb olcott:
On 10/22/2025 7:51 AM, dbush wrote:
On 10/22/2025 8:28 AM, olcott wrote:
Who did it wrong?That they can't even do a simple trace of DD correctly simulated by
HHH according to the semantics of the C programming language
A partial simulation is incorrect if the program hasn’t halted yet.That's because DD is NOT correctly simulated by HHH because HHH aborts.I did not say a complete simulation.
On 10/22/2025 8:55 AM, olcott wrote:
On 10/22/2025 7:51 AM, dbush wrote:
On 10/22/2025 8:28 AM, olcott wrote:
On 10/22/2025 3:58 AM, Mikko wrote:That's because DD is NOT correctly simulated by HHH because HHH aborts.
On 2025-10-21 23:10:33 +0000, olcott said:
On 10/21/2025 4:50 AM, Mikko wrote:
On 2025-10-19 15:36:52 +0000, olcott said:
On 10/19/2025 5:38 AM, Mikko wrote:
On 2025-10-18 11:09:49 +0000, olcott said:
On 10/18/2025 5:02 AM, Mikko wrote:
On 2025-10-09 17:01:09 +0000, olcott said:That people get confused never has been my mistake.
On 10/9/2025 4:41 AM, Mikko wrote:
On 2025-10-09 03:54:13 +0000, olcott said:See my new post.
On 10/8/2025 4:40 AM, Mikko wrote:
On 2025-10-07 15:05:07 +0000, olcott said:
When we ask polar yes/no questions that have no >>>>>>>>>>>>>>>> correct yes/no answer these questions themselves >>>>>>>>>>>>>>>> are incorrect.
Whether we want to call them "incorrect" or not is >>>>>>>>>>>>>>> irrelevant. One
important thing about them is that in natural languages >>>>>>>>>>>>>>> there are
such questions, which can be useful to know. Such >>>>>>>>>>>>>>> questions are
also possible in some interpretations of some formal >>>>>>>>>>>>>>> lanuguages.
Therefore, when a formal lanugage is designed one may >>>>>>>>>>>>>>> want to make
such questions possible or impossible in the intended >>>>>>>>>>>>>>> interpretation.
That a halt decider gets fooled by a simple input
that calls itself means that the requirements are
incorrect.
What gets fooled is not a halt deciders. Requirements are >>>>>>>>>>>>> correct
as they specify about every Turing machine whether is is a >>>>>>>>>>>>> halt
decider. The requirements need not serve any other purpose. >>>>>>>>>>>>
[Halting problem proof converted to Liar Paradox ---
2004 post converted to C]
Nothing there contradicts what I said above, although many other >>>>>>>>>>> errors have been found in the discussion following that post. >>>>>>>>>>
If a large number of people gets confused about the same thing >>>>>>>>> then
that mean a lack of clarity in presentation.
Most probably. There is also the factor of bias to
want to prove me wrong at a much higher priority
than understanding what I say.
I guess the reason why they (or at least some of them) want to prove >>>>>>> you wrong is that you have said several times something that can be >>>>>>> understood and is wrong.
iff (if and only if) you never understand my rebuttal
and or make sure that you never pay enough attention
to my rebuttal because you are to sure that I must be
wrong.
I don't believe anything you have written wnywhere reveals anything
about the motives of other people.
That they can't even do a simple trace of DD
correctly simulated by HHH according to the
semantics of the C programming language
I did not say a complete simulation.
You implicitly said so when you said "correctly simulated".
If that's not what you meant, then you just admitted that DD is NOT correctly simulated by HH.--
On 10/22/2025 8:02 AM, dbush wrote:
On 10/22/2025 8:55 AM, olcott wrote:
On 10/22/2025 7:51 AM, dbush wrote:
On 10/22/2025 8:28 AM, olcott wrote:I did not say a complete simulation.
That they can't even do a simple trace of DDThat's because DD is NOT correctly simulated by HHH because HHH aborts. >>>
correctly simulated by HHH according to the
semantics of the C programming language
You implicitly said so when you said "correctly simulated".
That always make sure to exclude a complete
simulation for non-terminating inputs.
inputs. inputs. inputs. inputs. inputs. inputs.
Not any other damn thing in the universe.
If that's not what you meant, then you just admitted that DD is NOT
correctly simulated by HH.
On 10/22/2025 8:38 AM, joes wrote:
Am Wed, 22 Oct 2025 07:55:49 -0500 schrieb olcott:
On 10/22/2025 7:51 AM, dbush wrote:Who did it wrong?
On 10/22/2025 8:28 AM, olcott wrote:
That they can't even do a simple trace of DD correctly simulated by
HHH according to the semantics of the C programming language
No one ever made any attempt to do this at all.
A partial simulation is incorrect if the program hasn’t halted yet.That's because DD is NOT correctly simulated by HHH because HHH aborts. >>> I did not say a complete simulation.
No one ever tried to simulate five steps.
On 10/22/2025 3:58 AM, Mikko wrote:
On 2025-10-21 23:10:33 +0000, olcott said:
On 10/21/2025 4:50 AM, Mikko wrote:
On 2025-10-19 15:36:52 +0000, olcott said:
On 10/19/2025 5:38 AM, Mikko wrote:
On 2025-10-18 11:09:49 +0000, olcott said:
On 10/18/2025 5:02 AM, Mikko wrote:
On 2025-10-09 17:01:09 +0000, olcott said:
On 10/9/2025 4:41 AM, Mikko wrote:
On 2025-10-09 03:54:13 +0000, olcott said:See my new post.
On 10/8/2025 4:40 AM, Mikko wrote:
On 2025-10-07 15:05:07 +0000, olcott said:
When we ask polar yes/no questions that have no
correct yes/no answer these questions themselves
are incorrect.
Whether we want to call them "incorrect" or not is irrelevant. One >>>>>>>>>>>> important thing about them is that in natural languages there are >>>>>>>>>>>> such questions, which can be useful to know. Such questions are >>>>>>>>>>>> also possible in some interpretations of some formal lanuguages. >>>>>>>>>>>> Therefore, when a formal lanugage is designed one may want to make >>>>>>>>>>>> such questions possible or impossible in the intended interpretation.
That a halt decider gets fooled by a simple input
that calls itself means that the requirements are
incorrect.
What gets fooled is not a halt deciders. Requirements are correct >>>>>>>>>> as they specify about every Turing machine whether is is a halt >>>>>>>>>> decider. The requirements need not serve any other purpose. >>>>>>>>>
[Halting problem proof converted to Liar Paradox ---
2004 post converted to C]
Nothing there contradicts what I said above, although many other >>>>>>>> errors have been found in the discussion following that post.
That people get confused never has been my mistake.
If a large number of people gets confused about the same thing then >>>>>> that mean a lack of clarity in presentation.
Most probably. There is also the factor of bias to
want to prove me wrong at a much higher priority
than understanding what I say.
I guess the reason why they (or at least some of them) want to prove
you wrong is that you have said several times something that can be
understood and is wrong.
iff (if and only if) you never understand my rebuttal
and or make sure that you never pay enough attention
to my rebuttal because you are to sure that I must be
wrong.
I don't believe anything you have written wnywhere reveals anything
about the motives of other people.
That they can't even do a simple trace of DD
correctly simulated by HHH according to the
semantics of the C programming language when
they have been in the C group for decades seems
to indicate that they are flat out liars.
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