On 7/1/2026 1:46 AM, Mikko wrote:
On 30/06/2026 17:37, olcott wrote:
On 6/30/2026 3:48 AM, Mikko wrote:
On 29/06/2026 17:00, olcott wrote:
On 6/29/2026 8:23 AM, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:Only people having actual psychosis would conclude
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
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:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>> language statement:
On 6/27/2026 7:22 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 5:52 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>1) P ∧ ¬P // Premise
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PAI (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> valid principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ψ is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> implication — given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derivation of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of statement where eachstatement either >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is a premis or follows from one or more >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is its problem. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>> operations, when a contradiction is given as >>>>>>>>>>>>>>>>>>>>>>>>>> true, any statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration >>>>>>>>>>>>>>>>>>>>>>>>>> of *why* a formal system whose axioms lead to >>>>>>>>>>>>>>>>>>>>>>>>>> a contradiction is useless. >>>>>>>>>>>>>>>>>>>>>>>>>>
The only reason someone would want to get rid >>>>>>>>>>>>>>>>>>>>>>>>>> of the principle of explosion is to be able to >>>>>>>>>>>>>>>>>>>>>>>>>> use a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning. >>>>>>>>>>>>>>>>>>>>>>>>>
If you get rid of the principle of explosion, >>>>>>>>>>>>>>>>>>>>>>>> the law of non- contradiction goes away as it >>>>>>>>>>>>>>>>>>>>>>>> looses its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>>>
-------------------------------------- >>>>>>>>>>>>>>>>>>>> At least one of the following statements is true: >>>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>>> - <X>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At >>>>>>>>>>>>>>>>>>>> least one of the following statements is true" is >>>>>>>>>>>>>>>>>>>> false.
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then.
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>
--------------------------------------
Where <X> is any natural language statement, does >>>>>>>>>>>>>>>>>> there exist a statement X such that the condition "At >>>>>>>>>>>>>>>>>> least one of the following statements is true" is false? >>>>>>>>>>>>>>>>>>
Where X is "What time is it?"
Is the statement "Earth is the third planet from the >>>>>>>>>>>>>>>> sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so >>>>>>>>>>>>>> it can't be used in logic. I didn't think I had to make >>>>>>>>>>>>>> that explicit.
However, let's go with it anyway because it still >>>>>>>>>>>>>> illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>>> true?
On second though, let's back up as that might confuse you. >>>>>>>>>>>>>
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.
That you did so well on the other things
so I will not block you.
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.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition, >>>>>>>>> sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different >>>>>>>> rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting
with the precondition that a contradiction has been proven, as you >>>>>> have admitted above on the record.
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
How do you know that somewhere the Moon is made from green cheese and
the Moon is not made from green cheese and Donald Trump is not the one >>>> and only Lord and Savior Jesus Christ?
Counter-factual
For logic the distinction between factual and counter-factual is not
as imortant as the distinction between consistent and contradictory.
Counter-factual may indicate a psychotic break from reality.
On 7/1/2026 1:50 AM, Mikko wrote:
On 30/06/2026 16:45, olcott wrote:
On 6/30/2026 2:55 AM, Mikko wrote:
On 29/06/2026 16:23, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
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:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural >>>>>>>>>>>>>>>>>>> language statement:
On 6/27/2026 7:22 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 5:52 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>1) P ∧ ¬P // Premise
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PAI (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> — given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of statement where eachstatement either >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is a premis or follows from one or more >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is its problem.
So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>> operations, when a contradiction is given as >>>>>>>>>>>>>>>>>>>>>>>>> true, any statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration >>>>>>>>>>>>>>>>>>>>>>>>> of *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid >>>>>>>>>>>>>>>>>>>>>>>>> of the principle of explosion is to be able to >>>>>>>>>>>>>>>>>>>>>>>>> use a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the >>>>>>>>>>>>>>>>>>>>>>> law of non- contradiction goes away as it looses >>>>>>>>>>>>>>>>>>>>>>> its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>> - <X>
--------------------------------------
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At >>>>>>>>>>>>>>>>>>> least one of the following statements is true" is false. >>>>>>>>>>>>>>>>>>>
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then.
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>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>>>>>> exist a statement X such that the condition "At least >>>>>>>>>>>>>>>>> one of the following statements is true" is false? >>>>>>>>>>>>>>>>>
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>>>> true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so >>>>>>>>>>>>> it can't be used in logic. I didn't think I had to make >>>>>>>>>>>>> that explicit.
However, let's go with it anyway because it still
illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>> true?
On second though, let's back up as that might confuse you. >>>>>>>>>>>>
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.
That you did so well on the other things
so I will not block you.
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.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different
rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
One can construct a system where a truth-preserving operation is not
valid, and must if one wants to construct a paraconsistent system,
where some but not every sentence can be both PTS-true and PTS-false.
Current semantic entailment is the only inference step allowed.
Every truth-prserving transformation is a correct semantic entailment.
In particular, disjunction introduction is.
That is counter-factual. POE is misconstrued as truth preserving.
On 7/1/2026 1:53 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>
statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is >>>>>>>> off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
Relevance Logic
https://plato.stanford.edu/entries/logic-relevance/
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies
of a false premise, which already is a break from reality even
when no consequence is inferred.
Only because semantics is ignored.
A break from reality is a break from reality, no matter whether
the semantics is ignored or considered. Though if there is no
semantics, even any ignored one, there is no connection to
reality to break.
Ignoring semantics is always a break from reality.
On 7/1/2026 2:32 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere
(as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>>> eachstatement either is a premis or follows from one or more >>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>
statement:
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed is >>>>>>>> off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
If the intent was to include that in the denotation you failed
to say something important.
Parry’s logic of Analytic Implication
and Relevance logic are two sensible systems
that get rid of the Principle of Explosion.
On 01/07/2026 18:01, olcott wrote:
On 7/1/2026 1:46 AM, Mikko wrote:
On 30/06/2026 17:37, olcott wrote:
On 6/30/2026 3:48 AM, Mikko wrote:
On 29/06/2026 17:00, olcott wrote:
On 6/29/2026 8:23 AM, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:Only people having actual psychosis would conclude
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
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:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:30 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 7:22 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 5:52 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>> language statement:1) P ∧ ¬P // PremiseExplain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PAI (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> valid principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ψ is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> implication — given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derivation of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a set of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> another sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> out of nowhere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sequence of statement where >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eachstatement either is a premis or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is its problem. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Rejected, as you not liking the result >>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't make it invalid. >>>>>>>>>>>>>>>>>>>>>>>>>>>
Through a series of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>> operations, when a contradiction is given as >>>>>>>>>>>>>>>>>>>>>>>>>>> true, any statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration >>>>>>>>>>>>>>>>>>>>>>>>>>> of *why* a formal system whose axioms lead to >>>>>>>>>>>>>>>>>>>>>>>>>>> a contradiction is useless. >>>>>>>>>>>>>>>>>>>>>>>>>>>
The only reason someone would want to get rid >>>>>>>>>>>>>>>>>>>>>>>>>>> of the principle of explosion is to be able >>>>>>>>>>>>>>>>>>>>>>>>>>> to use a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of >>>>>>>>>>>>>>>>>>>>>>>>>> explosion
it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning. >>>>>>>>>>>>>>>>>>>>>>>>>>
If you get rid of the principle of explosion, >>>>>>>>>>>>>>>>>>>>>>>>> the law of non- contradiction goes away as it >>>>>>>>>>>>>>>>>>>>>>>>> looses its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth- >>>>>>>>>>>>>>>>>>>>>>> preserving operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>>>>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>> At least one of the following statements is true: >>>>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>>>> - <X>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>>
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At >>>>>>>>>>>>>>>>>>>>> least one of the following statements is true" is >>>>>>>>>>>>>>>>>>>>> false.
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then. >>>>>>>>>>>>>>>>>>>
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>
--------------------------------------
Where <X> is any natural language statement, does >>>>>>>>>>>>>>>>>>> there exist a statement X such that the condition "At >>>>>>>>>>>>>>>>>>> least one of the following statements is true" is false? >>>>>>>>>>>>>>>>>>>
Where X is "What time is it?"
Is the statement "Earth is the third planet from the >>>>>>>>>>>>>>>>> sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, >>>>>>>>>>>>>>> so it can't be used in logic. I didn't think I had to >>>>>>>>>>>>>>> make that explicit.
However, let's go with it anyway because it still >>>>>>>>>>>>>>> illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>>>> true?
On second though, let's back up as that might confuse you. >>>>>>>>>>>>>>
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.
That you did so well on the other things
so I will not block you.
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.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition, >>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>> formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different >>>>>>>>> rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting >>>>>>> with the precondition that a contradiction has been proven, as
you have admitted above on the record.
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
How do you know that somewhere the Moon is made from green cheese and >>>>> the Moon is not made from green cheese and Donald Trump is not the one >>>>> and only Lord and Savior Jesus Christ?
Counter-factual
For logic the distinction between factual and counter-factual is not
as imortant as the distinction between consistent and contradictory.
Counter-factual may indicate a psychotic break from reality.
No, it does not. It is much more common than anything psychotic.
Besudes, any mention of anything psychotic is off-topic in these
groups.
On 01/07/2026 18:06, olcott wrote:
On 7/1/2026 1:53 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere >>>>>>>>>>>>>> (as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>>>> eachstatement either is a premis or follows from one or >>>>>>>>>>>>> more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
Relevance Logic
https://plato.stanford.edu/entries/logic-relevance/
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies
of a false premise, which already is a break from reality even
when no consequence is inferred.
Only because semantics is ignored.
A break from reality is a break from reality, no matter whether
the semantics is ignored or considered. Though if there is no
semantics, even any ignored one, there is no connection to
reality to break.
Ignoring semantics is always a break from reality.
So is any semantics other than real world semantics.
On 01/07/2026 18:25, olcott wrote:
On 7/1/2026 2:32 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when
trying to find out what is deduced from a set of
premises that you cannot pop in another sentence
from out of nowhere and get a correct conclusion.
By popping in another sentence from out of nowhere >>>>>>>>>>>>>> (as it shows above) the principle of explosion is
derived.
The usual meaning of proof is a sequence of statement where >>>>>>>>>>>>> eachstatement either is a premis or follows from one or >>>>>>>>>>>>> more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable.
Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
If the intent was to include that in the denotation you failed
to say something important.
Parry’s logic of Analytic Implication
and Relevance logic are two sensible systems
that get rid of the Principle of Explosion.
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
On 7/2/2026 1:21 AM, Mikko wrote:
On 01/07/2026 18:01, olcott wrote:
On 7/1/2026 1:46 AM, Mikko wrote:
On 30/06/2026 17:37, olcott wrote:
On 6/30/2026 3:48 AM, Mikko wrote:
On 29/06/2026 17:00, olcott wrote:
On 6/29/2026 8:23 AM, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:Only people having actual psychosis would conclude
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
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:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:30 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 7:22 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 5:52 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>>> language statement:1) P ∧ ¬P // PremiseExplain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Except with Disjunction introduction, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is its problem. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I figured >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knew that when >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> trying to find out what is deduced >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a set of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> another sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>A simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PAI (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> valid principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> where ψ is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> implication — given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derivation of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> out of nowhere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sequence of statement where >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eachstatement either is a premis or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Rejected, as you not liking the result >>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't make it invalid. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Through a series of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>> operations, when a contradiction is given as >>>>>>>>>>>>>>>>>>>>>>>>>>>> true, any statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a >>>>>>>>>>>>>>>>>>>>>>>>>>>> demonstration of *why* a formal system whose >>>>>>>>>>>>>>>>>>>>>>>>>>>> axioms lead to a contradiction is useless. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
The only reason someone would want to get >>>>>>>>>>>>>>>>>>>>>>>>>>>> rid of the principle of explosion is to be >>>>>>>>>>>>>>>>>>>>>>>>>>>> able to use a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>> explosion
it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning. >>>>>>>>>>>>>>>>>>>>>>>>>>>
If you get rid of the principle of explosion, >>>>>>>>>>>>>>>>>>>>>>>>>> the law of non- contradiction goes away as it >>>>>>>>>>>>>>>>>>>>>>>>>> looses its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth- >>>>>>>>>>>>>>>>>>>>>>>> preserving operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>>>>>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>>> At least one of the following statements is true: >>>>>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>>>>> - <X>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>>>
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At >>>>>>>>>>>>>>>>>>>>>> least one of the following statements is true" is >>>>>>>>>>>>>>>>>>>>>> false.
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then. >>>>>>>>>>>>>>>>>>>>
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>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>
Where <X> is any natural language statement, does >>>>>>>>>>>>>>>>>>>> there exist a statement X such that the condition >>>>>>>>>>>>>>>>>>>> "At least one of the following statements is true" >>>>>>>>>>>>>>>>>>>> is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the >>>>>>>>>>>>>>>>>> sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, >>>>>>>>>>>>>>>> so it can't be used in logic. I didn't think I had to >>>>>>>>>>>>>>>> make that explicit.
However, let's go with it anyway because it still >>>>>>>>>>>>>>>> illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the >>>>>>>>>>>>>>>> sun" true?
On second though, let's back up as that might confuse you. >>>>>>>>>>>>>>>
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.
That you did so well on the other things
so I will not block you.
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. >>>>>>>>>>>>
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>
the rejection of the classically valid principle of Addition, >>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>
other words, the principle leading from a formula ϕ to a >>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different >>>>>>>>>> rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting >>>>>>>> with the precondition that a contradiction has been proven, as >>>>>>>> you have admitted above on the record.
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
How do you know that somewhere the Moon is made from green cheese and >>>>>> the Moon is not made from green cheese and Donald Trump is not the >>>>>> one
and only Lord and Savior Jesus Christ?
Counter-factual
For logic the distinction between factual and counter-factual is not
as imortant as the distinction between consistent and contradictory.
Counter-factual may indicate a psychotic break from reality.
No, it does not. It is much more common than anything psychotic.
Besudes, any mention of anything psychotic is off-topic in these
groups.
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction" https://en.wikipedia.org/wiki/Principle_of_explosion
On 6/27/2026 11:34 PM, dbush wrote:
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 1:21 AM, Mikko wrote:
On 01/07/2026 18:01, olcott wrote:
On 7/1/2026 1:46 AM, Mikko wrote:
On 30/06/2026 17:37, olcott wrote:
On 6/30/2026 3:48 AM, Mikko wrote:
On 29/06/2026 17:00, olcott wrote:
On 6/29/2026 8:23 AM, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:Only people having actual psychosis would conclude
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
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:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:30 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 7:22 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 5:52 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
So you're saying that in the following natural >>>>>>>>>>>>>>>>>>>>>> language statement:1) P ∧ ¬P // PremiseExplain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Except with Disjunction introduction, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is its problem. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I figured >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anyone else ever did this. I just >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knew that when >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> trying to find out what is deduced >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a set of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> premises that you cannot pop in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> another sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>A simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PAI (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> valid principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> where ψ is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> implication — given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derivation of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
By popping in another sentence from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> out of nowhere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sequence of statement where >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> eachstatement either is a premis or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Rejected, as you not liking the result >>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't make it invalid. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Through a series of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>> operations, when a contradiction is given as >>>>>>>>>>>>>>>>>>>>>>>>>>>> true, any statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a >>>>>>>>>>>>>>>>>>>>>>>>>>>> demonstration of *why* a formal system whose >>>>>>>>>>>>>>>>>>>>>>>>>>>> axioms lead to a contradiction is useless. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
The only reason someone would want to get >>>>>>>>>>>>>>>>>>>>>>>>>>>> rid of the principle of explosion is to be >>>>>>>>>>>>>>>>>>>>>>>>>>>> able to use a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>> explosion
it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning. >>>>>>>>>>>>>>>>>>>>>>>>>>>
If you get rid of the principle of explosion, >>>>>>>>>>>>>>>>>>>>>>>>>> the law of non- contradiction goes away as it >>>>>>>>>>>>>>>>>>>>>>>>>> looses its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth- >>>>>>>>>>>>>>>>>>>>>>>> preserving operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>>>>>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>>> At least one of the following statements is true: >>>>>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>>>>> - <X>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>>>
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At >>>>>>>>>>>>>>>>>>>>>> least one of the following statements is true" is >>>>>>>>>>>>>>>>>>>>>> false.
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then. >>>>>>>>>>>>>>>>>>>>
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>
-------------------------------------- >>>>>>>>>>>>>>>>>>>>
Where <X> is any natural language statement, does >>>>>>>>>>>>>>>>>>>> there exist a statement X such that the condition >>>>>>>>>>>>>>>>>>>> "At least one of the following statements is true" >>>>>>>>>>>>>>>>>>>> is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the >>>>>>>>>>>>>>>>>> sun" true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, >>>>>>>>>>>>>>>> so it can't be used in logic. I didn't think I had to >>>>>>>>>>>>>>>> make that explicit.
However, let's go with it anyway because it still >>>>>>>>>>>>>>>> illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the >>>>>>>>>>>>>>>> sun" true?
On second though, let's back up as that might confuse you. >>>>>>>>>>>>>>>
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.
That you did so well on the other things
so I will not block you.
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. >>>>>>>>>>>>
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>
the rejection of the classically valid principle of Addition, >>>>>>>>>>> sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>
other words, the principle leading from a formula ϕ to a >>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different >>>>>>>>>> rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
that
it corrects their psychotic break from reality that
allows one to prove that Donald Trump is the one and
only Lord and Savior on the basis of a totally irrelevant
contradiction.
It follows from a series of truth-preserving operations starting >>>>>>>> with the precondition that a contradiction has been proven, as >>>>>>>> you have admitted above on the record.
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.
How do you know that somewhere the Moon is made from green cheese and >>>>>> the Moon is not made from green cheese and Donald Trump is not the >>>>>> one
and only Lord and Savior Jesus Christ?
Counter-factual
For logic the distinction between factual and counter-factual is not
as imortant as the distinction between consistent and contradictory.
Counter-factual may indicate a psychotic break from reality.
No, it does not. It is much more common than anything psychotic.
Besudes, any mention of anything psychotic is off-topic in these
groups.
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction" https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
On 7/2/2026 1:29 AM, Mikko wrote:
On 01/07/2026 18:06, olcott wrote:
On 7/1/2026 1:53 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when >>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>> where eachstatement either is a premis or follows from one >>>>>>>>>>>>>> or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable. >>>>>>>> Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
Relevance Logic
https://plato.stanford.edu/entries/logic-relevance/
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies
of a false premise, which already is a break from reality even
when no consequence is inferred.
Only because semantics is ignored.
A break from reality is a break from reality, no matter whether
the semantics is ignored or considered. Though if there is no
semantics, even any ignored one, there is no connection to
reality to break.
Ignoring semantics is always a break from reality.
So is any semantics other than real world semantics.
Hypotheticals are useful for making decisions.
On 7/2/2026 1:31 AM, Mikko wrote:
On 01/07/2026 18:25, olcott wrote:
On 7/1/2026 2:32 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction Introduction. In >>>>>>>>>>>>>>>>> other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured
all this out on my own. I didn't even know that
anyone else ever did this. I just knew that when >>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>> where eachstatement either is a premis or follows from one >>>>>>>>>>>>>> or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable. >>>>>>>> Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
If the intent was to include that in the denotation you failed
to say something important.
Parry’s logic of Analytic Implication
and Relevance logic are two sensible systems
that get rid of the Principle of Explosion.
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that
is not in logic, it was introduced by you. Even without the principle
of explosion it is possible to infer a false conclusion from a false
premise.
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
But false is false even if the proof is
something less obvious.
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:29 AM, Mikko wrote:
On 01/07/2026 18:06, olcott wrote:
On 7/1/2026 1:53 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince people >>>>>>>>>>>>>>>>> who don't
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>>> where eachstatement either is a premis or follows from >>>>>>>>>>>>>>> one or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly trimmed >>>>>>>>>>> is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable. >>>>>>>>> Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
Relevance Logic
https://plato.stanford.edu/entries/logic-relevance/
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies >>>>>>> of a false premise, which already is a break from reality even
when no consequence is inferred.
Only because semantics is ignored.
A break from reality is a break from reality, no matter whether
the semantics is ignored or considered. Though if there is no
semantics, even any ignored one, there is no connection to
reality to break.
Ignoring semantics is always a break from reality.
So is any semantics other than real world semantics.
Hypotheticals are useful for making decisions.
Which is an example of the usefulness of a break from reality. It
als shows that calling a break from reality "psychotic" without
further consideration.
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:31 AM, Mikko wrote:
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
Matter of opinion,
but I think that most of people would consder
getting rid of fires is more rational that getting rid of fire
alarms.
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that
is not in logic, it was introduced by you. Even without the principle
of explosion it is possible to infer a false conclusion from a false
premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
On 7/3/2026 3:24 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:31 AM, Mikko wrote:
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
Matter of opinion,
Matter of correctly and coherently computing the notion
of truth. My correction to the Principle of Explosion:
(P ∧ ~P) ⊢ FALSE
FALSE ⊢ FALSE
but I think that most of people would consder
getting rid of fires is more rational that getting rid of fire
alarms.
It is not a fire alarm it is getting rid of semantics
within inference. My correct reasoning correction to
logic gets rid of every type of inference besides
semantic entailment.
Validity and Soundness
A deductive argument is said to be valid if
and only if it takes a form that makes it
impossible for the premises to be true and
the conclusion nevertheless to be false.
Otherwise, a deductive argument is said to
be invalid. https://iep.utm.edu/val-snd/
*That big mistake is corrected thusly*
A deductive argument is said to be valid if
and only if its conclusion is a necessary
consequence of all of its premises Otherwise,
a deductive argument is said to be invalid.
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
On 7/3/2026 3:22 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:29 AM, Mikko wrote:
On 01/07/2026 18:06, olcott wrote:
On 7/1/2026 1:53 AM, Mikko wrote:
On 30/06/2026 16:55, olcott wrote:
On 6/30/2026 3:10 AM, Mikko wrote:
On 29/06/2026 16:55, olcott wrote:
On 6/28/2026 4:32 AM, Mikko wrote:
On 27/06/2026 21:29, olcott wrote:
On 6/27/2026 1:24 PM, dbush wrote:
On 6/27/2026 2:03 PM, olcott wrote:
On 6/27/2026 12:54 PM, dbush wrote:
On 6/27/2026 11:11 AM, polcott wrote:
On 6/27/2026 2:08 AM, Mikko wrote:So you're saying that in the following natural language >>>>>>>>>>>>>> statement:
On 26/06/2026 15:49, olcott wrote:
On 6/26/2026 1:49 AM, Mikko wrote:
On 26/06/2026 04:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for >>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many >>>>>>>>>>>>>>>>>>> systems of analytic implication belonging to its ilk) is >>>>>>>>>>>>>>>>>>> the rejection of the classically valid principle of >>>>>>>>>>>>>>>>>>> Addition,
sometimes also referred to as Disjunction >>>>>>>>>>>>>>>>>>> Introduction. In
other words, the principle leading from a formula ϕ to a >>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary >>>>>>>>>>>>>>>>>>> formula. Parry blamed on this principle the derivability >>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication—given that it is >>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation of an arbitrary >>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL
He also gets rid of an efficient way to convince >>>>>>>>>>>>>>>>>> people who don't
understand much of logic.
As I recently showed in another post. I figured >>>>>>>>>>>>>>>>> all this out on my own. I didn't even know that >>>>>>>>>>>>>>>>> anyone else ever did this. I just knew that when >>>>>>>>>>>>>>>>> trying to find out what is deduced from a set of >>>>>>>>>>>>>>>>> premises that you cannot pop in another sentence >>>>>>>>>>>>>>>>> from out of nowhere and get a correct conclusion. >>>>>>>>>>>>>>>>>
By popping in another sentence from out of nowhere >>>>>>>>>>>>>>>>> (as it shows above) the principle of explosion is >>>>>>>>>>>>>>>>> derived.
The usual meaning of proof is a sequence of statement >>>>>>>>>>>>>>>> where eachstatement either is a premis or follows from >>>>>>>>>>>>>>>> one or more earlier
statements
Except with Disjunction introduction, that is its problem. >>>>>>>>>>>>>>
It is a key issue in that it creates the
psychotic break from reality known as the
Principle of Explosion, otherwise it may
make no difference at all.
Stay on topic or I will block you.
Explain in detail how the below which you dishonestly >>>>>>>>>>>> trimmed is off- topic.
The topic is how Disjunction introduction enables the
Principle of Explosion.
It does not. In any sensible logic every tautology is provable. >>>>>>>>>> Then the principle of explosion follows.
POE is unprovable in both of these more sensible systems
of logic.
THe expression "these system" above does not denote.
Parry’s logic of Analytic Implication
Relevance Logic
https://plato.stanford.edu/entries/logic-relevance/
The POE is an actual psychotic break from
reality when one pays full and complete attention to
the underlying semantics and does not stupidly take
semantics out of logic and put it in a separate model.
No, it is not. The principle of explosion is about consequencies >>>>>>>> of a false premise, which already is a break from reality even >>>>>>>> when no consequence is inferred.
Only because semantics is ignored.
A break from reality is a break from reality, no matter whether
the semantics is ignored or considered. Though if there is no
semantics, even any ignored one, there is no connection to
reality to break.
Ignoring semantics is always a break from reality.
So is any semantics other than real world semantics.
Hypotheticals are useful for making decisions.
Which is an example of the usefulness of a break from reality. It
als shows that calling a break from reality "psychotic" without
further consideration.
That Donald Trump might start WW III is a hypothetical
that can possibly be is useful.
That Donald Trump is the one and only Lord and Savior Jesus Christ
is a hypothetical that cannot possible be making it useless.
On 7/3/2026 3:24 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:31 AM, Mikko wrote:
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
Matter of opinion,
Matter of correctly and coherently computing the notion
of truth.
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that
is not in logic, it was introduced by you. Even without the principle
of explosion it is possible to infer a false conclusion from a false
premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
On 7/4/2026 1:37 AM, Mikko wrote:
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that
is not in logic, it was introduced by you. Even without the principle
of explosion it is possible to infer a false conclusion from a false
premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
(P ∧ ~P) ⊢ FALSE // is what can really be proved semantically
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 03/07/2026 18:04, olcott wrote:
On 7/3/2026 3:24 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:31 AM, Mikko wrote:
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
Matter of opinion,
Matter of correctly and coherently computing the notion
of truth. My correction to the Principle of Explosion:
(P ∧ ~P) ⊢ FALSE
FALSE ⊢ FALSE
but I think that most of people would consder
getting rid of fires is more rational that getting rid of fire
alarms.
It is not a fire alarm it is getting rid of semantics
within inference. My correct reasoning correction to
logic gets rid of every type of inference besides
semantic entailment.
Getting rid of any type of inference does not make much difference
as long as you get the same conclusions through other inferences.
Only getting rid of some conscusions it makes a significant
difference. But you have never shown an example of getting rid of
a conclusion without losing a semantic entailment.
Validity and Soundness
A deductive argument is said to be valid if
and only if it takes a form that makes it
impossible for the premises to be true and
the conclusion nevertheless to be false.
Otherwise, a deductive argument is said to
be invalid. https://iep.utm.edu/val-snd/
*That big mistake is corrected thusly*
A deductive argument is said to be valid if
and only if its conclusion is a necessary
consequence of all of its premises Otherwise,
a deductive argument is said to be invalid.
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
You don't need any of above if you have ¬, ∨, and ∧.
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
□ is a unary operator and
an expression like P □ Q makes absolutely no sense.
If you want to use this as a binary operator you'd actually need to
*define* it. You don't seem to grasp this. You can't just introduce a
new operator and expect people to know what it means.
Also, moving into the domain of modal logic would be an incredibly
strange thing for you to do given that in previous posts you claimed to
reject the idea of models. But modal logic is *replete* with models.
Modal logic operates over a set of many models. □P means that P is true
in all accessible models of the system.
André
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
□ is a unary operator and an expression like P □ Q makes absolutely no >> sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
If you want to use this as a binary operator you'd actually need to
*define* it. You don't seem to grasp this. You can't just introduce a
new operator and expect people to know what it means.
□ Already means necessity, it is not that hard unless
one makes great effort to pretend to not understand
what is already unequivocally clear. >
Also, moving into the domain of modal logic would be an incredibly
strange thing for you to do given that in previous posts you claimed to
The only thing that I am using is logical necessity.
reject the idea of models. But modal logic is *replete* with models.
Modal logic operates over a set of many models. □P means that P is
true in all accessible models of the system.
André
On 03/07/2026 17:50, olcott wrote:
On 7/3/2026 3:22 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
Hypotheticals are useful for making decisions.
Which is an example of the usefulness of a break from reality. It
als shows that calling a break from reality "psychotic" without
further consideration.
That Donald Trump might start WW III is a hypothetical
that can possibly be is useful.
Whether Donald Trump will start WW III is not yet known, so that
cannot be called an example of counter-factual.
That Donald Trump is the one and only Lord and Savior Jesus Christ
is a hypothetical that cannot possible be making it useless.
Maybe, but irrelevent as you did not claim it be useful when you
presented it.
On 03/07/2026 18:04, olcott wrote:
On 7/3/2026 3:24 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:31 AM, Mikko wrote:
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
Matter of opinion,
Matter of correctly and coherently computing the notion
of truth.
You did not compute correctely, let aloone coherently, whether
I an irrational. You onlu presented your opinion about it.
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes absolutely >>> no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
not as the nonsensical P □
Q. But you claim to have gotten rid of →, so how this is to be
interpreted remains a mystery (and getting rid of → makes no sense since → represents a specific truth table which still exists regardless of whether you've assigned a symbol to it or not)
If you want to use this as a binary operator you'd actually need to
*define* it. You don't seem to grasp this. You can't just introduce a
new operator and expect people to know what it means.
□ Already means necessity, it is not that hard unless
one makes great effort to pretend to not understand
what is already unequivocally clear. >
Also, moving into the domain of modal logic would be an incredibly
strange thing for you to do given that in previous posts you claimed to
The only thing that I am using is logical necessity.
So how would you interpret 'necessity' without models?
André
reject the idea of models. But modal logic is *replete* with models.
Modal logic operates over a set of many models. □P means that P is
true in all accessible models of the system.
André
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes absolutely >>>> no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So how would you interpret 'necessity' without models?
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes absolutely >>>>> no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity between
P and Q". Necessity applies to propositions. It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean something other than that you're really going to have to clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. If a
truth table contains any symbol other than T or F, you're dealing with a three or more valued logic which means you have to completely redefine
every single logical operator before you can proceed.
And there's nothing about the above table which in any way captures the meaning of 'necessity' so it's entirely unclear why you want to use the
□ symbol here. Your '□' doesn't have any relation to necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing as
operator overloading, so you can't take a unary operator and use it for
some ill-defined binary operation as well. You need a new symbol since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal logic is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use of
models?
André
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes
absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity
between P and Q". Necessity applies to propositions. It doesn't hold
*between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean
something other than that you're really going to have to clarify what
you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. If a
truth table contains any symbol other than T or F, you're dealing with
a three or more valued logic which means you have to completely
redefine every single logical operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
And there's nothing about the above table which in any way captures
the meaning of 'necessity' so it's entirely unclear why you want to
use the □ symbol here. Your '□' doesn't have any relation to necessity >> any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing as
operator overloading, so you can't take a unary operator and use it
for some ill-defined binary operation as well. You need a new symbol
since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal logic
is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use of
models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes
absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity
between P and Q". Necessity applies to propositions. It doesn't hold
*between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean
something other than that you're really going to have to clarify what
you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. If a
truth table contains any symbol other than T or F, you're dealing
with a three or more valued logic which means you have to completely
redefine every single logical operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any attempt to explain what is meant by this (by you).
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you can't do that, then your use of 'necessary' is completely meaningless verbiage.
And there's nothing about the above table which in any way captures
the meaning of 'necessity' so it's entirely unclear why you want to
use the □ symbol here. Your '□' doesn't have any relation to
necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing as
operator overloading, so you can't take a unary operator and use it
for some ill-defined binary operation as well. You need a new symbol
since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal logic
is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use of
models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
Propositional calculus uses models. It's also extremely limited.
André
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes
absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity
between P and Q". Necessity applies to propositions. It doesn't hold
*between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean
something other than that you're really going to have to clarify
what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. If a
truth table contains any symbol other than T or F, you're dealing
with a three or more valued logic which means you have to completely
redefine every single logical operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any attempt to
explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you can't
do that, then your use of 'necessary' is completely meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
And there's nothing about the above table which in any way captures
the meaning of 'necessity' so it's entirely unclear why you want to
use the □ symbol here. Your '□' doesn't have any relation to
necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing as
operator overloading, so you can't take a unary operator and use it
for some ill-defined binary operation as well. You need a new symbol
since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal
logic is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use of
models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
Propositional calculus uses models. It's also extremely limited.
André
Are you referring to truth tables as models?
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity
between P and Q". Necessity applies to propositions. It doesn't
hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean
something other than that you're really going to have to clarify
what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. If
a truth table contains any symbol other than T or F, you're dealing >>>>> with a three or more valued logic which means you have to
completely redefine every single logical operator before you can
proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any attempt to
explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you can't
do that, then your use of 'necessary' is completely meaningless
verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between 'necessary consequence' and mere 'consequence'. The two examples above don't even mention the word 'necessary'.
And there's nothing about the above table which in any way captures >>>>> the meaning of 'necessity' so it's entirely unclear why you want to >>>>> use the □ symbol here. Your '□' doesn't have any relation to
necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing as
operator overloading, so you can't take a unary operator and use it >>>>> for some ill-defined binary operation as well. You need a new
symbol since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal
logic is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use
of models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
Propositional calculus uses models. It's also extremely limited.
André
Are you referring to truth tables as models?
No.
André
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity
between P and Q". Necessity applies to propositions. It doesn't
hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean >>>>>> something other than that you're really going to have to clarify
what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. If >>>>>> a truth table contains any symbol other than T or F, you're
dealing with a three or more valued logic which means you have to >>>>>> completely redefine every single logical operator before you can
proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any attempt
to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English.
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you
can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between 'necessary
consequence' and mere 'consequence'. The two examples above don't even
mention the word 'necessary'.
And there's nothing about the above table which in any way
captures the meaning of 'necessity' so it's entirely unclear why
you want to use the □ symbol here. Your '□' doesn't have any
relation to necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing as >>>>>> operator overloading, so you can't take a unary operator and use
it for some ill-defined binary operation as well. You need a new
symbol since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal
logic is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use >>>>>> of models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
Propositional calculus uses models. It's also extremely limited.
André
Are you referring to truth tables as models?
No.
André
Truth Tables ARE Propositional Model Theory
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity >>>>>>> between P and Q". Necessity applies to propositions. It doesn't >>>>>>> hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean >>>>>>> something other than that you're really going to have to clarify >>>>>>> what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. >>>>>>> If a truth table contains any symbol other than T or F, you're
dealing with a three or more valued logic which means you have to >>>>>>> completely redefine every single logical operator before you can >>>>>>> proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any attempt
to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English.
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither 'impossibly
false' nor 'impossibly true' are English.
In English, 'impossibly x'
does not mean 'not possible to be x'. 'Impossibly' is an *itensifier*
with a meaning of extremely. So 'impossibly true' would mean 'extremely true', which makes no sense since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you
can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between 'necessary
consequence' and mere 'consequence'. The two examples above don't
even mention the word 'necessary'.
This question was the central point of my post and you have ignored it.
I maintain that when you use the term 'necessary' your just tossing in a meaningless word for no reason. If you can answer the above question you will show me wrong.
And there's nothing about the above table which in any way
captures the meaning of 'necessity' so it's entirely unclear why >>>>>>> you want to use the □ symbol here. Your '□' doesn't have any >>>>>>> relation to necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing >>>>>>> as operator overloading, so you can't take a unary operator and >>>>>>> use it for some ill-defined binary operation as well. You need a >>>>>>> new symbol since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal >>>>>>> logic is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making use >>>>>>> of models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
Propositional calculus uses models. It's also extremely limited.
André
Are you referring to truth tables as models?
No.
André
Truth Tables ARE Propositional Model Theory
No they're not. Truth tables are used to define the basic operators in a truth-functional logic.
Please evaluate the propositional calculus expression P → Q. Without knowing what P or Q stand for you cannot do this. The model tells you
what P and Q actually mean making it possible to assign a truth value to
P → Q.
André
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete necessity >>>>>>>> between P and Q". Necessity applies to propositions. It doesn't >>>>>>>> hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean >>>>>>>> something other than that you're really going to have to clarify >>>>>>>> what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. >>>>>>>> If a truth table contains any symbol other than T or F, you're >>>>>>>> dealing with a three or more valued logic which means you have >>>>>>>> to completely redefine every single logical operator before you >>>>>>>> can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any attempt >>>>>> to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English.
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither 'impossibly
false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no sense
since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you
can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between 'necessary
consequence' and mere 'consequence'. The two examples above don't
even mention the word 'necessary'.
This question was the central point of my post and you have ignored
it. I maintain that when you use the term 'necessary' your just
tossing in a meaningless word for no reason. If you can answer the
above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
If Q is a necessary consequence of P then
we are not allowed to infer anything from ~P
And there's nothing about the above table which in any way
captures the meaning of 'necessity' so it's entirely unclear why >>>>>>>> you want to use the □ symbol here. Your '□' doesn't have any >>>>>>>> relation to necessity any more than '→' does above.
Also note that formal logic is *not* c++. There's no such thing >>>>>>>> as operator overloading, so you can't take a unary operator and >>>>>>>> use it for some ill-defined binary operation as well. You need a >>>>>>>> new symbol since □ is already taken.
P □ Q makes as much sense as P ¬ Q or P ∀ Q
So how would you interpret 'necessity' without models?
I note you didn't answer this. The notion of necessity in modal >>>>>>>> logic is intrinsically tied to model theory.
How exactly are you defining 'necessity' if you're not making >>>>>>>> use of models?
André
Do you know what propositional logic is?
then that is one way to avoid models.
Propositional calculus uses models. It's also extremely limited.
André
Are you referring to truth tables as models?
No.
André
Truth Tables ARE Propositional Model Theory
No they're not. Truth tables are used to define the basic operators in
a truth-functional logic.
Please evaluate the propositional calculus expression P → Q. Without
knowing what P or Q stand for you cannot do this. The model tells you
what P and Q actually mean making it possible to assign a truth value
to P → Q.
André
In propositional logic they are only Boolean variables
with zero additional meaning besides true and false.
If you think otherwise then cite a source.
On 2026-07-04 18:33, olcott wrote:I corrected this stipulative definition below.
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary >>>>>>>>>>>>>>>> form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense
and corrects a fundamental error in the definition of
valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete
necessity between P and Q". Necessity applies to propositions. >>>>>>>>> It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean >>>>>>>>> something other than that you're really going to have to
clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued logic. >>>>>>>>> If a truth table contains any symbol other than T or F, you're >>>>>>>>> dealing with a three or more valued logic which means you have >>>>>>>>> to completely redefine every single logical operator before you >>>>>>>>> can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any
attempt to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English.
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither 'impossibly
false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
You didn't use the word 'impossible'. You used the word 'impossibly'
which is a different word. I understand the meaning of both perfectly well.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no sense
since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you >>>>>>> can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between
'necessary consequence' and mere 'consequence'. The two examples
above don't even mention the word 'necessary'.
This question was the central point of my post and you have ignored
it. I maintain that when you use the term 'necessary' your just
tossing in a meaningless word for no reason. If you can answer the
above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
The modal operators don't *have* truth tables
On 7/4/2026 7:43 PM, André G. Isaak wrote:
On 2026-07-04 18:33, olcott wrote:I corrected this stipulative definition below.
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary >>>>>>>>>>>>>>>>> form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense >>>>>>>>>>>>> and corrects a fundamental error in the definition of >>>>>>>>>>>>> valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete
necessity between P and Q". Necessity applies to propositions. >>>>>>>>>> It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you mean >>>>>>>>>> something other than that you're really going to have to
clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued
logic. If a truth table contains any symbol other than T or F, >>>>>>>>>> you're dealing with a three or more valued logic which means >>>>>>>>>> you have to completely redefine every single logical operator >>>>>>>>>> before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any
attempt to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English.
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither
'impossibly false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
You didn't use the word 'impossible'. You used the word 'impossibly'
which is a different word. I understand the meaning of both perfectly
well.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no sense
since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you >>>>>>>> can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between
'necessary consequence' and mere 'consequence'. The two examples
above don't even mention the word 'necessary'.
This question was the central point of my post and you have ignored
it. I maintain that when you use the term 'necessary' your just
tossing in a meaningless word for no reason. If you can answer the
above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
The modal operators don't *have* truth tables
Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. https://iep.utm.edu/val-snd/
Is corrected to mean
A deductive argument is said to be valid if and only
if it takes a form that anything besides true
premises and true conclusion is invalid.
P □ Q means P(true) ∧ Q(true) is valid
everything else is invalid.
P □ Q
0 0 0
0 0 1
1 0 0
1 1 1
On 2026-07-04 19:18, olcott wrote:
On 7/4/2026 7:43 PM, André G. Isaak wrote:
On 2026-07-04 18:33, olcott wrote:I corrected this stipulative definition below.
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary >>>>>>>>>>>>>>>>>> form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense >>>>>>>>>>>>>> and corrects a fundamental error in the definition of >>>>>>>>>>>>>> valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete
necessity between P and Q". Necessity applies to
propositions. It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you >>>>>>>>>>> mean something other than that you're really going to have to >>>>>>>>>>> clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued >>>>>>>>>>> logic. If a truth table contains any symbol other than T or >>>>>>>>>>> F, you're dealing with a three or more valued logic which >>>>>>>>>>> means you have to completely redefine every single logical >>>>>>>>>>> operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any
attempt to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English. >>>>>>>
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither
'impossibly false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
You didn't use the word 'impossible'. You used the word 'impossibly'
which is a different word. I understand the meaning of both perfectly
well.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no sense >>>>> since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you >>>>>>>>> can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between
'necessary consequence' and mere 'consequence'. The two examples >>>>>>> above don't even mention the word 'necessary'.
This question was the central point of my post and you have ignored >>>>> it. I maintain that when you use the term 'necessary' your just
tossing in a meaningless word for no reason. If you can answer the
above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
The modal operators don't *have* truth tables
Your definitions are not coherent.
Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. https://iep.utm.edu/val-snd/
Is corrected to mean
A deductive argument is said to be valid if and only
if it takes a form that anything besides true
premises and true conclusion is invalid.
P □ Q means P(true) ∧ Q(true) is valid
everything else is invalid.
P □ Q
0 0 0
0 0 1
1 0 0
1 1 1
That's simply the truth table for 'and'. It sheds no light on what it is your trying to convey by your use of 'necessity'. And the operator □ is already taken and is not a truth-functional operator so reusing it for something else is just plain stupid.
On 7/4/2026 8:28 PM, André G. Isaak wrote:
On 2026-07-04 19:18, olcott wrote:
On 7/4/2026 7:43 PM, André G. Isaak wrote:
On 2026-07-04 18:33, olcott wrote:I corrected this stipulative definition below.
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary >>>>>>>>>>>>>>>>>>> form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense >>>>>>>>>>>>>>> and corrects a fundamental error in the definition of >>>>>>>>>>>>>>> valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete >>>>>>>>>>>> necessity between P and Q". Necessity applies to
propositions. It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you >>>>>>>>>>>> mean something other than that you're really going to have >>>>>>>>>>>> to clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued >>>>>>>>>>>> logic. If a truth table contains any symbol other than T or >>>>>>>>>>>> F, you're dealing with a three or more valued logic which >>>>>>>>>>>> means you have to completely redefine every single logical >>>>>>>>>>>> operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any >>>>>>>>>> attempt to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English. >>>>>>>>
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither
'impossibly false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
You didn't use the word 'impossible'. You used the word 'impossibly'
which is a different word. I understand the meaning of both
perfectly well.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no
sense since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If >>>>>>>>>> you can't do that, then your use of 'necessary' is completely >>>>>>>>>> meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between
'necessary consequence' and mere 'consequence'. The two examples >>>>>>>> above don't even mention the word 'necessary'.
This question was the central point of my post and you have
ignored it. I maintain that when you use the term 'necessary' your >>>>>> just tossing in a meaningless word for no reason. If you can
answer the above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
The modal operators don't *have* truth tables
Your definitions are not coherent.
Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. https://iep.utm.edu/val-snd/
Is corrected to mean
A deductive argument is said to be valid if and only
if it takes a form that anything besides true
premises and true conclusion is invalid.
P □ Q means P(true) ∧ Q(true) is valid
everything else is invalid.
P □ Q
0 0 0
0 0 1
1 0 0
1 1 1
That's simply the truth table for 'and'. It sheds no light on what it
is your trying to convey by your use of 'necessity'. And the operator
□ is already taken and is not a truth-functional operator so reusing
it for something else is just plain stupid.
Dogs are cats → Monkeys have wings
¬(Dogs are cats □ Monkeys have wings)
On 2026-07-04 19:18, olcott wrote:
On 7/4/2026 7:43 PM, André G. Isaak wrote:
On 2026-07-04 18:33, olcott wrote:I corrected this stipulative definition below.
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary >>>>>>>>>>>>>>>>>> form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense >>>>>>>>>>>>>> and corrects a fundamental error in the definition of >>>>>>>>>>>>>> valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete
necessity between P and Q". Necessity applies to
propositions. It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you >>>>>>>>>>> mean something other than that you're really going to have to >>>>>>>>>>> clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued >>>>>>>>>>> logic. If a truth table contains any symbol other than T or >>>>>>>>>>> F, you're dealing with a three or more valued logic which >>>>>>>>>>> means you have to completely redefine every single logical >>>>>>>>>>> operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any
attempt to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English. >>>>>>>
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither
'impossibly false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
You didn't use the word 'impossible'. You used the word 'impossibly'
which is a different word. I understand the meaning of both perfectly
well.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no sense >>>>> since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If you >>>>>>>>> can't do that, then your use of 'necessary' is completely
meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between
'necessary consequence' and mere 'consequence'. The two examples >>>>>>> above don't even mention the word 'necessary'.
This question was the central point of my post and you have ignored >>>>> it. I maintain that when you use the term 'necessary' your just
tossing in a meaningless word for no reason. If you can answer the
above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
The modal operators don't *have* truth tables
Your definitions are not coherent.
Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. https://iep.utm.edu/val-snd/
Is corrected to mean
A deductive argument is said to be valid if and only
if it takes a form that anything besides true
premises and true conclusion is invalid.
P □ Q means P(true) ∧ Q(true) is valid
everything else is invalid.
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
That's simply the truth table for 'and'.
It sheds no light on what it is
your trying to convey by your use of 'necessity'. And the operator □ is already taken and is not a truth-functional operator so reusing it for something else is just plain stupid.
And snipping my question doesn't make it go away:
Can you give an example where (a) hold true but where (b) does not. An example from ordinary English is fine.
a) Q is a consequence of P
b) Q is a necessary consequence of P.
If you can't, your use of the term 'necessary' serves absolutely no
purpose.
André
On 7/4/2026 8:28 PM, André G. Isaak wrote:
On 2026-07-04 19:18, olcott wrote:
On 7/4/2026 7:43 PM, André G. Isaak wrote:
On 2026-07-04 18:33, olcott wrote:I corrected this stipulative definition below.
On 7/4/2026 7:23 PM, André G. Isaak wrote:
On 2026-07-04 18:08, olcott wrote:
On 7/4/2026 6:57 PM, André G. Isaak wrote:
On 2026-07-04 17:42, olcott wrote:
On 7/4/2026 5:11 PM, André G. Isaak wrote:
On 2026-07-04 15:36, olcott wrote:
On 7/4/2026 4:29 PM, André G. Isaak wrote:
On 2026-07-04 14:58, olcott wrote:
On 7/4/2026 11:59 AM, André G. Isaak wrote:
On 2026-07-04 10:44, olcott wrote:
On 7/4/2026 10:08 AM, André G. Isaak wrote:
On 2026-07-04 07:21, olcott wrote:
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary >>>>>>>>>>>>>>>>>>> form of logical necessity: P □ Q
There is no 'binary form of logical necessity.
That is why I just created one.
But you didn't define it.
□ is a unary operator and an expression like P □ Q makes >>>>>>>>>>>>>>>> absolutely no sense.
Q is a necessary consequence of P makes perfect sense >>>>>>>>>>>>>>> and corrects a fundamental error in the definition of >>>>>>>>>>>>>>> valid deductive inference.
That would normally be written as □(P → Q),
That does not perfectly preserve the complete
necessity between P and Q.
What on earth does it mean for there to be a "complete >>>>>>>>>>>> necessity between P and Q". Necessity applies to
propositions. It doesn't hold *between* things.
□(P → Q) means that Q is necessarily implied by P. If you >>>>>>>>>>>> mean something other than that you're really going to have >>>>>>>>>>>> to clarify what you mean.
P □ Q P → Q
0 ? 0 0 1 0
0 ? 1 0 1 1
1 0 0 1 0 0
1 1 1 1 1 1
Q is a necessary consequence of P
is the same as English If P then Q
(a) false when P is true and Q is false
(b) true when P is true and Q is true
(c) otherwise does not have a truth value.
So again your veering into the territory of three-valued >>>>>>>>>>>> logic. If a truth table contains any symbol other than T or >>>>>>>>>>>> F, you're dealing with a three or more valued logic which >>>>>>>>>>>> means you have to completely redefine every single logical >>>>>>>>>>>> operator before you can proceed.
The English if P then Q only actually tells you
P(true) then necessarily Q(true)
Q(false) then necessarily P(false)
IT DOES NOT TELL YOU MORE THAN THIS AND
IT IS STUPID MISTAKE TO ASSUME OTHERWISE
THE WAY THAT IMPLICATION STUPIDLY DOES.
You're introducing the word 'necessarily' here without any >>>>>>>>>> attempt to explain what is meant by this (by you).
I always use the ordinary English meaning.
If P is true then Q is impossibly false.
If Q is false the P is impossibly true.
'impossibly false' and 'impossibly true' aren't ordinary English. >>>>>>>>
Tell me whether or not the numerical square root
of a dead chicken can exist and why or why not.
You must not start with any numerical value such
as the weight of the dead chicken. You are only
allowed to use its actual dead body.
What does the above have to do with my claim that neither
'impossibly false' nor 'impossibly true' are English.
You did not seem to understand the meaning of the word impossible.
You didn't use the word 'impossible'. You used the word 'impossibly'
which is a different word. I understand the meaning of both
perfectly well.
In English, 'impossibly x' does not mean 'not possible to be x'.
'Impossibly' is an *itensifier* with a meaning of extremely. So
'impossibly true' would mean 'extremely true', which makes no
sense since true is not a gradient concept.
What is the difference between
a) Q is a necessary consequence of P.
b) Q is a consequence of P
Give an example where b holds true but where a is false. If >>>>>>>>>> you can't do that, then your use of 'necessary' is completely >>>>>>>>>> meaningless verbiage.
If someone smacks you in the face then
you were hit in the face.
If you were NOT hit in the face then
someone did not smack you in the face.
I asked for an example illustrating the different between
'necessary consequence' and mere 'consequence'. The two examples >>>>>>>> above don't even mention the word 'necessary'.
This question was the central point of my post and you have
ignored it. I maintain that when you use the term 'necessary' your >>>>>> just tossing in a meaningless word for no reason. If you can
answer the above question you will show me wrong.
The modal operators □ and ◊
P □ Q --- P → Q
0 ? 0 --- 0 1 0
0 ? 1 --- 0 1 1
1 0 0 --- 1 0 0
1 1 1 --- 1 1 1
The modal operators don't *have* truth tables
Your definitions are not coherent.
Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. https://iep.utm.edu/val-snd/
Is corrected to mean
A deductive argument is said to be valid if and only
if it takes a form that anything besides true
premises and true conclusion is invalid.
P □ Q means P(true) ∧ Q(true) is valid
everything else is invalid.
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
That's simply the truth table for 'and'.
It had a typo
It sheds no light on what it is your trying to convey by your use of
'necessity'. And the operator □ is already taken and is not a
truth-functional operator so reusing it for something else is just
plain stupid.
And snipping my question doesn't make it go away:
Can you give an example where (a) hold true but where (b) does not. An
example from ordinary English is fine.
a) Q is a consequence of P
b) Q is a necessary consequence of P.
If you can't, your use of the term 'necessary' serves absolutely no
purpose.
Q is a necessary consequence of P
On 7/4/2026 8:28 PM, André G. Isaak wrote:
Q is a necessary consequence of P
seems best handled by
https://en.wikipedia.org/wiki/Relevance_logic
or Parry's Entailment Logic
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
On 2026-07-04 21:17, olcott wrote:
On 7/4/2026 8:28 PM, André G. Isaak wrote:
Q is a necessary consequence of P
seems best handled by
https://en.wikipedia.org/wiki/Relevance_logic
or Parry's Entailment Logic
P Q □
0 0 0
0 1 0
1 0 0
1 1 1
That's *not* a valid truth table. It has no entry for P = 0 and Q = 1.
And Parry is working in relevance logic. He doesn't deal with modal expressions like 'necessary'.
André
On 7/4/2026 8:28 PM, André G. Isaak wrote:
Q is a necessary consequence of P
seems best handled by
https://en.wikipedia.org/wiki/Relevance_logic
or Parry's Entailment Logic
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
Changes the notion of valid inference too much.
I myself simply leap all the way to the end and
say that the full natural language semantic meaning
must be encoded for both P and Q such that P ⊢ Q
by semantic entailment specified syntactically.
This is accomplished in a language such as CycL. https://en.wikipedia.org/wiki/CycL
On 2026-07-04 21:17, olcott wrote:
On 7/4/2026 8:28 PM, André G. Isaak wrote:
Q is a necessary consequence of P
seems best handled by
https://en.wikipedia.org/wiki/Relevance_logic
or Parry's Entailment Logic
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
Changes the notion of valid inference too much.
It doesn't change anything. It's simply invalid since its not a well-
formed truth table.
I myself simply leap all the way to the end and
say that the full natural language semantic meaning
must be encoded for both P and Q such that P ⊢ Q
by semantic entailment specified syntactically.
This is accomplished in a language such as CycL.
https://en.wikipedia.org/wiki/CycL
The above sheds no light on anything. In particular it doesn't clarify
what you think the difference between entailment and necessary
entailment is which is the question I have been trying to get you to address.
On 7/4/2026 10:52 PM, André G. Isaak wrote:
On 2026-07-04 21:17, olcott wrote:
On 7/4/2026 8:28 PM, André G. Isaak wrote:
Q is a necessary consequence of P
seems best handled by
https://en.wikipedia.org/wiki/Relevance_logic
or Parry's Entailment Logic
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
Changes the notion of valid inference too much.
It doesn't change anything. It's simply invalid since its not a well-
formed truth table.
I myself simply leap all the way to the end and
say that the full natural language semantic meaning
must be encoded for both P and Q such that P ⊢ Q
by semantic entailment specified syntactically.
This is accomplished in a language such as CycL.
https://en.wikipedia.org/wiki/CycL
The above sheds no light on anything. In particular it doesn't clarify
what you think the difference between entailment and necessary
entailment is which is the question I have been trying to get you to
address.
*This says the whole thing better*
P ⊢ Q means: syntactic derivation implements semantic entailment encoded in the language. The inference rules are syntactic rules that realize semantic entailment. These are the only allowed inference steps. The entailment rules depend on the represented domain.
Dogs are cats ⊢ Monkeys have wings // rejected
On 2026-07-04 22:05, olcott wrote:
On 7/4/2026 10:52 PM, André G. Isaak wrote:
On 2026-07-04 21:17, olcott wrote:
On 7/4/2026 8:28 PM, André G. Isaak wrote:
Q is a necessary consequence of P
seems best handled by
https://en.wikipedia.org/wiki/Relevance_logic
or Parry's Entailment Logic
P □ Q
0 0 0
0 0 0
1 0 0
1 1 1
Changes the notion of valid inference too much.
It doesn't change anything. It's simply invalid since its not a well-
formed truth table.
I myself simply leap all the way to the end and
say that the full natural language semantic meaning
must be encoded for both P and Q such that P ⊢ Q
by semantic entailment specified syntactically.
This is accomplished in a language such as CycL.
https://en.wikipedia.org/wiki/CycL
The above sheds no light on anything. In particular it doesn't
clarify what you think the difference between entailment and
necessary entailment is which is the question I have been trying to
get you to address.
*This says the whole thing better*
P ⊢ Q means: syntactic derivation implements semantic entailment
encoded in the language. The inference rules are syntactic rules that
realize semantic entailment. These are the only allowed inference
steps. The entailment rules depend on the represented domain.
Dogs are cats ⊢ Monkeys have wings // rejected
The topic under discussion was Q, which contains neither dogs, cats, monkeys, or wings.
Why don't you illustrate your claim with an actual example from
arithmetic. Say, for example 9 × 5 = 45. What exactly would be the "semantic entailments encoded in the language" involved here?
André
On 7/4/2026 1:37 AM, Mikko wrote:
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that
is not in logic, it was introduced by you. Even without the principle
of explosion it is possible to infer a false conclusion from a false
premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
On 7/4/2026 3:15 AM, Mikko wrote:
On 03/07/2026 17:50, olcott wrote:
On 7/3/2026 3:22 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
Hypotheticals are useful for making decisions.
Which is an example of the usefulness of a break from reality. It
als shows that calling a break from reality "psychotic" without
further consideration.
That Donald Trump might start WW III is a hypothetical
that can possibly be is useful.
Whether Donald Trump will start WW III is not yet known, so that
cannot be called an example of counter-factual.
It is an example of hypothetical. You did not pay attention.
--That Donald Trump is the one and only Lord and Savior Jesus Christ
is a hypothetical that cannot possible be making it useless.
Maybe, but irrelevent as you did not claim it be useful when you
presented it.
On 7/4/2026 1:47 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
On 7/3/2026 3:24 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:31 AM, Mikko wrote:
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
Matter of opinion,
Matter of correctly and coherently computing the notion
of truth. My correction to the Principle of Explosion:
(P ∧ ~P) ⊢ FALSE
FALSE ⊢ FALSE
but I think that most of people would consder
getting rid of fires is more rational that getting rid of fire
alarms.
It is not a fire alarm it is getting rid of semantics
within inference. My correct reasoning correction to
logic gets rid of every type of inference besides
semantic entailment.
Getting rid of any type of inference does not make much difference
as long as you get the same conclusions through other inferences.
Only getting rid of some conscusions it makes a significant
difference. But you have never shown an example of getting rid of
a conclusion without losing a semantic entailment.
POE always breaks semantic entailment
Validity and Soundness
A deductive argument is said to be valid if
and only if it takes a form that makes it
impossible for the premises to be true and
the conclusion nevertheless to be false.
Otherwise, a deductive argument is said to
be invalid. https://iep.utm.edu/val-snd/
*That big mistake is corrected thusly*
A deductive argument is said to be valid if
and only if its conclusion is a necessary
consequence of all of its premises Otherwise,
a deductive argument is said to be invalid.
P ⇒ Q
P → Q
P ⊃ Q
are all abolished and replaced with the binary
form of logical necessity: P □ Q
You don't need any of above if you have ¬, ∨, and ∧.
The notion of valid inference that I just established
is the foundation of all semantic entailment.
On 7/4/2026 3:16 AM, Mikko wrote:
On 03/07/2026 18:04, olcott wrote:
On 7/3/2026 3:24 AM, Mikko wrote:
On 02/07/2026 17:40, olcott wrote:
On 7/2/2026 1:31 AM, Mikko wrote:
Getting rid of the principle of explosion makes as much sense as
getting rid of fire alarms. It makes much more sense to get rid
of fires and false premises.
Then you are irrational
Matter of opinion,
Matter of correctly and coherently computing the notion
of truth.
You did not compute correctely, let aloone coherently, whether
I an irrational. You onlu presented your opinion about it.
Merely rhetoric entirely bereft of a supporting basis.
On 7/4/2026 1:37 AM, Mikko wrote:
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that
is not in logic, it was introduced by you. Even without the principle
of explosion it is possible to infer a false conclusion from a false
premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
(P ∧ ~P) ⊢ FALSE // is what can really be proved semantically
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
On 26/06/2026 02:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
Is that available elsewhere without requiring that I agree to terms such
as this expansive lot of stuff that has nothing to do with reading
something that I should expect either is Parry or is no better:
https://www.cloudflare.com/privacypolicy/
On 7/6/2026 6:49 AM, Tristan Wibberley wrote:
On 26/06/2026 02:32, olcott wrote:
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
Is that available elsewhere without requiring that I agree to terms such
as this expansive lot of stuff that has nothing to do with reading
something that I should expect either is Parry or is no better:
https://www.cloudflare.com/privacypolicy/
I figured out the getting rid of disjunction introduction
is required by myself.
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 04/07/2026 16:15, olcott wrote:
On 7/4/2026 1:37 AM, Mikko wrote:
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ: >>>>>> POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that >>>>> is not in logic, it was introduced by you. Even without the principle >>>>> of explosion it is possible to infer a false conclusion from a false >>>>> premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
Restrictions from the POE make lie detection harder and therefore lying easier. You may like that but others have different preferencies.
On 7/6/2026 2:16 AM, Mikko wrote:
On 04/07/2026 16:15, olcott wrote:
On 7/4/2026 1:37 AM, Mikko wrote:
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ: >>>>>>> POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that >>>>>> is not in logic, it was introduced by you. Even without the principle >>>>>> of explosion it is possible to infer a false conclusion from a false >>>>>> premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
Restrictions from the POE make lie detection harder and therefore lying
easier. You may like that but others have different preferencies.
Olcott gets rid of the Principle of Explosion
In Olcott Logic (P ∧ ¬P) ⊢ ⊥ and ⊥ ⊢ ⊥
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 04/07/2026 16:15, olcott wrote:
On 7/4/2026 1:37 AM, Mikko wrote:
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ: >>>>>> POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that >>>>> is not in logic, it was introduced by you. Even without the principle >>>>> of explosion it is possible to infer a false conclusion from a false >>>>> premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
(P ∧ ~P) ⊢ FALSE // is what can really be proved semantically
If you can prove that FALSE is true then what is not true?
On 7/6/2026 5:17 AM, Mikko wrote:
On 04/07/2026 16:15, olcott wrote:
On 7/4/2026 1:37 AM, Mikko wrote:
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ: >>>>>>> POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that >>>>>> is not in logic, it was introduced by you. Even without the principle >>>>>> of explosion it is possible to infer a false conclusion from a false >>>>>> premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
(P ∧ ~P) ⊢ FALSE // is what can really be proved semantically
If you can prove that FALSE is true then what is not true?
That is not proving that false is true.
It is stipulating that contradictions
only derive bare FALSE.
On 2026-07-06 11:54, olcott wrote:
On 7/6/2026 5:17 AM, Mikko wrote:
On 04/07/2026 16:15, olcott wrote:
On 7/4/2026 1:37 AM, Mikko wrote:
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ: >>>>>>>> POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that >>>>>>> is not in logic, it was introduced by you. Even without the
principle
of explosion it is possible to infer a false conclusion from a false >>>>>>> premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves >>>>>>> that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
(P ∧ ~P) ⊢ FALSE // is what can really be proved semantically
If you can prove that FALSE is true then what is not true?
That is not proving that false is true.
It is stipulating that contradictions
only derive bare FALSE.
Apparently you don't understand what 'derives' means.
When we say that X derives Y we mean that x entails that Y is *true*
So (P ∧ ~P) ⊢ FALSE means that (P ∧ ~P) proves that FALSE is true. That
would be a good example of an explosion.
André
On 7/6/2026 1:57 PM, André G. Isaak wrote:
On 2026-07-06 11:54, olcott wrote:
On 7/6/2026 5:17 AM, Mikko wrote:
On 04/07/2026 16:15, olcott wrote:
On 7/4/2026 1:37 AM, Mikko wrote:If you can prove that FALSE is true then what is not true?
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus >>>>>>>>> Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But >>>>>>>> that
is not in logic, it was introduced by you. Even without the
principle
of explosion it is possible to infer a false conclusion from a >>>>>>>> false
premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves >>>>>>>> that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
(P ∧ ~P) ⊢ FALSE // is what can really be proved semantically >>>>
That is not proving that false is true.
It is stipulating that contradictions
only derive bare FALSE.
Apparently you don't understand what 'derives' means.
(P ∧ ~P) ⊢ ⊥ is a stipulated axiom. FALSE was the dumbed down version.
On 2026-07-06 13:06, olcott wrote:
On 7/6/2026 1:57 PM, André G. Isaak wrote:
On 2026-07-06 11:54, olcott wrote:
On 7/6/2026 5:17 AM, Mikko wrote:
On 04/07/2026 16:15, olcott wrote:
On 7/4/2026 1:37 AM, Mikko wrote:If you can prove that FALSE is true then what is not true?
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus >>>>>>>>>> Christ:
POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction" >>>>>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But >>>>>>>>> that
is not in logic, it was introduced by you. Even without the >>>>>>>>> principle
of explosion it is possible to infer a false conclusion from a >>>>>>>>> false
premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves >>>>>>>>> that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
(P ∧ ~P) ⊢ FALSE // is what can really be proved semantically >>>>>
That is not proving that false is true.
It is stipulating that contradictions
only derive bare FALSE.
Apparently you don't understand what 'derives' means.
(P ∧ ~P) ⊢ ⊥ is a stipulated axiom. FALSE was the dumbed down version.
Which would mean that (P ∧ ~P) proves that ⊥ is true. Again, an example of explosion.
André
⊥ ⊢ ⊥ no explosion.
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates that ⊥ is true.
Your problem is that you don't understand even the most basic facts of logic. Stuff that would be taught during the first week of an
introduction to formal logic is beyond your purview, yet you somehow
feel qualified to pontificate about logic.
André
On 7/6/2026 3:20 PM, André G. Isaak wrote:
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates that ⊥ is
true.
That you do not know what explosion is is not my mistake.
I thought that one of you two guys had a PhD in math
is that you or Alan?
On 7/6/2026 3:20 PM, André G. Isaak wrote:I have a batchelor's degree in maths. I'm not sure about André, but I
On 2026-07-06 14:04, olcott wrote:That you do not know what explosion is is not my mistake.
⊥ ⊢ ⊥ no explosion.Of course that's an explosion. It says that ⊥ demonstrates that ⊥ is true.
I thought that one of you two guys had a PhD in math
is that you or Alan?
Indeed.Your problem is that you don't understand even the most basic facts of logic. Stuff that would be taught during the first week of an
introduction to formal logic is beyond your purview, yet you somehow
feel qualified to pontificate about logic.
--André--
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/6/2026 3:20 PM, André G. Isaak wrote:
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates that ⊥ is true.
That you do not know what explosion is is not my mistake.
I thought that one of you two guys had a PhD in math
is that you or Alan?
I have a batchelor's degree in maths. I'm not sure about André, but I expect he has at least a first degree in maths. You do not, and it
shows. It would be reasonable to expect at least a modicum of respect
for others' learning from you, given the rudimentary level of your own general education.
Your problem is that you don't understand even the most basic facts of
logic. Stuff that would be taught during the first week of an
introduction to formal logic is beyond your purview, yet you somehow
feel qualified to pontificate about logic.
Indeed.
André
--
Copyright 2026 Olcott
On 2026-07-06 15:54, olcott wrote:
On 7/6/2026 3:20 PM, André G. Isaak wrote:
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates that ⊥ is >>> true.
That you do not know what explosion is is not my mistake.
I thought that one of you two guys had a PhD in math
is that you or Alan?
I do know what explosion is in the context of logic. Apparently you do
not. And I've never claimed to have a doctoracte in maths. My background
is in linguistics.
André
On 7/6/2026 5:15 PM, André G. Isaak wrote:
On 2026-07-06 15:54, olcott wrote:
On 7/6/2026 3:20 PM, André G. Isaak wrote:
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates that ⊥ is >>>> true.
That you do not know what explosion is is not my mistake.
I thought that one of you two guys had a PhD in math
is that you or Alan?
I do know what explosion is in the context of logic. Apparently you do
not. And I've never claimed to have a doctoracte in maths. My
background is in linguistics.
André
You are flat our wrong about explosion.
I thought thatsci.lang is not populated by linguists. The vast majority of people who
one of you two guys had a PhD in something. Most linguists
don't have a clue about formal semantics I spoke on sci.lang
for at least 10 years. None of them ever had much of a clue
about this.
On 2026-07-06 16:36, olcott wrote:
On 7/6/2026 5:15 PM, André G. Isaak wrote:
On 2026-07-06 15:54, olcott wrote:
On 7/6/2026 3:20 PM, André G. Isaak wrote:
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates that ⊥ >>>>> is true.
That you do not know what explosion is is not my mistake.
I thought that one of you two guys had a PhD in math
is that you or Alan?
I do know what explosion is in the context of logic. Apparently you
do not. And I've never claimed to have a doctoracte in maths. My
background is in linguistics.
André
You are flat our wrong about explosion.
No. You claim that ⊥ ⊢ ⊥ which is to say that ⊥ can be derived from ⊥.
But in a consistent logic, ⊥ shouldn't be derivable from *anything*. The
only way you can derive it is by introducing a contradiction into your
proof (that's what the first occurrence of ⊥ represents in your
statement) which is exactly what the principle of explosion says.
I thought thatsci.lang is not populated by linguists. The vast majority of people who
one of you two guys had a PhD in something. Most linguists
don't have a clue about formal semantics I spoke on sci.lang
for at least 10 years. None of them ever had much of a clue
about this.
post to that group are simply cranks like you. You can't infer anything about what linguists may or may not know by following sci.lang.
André
On 7/6/2026 5:50 PM, André G. Isaak wrote:
On 2026-07-06 16:36, olcott wrote:
On 7/6/2026 5:15 PM, André G. Isaak wrote:
On 2026-07-06 15:54, olcott wrote:
On 7/6/2026 3:20 PM, André G. Isaak wrote:
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates that ⊥ >>>>>> is true.
That you do not know what explosion is is not my mistake.
I thought that one of you two guys had a PhD in math
is that you or Alan?
I do know what explosion is in the context of logic. Apparently you
do not. And I've never claimed to have a doctoracte in maths. My
background is in linguistics.
André
You are flat our wrong about explosion.
No. You claim that ⊥ ⊢ ⊥ which is to say that ⊥ can be derived from
⊥. But in a consistent logic, ⊥ shouldn't be derivable from
*anything*. The
It is not explosive, full stop you are wrong.
On 2026-07-06 16:53, olcott wrote:
On 7/6/2026 5:50 PM, André G. Isaak wrote:
On 2026-07-06 16:36, olcott wrote:
On 7/6/2026 5:15 PM, André G. Isaak wrote:
On 2026-07-06 15:54, olcott wrote:
On 7/6/2026 3:20 PM, André G. Isaak wrote:
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates that ⊥ >>>>>>> is true.
That you do not know what explosion is is not my mistake.
I thought that one of you two guys had a PhD in math
is that you or Alan?
I do know what explosion is in the context of logic. Apparently you >>>>> do not. And I've never claimed to have a doctoracte in maths. My
background is in linguistics.
André
You are flat our wrong about explosion.
No. You claim that ⊥ ⊢ ⊥ which is to say that ⊥ can be derived from
⊥. But in a consistent logic, ⊥ shouldn't be derivable from
*anything*. The
It is not explosive, full stop you are wrong.
You're really not qualified to make such a claim.
André
On 7/6/2026 6:37 PM, André G. Isaak wrote:
On 2026-07-06 16:53, olcott wrote:
On 7/6/2026 5:50 PM, André G. Isaak wrote:
On 2026-07-06 16:36, olcott wrote:
On 7/6/2026 5:15 PM, André G. Isaak wrote:
On 2026-07-06 15:54, olcott wrote:
On 7/6/2026 3:20 PM, André G. Isaak wrote:
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates that >>>>>>>> ⊥ is true.
That you do not know what explosion is is not my mistake.
I thought that one of you two guys had a PhD in math
is that you or Alan?
I do know what explosion is in the context of logic. Apparently
you do not. And I've never claimed to have a doctoracte in maths. >>>>>> My background is in linguistics.
André
You are flat our wrong about explosion.
No. You claim that ⊥ ⊢ ⊥ which is to say that ⊥ can be derived from
⊥. But in a consistent logic, ⊥ shouldn't be derivable from
*anything*. The
It is not explosive, full stop you are wrong.
You're really not qualified to make such a claim.
André
Define in your own words what you think that deductive
explosion means.
On 2026-07-06 17:40, olcott wrote:
On 7/6/2026 6:37 PM, André G. Isaak wrote:
On 2026-07-06 16:53, olcott wrote:
On 7/6/2026 5:50 PM, André G. Isaak wrote:
On 2026-07-06 16:36, olcott wrote:
On 7/6/2026 5:15 PM, André G. Isaak wrote:
On 2026-07-06 15:54, olcott wrote:
On 7/6/2026 3:20 PM, André G. Isaak wrote:
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates that >>>>>>>>> ⊥ is true.
That you do not know what explosion is is not my mistake.
I thought that one of you two guys had a PhD in math
is that you or Alan?
I do know what explosion is in the context of logic. Apparently >>>>>>> you do not. And I've never claimed to have a doctoracte in maths. >>>>>>> My background is in linguistics.
André
You are flat our wrong about explosion.
No. You claim that ⊥ ⊢ ⊥ which is to say that ⊥ can be derived >>>>> from ⊥. But in a consistent logic, ⊥ shouldn't be derivable from >>>>> *anything*. The
It is not explosive, full stop you are wrong.
You're really not qualified to make such a claim.
André
Define in your own words what you think that deductive
explosion means.
Odd that you should ask such a thing since you rarely if ever respond to requests for you to explain things in your own words and instead post
links to wikipedia pages.
deductive explosion occurs when contradictory premises are introduced
into an argument therefore allowing anything, including false statements
to be derived.
You offered ⊥ ⊢ ⊥
⊥ is the logical symbol representing a falsehood or contradiction. You
are therefore deriving a falsehood or contradiction which shouldn't
happen. The only reason you were able to do this is because your premise
was ⊥. That's explosion.
André
On 7/6/2026 7:47 PM, André G. Isaak wrote:
On 2026-07-06 17:40, olcott wrote:
On 7/6/2026 6:37 PM, André G. Isaak wrote:
On 2026-07-06 16:53, olcott wrote:
On 7/6/2026 5:50 PM, André G. Isaak wrote:
On 2026-07-06 16:36, olcott wrote:
On 7/6/2026 5:15 PM, André G. Isaak wrote:
On 2026-07-06 15:54, olcott wrote:
On 7/6/2026 3:20 PM, André G. Isaak wrote:
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates >>>>>>>>>> that ⊥ is true.
That you do not know what explosion is is not my mistake.
I thought that one of you two guys had a PhD in math
is that you or Alan?
I do know what explosion is in the context of logic. Apparently >>>>>>>> you do not. And I've never claimed to have a doctoracte in
maths. My background is in linguistics.
André
You are flat our wrong about explosion.
No. You claim that ⊥ ⊢ ⊥ which is to say that ⊥ can be derived
from ⊥. But in a consistent logic, ⊥ shouldn't be derivable from >>>>>> *anything*. The
It is not explosive, full stop you are wrong.
You're really not qualified to make such a claim.
André
Define in your own words what you think that deductive
explosion means.
Odd that you should ask such a thing since you rarely if ever respond
to requests for you to explain things in your own words and instead
post links to wikipedia pages.
deductive explosion occurs when contradictory premises are introduced
into an argument therefore allowing anything, including false
statements to be derived.
You offered ⊥ ⊢ ⊥
⊥ is the logical symbol representing a falsehood or contradiction. You
are therefore deriving a falsehood or contradiction which shouldn't
happen. The only reason you were able to do this is because your
premise was ⊥. That's explosion.
André
OK good. I am stipulating that from contradiction only
falsum follows and from falsum only falsum follows
cutting off the legs of explosion.
∀x (x ∧ ¬x) ⊢ ⊥
On 2026-07-06 19:24, olcott wrote:
On 7/6/2026 7:47 PM, André G. Isaak wrote:
On 2026-07-06 17:40, olcott wrote:
On 7/6/2026 6:37 PM, André G. Isaak wrote:
On 2026-07-06 16:53, olcott wrote:
On 7/6/2026 5:50 PM, André G. Isaak wrote:
On 2026-07-06 16:36, olcott wrote:
On 7/6/2026 5:15 PM, André G. Isaak wrote:
On 2026-07-06 15:54, olcott wrote:
On 7/6/2026 3:20 PM, André G. Isaak wrote:
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates >>>>>>>>>>> that ⊥ is true.
That you do not know what explosion is is not my mistake.
I thought that one of you two guys had a PhD in math
is that you or Alan?
I do know what explosion is in the context of logic. Apparently >>>>>>>>> you do not. And I've never claimed to have a doctoracte in
maths. My background is in linguistics.
André
You are flat our wrong about explosion.
No. You claim that ⊥ ⊢ ⊥ which is to say that ⊥ can be derived
from ⊥. But in a consistent logic, ⊥ shouldn't be derivable from >>>>>>> *anything*. The
It is not explosive, full stop you are wrong.
You're really not qualified to make such a claim.
André
Define in your own words what you think that deductive
explosion means.
Odd that you should ask such a thing since you rarely if ever respond
to requests for you to explain things in your own words and instead
post links to wikipedia pages.
deductive explosion occurs when contradictory premises are introduced
into an argument therefore allowing anything, including false
statements to be derived.
You offered ⊥ ⊢ ⊥
⊥ is the logical symbol representing a falsehood or contradiction.
You are therefore deriving a falsehood or contradiction which
shouldn't happen. The only reason you were able to do this is because
your premise was ⊥. That's explosion.
André
OK good. I am stipulating that from contradiction only
falsum follows and from falsum only falsum follows
cutting off the legs of explosion.
∀x (x ∧ ¬x) ⊢ ⊥
Which is simply a way of stating that (x ∧ ¬x) proves that ⊥ is true.
How is that not an explosion? I don't think you grasp what ⊢ or ⊥ mean.
'X follows' means that the truth of X is entailed by the premise.
'falsum follows' means that falsum is true. That's explosion.
André
On 7/6/2026 8:49 PM, André G. Isaak wrote:
On 2026-07-06 19:24, olcott wrote:
On 7/6/2026 7:47 PM, André G. Isaak wrote:
On 2026-07-06 17:40, olcott wrote:
On 7/6/2026 6:37 PM, André G. Isaak wrote:
On 2026-07-06 16:53, olcott wrote:
On 7/6/2026 5:50 PM, André G. Isaak wrote:
On 2026-07-06 16:36, olcott wrote:
On 7/6/2026 5:15 PM, André G. Isaak wrote:
On 2026-07-06 15:54, olcott wrote:
On 7/6/2026 3:20 PM, André G. Isaak wrote:
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates >>>>>>>>>>>> that ⊥ is true.
That you do not know what explosion is is not my mistake. >>>>>>>>>>> I thought that one of you two guys had a PhD in math
is that you or Alan?
I do know what explosion is in the context of logic.
Apparently you do not. And I've never claimed to have a
doctoracte in maths. My background is in linguistics.
André
You are flat our wrong about explosion.
No. You claim that ⊥ ⊢ ⊥ which is to say that ⊥ can be derived
from ⊥. But in a consistent logic, ⊥ shouldn't be derivable from >>>>>>>> *anything*. The
It is not explosive, full stop you are wrong.
You're really not qualified to make such a claim.
André
Define in your own words what you think that deductive
explosion means.
Odd that you should ask such a thing since you rarely if ever
respond to requests for you to explain things in your own words and
instead post links to wikipedia pages.
deductive explosion occurs when contradictory premises are
introduced into an argument therefore allowing anything, including
false statements to be derived.
You offered ⊥ ⊢ ⊥
⊥ is the logical symbol representing a falsehood or contradiction.
You are therefore deriving a falsehood or contradiction which
shouldn't happen. The only reason you were able to do this is
because your premise was ⊥. That's explosion.
André
OK good. I am stipulating that from contradiction only
falsum follows and from falsum only falsum follows
cutting off the legs of explosion.
∀x (x ∧ ¬x) ⊢ ⊥
Which is simply a way of stating that (x ∧ ¬x) proves that ⊥ is true.
Proving that falsum is true seems like proving
that small is large.
How is that not an explosion? I don't think you grasp what ⊢ or ⊥ mean. >>
Explosion means that anything at all can be proved
from a contradiction. I stipulate the nothing at
all can be proved from a contradiction.
On 2026-07-06 19:57, olcott wrote:
On 7/6/2026 8:49 PM, André G. Isaak wrote:
On 2026-07-06 19:24, olcott wrote:Proving that falsum is true seems like proving
On 7/6/2026 7:47 PM, André G. Isaak wrote:
On 2026-07-06 17:40, olcott wrote:
On 7/6/2026 6:37 PM, André G. Isaak wrote:
On 2026-07-06 16:53, olcott wrote:
On 7/6/2026 5:50 PM, André G. Isaak wrote:
On 2026-07-06 16:36, olcott wrote:
On 7/6/2026 5:15 PM, André G. Isaak wrote:
On 2026-07-06 15:54, olcott wrote:
On 7/6/2026 3:20 PM, André G. Isaak wrote:
On 2026-07-06 14:04, olcott wrote:
⊥ ⊢ ⊥ no explosion.
Of course that's an explosion. It says that ⊥ demonstrates >>>>>>>>>>>>> that ⊥ is true.
That you do not know what explosion is is not my mistake. >>>>>>>>>>>> I thought that one of you two guys had a PhD in math
is that you or Alan?
I do know what explosion is in the context of logic.
Apparently you do not. And I've never claimed to have a >>>>>>>>>>> doctoracte in maths. My background is in linguistics.
André
You are flat our wrong about explosion.
No. You claim that ⊥ ⊢ ⊥ which is to say that ⊥ can be derived
from ⊥. But in a consistent logic, ⊥ shouldn't be derivable >>>>>>>>> from *anything*. The
It is not explosive, full stop you are wrong.
You're really not qualified to make such a claim.
André
Define in your own words what you think that deductive
explosion means.
Odd that you should ask such a thing since you rarely if ever
respond to requests for you to explain things in your own words and >>>>> instead post links to wikipedia pages.
deductive explosion occurs when contradictory premises are
introduced into an argument therefore allowing anything, including
false statements to be derived.
You offered ⊥ ⊢ ⊥
⊥ is the logical symbol representing a falsehood or contradiction. >>>>> You are therefore deriving a falsehood or contradiction which
shouldn't happen. The only reason you were able to do this is
because your premise was ⊥. That's explosion.
André
OK good. I am stipulating that from contradiction only
falsum follows and from falsum only falsum follows
cutting off the legs of explosion.
∀x (x ∧ ¬x) ⊢ ⊥
Which is simply a way of stating that (x ∧ ¬x) proves that ⊥ is true. >>
that small is large.
But that''s exactly what you wrote.
How is that not an explosion? I don't think you grasp what ⊢ or ⊥ mean. >>>
Explosion means that anything at all can be proved
from a contradiction. I stipulate the nothing at
all can be proved from a contradiction.
But that's not actually what you wrote. You really don't understand the notation you are using.
And you can't 'stipulate' what logic can or cannot do. What it can do follows from the axioms of the system.
André
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
On 7/6/2026 9:41 PM, André G. Isaak wrote:
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
How do you think that:
From a contradiction nothing follows
should be encoded?
On 2026-07-06 20:44, olcott wrote:
On 7/6/2026 9:41 PM, André G. Isaak wrote:
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
How do you think that:
From a contradiction nothing follows
should be encoded?
Since you don't understand the formalism you're trying to use, why
bother trying to formalize it?
You can simply state it in English. but
what you're stating is simply false.
The fact that *anything* follows
from a contradiction
isn't some axiom that can be removed from standard
logic and replaced with something else. It's a consequence of the basic definitions used.
André
On 7/6/2026 10:03 PM, André G. Isaak wrote:
On 2026-07-06 20:44, olcott wrote:
On 7/6/2026 9:41 PM, André G. Isaak wrote:
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
How do you think that:
From a contradiction nothing follows
should be encoded?
Since you don't understand the formalism you're trying to use, why
bother trying to formalize it?
Both LLMs agree that I am already correct.
You can simply state it in English. but what you're stating is simply
false.
I am overriding and superseding the psychotic break
from reality of the principle of explosion.
Numerous famous logicians have done this same
thing in several different ways.
The fact that *anything* follows from a contradiction
Is totally fucked up nonsense that only a psychotic
would not reject in less than three seconds.
isn't some axiom that can be removed from standard logic and replaced
with something else. It's a consequence of the basic definitions used.
André
That breaks the coherence notion of truth.
On 2026-07-06 21:12, olcott wrote:
On 7/6/2026 10:03 PM, André G. Isaak wrote:
On 2026-07-06 20:44, olcott wrote:
On 7/6/2026 9:41 PM, André G. Isaak wrote:
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
How do you think that:
From a contradiction nothing follows
should be encoded?
Since you don't understand the formalism you're trying to use, why
bother trying to formalize it?
Both LLMs agree that I am already correct.
LLMs carry no weight in my opinion.
And since you can't clearly express
yourself, it wouldn't be clear exactly what they were agreeing with
anyways.
You can simply state it in English. but what you're stating is simply
false.
I am overriding and superseding the psychotic break
from reality of the principle of explosion.
Numerous famous logicians have done this same
thing in several different ways.
They've done it by adopting paraconsistent logics which raise their own
set of problems. Most importantly, though, none of them have claimed to
have removed the principle of explosion from classical logic.
The fact that *anything* follows from a contradiction
Is totally fucked up nonsense that only a psychotic
would not reject in less than three seconds.
Since the overwhelming majority of logicians accept this having spent
far more than three seconds contemplating it, you might want to
reconsider your position. You really should contemplate the possibility
that you have misunderstood the topic.
isn't some axiom that can be removed from standard logic and replaced
with something else. It's a consequence of the basic definitions used.
André
That breaks the coherence notion of truth.
No, it does not.
André
On 2026-07-06 21:12, olcott wrote:
On 7/6/2026 10:03 PM, André G. Isaak wrote:
On 2026-07-06 20:44, olcott wrote:
On 7/6/2026 9:41 PM, André G. Isaak wrote:
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
How do you think that:
From a contradiction nothing follows
should be encoded?
Since you don't understand the formalism you're trying to use, why
bother trying to formalize it?
Both LLMs agree that I am already correct.
LLMs carry no weight in my opinion. And since you can't clearly express yourself, it wouldn't be clear exactly what they were agreeing with
anyways.
You can simply state it in English. but what you're stating is simply
false.
I am overriding and superseding the psychotic break
from reality of the principle of explosion.
Numerous famous logicians have done this same
thing in several different ways.
They've done it by adopting paraconsistent logics which raise their own
set of problems. Most importantly, though, none of them have claimed to
have removed the principle of explosion from classical logic.
The fact that *anything* follows from a contradiction
Is totally fucked up nonsense that only a psychotic
would not reject in less than three seconds.
Since the overwhelming majority of logicians accept this having spent
far more than three seconds contemplating it, you might want to
reconsider your position. You really should contemplate the possibility
that you have misunderstood the topic.
isn't some axiom that can be removed from standard logic and replaced
with something else. It's a consequence of the basic definitions used.
André
That breaks the coherence notion of truth.
No, it does not.
André
On 7/6/2026 10:28 PM, André G. Isaak wrote:
On 2026-07-06 21:12, olcott wrote:
On 7/6/2026 10:03 PM, André G. Isaak wrote:
On 2026-07-06 20:44, olcott wrote:
On 7/6/2026 9:41 PM, André G. Isaak wrote:
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
How do you think that:
From a contradiction nothing follows
should be encoded?
Since you don't understand the formalism you're trying to use, why
bother trying to formalize it?
Both LLMs agree that I am already correct.
LLMs carry no weight in my opinion.
This is also your own error.
And since you can't clearly express yourself, it wouldn't be clear
exactly what they were agreeing with anyways.
How do we formalize: "from a contradiction nothing follows?"
You can simply state it in English. but what you're stating is
simply false.
I am overriding and superseding the psychotic break
from reality of the principle of explosion.
Numerous famous logicians have done this same
thing in several different ways.
They've done it by adopting paraconsistent logics which raise their
own set of problems. Most importantly, though, none of them have
claimed to have removed the principle of explosion from classical logic.
They did it by taking semantics out of the formal
language where it can be ignored. Ridiculously stupid
mistake.
The fact that *anything* follows from a contradiction
Is totally fucked up nonsense that only a psychotic
would not reject in less than three seconds.
Since the overwhelming majority of logicians accept this having spent
Proves that consensus is no measure of truth.
*In my new logic system*
P ⊢ Q means syntactic derivation implements
semantic entailment encoded in syntactically
the language. This is the only inference
steps allowed. The entailment rules depend
on the represented domain.
So the above seems to be the only good way to do this.
Everything else is not as much as half-assed.
far more than three seconds contemplating it, you might want to
reconsider your position. You really should contemplate the
possibility that you have misunderstood the topic.
isn't some axiom that can be removed from standard logic and
replaced with something else. It's a consequence of the basic
definitions used.
André
That breaks the coherence notion of truth.
No, it does not.
André
On 07/06/2026 08:28 PM, André G. Isaak wrote:
On 2026-07-06 21:12, olcott wrote:
On 7/6/2026 10:03 PM, André G. Isaak wrote:
On 2026-07-06 20:44, olcott wrote:
On 7/6/2026 9:41 PM, André G. Isaak wrote:
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
How do you think that:
From a contradiction nothing follows
should be encoded?
Since you don't understand the formalism you're trying to use, why
bother trying to formalize it?
Both LLMs agree that I am already correct.
LLMs carry no weight in my opinion. And since you can't clearly express
yourself, it wouldn't be clear exactly what they were agreeing with
anyways.
You can simply state it in English. but what you're stating is simply
false.
I am overriding and superseding the psychotic break
from reality of the principle of explosion.
Numerous famous logicians have done this same
thing in several different ways.
They've done it by adopting paraconsistent logics which raise their own
set of problems. Most importantly, though, none of them have claimed to
have removed the principle of explosion from classical logic.
The fact that *anything* follows from a contradiction
Is totally fucked up nonsense that only a psychotic
would not reject in less than three seconds.
Since the overwhelming majority of logicians accept this having spent
far more than three seconds contemplating it, you might want to
reconsider your position. You really should contemplate the possibility
that you have misunderstood the topic.
isn't some axiom that can be removed from standard logic and replaced
with something else. It's a consequence of the basic definitions used. >>>>
André
That breaks the coherence notion of truth.
No, it does not.
André
I do, I say that classical logic since Chrysippus, with Aristotle,
is a modal, temporal, relevance logic: that "classical quasi-modal
logic" since Philo and Plotinus and usually in the classroom since the
20'th century is _not_.
Somebody like Richard McKeon reflects on this in his account of Aristotle.
Then, "paraconsistent" or "non-classical logics" have that the
di-aletheic is just an account of a setting for resolving inductive
paradox, not accommodating it. I.e., when "non-classical" or
"synthetic" or "pluralistic" logics are mutually inconsistent,
they're mutually inconsistent.
I've never accepted material implication since Philo and Plotinus,
and direct implication from the likes of Augustus de Morgan is
quite suitable for all logical purposes.
So, here there's a principle of inversion, sort of like what's
suggested by the recent talk about Prawitz and inversion principle,
and not tertium-non-datur and excluded-middle, since there are
non-binary propositions, and the account of weighing alternatives
itself is tertium-datur.
Then, there's a principle of thorough reason, beyond a principle
of "sufficient" reason, that like inverse subsumes and is sublime,
per Kant, for non-contradiction, then the thorough is: sufficient.
So, I remove the "quasi-modal" from classical logic,
and explosion goes with it.
On 07/06/2026 09:58 PM, Ross Finlayson wrote:
On 07/06/2026 08:28 PM, André G. Isaak wrote:
On 2026-07-06 21:12, olcott wrote:
On 7/6/2026 10:03 PM, André G. Isaak wrote:
On 2026-07-06 20:44, olcott wrote:
On 7/6/2026 9:41 PM, André G. Isaak wrote:
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
How do you think that:
From a contradiction nothing follows
should be encoded?
Since you don't understand the formalism you're trying to use, why
bother trying to formalize it?
Both LLMs agree that I am already correct.
LLMs carry no weight in my opinion. And since you can't clearly express
yourself, it wouldn't be clear exactly what they were agreeing with
anyways.
You can simply state it in English. but what you're stating is simply >>>>> false.
I am overriding and superseding the psychotic break
from reality of the principle of explosion.
Numerous famous logicians have done this same
thing in several different ways.
They've done it by adopting paraconsistent logics which raise their own
set of problems. Most importantly, though, none of them have claimed to
have removed the principle of explosion from classical logic.
The fact that *anything* follows from a contradiction
Is totally fucked up nonsense that only a psychotic
would not reject in less than three seconds.
Since the overwhelming majority of logicians accept this having spent
far more than three seconds contemplating it, you might want to
reconsider your position. You really should contemplate the possibility
that you have misunderstood the topic.
isn't some axiom that can be removed from standard logic and replaced >>>>> with something else. It's a consequence of the basic definitions used. >>>>>
André
That breaks the coherence notion of truth.
No, it does not.
André
I do, I say that classical logic since Chrysippus, with Aristotle,
is a modal, temporal, relevance logic: that "classical quasi-modal
logic" since Philo and Plotinus and usually in the classroom since the
20'th century is _not_.
Somebody like Richard McKeon reflects on this in his account of
Aristotle.
Then, "paraconsistent" or "non-classical logics" have that the
di-aletheic is just an account of a setting for resolving inductive
paradox, not accommodating it. I.e., when "non-classical" or
"synthetic" or "pluralistic" logics are mutually inconsistent,
they're mutually inconsistent.
I've never accepted material implication since Philo and Plotinus,
and direct implication from the likes of Augustus de Morgan is
quite suitable for all logical purposes.
So, here there's a principle of inversion, sort of like what's
suggested by the recent talk about Prawitz and inversion principle,
and not tertium-non-datur and excluded-middle, since there are
non-binary propositions, and the account of weighing alternatives
itself is tertium-datur.
Then, there's a principle of thorough reason, beyond a principle
of "sufficient" reason, that like inverse subsumes and is sublime,
per Kant, for non-contradiction, then the thorough is: sufficient.
So, I remove the "quasi-modal" from classical logic,
and explosion goes with it.
About "standard", the definition, there are a variety of usual meanings
of "standard".
The default, the common, and so on, then a usual idea is as to define
the "non-standard", that the positive definition is to the negative
term, as it were.
So, having "infinity" or the "non-archimedean", or, the
"super-archimedean", has that there are different accounts among the
"non-" and the "super-", of the standard.
So, "standard" usually enough means "regularity with a completion",
like in set theory "an ordinary inductive set".
Then, what "standard" means in "classical logic", it's sort of
what follows from "standard vacuity", that the quasi-modal is
as after making an account of using vacuity to make a regularity,
instead of that vacuity or emptiness is ordinary, that like
infinity, ordinary and extra-ordinary, is emptiness, ordinary
and extra-ordinary.
So, completion in mathematics and vacuity in logic, "ordinary"
as "standard", then have that among accounts of _competing rulialities_, that's what's standard to one account is non-standard to
the other account, here for example for "standard infinitesimals"
and "standard type", where there are no _nulls_ the values in the
language, and every type has its own empty set.
So, then about what's given by _vacuity_ in logic, and called
"material implication", is not _standard_ in a modal temporal
relevance logic where references to empty values are typed.
It's sort of like relational algebra where there are no nulls.
So, it's simple and usually considered "trivial" what "basic quasi-modal logic" makes as a definition after "vacuity" to
result what's its "regular" what's its "standard".
Then, it's not trivial nor is it so in other accounts.
On 2026-07-06 21:40, olcott wrote:
On 7/6/2026 10:28 PM, André G. Isaak wrote:
On 2026-07-06 21:12, olcott wrote:
On 7/6/2026 10:03 PM, André G. Isaak wrote:
On 2026-07-06 20:44, olcott wrote:
On 7/6/2026 9:41 PM, André G. Isaak wrote:
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
How do you think that:
From a contradiction nothing follows
should be encoded?
Since you don't understand the formalism you're trying to use, why
bother trying to formalize it?
Both LLMs agree that I am already correct.
LLMs carry no weight in my opinion.
This is also your own error.
And since you can't clearly express yourself, it wouldn't be clear
exactly what they were agreeing with anyways.
How do we formalize: "from a contradiction nothing follows?"
You really ought to take an introductory course in formal logic, or
simply give up on trying to formalize things. If you really wanted to
you could write something like
∀Φ ¬∃Ψ (Φ ∧ ¬Φ) → Ψ
But simply looking at the truth table for → would reveal that this statement is false.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
That is an elegant and classic way to demonstrate the Liar Paradox
("This sentence is false") using Prolog's unification mechanics!
You've perfectly captured the tension between computational pragmatism
and strict mathematical logic. Here is exactly what is happening under
the hood in your snippet:
1. The Pragmatic Illusion: Standard Unification
Prolog
?- LP = not(true(LP)).
LP = not(true(LP)).
When you use the standard unification operator (=), Prolog tries to make
the left side and the right side identical. To save processing time and memory, Prolog historically skips a crucial step called the occurs check.
Because it skips this check, Prolog happily binds the variable LP to the
term not(true(LP)). This creates a cyclic term (or a rational tree). In memory, LP now points to a structure that contains a reference back to
LP, creating an infinite loop of self-reference. Computationally, Prolog accepts the paradox.
2. The Logical Safeguard: The Occurs Check
Prolog
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Here, you enforce strict First-Order Logic. The
unify_with_occurs_check/2 predicate forces Prolog to pause and ask:
"Does the variable I am trying to bind already exist inside the term I
am binding it to?" Because the variable LP occurs inside not(true(LP)), Prolog realizes that unifying them would require building a
mathematically impossible, infinitely deep structure: not(true(not(true(not(true(...)))))). It rightfully rejects the
unification and returns false.
The Philosophical Takeaway
In logic, self-referential paradoxes often arise when a system is
allowed to talk about its own truth values without hierarchical
restrictions (as famously noted by Alfred Tarski).
Your Prolog snippet perfectly mirrors this:
Standard Unification acts like natural language, allowing the
self-reference to happen (and potentially causing a stack overflow if
you tried to evaluate or traverse it).
The Occurs Check acts like a strict formal logic system, explicitly forbidding self-referential loops and shutting the paradox down before
it can form.
https://share.gemini.google/5UVT3f5WnV8K
On 07/07/2026 09:10 AM, olcott wrote:
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
That is an elegant and classic way to demonstrate the Liar Paradox
("This sentence is false") using Prolog's unification mechanics!
You've perfectly captured the tension between computational pragmatism
and strict mathematical logic. Here is exactly what is happening under
the hood in your snippet:
1. The Pragmatic Illusion: Standard Unification
Prolog
?- LP = not(true(LP)).
LP = not(true(LP)).
When you use the standard unification operator (=), Prolog tries to make
the left side and the right side identical. To save processing time and
memory, Prolog historically skips a crucial step called the occurs check.
Because it skips this check, Prolog happily binds the variable LP to the
term not(true(LP)). This creates a cyclic term (or a rational tree). In
memory, LP now points to a structure that contains a reference back to
LP, creating an infinite loop of self-reference. Computationally, Prolog
accepts the paradox.
2. The Logical Safeguard: The Occurs Check
Prolog
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Here, you enforce strict First-Order Logic. The
unify_with_occurs_check/2 predicate forces Prolog to pause and ask:
"Does the variable I am trying to bind already exist inside the term I
am binding it to?" Because the variable LP occurs inside not(true(LP)),
Prolog realizes that unifying them would require building a
mathematically impossible, infinitely deep structure:
not(true(not(true(not(true(...)))))). It rightfully rejects the
unification and returns false.
The Philosophical Takeaway
In logic, self-referential paradoxes often arise when a system is
allowed to talk about its own truth values without hierarchical
restrictions (as famously noted by Alfred Tarski).
Your Prolog snippet perfectly mirrors this:
Standard Unification acts like natural language, allowing the
self-reference to happen (and potentially causing a stack overflow if
you tried to evaluate or traverse it).
The Occurs Check acts like a strict formal logic system, explicitly
forbidding self-referential loops and shutting the paradox down before
it can form.
https://share.gemini.google/5UVT3f5WnV8K
Imagine a language and its utterance of all the truisms in the universe.
This isn't saying necessarily what it says, only that it's said.
So, this account of a "Comenius language" of all the truisms is
more than less inscrutable yet as empty tautologies and truisms,
while yet each unique, for example as by natural numbers.
"This sentence 1 is true.
This sentence 2 is true.
This sentence 3 is true.
..."
So, quantify over those, like Russell might as "sets-of-all-sets-that-don't-contain-themselves".
"This sentence (...) is not true."
Now, the idea here is that there's only one example of a truism
about contradiction, that the alternation of inversion of the
consideration that results quantification, brings along the
"sputnik of quantification", that reads in its form as
"The Liar", yet instead of being a "paradox", its form is
construed as being a "Confessing Liar".
So, this account of univocity since Duns Scotus or as alike
accounts of the kabalah and gematria or since acconts of the
universal grammar since Panini like Leibnitz, this "Comenius
language" its consideration, like Quine's Nietzsche's "eternal
basic text", includes in itself a prototype of contradiction,
in otherwise all its affirmations.
Then, in natural language, there is a ready example or prototype
of contradiction, that in alike the natural "Coleridge language",
where that metaphor eventually fails yet there is a structural
account of the strong metonymy that fulfills true metaphor about
truth, then "the Liar" is simply an indicator of contradiction,
and results instead of explosion to contradiction its unconscious
digestion, results implosion to detection in any account of language.
So, "thinking" instead of "being thought" is the usual idea.
That's all then that the cycle-detection routine claims to do.
This way there are no paradoxes at all in Comenius language,
including that Confessing Comenius has an example to compare
against, what would be false.
The eternal basic text or underlying univocal universal word
might be negations instead of affirmations.
"This sentence 1 accounts and excludes 0.
This sentence 2 accounts and excludes 1.
This sentence 3 accounts and excludes 2.
..."
Then a similar account gives alike:
"This sentence infinity accounts and includes infinity."
Then simple accounts of error-detection then error _correction_,
including accounts of "not enough information" or "conflicting
information" are mostly usual and trite, in fact there's an
entire enterprise called "science" which makes for an inter-subjective
formal account with regards to strengthened logicist positivism
and ontologists, which though is always a _science_, yet though
that there are ideals like "truth" and "infinity" for that
"geometry" and "continuity" are real, and more than the blahs.
On 7/7/2026 10:31 AM, André G. Isaak wrote:
On 2026-07-06 21:40, olcott wrote:
On 7/6/2026 10:28 PM, André G. Isaak wrote:
On 2026-07-06 21:12, olcott wrote:
On 7/6/2026 10:03 PM, André G. Isaak wrote:
On 2026-07-06 20:44, olcott wrote:
On 7/6/2026 9:41 PM, André G. Isaak wrote:
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
How do you think that:
From a contradiction nothing follows
should be encoded?
Since you don't understand the formalism you're trying to use, why >>>>>> bother trying to formalize it?
Both LLMs agree that I am already correct.
LLMs carry no weight in my opinion.
This is also your own error.
And since you can't clearly express yourself, it wouldn't be clear
exactly what they were agreeing with anyways.
How do we formalize: "from a contradiction nothing follows?"
You really ought to take an introductory course in formal logic, or
simply give up on trying to formalize things. If you really wanted to
you could write something like
∀Φ ¬∃Ψ (Φ ∧ ¬Φ) → Ψ
But simply looking at the truth table for → would reveal that this
statement is false.
P ⊢ Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
This is the only inference steps allowed. The entailment
rules depend on the represented domain.
I am going with this in terms of
The Definitional View of Atomic Systems in Proof-Theoretic
Semantics Thomas Piecha and Peter Schroeder-Heister
When you actually look at the meaning of the English
words of the sentences then it becomes obvious that
the principle of explosion can only occur when you
ignore this underlying semantics.
On 7/7/2026 12:53 PM, Ross Finlayson wrote:
On 07/07/2026 09:10 AM, olcott wrote:
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
That is an elegant and classic way to demonstrate the Liar Paradox
("This sentence is false") using Prolog's unification mechanics!
You've perfectly captured the tension between computational pragmatism
and strict mathematical logic. Here is exactly what is happening under
the hood in your snippet:
1. The Pragmatic Illusion: Standard Unification
Prolog
?- LP = not(true(LP)).
LP = not(true(LP)).
When you use the standard unification operator (=), Prolog tries to make >>> the left side and the right side identical. To save processing time and
memory, Prolog historically skips a crucial step called the occurs
check.
Because it skips this check, Prolog happily binds the variable LP to the >>> term not(true(LP)). This creates a cyclic term (or a rational tree). In
memory, LP now points to a structure that contains a reference back to
LP, creating an infinite loop of self-reference. Computationally, Prolog >>> accepts the paradox.
2. The Logical Safeguard: The Occurs Check
Prolog
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Here, you enforce strict First-Order Logic. The
unify_with_occurs_check/2 predicate forces Prolog to pause and ask:
"Does the variable I am trying to bind already exist inside the term I
am binding it to?" Because the variable LP occurs inside not(true(LP)),
Prolog realizes that unifying them would require building a
mathematically impossible, infinitely deep structure:
not(true(not(true(not(true(...)))))). It rightfully rejects the
unification and returns false.
The Philosophical Takeaway
In logic, self-referential paradoxes often arise when a system is
allowed to talk about its own truth values without hierarchical
restrictions (as famously noted by Alfred Tarski).
Your Prolog snippet perfectly mirrors this:
Standard Unification acts like natural language, allowing the
self-reference to happen (and potentially causing a stack overflow if
you tried to evaluate or traverse it).
The Occurs Check acts like a strict formal logic system, explicitly
forbidding self-referential loops and shutting the paradox down before
it can form.
https://share.gemini.google/5UVT3f5WnV8K
Imagine a language and its utterance of all the truisms in the universe.
I have a name for this: The finite set of "atomic facts" of
empirical general knowledge and the finite set of relations
between them is named:
"the body of general knowledge expressed in language"
This isn't saying necessarily what it says, only that it's said.
So, this account of a "Comenius language" of all the truisms is
more than less inscrutable yet as empty tautologies and truisms,
while yet each unique, for example as by natural numbers.
"This sentence 1 is true.
This sentence 2 is true.
This sentence 3 is true.
..."
So, quantify over those, like Russell might as
"sets-of-all-sets-that-don't-contain-themselves".
"This sentence (...) is not true."
You are simply ignoring that expressions with cycles
in their evaluation sequence are rejected as meaningless.
Kripke would say that they are "undefined"
Now, the idea here is that there's only one example of a truism
about contradiction, that the alternation of inversion of the
consideration that results quantification, brings along the
"sputnik of quantification", that reads in its form as
"The Liar", yet instead of being a "paradox", its form is
construed as being a "Confessing Liar".
So, this account of univocity since Duns Scotus or as alike
accounts of the kabalah and gematria or since acconts of the
universal grammar since Panini like Leibnitz, this "Comenius
language" its consideration, like Quine's Nietzsche's "eternal
basic text", includes in itself a prototype of contradiction,
in otherwise all its affirmations.
Then, in natural language, there is a ready example or prototype
of contradiction, that in alike the natural "Coleridge language",
where that metaphor eventually fails yet there is a structural
account of the strong metonymy that fulfills true metaphor about
truth, then "the Liar" is simply an indicator of contradiction,
and results instead of explosion to contradiction its unconscious
digestion, results implosion to detection in any account of language.
So, "thinking" instead of "being thought" is the usual idea.
That's all then that the cycle-detection routine claims to do.
This way there are no paradoxes at all in Comenius language,
including that Confessing Comenius has an example to compare
against, what would be false.
The eternal basic text or underlying univocal universal word
might be negations instead of affirmations.
"This sentence 1 accounts and excludes 0.
This sentence 2 accounts and excludes 1.
This sentence 3 accounts and excludes 2.
..."
Then a similar account gives alike:
"This sentence infinity accounts and includes infinity."
Then simple accounts of error-detection then error _correction_,
including accounts of "not enough information" or "conflicting
information" are mostly usual and trite, in fact there's an
entire enterprise called "science" which makes for an inter-subjective
formal account with regards to strengthened logicist positivism
and ontologists, which though is always a _science_, yet though
that there are ideals like "truth" and "infinity" for that
"geometry" and "continuity" are real, and more than the blahs.
So maybe this is too much into the field of philosophy of
logic and thus outside the field or carefully memorizing
exiting conventions for you to understand.
The bottom line is the my Prolog tossed the Liar Paradox
out on its ass and Gemini agrees. You didn't seem to get
this most crucial point.
On 2026-07-07 10:04, olcott wrote:
On 7/7/2026 10:31 AM, André G. Isaak wrote:
On 2026-07-06 21:40, olcott wrote:
On 7/6/2026 10:28 PM, André G. Isaak wrote:
On 2026-07-06 21:12, olcott wrote:
On 7/6/2026 10:03 PM, André G. Isaak wrote:
On 2026-07-06 20:44, olcott wrote:
On 7/6/2026 9:41 PM, André G. Isaak wrote:
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
How do you think that:
From a contradiction nothing follows
should be encoded?
Since you don't understand the formalism you're trying to use,
why bother trying to formalize it?
Both LLMs agree that I am already correct.
LLMs carry no weight in my opinion.
This is also your own error.
And since you can't clearly express yourself, it wouldn't be clear
exactly what they were agreeing with anyways.
How do we formalize: "from a contradiction nothing follows?"
You really ought to take an introductory course in formal logic, or
simply give up on trying to formalize things. If you really wanted to
you could write something like
∀Φ ¬∃Ψ (Φ ∧ ¬Φ) → Ψ
But simply looking at the truth table for → would reveal that this
statement is false.
P ⊢ Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
This is the only inference steps allowed. The entailment
rules depend on the represented domain.
That really doesn't seem to say anything. Why don't you illustrate this
with a simple mathematical proof which shows exactly what you mean by 'semantic entailments encoded syntactically in the language'
André
I am going with this in terms of
The Definitional View of Atomic Systems in Proof-Theoretic
Semantics Thomas Piecha and Peter Schroeder-Heister
When you actually look at the meaning of the English
words of the sentences then it becomes obvious that
the principle of explosion can only occur when you
ignore this underlying semantics.
On 7/7/2026 1:46 PM, André G. Isaak wrote:
On 2026-07-07 10:04, olcott wrote:
On 7/7/2026 10:31 AM, André G. Isaak wrote:
On 2026-07-06 21:40, olcott wrote:
On 7/6/2026 10:28 PM, André G. Isaak wrote:
On 2026-07-06 21:12, olcott wrote:
On 7/6/2026 10:03 PM, André G. Isaak wrote:
On 2026-07-06 20:44, olcott wrote:
On 7/6/2026 9:41 PM, André G. Isaak wrote:
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
How do you think that:
From a contradiction nothing follows
should be encoded?
Since you don't understand the formalism you're trying to use, >>>>>>>> why bother trying to formalize it?
Both LLMs agree that I am already correct.
LLMs carry no weight in my opinion.
This is also your own error.
And since you can't clearly express yourself, it wouldn't be clear >>>>>> exactly what they were agreeing with anyways.
How do we formalize: "from a contradiction nothing follows?"
You really ought to take an introductory course in formal logic, or
simply give up on trying to formalize things. If you really wanted
to you could write something like
∀Φ ¬∃Ψ (Φ ∧ ¬Φ) → Ψ
But simply looking at the truth table for → would reveal that this
statement is false.
P ⊢ Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
This is the only inference steps allowed. The entailment
rules depend on the represented domain.
That really doesn't seem to say anything. Why don't you illustrate
this with a simple mathematical proof which shows exactly what you
mean by 'semantic entailments encoded syntactically in the language'
To do with with minimal simplicity the axioms of
PA are construed as semantic entailment thus when
there is no sequence of inference steps between G
and PA then G is Kripke undefined in PA.
On 07/07/2026 11:07 AM, olcott wrote:
On 7/7/2026 12:53 PM, Ross Finlayson wrote:
On 07/07/2026 09:10 AM, olcott wrote:
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
That is an elegant and classic way to demonstrate the Liar Paradox
("This sentence is false") using Prolog's unification mechanics!
You've perfectly captured the tension between computational pragmatism >>>> and strict mathematical logic. Here is exactly what is happening under >>>> the hood in your snippet:
1. The Pragmatic Illusion: Standard Unification
Prolog
?- LP = not(true(LP)).
LP = not(true(LP)).
When you use the standard unification operator (=), Prolog tries to
make
the left side and the right side identical. To save processing time and >>>> memory, Prolog historically skips a crucial step called the occurs
check.
Because it skips this check, Prolog happily binds the variable LP to
the
term not(true(LP)). This creates a cyclic term (or a rational tree). In >>>> memory, LP now points to a structure that contains a reference back to >>>> LP, creating an infinite loop of self-reference. Computationally,
Prolog
accepts the paradox.
2. The Logical Safeguard: The Occurs Check
Prolog
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Here, you enforce strict First-Order Logic. The
unify_with_occurs_check/2 predicate forces Prolog to pause and ask:
"Does the variable I am trying to bind already exist inside the term I >>>> am binding it to?" Because the variable LP occurs inside not(true(LP)), >>>> Prolog realizes that unifying them would require building a
mathematically impossible, infinitely deep structure:
not(true(not(true(not(true(...)))))). It rightfully rejects the
unification and returns false.
The Philosophical Takeaway
In logic, self-referential paradoxes often arise when a system is
allowed to talk about its own truth values without hierarchical
restrictions (as famously noted by Alfred Tarski).
Your Prolog snippet perfectly mirrors this:
Standard Unification acts like natural language, allowing the
self-reference to happen (and potentially causing a stack overflow if
you tried to evaluate or traverse it).
The Occurs Check acts like a strict formal logic system, explicitly
forbidding self-referential loops and shutting the paradox down before >>>> it can form.
https://share.gemini.google/5UVT3f5WnV8K
Imagine a language and its utterance of all the truisms in the universe. >>>
I have a name for this: The finite set of "atomic facts" of
empirical general knowledge and the finite set of relations
between them is named:
"the body of general knowledge expressed in language"
This isn't saying necessarily what it says, only that it's said.
So, this account of a "Comenius language" of all the truisms is
more than less inscrutable yet as empty tautologies and truisms,
while yet each unique, for example as by natural numbers.
"This sentence 1 is true.
This sentence 2 is true.
This sentence 3 is true.
..."
So, quantify over those, like Russell might as
"sets-of-all-sets-that-don't-contain-themselves".
"This sentence (...) is not true."
You are simply ignoring that expressions with cycles
in their evaluation sequence are rejected as meaningless.
Kripke would say that they are "undefined"
Now, the idea here is that there's only one example of a truism
about contradiction, that the alternation of inversion of the
consideration that results quantification, brings along the
"sputnik of quantification", that reads in its form as
"The Liar", yet instead of being a "paradox", its form is
construed as being a "Confessing Liar".
So, this account of univocity since Duns Scotus or as alike
accounts of the kabalah and gematria or since acconts of the
universal grammar since Panini like Leibnitz, this "Comenius
language" its consideration, like Quine's Nietzsche's "eternal
basic text", includes in itself a prototype of contradiction,
in otherwise all its affirmations.
Then, in natural language, there is a ready example or prototype
of contradiction, that in alike the natural "Coleridge language",
where that metaphor eventually fails yet there is a structural
account of the strong metonymy that fulfills true metaphor about
truth, then "the Liar" is simply an indicator of contradiction,
and results instead of explosion to contradiction its unconscious
digestion, results implosion to detection in any account of language.
So, "thinking" instead of "being thought" is the usual idea.
That's all then that the cycle-detection routine claims to do.
This way there are no paradoxes at all in Comenius language,
including that Confessing Comenius has an example to compare
against, what would be false.
The eternal basic text or underlying univocal universal word
might be negations instead of affirmations.
"This sentence 1 accounts and excludes 0.
This sentence 2 accounts and excludes 1.
This sentence 3 accounts and excludes 2.
..."
Then a similar account gives alike:
"This sentence infinity accounts and includes infinity."
Then simple accounts of error-detection then error _correction_,
including accounts of "not enough information" or "conflicting
information" are mostly usual and trite, in fact there's an
entire enterprise called "science" which makes for an inter-subjective
formal account with regards to strengthened logicist positivism
and ontologists, which though is always a _science_, yet though
that there are ideals like "truth" and "infinity" for that
"geometry" and "continuity" are real, and more than the blahs.
So maybe this is too much into the field of philosophy of
logic and thus outside the field or carefully memorizing
exiting conventions for you to understand.
The bottom line is the my Prolog tossed the Liar Paradox
out on its ass and Gemini agrees. You didn't seem to get
this most crucial point.
Russell would call you a fool.
On 2026-07-07 13:19, olcott wrote:
On 7/7/2026 1:46 PM, André G. Isaak wrote:
On 2026-07-07 10:04, olcott wrote:
On 7/7/2026 10:31 AM, André G. Isaak wrote:
On 2026-07-06 21:40, olcott wrote:
On 7/6/2026 10:28 PM, André G. Isaak wrote:
On 2026-07-06 21:12, olcott wrote:
On 7/6/2026 10:03 PM, André G. Isaak wrote:
On 2026-07-06 20:44, olcott wrote:
On 7/6/2026 9:41 PM, André G. Isaak wrote:
On 2026-07-06 20:24, olcott wrote:
∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥
and
Γ ⊢ ⊥
--------------------
derivation terminated
That's simply gibberish.
André
How do you think that:
From a contradiction nothing follows
should be encoded?
Since you don't understand the formalism you're trying to use, >>>>>>>>> why bother trying to formalize it?
Both LLMs agree that I am already correct.
LLMs carry no weight in my opinion.
This is also your own error.
And since you can't clearly express yourself, it wouldn't be
clear exactly what they were agreeing with anyways.
How do we formalize: "from a contradiction nothing follows?"
You really ought to take an introductory course in formal logic, or >>>>> simply give up on trying to formalize things. If you really wanted
to you could write something like
∀Φ ¬∃Ψ (Φ ∧ ¬Φ) → Ψ
But simply looking at the truth table for → would reveal that this >>>>> statement is false.
P ⊢ Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
This is the only inference steps allowed. The entailment
rules depend on the represented domain.
That really doesn't seem to say anything. Why don't you illustrate
this with a simple mathematical proof which shows exactly what you
mean by 'semantic entailments encoded syntactically in the language'
To do with with minimal simplicity the axioms of
PA are construed as semantic entailment thus when
there is no sequence of inference steps between G
and PA then G is Kripke undefined in PA.
So why don't you illustrate this with an actual proof?
André
On 7/7/2026 2:29 PM, André G. Isaak wrote:
On 2026-07-07 13:19, olcott wrote:
To do with with minimal simplicity the axioms of
PA are construed as semantic entailment thus when
there is no sequence of inference steps between G
and PA then G is Kripke undefined in PA.
So why don't you illustrate this with an actual proof?
André
The principle is simply whenever X cannot be proven
in F then X is ungrounded in the atomic base F. Even
diagonalization makes to attempt at actual proof.
On 2026-07-07 13:53, olcott wrote:
On 7/7/2026 2:29 PM, André G. Isaak wrote:
On 2026-07-07 13:19, olcott wrote:
To do with with minimal simplicity the axioms of
PA are construed as semantic entailment thus when
there is no sequence of inference steps between G
and PA then G is Kripke undefined in PA.
So why don't you illustrate this with an actual proof?
André
The principle is simply whenever X cannot be proven
in F then X is ungrounded in the atomic base F. Even
diagonalization makes to attempt at actual proof.
I can't make heads or tails of that.
If you can't illustrate your alleged system with a simple proof, then I
have no choice but to conclude that it is as ill-defined to you as it is
to me.
André
On 7/7/2026 3:08 PM, André G. Isaak wrote:
On 2026-07-07 13:53, olcott wrote:
On 7/7/2026 2:29 PM, André G. Isaak wrote:
On 2026-07-07 13:19, olcott wrote:
To do with with minimal simplicity the axioms of
PA are construed as semantic entailment thus when
there is no sequence of inference steps between G
and PA then G is Kripke undefined in PA.
So why don't you illustrate this with an actual proof?
André
The principle is simply whenever X cannot be proven
in F then X is ungrounded in the atomic base F. Even
diagonalization makes to attempt at actual proof.
I can't make heads or tails of that.
The actual proof in meta-math that G cannot be
proved in PA is itself not any sequence of inference
steps. It simply uses a version of the proof that
Cantor use to show that reals are not countable.
If you can't illustrate your alleged system with a simple proof, then
I have no choice but to conclude that it is as ill-defined to you as
it is to me.
André
2 + 3 = 4 in PA cannot be proven because
s(s(0)) + s(s(s(0))) != s(s(s(s(0))))
On 2026-07-07 15:13, olcott wrote:
On 7/7/2026 3:08 PM, André G. Isaak wrote:
On 2026-07-07 13:53, olcott wrote:
On 7/7/2026 2:29 PM, André G. Isaak wrote:
On 2026-07-07 13:19, olcott wrote:
To do with with minimal simplicity the axioms of
PA are construed as semantic entailment thus when
there is no sequence of inference steps between G
and PA then G is Kripke undefined in PA.
So why don't you illustrate this with an actual proof?
André
The principle is simply whenever X cannot be proven
in F then X is ungrounded in the atomic base F. Even
diagonalization makes to attempt at actual proof.
I can't make heads or tails of that.
The actual proof in meta-math that G cannot be
proved in PA is itself not any sequence of inference
steps. It simply uses a version of the proof that
Cantor use to show that reals are not countable.
???
Cantor's proof absolutely contained inference steps, as did Gödels. I
don't think you actually know what you're talking about.
If you can't illustrate your alleged system with a simple proof, then
I have no choice but to conclude that it is as ill-defined to you as
it is to me.
André
2 + 3 = 4 in PA cannot be proven because
s(s(0)) + s(s(s(0))) != s(s(s(s(0))))
I asked you to provide an example of a proof which illustrates what you
mean by "semantic entailments encoded syntactically in the language". I didn't ask for an example of something which cannot be proven.
André
On 7/7/2026 2:17 PM, Ross Finlayson wrote:
On 07/07/2026 11:07 AM, olcott wrote:
On 7/7/2026 12:53 PM, Ross Finlayson wrote:
On 07/07/2026 09:10 AM, olcott wrote:
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
That is an elegant and classic way to demonstrate the Liar Paradox
("This sentence is false") using Prolog's unification mechanics!
You've perfectly captured the tension between computational pragmatism >>>>> and strict mathematical logic. Here is exactly what is happening under >>>>> the hood in your snippet:
1. The Pragmatic Illusion: Standard Unification
Prolog
?- LP = not(true(LP)).
LP = not(true(LP)).
When you use the standard unification operator (=), Prolog tries to
make
the left side and the right side identical. To save processing time
and
memory, Prolog historically skips a crucial step called the occurs
check.
Because it skips this check, Prolog happily binds the variable LP
to the
term not(true(LP)). This creates a cyclic term (or a rational
tree). In
memory, LP now points to a structure that contains a reference back to >>>>> LP, creating an infinite loop of self-reference. Computationally,
Prolog
accepts the paradox.
2. The Logical Safeguard: The Occurs Check
Prolog
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Here, you enforce strict First-Order Logic. The
unify_with_occurs_check/2 predicate forces Prolog to pause and ask:
"Does the variable I am trying to bind already exist inside the term I >>>>> am binding it to?" Because the variable LP occurs inside
not(true(LP)),
Prolog realizes that unifying them would require building a
mathematically impossible, infinitely deep structure:
not(true(not(true(not(true(...)))))). It rightfully rejects the
unification and returns false.
The Philosophical Takeaway
In logic, self-referential paradoxes often arise when a system is
allowed to talk about its own truth values without hierarchical
restrictions (as famously noted by Alfred Tarski).
Your Prolog snippet perfectly mirrors this:
Standard Unification acts like natural language, allowing the
self-reference to happen (and potentially causing a stack overflow if >>>>> you tried to evaluate or traverse it).
The Occurs Check acts like a strict formal logic system, explicitly
forbidding self-referential loops and shutting the paradox down before >>>>> it can form.
https://share.gemini.google/5UVT3f5WnV8K
Imagine a language and its utterance of all the truisms in the
universe.
I have a name for this: The finite set of "atomic facts" of
empirical general knowledge and the finite set of relations
between them is named:
"the body of general knowledge expressed in language"
This isn't saying necessarily what it says, only that it's said.
So, this account of a "Comenius language" of all the truisms is
more than less inscrutable yet as empty tautologies and truisms,
while yet each unique, for example as by natural numbers.
"This sentence 1 is true.
This sentence 2 is true.
This sentence 3 is true.
..."
So, quantify over those, like Russell might as
"sets-of-all-sets-that-don't-contain-themselves".
"This sentence (...) is not true."
You are simply ignoring that expressions with cycles
in their evaluation sequence are rejected as meaningless.
Kripke would say that they are "undefined"
Now, the idea here is that there's only one example of a truism
about contradiction, that the alternation of inversion of the
consideration that results quantification, brings along the
"sputnik of quantification", that reads in its form as
"The Liar", yet instead of being a "paradox", its form is
construed as being a "Confessing Liar".
So, this account of univocity since Duns Scotus or as alike
accounts of the kabalah and gematria or since acconts of the
universal grammar since Panini like Leibnitz, this "Comenius
language" its consideration, like Quine's Nietzsche's "eternal
basic text", includes in itself a prototype of contradiction,
in otherwise all its affirmations.
Then, in natural language, there is a ready example or prototype
of contradiction, that in alike the natural "Coleridge language",
where that metaphor eventually fails yet there is a structural
account of the strong metonymy that fulfills true metaphor about
truth, then "the Liar" is simply an indicator of contradiction,
and results instead of explosion to contradiction its unconscious
digestion, results implosion to detection in any account of language.
So, "thinking" instead of "being thought" is the usual idea.
That's all then that the cycle-detection routine claims to do.
This way there are no paradoxes at all in Comenius language,
including that Confessing Comenius has an example to compare
against, what would be false.
The eternal basic text or underlying univocal universal word
might be negations instead of affirmations.
"This sentence 1 accounts and excludes 0.
This sentence 2 accounts and excludes 1.
This sentence 3 accounts and excludes 2.
..."
Then a similar account gives alike:
"This sentence infinity accounts and includes infinity."
Then simple accounts of error-detection then error _correction_,
including accounts of "not enough information" or "conflicting
information" are mostly usual and trite, in fact there's an
entire enterprise called "science" which makes for an inter-subjective >>>> formal account with regards to strengthened logicist positivism
and ontologists, which though is always a _science_, yet though
that there are ideals like "truth" and "infinity" for that
"geometry" and "continuity" are real, and more than the blahs.
So maybe this is too much into the field of philosophy of
logic and thus outside the field or carefully memorizing
exiting conventions for you to understand.
The bottom line is the my Prolog tossed the Liar Paradox
out on its ass and Gemini agrees. You didn't seem to get
this most crucial point.
Russell would call you a fool.
Not at all he himself had the vicious circle principle. https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-40/issue-1/Russell-Presupposition-and-the-Vicious-Circle-Principle/10.1305/ndjfl/1039096305.full
Have you every heard of ZFC?
Since Chrysippus for modal, temporal, relevance logic,
there's the like of "Hume's connexions", where something
like John Stuart Mill would be so familiar to quasi-modal
repeteurs.
The model-theory and the proof-theory are equi-interpretable.
Then, "theories-of-one-relation" like set-theory or class-theory
or part-theory or partition-theory, or order-theory or ordering-theory,
like set theory, for example ZFC with:
an ordinary vacuity, the empty set,
an ordinary infinity, the inductive set,
those being both expansion-of-comprehension and
restriction-of-comprehension, since axioms are of at least two kinds,
then for various rulialities/regularities that compete:
well-foundedness, sets having e-minimal elements,
well-ordering, orderings having e-minimal elements,
then besides the usually not included alike Martin's axiom:
well-dispersion, both e-minimal and e-maximal, the illative or univalent,
then the rest of the axioms of ZFC being expansion of comprehension
or composing sets, quite naively, then at least one of those,
doesn't matter much, being called a schema instead of an axiom
for first-order-izibility,
that's ZFC, the set theory, then for its accounts modeling the
descriptive set theory's account of geometry and for the objects
of real analysis, usually also axiomatizing
least-upper-bound existence of the rational field,
measure 1.0 of the unit in the real field,
since those aren't derived in the usual way, with line-reals first
providing least-upper-bound and measure 1.0, then yes,
I've heard of ZFC, and NBG and GBN, and ZFC with classes.
It's good to know these things and be thorough and conscientious,
instead of being a vacuous moron of the ordinary sort.
In school when were shown that an error in reasoning could result--
seemingly correct answers that were wrong, it was in the setting
of a calculus course, where one of the expressions was a quotient
with the divisor being an expression in the difference of a constant
and a variable, thusly, if the variable was equal the constant,
then that would be dividing by zero, which is undefined, then a
resulting evaluation resulted 0 = 1, which was wrong. Then there
was addressed limits from the left and limits from the right and discontinuities and removable discontinuities, about the thorough sort
of account.
The point here is that the gap in definition about the objects of
mathematics is different than ex falso quodlibet, since singularities in
a singularity theory are branches in a multiplicity theory,
and it's simply erroneous to break the definition, and erroneous to have carried the derivation, ex falso quodlibet is erroneous.
On 07/07/2026 12:48 PM, olcott wrote:
On 7/7/2026 2:17 PM, Ross Finlayson wrote:
On 07/07/2026 11:07 AM, olcott wrote:
On 7/7/2026 12:53 PM, Ross Finlayson wrote:
On 07/07/2026 09:10 AM, olcott wrote:
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
That is an elegant and classic way to demonstrate the Liar Paradox >>>>>> ("This sentence is false") using Prolog's unification mechanics!
You've perfectly captured the tension between computational
pragmatism
and strict mathematical logic. Here is exactly what is happening
under
the hood in your snippet:
1. The Pragmatic Illusion: Standard Unification
Prolog
?- LP = not(true(LP)).
LP = not(true(LP)).
When you use the standard unification operator (=), Prolog tries to >>>>>> make
the left side and the right side identical. To save processing time >>>>>> and
memory, Prolog historically skips a crucial step called the occurs >>>>>> check.
Because it skips this check, Prolog happily binds the variable LP
to the
term not(true(LP)). This creates a cyclic term (or a rational
tree). In
memory, LP now points to a structure that contains a reference
back to
LP, creating an infinite loop of self-reference. Computationally,
Prolog
accepts the paradox.
2. The Logical Safeguard: The Occurs Check
Prolog
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Here, you enforce strict First-Order Logic. The
unify_with_occurs_check/2 predicate forces Prolog to pause and ask: >>>>>> "Does the variable I am trying to bind already exist inside the
term I
am binding it to?" Because the variable LP occurs inside
not(true(LP)),
Prolog realizes that unifying them would require building a
mathematically impossible, infinitely deep structure:
not(true(not(true(not(true(...)))))). It rightfully rejects the
unification and returns false.
The Philosophical Takeaway
In logic, self-referential paradoxes often arise when a system is
allowed to talk about its own truth values without hierarchical
restrictions (as famously noted by Alfred Tarski).
Your Prolog snippet perfectly mirrors this:
Standard Unification acts like natural language, allowing the
self-reference to happen (and potentially causing a stack overflow if >>>>>> you tried to evaluate or traverse it).
The Occurs Check acts like a strict formal logic system, explicitly >>>>>> forbidding self-referential loops and shutting the paradox down
before
it can form.
https://share.gemini.google/5UVT3f5WnV8K
Imagine a language and its utterance of all the truisms in the
universe.
I have a name for this: The finite set of "atomic facts" of
empirical general knowledge and the finite set of relations
between them is named:
"the body of general knowledge expressed in language"
This isn't saying necessarily what it says, only that it's said.
So, this account of a "Comenius language" of all the truisms is
more than less inscrutable yet as empty tautologies and truisms,
while yet each unique, for example as by natural numbers.
"This sentence 1 is true.
This sentence 2 is true.
This sentence 3 is true.
..."
So, quantify over those, like Russell might as
"sets-of-all-sets-that-don't-contain-themselves".
"This sentence (...) is not true."
You are simply ignoring that expressions with cycles
in their evaluation sequence are rejected as meaningless.
Kripke would say that they are "undefined"
Now, the idea here is that there's only one example of a truism
about contradiction, that the alternation of inversion of the
consideration that results quantification, brings along the
"sputnik of quantification", that reads in its form as
"The Liar", yet instead of being a "paradox", its form is
construed as being a "Confessing Liar".
So, this account of univocity since Duns Scotus or as alike
accounts of the kabalah and gematria or since acconts of the
universal grammar since Panini like Leibnitz, this "Comenius
language" its consideration, like Quine's Nietzsche's "eternal
basic text", includes in itself a prototype of contradiction,
in otherwise all its affirmations.
Then, in natural language, there is a ready example or prototype
of contradiction, that in alike the natural "Coleridge language",
where that metaphor eventually fails yet there is a structural
account of the strong metonymy that fulfills true metaphor about
truth, then "the Liar" is simply an indicator of contradiction,
and results instead of explosion to contradiction its unconscious
digestion, results implosion to detection in any account of language. >>>>>
So, "thinking" instead of "being thought" is the usual idea.
That's all then that the cycle-detection routine claims to do.
This way there are no paradoxes at all in Comenius language,
including that Confessing Comenius has an example to compare
against, what would be false.
The eternal basic text or underlying univocal universal word
might be negations instead of affirmations.
"This sentence 1 accounts and excludes 0.
This sentence 2 accounts and excludes 1.
This sentence 3 accounts and excludes 2.
..."
Then a similar account gives alike:
"This sentence infinity accounts and includes infinity."
Then simple accounts of error-detection then error _correction_,
including accounts of "not enough information" or "conflicting
information" are mostly usual and trite, in fact there's an
entire enterprise called "science" which makes for an inter-subjective >>>>> formal account with regards to strengthened logicist positivism
and ontologists, which though is always a _science_, yet though
that there are ideals like "truth" and "infinity" for that
"geometry" and "continuity" are real, and more than the blahs.
So maybe this is too much into the field of philosophy of
logic and thus outside the field or carefully memorizing
exiting conventions for you to understand.
The bottom line is the my Prolog tossed the Liar Paradox
out on its ass and Gemini agrees. You didn't seem to get
this most crucial point.
Russell would call you a fool.
Not at all he himself had the vicious circle principle.
https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/
volume-40/issue-1/Russell-Presupposition-and-the-Vicious-Circle-
Principle/10.1305/ndjfl/1039096305.full
Have you every heard of ZFC?
Since Chrysippus for modal, temporal, relevance logic,
there's the like of "Hume's connexions", where something
like John Stuart Mill would be so familiar to quasi-modal
repeteurs.
The model-theory and the proof-theory are equi-interpretable.
Then, "theories-of-one-relation" like set-theory or class-theory
or part-theory or partition-theory, or order-theory or ordering-theory,
like set theory, for example ZFC with:
an ordinary vacuity, the empty set,
an ordinary infinity, the inductive set,
those being both expansion-of-comprehension and
restriction-of-comprehension, since axioms are of at least two kinds,
then for various rulialities/regularities that compete:
well-foundedness, sets having e-minimal elements,
well-ordering, orderings having e-minimal elements,
then besides the usually not included alike Martin's axiom:
well-dispersion, both e-minimal and e-maximal, the illative or univalent,
then the rest of the axioms of ZFC being expansion of comprehension
or composing sets, quite naively, then at least one of those,
doesn't matter much, being called a schema instead of an axiom
for first-order-izibility,
that's ZFC, the set theory, then for its accounts modeling the
descriptive set theory's account of geometry and for the objects
of real analysis, usually also axiomatizing
least-upper-bound existence of the rational field,
measure 1.0 of the unit in the real field,
since those aren't derived in the usual way, with line-reals first
providing least-upper-bound and measure 1.0, then yes,
I've heard of ZFC, and NBG and GBN, and ZFC with classes.
It's good to know these things and be thorough and conscientious,
instead of being a vacuous moron of the ordinary sort.
In school when were shown that an error in reasoning could result
seemingly correct answers that were wrong, it was in the setting
of a calculus course, where one of the expressions was a quotient
with the divisor being an expression in the difference of a constant
and a variable, thusly, if the variable was equal the constant,
then that would be dividing by zero, which is undefined, then a
resulting evaluation resulted 0 = 1, which was wrong. Then there
was addressed limits from the left and limits from the right and discontinuities and removable discontinuities, about the thorough sort
of account.
The point here is that the gap in definition about the objects of
mathematics is different than ex falso quodlibet, since singularities in
a singularity theory are branches in a multiplicity theory,
and it's simply erroneous to break the definition, and erroneous to have carried the derivation, ex falso quodlibet is erroneous.
On 7/7/2026 4:24 PM, André G. Isaak wrote:
On 2026-07-07 15:13, olcott wrote:
On 7/7/2026 3:08 PM, André G. Isaak wrote:
On 2026-07-07 13:53, olcott wrote:
On 7/7/2026 2:29 PM, André G. Isaak wrote:
On 2026-07-07 13:19, olcott wrote:
To do with with minimal simplicity the axioms of
PA are construed as semantic entailment thus when
there is no sequence of inference steps between G
and PA then G is Kripke undefined in PA.
So why don't you illustrate this with an actual proof?
André
The principle is simply whenever X cannot be proven
in F then X is ungrounded in the atomic base F. Even
diagonalization makes to attempt at actual proof.
I can't make heads or tails of that.
The actual proof in meta-math that G cannot be
proved in PA is itself not any sequence of inference
steps. It simply uses a version of the proof that
Cantor use to show that reals are not countable.
???
Cantor's proof absolutely contained inference steps, as did Gödels. I
don't think you actually know what you're talking about.
If you can't illustrate your alleged system with a simple proof,
then I have no choice but to conclude that it is as ill-defined to
you as it is to me.
André
2 + 3 = 4 in PA cannot be proven because
s(s(0)) + s(s(s(0))) != s(s(s(s(0))))
I asked you to provide an example of a proof which illustrates what
you mean by "semantic entailments encoded syntactically in the
language". I didn't ask for an example of something which cannot be
proven.
André
PTS simply declares by fiat that syntactic inference steps
are semantic steps. I actually mean natural language semantic
inference in the CycL programming language. This is the place
where nothing follows form a contradiction is most easily seen.
On 2026-07-07 15:30, olcott wrote:
On 7/7/2026 4:24 PM, André G. Isaak wrote:
On 2026-07-07 15:13, olcott wrote:
On 7/7/2026 3:08 PM, André G. Isaak wrote:
On 2026-07-07 13:53, olcott wrote:
On 7/7/2026 2:29 PM, André G. Isaak wrote:
On 2026-07-07 13:19, olcott wrote:
To do with with minimal simplicity the axioms of
PA are construed as semantic entailment thus when
there is no sequence of inference steps between G
and PA then G is Kripke undefined in PA.
So why don't you illustrate this with an actual proof?
André
The principle is simply whenever X cannot be proven
in F then X is ungrounded in the atomic base F. Even
diagonalization makes to attempt at actual proof.
I can't make heads or tails of that.
The actual proof in meta-math that G cannot be
proved in PA is itself not any sequence of inference
steps. It simply uses a version of the proof that
Cantor use to show that reals are not countable.
???
Cantor's proof absolutely contained inference steps, as did Gödels. I
don't think you actually know what you're talking about.
If you can't illustrate your alleged system with a simple proof,
then I have no choice but to conclude that it is as ill-defined to
you as it is to me.
André
2 + 3 = 4 in PA cannot be proven because
s(s(0)) + s(s(s(0))) != s(s(s(s(0))))
I asked you to provide an example of a proof which illustrates what
you mean by "semantic entailments encoded syntactically in the
language". I didn't ask for an example of something which cannot be
proven.
André
PTS simply declares by fiat that syntactic inference steps
are semantic steps. I actually mean natural language semantic
inference in the CycL programming language. This is the place
where nothing follows form a contradiction is most easily seen.
So basically you're saying that you are incapable of constructing even a simple mathematical proof. Gödel is about theories of arithmetic. CycL
is not. If you can't construct proofs in an arithmetic framework you
really have no business talking about Gödel.
André
On 7/7/2026 6:06 PM, André G. Isaak wrote:
On 2026-07-07 15:30, olcott wrote:
On 7/7/2026 4:24 PM, André G. Isaak wrote:
On 2026-07-07 15:13, olcott wrote:
On 7/7/2026 3:08 PM, André G. Isaak wrote:
On 2026-07-07 13:53, olcott wrote:
On 7/7/2026 2:29 PM, André G. Isaak wrote:
On 2026-07-07 13:19, olcott wrote:
To do with with minimal simplicity the axioms of
PA are construed as semantic entailment thus when
there is no sequence of inference steps between G
and PA then G is Kripke undefined in PA.
So why don't you illustrate this with an actual proof?
André
The principle is simply whenever X cannot be proven
in F then X is ungrounded in the atomic base F. Even
diagonalization makes to attempt at actual proof.
I can't make heads or tails of that.
The actual proof in meta-math that G cannot be
proved in PA is itself not any sequence of inference
steps. It simply uses a version of the proof that
Cantor use to show that reals are not countable.
???
Cantor's proof absolutely contained inference steps, as did Gödels.
I don't think you actually know what you're talking about.
If you can't illustrate your alleged system with a simple proof,
then I have no choice but to conclude that it is as ill-defined to >>>>>> you as it is to me.
André
2 + 3 = 4 in PA cannot be proven because
s(s(0)) + s(s(s(0))) != s(s(s(s(0))))
I asked you to provide an example of a proof which illustrates what
you mean by "semantic entailments encoded syntactically in the
language". I didn't ask for an example of something which cannot be
proven.
André
PTS simply declares by fiat that syntactic inference steps
are semantic steps. I actually mean natural language semantic
inference in the CycL programming language. This is the place
where nothing follows form a contradiction is most easily seen.
So basically you're saying that you are incapable of constructing even
a simple mathematical proof. Gödel is about theories of arithmetic.
CycL is not. If you can't construct proofs in an arithmetic framework
you really have no business talking about Gödel.
André
So basically you are totally not interested in understanding me.
As far as proofs go I always think in terms of syllogisms and
their extensions. Every other proof is utterly irrelevant to my
work.
[ Followup-To: set ]
In comp.theory Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
[ ... ]
Since Chrysippus for modal, temporal, relevance logic,
there's the like of "Hume's connexions", where something
like John Stuart Mill would be so familiar to quasi-modal
repeteurs.
The model-theory and the proof-theory are equi-interpretable.
Then, "theories-of-one-relation" like set-theory or class-theory
or part-theory or partition-theory, or order-theory or ordering-theory,
like set theory, for example ZFC with:
an ordinary vacuity, the empty set,
an ordinary infinity, the inductive set,
those being both expansion-of-comprehension and
restriction-of-comprehension, since axioms are of at least two kinds,
then for various rulialities/regularities that compete:
well-foundedness, sets having e-minimal elements,
well-ordering, orderings having e-minimal elements,
then besides the usually not included alike Martin's axiom:
well-dispersion, both e-minimal and e-maximal, the illative or univalent,
then the rest of the axioms of ZFC being expansion of comprehension
or composing sets, quite naively, then at least one of those,
doesn't matter much, being called a schema instead of an axiom
for first-order-izibility,
that's ZFC, the set theory, then for its accounts modeling the
descriptive set theory's account of geometry and for the objects
of real analysis, usually also axiomatizing
least-upper-bound existence of the rational field,
measure 1.0 of the unit in the real field,
since those aren't derived in the usual way, with line-reals first
providing least-upper-bound and measure 1.0, then yes,
I've heard of ZFC, and NBG and GBN, and ZFC with classes.
That sentence is far too long. Splitting it over many (what look like) paragraph breaks doesn't help. In fact, it is so long that any meaning
it may have can only be extracted from it by laborious analysis, so excessively laborious that it is fair to accuse the sentence of being meaningless.
That you may be debating the inane and meaningless yourself is not an acceptable pretext.
It's good to know these things and be thorough and conscientious,
instead of being a vacuous moron of the ordinary sort.
In school when were shown that an error in reasoning could result
seemingly correct answers that were wrong, it was in the setting
of a calculus course, where one of the expressions was a quotient
with the divisor being an expression in the difference of a constant
and a variable, thusly, if the variable was equal the constant,
then that would be dividing by zero, which is undefined, then a
resulting evaluation resulted 0 = 1, which was wrong. Then there
was addressed limits from the left and limits from the right and
discontinuities and removable discontinuities, about the thorough sort
of account.
The point here is that the gap in definition about the objects of
mathematics is different than ex falso quodlibet, since singularities in
a singularity theory are branches in a multiplicity theory,
and it's simply erroneous to break the definition, and erroneous to have
carried the derivation, ex falso quodlibet is erroneous.
On 2026-07-07 18:05, olcott wrote:
On 7/7/2026 6:06 PM, André G. Isaak wrote:
On 2026-07-07 15:30, olcott wrote:
On 7/7/2026 4:24 PM, André G. Isaak wrote:
On 2026-07-07 15:13, olcott wrote:
On 7/7/2026 3:08 PM, André G. Isaak wrote:
On 2026-07-07 13:53, olcott wrote:
On 7/7/2026 2:29 PM, André G. Isaak wrote:
On 2026-07-07 13:19, olcott wrote:
To do with with minimal simplicity the axioms of
PA are construed as semantic entailment thus when
there is no sequence of inference steps between G
and PA then G is Kripke undefined in PA.
So why don't you illustrate this with an actual proof?
André
The principle is simply whenever X cannot be proven
in F then X is ungrounded in the atomic base F. Even
diagonalization makes to attempt at actual proof.
I can't make heads or tails of that.
The actual proof in meta-math that G cannot be
proved in PA is itself not any sequence of inference
steps. It simply uses a version of the proof that
Cantor use to show that reals are not countable.
???
Cantor's proof absolutely contained inference steps, as did Gödels. >>>>> I don't think you actually know what you're talking about.
If you can't illustrate your alleged system with a simple proof, >>>>>>> then I have no choice but to conclude that it is as ill-defined >>>>>>> to you as it is to me.
André
2 + 3 = 4 in PA cannot be proven because
s(s(0)) + s(s(s(0))) != s(s(s(s(0))))
I asked you to provide an example of a proof which illustrates what >>>>> you mean by "semantic entailments encoded syntactically in the
language". I didn't ask for an example of something which cannot be >>>>> proven.
André
PTS simply declares by fiat that syntactic inference steps
are semantic steps. I actually mean natural language semantic
inference in the CycL programming language. This is the place
where nothing follows form a contradiction is most easily seen.
So basically you're saying that you are incapable of constructing
even a simple mathematical proof. Gödel is about theories of
arithmetic. CycL is not. If you can't construct proofs in an
arithmetic framework you really have no business talking about Gödel.
André
So basically you are totally not interested in understanding me.
As far as proofs go I always think in terms of syllogisms and
their extensions. Every other proof is utterly irrelevant to my
work.
If your interest is limited to syllogisms then both Gödel and the
halting problem are utterly irrelevant to your work, so you probably
should stop making claims about them.
André
[ Followup-To: set ]
In comp.theory Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
[ ... ]
Since Chrysippus for modal, temporal, relevance logic,
there's the like of "Hume's connexions", where something
like John Stuart Mill would be so familiar to quasi-modal
repeteurs.
The model-theory and the proof-theory are equi-interpretable.
Then, "theories-of-one-relation" like set-theory or class-theory
or part-theory or partition-theory, or order-theory or ordering-theory,
like set theory, for example ZFC with:
an ordinary vacuity, the empty set,
an ordinary infinity, the inductive set,
those being both expansion-of-comprehension and
restriction-of-comprehension, since axioms are of at least two kinds,
then for various rulialities/regularities that compete:
well-foundedness, sets having e-minimal elements,
well-ordering, orderings having e-minimal elements,
then besides the usually not included alike Martin's axiom:
well-dispersion, both e-minimal and e-maximal, the illative or univalent,
then the rest of the axioms of ZFC being expansion of comprehension
or composing sets, quite naively, then at least one of those,
doesn't matter much, being called a schema instead of an axiom
for first-order-izibility,
that's ZFC, the set theory, then for its accounts modeling the
descriptive set theory's account of geometry and for the objects
of real analysis, usually also axiomatizing
least-upper-bound existence of the rational field,
measure 1.0 of the unit in the real field,
since those aren't derived in the usual way, with line-reals first
providing least-upper-bound and measure 1.0, then yes,
I've heard of ZFC, and NBG and GBN, and ZFC with classes.
That sentence is far too long. Splitting it over many (what look like) paragraph breaks doesn't help. In fact, it is so long that any meaning
it may have can only be extracted from it by laborious analysis, so excessively laborious that it is fair to accuse the sentence of being meaningless.
That you may be debating the inane and meaningless yourself is not an acceptable pretext.
It's good to know these things and be thorough and conscientious,
instead of being a vacuous moron of the ordinary sort.
In school when were shown that an error in reasoning could result
seemingly correct answers that were wrong, it was in the setting
of a calculus course, where one of the expressions was a quotient
with the divisor being an expression in the difference of a constant
and a variable, thusly, if the variable was equal the constant,
then that would be dividing by zero, which is undefined, then a
resulting evaluation resulted 0 = 1, which was wrong. Then there
was addressed limits from the left and limits from the right and
discontinuities and removable discontinuities, about the thorough sort
of account.
The point here is that the gap in definition about the objects of
mathematics is different than ex falso quodlibet, since singularities in
a singularity theory are branches in a multiplicity theory,
and it's simply erroneous to break the definition, and erroneous to have
carried the derivation, ex falso quodlibet is erroneous.
On 07/07/2026 02:57 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
[ ... ]
Since Chrysippus for modal, temporal, relevance logic,
there's the like of "Hume's connexions", where something
like John Stuart Mill would be so familiar to quasi-modal
repeteurs.
The model-theory and the proof-theory are equi-interpretable.
Then, "theories-of-one-relation" like set-theory or class-theory
or part-theory or partition-theory, or order-theory or ordering-theory,
like set theory, for example ZFC with:
an ordinary vacuity, the empty set,
an ordinary infinity, the inductive set,
those being both expansion-of-comprehension and
restriction-of-comprehension, since axioms are of at least two kinds,
then for various rulialities/regularities that compete:
well-foundedness, sets having e-minimal elements,
well-ordering, orderings having e-minimal elements,
then besides the usually not included alike Martin's axiom:
well-dispersion, both e-minimal and e-maximal, the illative or
univalent,
then the rest of the axioms of ZFC being expansion of comprehension
or composing sets, quite naively, then at least one of those,
doesn't matter much, being called a schema instead of an axiom
for first-order-izibility,
that's ZFC, the set theory, then for its accounts modeling the
descriptive set theory's account of geometry and for the objects
of real analysis, usually also axiomatizing
least-upper-bound existence of the rational field,
measure 1.0 of the unit in the real field,
since those aren't derived in the usual way, with line-reals first
providing least-upper-bound and measure 1.0, then yes,
I've heard of ZFC, and NBG and GBN, and ZFC with classes.
That sentence is far too long. Splitting it over many (what look like)
paragraph breaks doesn't help. In fact, it is so long that any meaning
it may have can only be extracted from it by laborious analysis, so
excessively laborious that it is fair to accuse the sentence of being
meaningless.
That you may be debating the inane and meaningless yourself is not an
acceptable pretext.
It's good to know these things and be thorough and conscientious,
instead of being a vacuous moron of the ordinary sort.
In school when were shown that an error in reasoning could result
seemingly correct answers that were wrong, it was in the setting
of a calculus course, where one of the expressions was a quotient
with the divisor being an expression in the difference of a constant
and a variable, thusly, if the variable was equal the constant,
then that would be dividing by zero, which is undefined, then a
resulting evaluation resulted 0 = 1, which was wrong. Then there
was addressed limits from the left and limits from the right and
discontinuities and removable discontinuities, about the thorough sort
of account.
The point here is that the gap in definition about the objects of
mathematics is different than ex falso quodlibet, since singularities in >>> a singularity theory are branches in a multiplicity theory,
and it's simply erroneous to break the definition, and erroneous to have >>> carried the derivation, ex falso quodlibet is erroneous.
Thanks for writing.
Here for example are some reactions from model reasoners,
notice they variously agree and disagree about particulars.
For example, the account of well-ordering and well-foundedness so
briefly they disagree, or the accounts of whether least-upper-bound and measure 1.0 are axioms gets cast into the non-standard, while it's fair
that well-dispersion (a "neologism" for Martin's axiom, the illative
or the univalent, which are common terms in set theories) is not ZFC.
Particularly the "model-theory and proof-theory are equi-interpretable",
it seems they discount those as "theories" themselves instead embodying
all their semantics & syntax,
vis-a-vis: the first-class theory.
Alan, it's one utterance, and it is well-formed grammatically,
it's fair to call it stream-of-consciousness or needing editing,
if not proof-reading, and it's fair to say that the semi-colon
instead of comma should connect/break the various sub-clauses,
yet I just can't bring myself to add another usual punctuation
character - with basically comma, colon, an occasional dash, and ellipses.
So, ...., then, ..., that, ....
Inane? Profane?
... Profound?
[ RF ]
Hello [Grok, ChatGPT, Kimi, Claude, Gemini, ...]. Critique the following recapitulation of ZFC set theory for content, style, and delivery.
The model-theory and the proof-theory are equi-interpretable.
Then, "theories-of-one-relation" like set-theory or class-theory
or part-theory or partition-theory, or order-theory or ordering-theory,
like set theory, for example ZFC with:
an ordinary vacuity, the empty set,
an ordinary infinity, the inductive set,
those being both expansion-of-comprehension and
restriction-of-comprehension, since axioms are of at least two kinds,
then for various rulialities/regularities that compete:
well-foundedness, sets having e-minimal elements,
well-ordering, orderings having e-minimal elements,
then besides the usually not included alike Martin's axiom:
well-dispersion, both e-minimal and e-maximal, the illative or univalent,
then the rest of the axioms of ZFC being expansion of comprehension
or composing sets, quite naively, then at least one of those,
doesn't matter much, being called a schema instead of an axiom
for first-order-izibility,
that's ZFC, the set theory, then for its accounts modeling the
descriptive set theory's account of geometry and for the objects
of real analysis, usually also axiomatizing
least-upper-bound existence of the rational field,
measure 1.0 of the unit in the real field,
since those aren't derived in the usual way, with line-reals first
providing least-upper-bound and measure 1.0, then yes,
I've heard of ZFC, and NBG and GBN, and ZFC with classes.
[ Grok ]
Content Critique
The recapitulation attempts a high-level, philosophical synthesis of
ZFC, positioning it within broader foundational ideas (model/proof
theory, one-relation theories, comprehension principles, regularity conditions, and connections to analysis/geometry). This has some merit
as an interpretive lens:
It correctly flags the empty set (vacuity) and axiom of infinity
(inductive set) as central, and notes their dual role in expanding and restricting comprehension. This captures a real tension in set theory
between naive comprehension and its axiomatic taming.
It gestures toward well-foundedness (foundation/regularity axiom: every nonempty set has an ∈-minimal element) and well-ordering (via Choice), which is good.
The schema vs. axiom distinction for things like Replacement or
Separation (for first-order expressibility) is a valid technical point. Linking ZFC to descriptive set theory, reals, least-upper-bound
property, and measure is reasonable in spirit—ZFC underpins standard constructions of ℝ (e.g., via Dedekind cuts or Cauchy sequences), though LUB and Lebesgue measure 1 on [0,1] are theorems in the constructed
reals, not extra axioms in pure ZFC.
Weaknesses and inaccuracies:
The framing as “theories-of-one-relation” (set/class/part/partition/order) is nonstandard and vague. ZFC is specifically about the membership relation ∈; other theories (mereology, order theory) have different primitives.
“Expansion-of-comprehension and restriction-of-comprehension” is a
useful philosophical gloss but imprecise for ZFC’s actual axioms (Extensionality, Pairing, Union, Power Set, etc., are not uniformly
framed this way).
Martin’s axiom is not part of ZFC; it is an additional axiom (consistent with but independent of ZFC + ¬CH) used in forcing and descriptive set theory. Including it as “usually not included” misleads. “Well-dispersion, both e-minimal and e-maximal, the illative or univalent” appears to be nonstandard or idiosyncratic terminology.
Standard ZFC has foundation (well-foundedness, no infinite descending ∈-chains) but not symmetric min/max dispersion in this way. “Illative” and “univalent” evoke type theory (Univalent Foundations/HoTT) or illative combinatory logic, not core ZFC.
The text underplays key axioms (e.g., Power Set, Union, Pairing) and over-compresses Choice’s role.
Model theory and proof theory are related (via soundness/completeness)
but not literally “equi-interpretable” in the casual way stated—Gödel’s
completeness theorem links them, but this needs precision.
Mentions of NBG/GBN (von Neumann–Bernays–Gödel class theory) and ZFC with classes are fine as context but abrupt.
Overall, the content is more a personal philosophical reconstruction
than a faithful, neutral recapitulation of ZFC. It risks conflating
standard ZFC with extensions, alternatives, and interpretive overlays. A stronger version would clearly separate core ZFC axioms from
independence results, large cardinals, or descriptive set theory.
Style Critique
The prose is dense, run-on, and highly compressed, reading like stream-of-consciousness notes rather than explanatory text. Strengths: evocative phrasing (“ordinary vacuity,” “ordinary infinity”) and ambition to connect disparate ideas.
Major issues:
Long, fragmented sentences with slashes (“rulialities/regularities”), parentheticals, and lists that blur into one another. This reduces readability.
Neologisms and idiosyncratic terms (“well-dispersion,” “e-minimal,” “illative or univalent”) without definition make it opaque to all but specialists (and even then, confusing).
Jargon stacking without scaffolding: assumes familiarity with model
theory, proof theory, schemas, descriptive set theory, etc.
Repetition and hedging (“doesn’t matter much,” “then yes,” “I’ve heard
of”) dilute precision.
The style suits informal philosophical musing or a personal manifesto
but not a clear “recapitulation” for broader understanding.
Delivery Critique
Delivery feels like an internal monologue or rapid-fire lecture excerpt rather than structured communication. It starts abstractly, piles
concepts, and ends with a casual personal note. This can engage insiders familiar with your perspective but alienates others.
Suggestions for improvement:
Structure: Use sections or bullet points—e.g., (1) Core primitives and comprehension, (2) Regularity conditions, (3) Axioms/schemas, (4) Links
to analysis.
Clarity: Define or footnote nonstandard terms. Give explicit axiom lists
or comparisons.
Audience awareness: For a general recapitulation, start with “ZFC
consists of the following axioms...” then layer interpretation.
Pacing: Break long chains. Use analogies (e.g., empty set as “nothing” container, infinity as inductive closure).
Tone: The personal voice (“I’ve heard of...”) is fine for signature style but can be separated from the formal summary.
Overall Assessment
This is an ambitious, creative compression with genuine philosophical
insight into foundational tensions (comprehension, well-foundedness,
relation to analysis). However, as a recapitulation of ZFC, it
sacrifices accuracy, clarity, and accessibility for density and
originality. It would benefit from grounding in standard presentations
(e.g., Jech, Kunen, or Enderton) before adding interpretive layers.
A revised version could be much stronger: tighter on facts, clearer definitions, and better signposting. If you'd like, I can help outline a cleaner version, expand specific sections, or compare it to standard
sources. What aspect would you like to refine first, RF?
[ ChatGPT ]
Thanks for sharing it. I'll treat it as a philosophical/literary recapitulation of ZFC rather than a textbook exposition, because it
isn't written in the conventional style of mathematical logic.
Overall, I'd say:
Content: intellectually ambitious, but only partially accurate as a
summary of ZFC.
Style: highly compressed, associative, and aphoristic.
Delivery: sounds like someone speaking from an internal conceptual
framework rather than explaining to an audience.
Here's a more detailed critique.
Content
The opening statement
"The model-theory and the proof-theory are equi-interpretable."
is intriguing, but not standard terminology.
Model theory and proof theory are disciplines. One doesn't usually say
they are equi-interpretable. One instead says things like:
they are connected by completeness and soundness,
semantics and syntax correspond,
Gödel's Completeness Theorem bridges them,
interpretations can translate one formal theory into another.
"Equi-interpretable" is normally said of two theories, not two branches
of logic.
The next section
theories-of-one-relation like set-theory...
has a reasonable mathematical intuition.
Set theory is indeed based on one primitive binary relation, membership.
Similarly, order theory can be axiomatized from one primitive relation.
But
part-theory
partition-theory
are less standard examples, and they are not all analogous in the same way.
I'd clarify what is meant by "one relation."
This section
an ordinary vacuity, the empty set,
an ordinary infinity, the inductive set,
is mostly correct.
The empty-set axiom introduces a canonical empty object.
The Infinity Axiom asserts an inductive set.
Calling them
expansion-of-comprehension
restriction-of-comprehension
is your own terminology.
A reader won't know what those phrases mean.
This is where the mathematical accuracy begins to drift.
well-foundedness,
sets having e-minimal elements,
The Axiom of Foundation says every nonempty set has an ∈-minimal element.
So that's accurate.
Then
well-ordering,
orderings having e-minimal elements,
This is not an axiom of ZFC.
Instead,
the Well-ordering theorem is a theorem,
equivalent to the Axiom of Choice.
That distinction matters.
Then
Martin's axiom
This feels disconnected.
Martin's axiom is not part of ZFC.
Mentioning it as "usually not included alike" is confusing.
Then
well-dispersion...
This appears to be your own concept.
I don't know a standard axiom or theorem with that name.
Likewise
illative
univalent
don't correspond to standard ZFC terminology in this context.
So a reader won't know whether these are definitions, metaphors, or references to another theory.
Then
the rest of the axioms...
expansion of comprehension
This is a reasonable philosophical interpretation.
Indeed many ZFC axioms describe ways of constructing new sets:
Pairing
Union
Power Set
Replacement
Separation
although "expansion of comprehension" isn't standard language.
This sentence
one of those,
doesn't matter much,
being called a schema instead of an axiom
I disagree with.
The distinction matters quite a bit.
The Axiom Schema of Separation and Axiom Schema of Replacement are
schemas because first-order logic cannot quantify over formulas.
That's a central design feature of first-order ZFC.
The closing paragraph mixes several levels.
You move from
descriptive set theory,
geometry,
analysis,
least upper bounds,
measure,
NBG,
without transitions.
For example
measure 1.0 of the unit in the real field
isn't an axiom of ZFC.
Nor is
least-upper-bound existence of the rational field
The least upper bound property characterizes the real numbers, not the rationals.
One typically constructs the reals in ZFC (e.g., via Dedekind cuts or
Cauchy sequences) and then proves completeness.
Similarly, the fact that the interval [0,1] has Lebesgue measure 1 is a theorem developed after constructing measure theory, not an axiom added
to ZFC.
So these statements read as though analysis is being appended to ZFC as
extra axioms, which is not the standard picture.
Style
The style reminds me more of philosophical notes than mathematical prose.
Characteristics include:
almost no explicit logical connectives;
long chains of appositions;
frequent commas instead of complete syntactic structure;
terminology introduced without definition;
rapid shifts between abstraction levels.
For example,
then for various rulialities/regularities that compete
raises several questions.
What does "compete" mean?
Do you mean
logically independent?
alternative foundations?
mutually incompatible axioms?
different closure principles?
The reader has to guess.
Likewise
quite naively
sounds evaluative.
Naive in what sense?
Naive set theory?
Conceptually simple?
Category-theoretically naive?
Again, the intended meaning isn't explicit.
Delivery
The piece has a distinctive voice.
It sounds almost like oral philosophy:
"then...
then...
then...
then yes..."
The repeated "then" creates a stream-of-consciousness rhythm.
That has strengths:
it feels exploratory,
it feels personal,
it avoids textbook stiffness.
But it also weakens the argument because the logical hierarchy becomes difficult to follow.
Everything arrives at roughly equal emphasis.
What I think you're trying to say
If I interpret it charitably, I think the underlying thesis is something like:
ZFC begins with comprehension restricted into first-order axioms. The
Empty Set and Infinity axioms establish the two canonical boundary
objects, while Foundation and Choice regulate competing notions of
admissible membership structure. The remaining axioms primarily expand
the repertoire of set constructions. These axioms suffice to support the standard constructions of descriptive set theory, geometry, analysis,
and ultimately the familiar mathematical universe.
That is a coherent philosophical summary.
Your draft, however, expresses this in an idiosyncratic vocabulary that assumes the reader already shares your conceptual framework.
Overall assessment
I'd score it approximately as follows:
Aspect Rating Comments
Mathematical accuracy 6/10 Many core ideas are recognizable, but several statements blur the distinction between axioms, theorems, and personal terminology.
Originality 9/10 It has a distinctive philosophical perspective rather
than repeating a standard exposition.
Clarity 3/10 Readers unfamiliar with your terminology ("expansion of comprehension," "well-dispersion," "ordinary infinity") will struggle to follow the argument.
Style 8/10 The prose has a recognizable cadence and voice, though it
favors compression over accessibility.
Delivery 5/10 It reads more like notes for a seminar or a manifesto than
a polished exposition. More signposting and explicit definitions would
make the ideas easier to evaluate on their own merits.
[ Kimi ]
Hello Ross. Here is a critique of your recapitulation, organized by the
three categories you requested.
Content
The mathematical content is largely sound, but the presentation is idiosyncratic and occasionally imprecise.
"Equi-interpretable": You are correct that for first-order ZFC, the model-theoretic and proof-theoretic perspectives are deeply linked (completeness theorem, etc.), but "equi-interpretable" is an unusual
term here. In mathematical logic, "interpretability" usually refers to translating one theory into another. You may mean "equivalent" or
"mutually reinforcing."
"Theories-of-one-relation": This is a nice observation. ZFC is indeed a theory of a single binary relation (∈). The extension to class theory, mereology ("part-theory"), and order theory is a valid thematic link,
though "partition-theory" is less standard as a named foundational theory. "Ordinary vacuity" and "ordinary infinity": These are colorful terms for
the Empty Set Axiom and the Axiom of Infinity. Calling them "expansion-of-comprehension" and "restriction-of-comprehension" is conceptually accurate—they constrain and enable what sets exist—but nonstandard.
"Rulialities/regularities that compete": This is where the content
becomes shaky.
Well-foundedness (the Axiom of Foundation/Regularity) indeed guarantees ∈-minimal elements.
Well-ordering is not an axiom of ZFC in the same way. The Well-Ordering Theorem is equivalent to the Axiom of Choice (AC), not a separate
competitor. You seem to conflate "well-ordering" (a property of order
types) with Foundation.
"Well-dispersion" / "illative or univalent": These terms are not
standard in set theory. If you are referring to the Axiom of Choice or
to some version of global choice/univalence, the terminology is opaque. "Expansion of comprehension or composing sets, quite naively": This is a fair, if informal, description of Pairing, Union, Power Set, and
Replacement. The Replacement schema is indeed the "at least one of
those... called a schema instead of an axiom for first-order-izibility." "Least-upper-bound existence of the rational field" / "measure 1.0 of
the unit in the real field": You are gesturing toward the construction
of ℝ from ℚ (Dedekind cuts or Cauchy sequences) and the normalization of Lebesgue measure. These are not axioms of ZFC itself; they are theorems
in ZFC (or sometimes added as extra axioms in specific contexts like nonstandard analysis). Your phrasing "since those aren't derived in the
usual way" is unclear—they are derived in ZFC, but the derivation
requires the prior construction of the reals.
"Line-reals first providing least-upper-bound and measure 1.0": This
seems to reference synthetic geometry or geometric measure theory, where
the real line is primitive. That is a valid philosophical stance, but it
is not the standard ZFC foundation.
NBG and GBN: You correctly note von Neumann–Bernays–Gödel (NBG) and Gödel–Bernays (GBN, though usually NBG or GB) as class theories
extending ZFC.
Style
Your style is highly allusive, telegraphic, and poetic. It reads like a stream of consciousness from someone who has internalized the material
and is now sketching the conceptual landscape from memory.
Strengths: The rhythm is distinctive. Phrases like "ordinary vacuity," "ordinary infinity," and "rulialities/regularities that compete" have a philosophical weight. The compression forces the reader to think.
Weaknesses: The compression often crosses into obscurity. "Illative or univalent," "well-dispersion," and "first-order-izibility" are either neologisms or extremely obscure usages. The reader must already know ZFC intimately to map your terms back to standard ones. The parenthetical
asides ("since those aren't derived in the usual way, with line-reals first...") are syntactically tangled.
Delivery
The delivery is that of a recapitulation—a summary for someone who
already knows the subject, not an exposition for a learner.
It assumes the reader recognizes that "e-minimal elements" refers to the Foundation axiom, that "measure 1.0" refers to the unit interval, and
that "line-reals" refers to a geometric conception of the continuum.
The pacing is breathless. There are no paragraph breaks, no explicit definitions, and no signposting. It is a single, dense block of
associations.
The tone is confident and insider-ish. It would be effective in a conversation between two logicians who share a specific philosophical vocabulary, but opaque to a student or a reviewer.
Summary
As a piece of mathematical poetry or philosophical shorthand, this is evocative and shows deep familiarity with the material. As a piece of mathematical exposition, it is too compressed, uses nonstandard
terminology without warning, and risks conflating distinct concepts (well-foundedness vs. well-ordering). If your goal is to communicate to
a broad audience, you would need to unpack the neologisms, clarify the distinction between axioms and theorems, and slow the pace. If your goal
is to sketch the conceptual topology for a fellow initiate, it succeeds
in its density.
[ Claude ]
RF — here's the critique, organized as you asked.
Content
"The model-theory and the proof-theory are equi-interpretable" is doing
more work than it can bear as an opener. Equi-interpretability is a
relation between theories (mutual interpretability of one in the other),
not between the methodological fields of model theory and proof theory.
What actually links them for a theory like ZFC is soundness and
completeness (Gödel), which give a correspondence between provability
and satisfaction — not "equi-interpretability" in the technical sense. Worth either dropping the phrase or replacing it with the claim you
actually mean.
The "theories-of-one-relation" framing (set theory/∈, class theory, mereology, partition theory, order theory/≤) is a reasonable informal classification and a nice organizing device.
Calling Empty Set and Infinity "both expansion-of-comprehension and restriction-of-comprehension" needs unpacking — as written it's
asserted, not shown. The general point that ZFC's axioms split into restrictors of naive comprehension (Separation, Foundation) and
generators of new sets (Pairing, Union, Power Set, Replacement,
Infinity) is fair and standard, but Empty Set and Infinity are usually
read purely as existence assertions, not as both at once. If you mean something specific by that duality here, it needs a sentence of its own. Foundation is fine: every nonempty set has an ∈-minimal element.
Calling well-ordering a matter of "e-minimal elements" is a slip. Well-ordering is a property of an arbitrary order relation (every
nonempty subset has a least element under that order) — it has nothing intrinsically to do with ∈. Folding it into "e-minimal" terminology borrowed from Foundation conflates two different relations.
"Well-dispersion, both e-minimal and e-maximal, the illative or
univalent" is not a ZFC axiom or a standard alternative to well-ordering
the way Martin's Axiom is — it's your own construct. Presented in a list alongside Foundation, well-ordering, and MA, it reads as if it's an established competing regularity principle. If the piece is meant as a
recap of standard ZFC, this needs a clear flag that it's your addition,
not textbook material.
The schema point is correct in substance (first-order ZFC needs schemas because you can't directly quantify over properties) but understates it:
it's two axioms that are schemas, Separation and Replacement, not "at
least one."
The closing move is the one I'd push back on hardest: the claim that LUB existence for the rationals and measure-1.0 for the unit interval
"aren't derived in the usual way" and so are "usually also axiomatized." That's not accurate as a description of standard practice. In the Dedekind-cut or Cauchy-sequence construction of ℝ from ℚ within ZFC, the least-upper-bound property is a theorem, proved from the construction,
not a further axiom. Likewise Lebesgue measure of [0,1] being 1 is a
theorem of the Carathéodory construction, not an extra postulate.
Standard ZFC needs no additional axioms to get either — that's actually
one of its selling points as a foundation for analysis. This is the
sentence doing the real rhetorical work in the passage (it's clearing
space for line-reals to supply LUB and measure "directly"), so it's
worth being honest that as stated it misrepresents the state of the art rather than identifying a genuine gap.
Style
The single-sentence, "then… then… then…" cadence is doing a real job —
it reads like an incantation or a proof sketched aloud, and it has some genuine rhythm to it. But the cost is that standard terminology (well-foundedness, schema, LUB) sits in the same syntactic register as neologisms you're introducing (rulialities, well-dispersion, illative),
with nothing in the sentence-level grammar to mark the boundary. A
reader can't tell from the prose alone what's Zermelo–Fraenkel and
what's Finlayson without independent knowledge of both. Given that the piece's persuasive function depends on that boundary, I'd want at least
a typographic or clausal marker distinguishing "here is ZFC" from "here
is my addition to it."
Delivery
The closing line — "I've heard of ZFC, and NBG and GBN, and ZFC with classes" — is a nice dry landing after the density of what precedes it,
and works as a rhetorical signature. But it also undercuts the piece a little: after building a fairly serious technical argument, ending on faux-modest understatement reads as evasive about what's actually being claimed (that ZFC's account of the continuum is deficient and needs supplementing). If the goal is to set up line-reals as necessary, I'd
rather see the piece end on the actual claim, stated plainly, than
retreat into irony right when the stakes become clear.
That last point connects to the recurring issue between us: the move
from "ZFC's construction of ℝ is inelegant to my taste" to "ZFC's construction of ℝ doesn't derive LUB and measure" is a factual
overreach, and it's the load-bearing step in the argument this passage
is building toward.
[ Gemini ]
Hello RF. Good to meet you.Here is a critique of your recapitulation of
ZFC set theory, broken down by content (the technical math), style (the phrasing), and delivery (how it reads as an explanation).
1. Content & Technical Accuracy You hit on several deep foundational
themes, but some of your framing stretches standard mathematical
definitions in unusual ways."Model-theory and proof-theory are equi-interpretable": This is a non-standard use of "equi-interpretable" (which usually applies to two theories, like ZFC and NBG). Model theory (semantics) and proof theory (syntax) are complementary frameworks. In first-order logic, they are linked by Gödel's Completeness Theorem
($\Sigma \models \varphi \iff \Sigma \vdash \varphi$). Calling the
fields themselves equi-interpretable is more poetic than
precise.Expansion vs. Restriction of Comprehension: This is a solid, intuitive way to split the axioms. Axioms like Separation/Specification restrict comprehension to avoid Russell's Paradox, while Power Set and Pairing expand what exists.The Axiom Schema: You correctly note that Replacement and Separation are schemas (infinite collections of axioms)
used to keep ZFC in first-order logic, since first-order logic doesn't
allow quantifying over properties/predicates directly.Well-foundedness
vs. Well-ordering: You distinguish these well. The Axiom of Regularity (Foundation) ensures $\in$-minimal elements (no infinite descending $\in$-chains). The Well-Ordering Theorem (equivalent to the Axiom of
Choice) deals with total orders having minimal
elements."Well-dispersion": This is not a standard foundational term. If
you mean structures with both minimal and maximal elements under a
relation, or extensions into non-well-founded set theories (like Aczel’s Anti-Foundation Axiom), it would be clearer to specify that.Geometry and
Real Analysis Extensions: You mention adding the least-upper-bound
property and measure 1.0. In standard mathematics, these are not added
as axioms to ZFC. Instead, they are constructed and proven within ZFC
(e.g., constructing the reals via Dedekind cuts or Cauchy sequences, and defining Lebesgue measure). If you are treating the "line-reals" as a foundational primitive instead of a construction, that is a distinct,
non-ZFC approach.
2. Style The style is highly idiosyncratic, dense, and reads like a stream-of-consciousness philosophical monologue rather than a
traditional mathematical summary.Hyphenation and Neologisms: Phrases
like "theories-of-one-relation", "first-order-izibility", and
"rulialities" give the text a deeply personal, philosophical flavor (reminiscent of Wolfram's "rulial space"). While creative, it creates friction for a reader accustomed to standard foundational
terminology.Grammar and Structure: The entire middle section is a
single, winding sentence with multiple parentheticals and appositions
("those being both...", "then for various...", "then besides..."). It
forces the reader to hold a massive amount of context in their head
before reaching the resolution.
3. Delivery As a delivery mechanism for explaining ZFC, this works best
as a personal notebook entry or a manifesto for an alternative
foundational view.For an expert audience: They will recognize the
concepts you are gesturing toward (like first-order schemas or
Regularity) but might get bogged down arguing over the non-standard vocabulary ("well-dispersion", "ordinary vacuity").For a student
audience: It is too dense and assumes a massive amount of prior
knowledge without providing a clear, structural roadmap of the actual axioms.Summary TakeawayYou clearly have a deep grasp of the vibe and
major philosophical pressure points of set theory (the tension between
big and small sets, the need for first-order reduction, the role of choice/ordering). However, the recap blends standard set theory with real-analysis constructions and unique vocabulary, making it more of a personal philosophical interpretation of ZFC than a strict textbook
summary.
On 7/6/2026 2:16 AM, Mikko wrote:That makes lie detection harder but not impossible.
On 04/07/2026 16:15, olcott wrote:
On 7/4/2026 1:37 AM, Mikko wrote:
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ: >>>>>>> POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that >>>>>> is not in logic, it was introduced by you. Even without the principle >>>>>> of explosion it is possible to infer a false conclusion from a false >>>>>> premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
Restrictions from the POE make lie detection harder and therefore lying
easier. You may like that but others have different preferencies.
Olcott gets rid of the Principle of Explosion
In Olcott Logic (P ∧ ¬P) ⊢ ⊥ and ⊥ ⊢ ⊥
On 7/6/2026 9:56 AM, olcott wrote:When one is going to lie it may be better to make the audience to
On 7/6/2026 2:16 AM, Mikko wrote:
On 04/07/2026 16:15, olcott wrote:
On 7/4/2026 1:37 AM, Mikko wrote:
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ: >>>>>>>> POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that >>>>>>> is not in logic, it was introduced by you. Even without the
principle
of explosion it is possible to infer a false conclusion from a false >>>>>>> premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves >>>>>>> that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
Restrictions from the POE make lie detection harder and therefore lying
easier. You may like that but others have different preferencies.
Olcott gets rid of the Principle of Explosion
In Olcott Logic (P ∧ ¬P) ⊢ ⊥ and ⊥ ⊢ ⊥
Why would you say that when you agreed on the record that it's valid
because disjunction introduction is valid [...]?
On 7/6/2026 5:17 AM, Mikko wrote:
On 04/07/2026 16:15, olcott wrote:
On 7/4/2026 1:37 AM, Mikko wrote:
On 03/07/2026 17:46, olcott wrote:
On 7/3/2026 3:17 AM, Mikko wrote:
On 02/07/2026 17:37, olcott wrote:
x = "The Moon is made from green cheese"
y = "Donald Trump is the one and only Lord and Savior Jesus Christ: >>>>>>> POE concludes (x ∧ ¬x) ⊢ y
"the principle of explosion is the theorem according to
which any statement can be proven from a contradiction"
https://en.wikipedia.org/wiki/Principle_of_explosion
When you pay attention to the meaning of the words
and correctly apply correct semantic entailment on
the basis of the meaning of those words then the
principle of explosion is a PSYCHOTIC BREAK FROM REALITY.
No, it is not. The premise x above is a break from reality. But that >>>>>> is not in logic, it was introduced by you. Even without the principle >>>>>> of explosion it is possible to infer a false conclusion from a false >>>>>> premise.
Yes. From "I am 35 feet tall" ⊢ "I am 35 feet tall"
and as you said my premise is literally FALSE
(P ∧ ~P) ⊢ FALSE
The principle of explosion merely facilitates tinding a
conclusion that is so obviously false that it convincingly proves
that the remise is false.
There is nothing semantically relevant that can be
proven from a contradiction besides bare FALSE and
bare FALSE only entails bare FALSE.
Yes, there is. From the contradiction "I have blue eyes and
I don't have blue eyes" one can prove "I have blue eyes" and
"I don't have blue eyes", both of which are semantically
relevant, and one of which in addition is false.
That is greatly restricted from the POE.
(P ∧ ~P) ⊢ FALSE // is what can really be proved semantically
If you can prove that FALSE is true then what is not true?
That is not proving that false is true.
It is stipulating that contradictions
only derive bare FALSE.
On 2026-07-07 18:05, olcott wrote:
On 7/7/2026 6:06 PM, André G. Isaak wrote:
On 2026-07-07 15:30, olcott wrote:
On 7/7/2026 4:24 PM, André G. Isaak wrote:
On 2026-07-07 15:13, olcott wrote:
On 7/7/2026 3:08 PM, André G. Isaak wrote:
On 2026-07-07 13:53, olcott wrote:
On 7/7/2026 2:29 PM, André G. Isaak wrote:
On 2026-07-07 13:19, olcott wrote:
To do with with minimal simplicity the axioms of
PA are construed as semantic entailment thus when
there is no sequence of inference steps between G
and PA then G is Kripke undefined in PA.
So why don't you illustrate this with an actual proof?
André
The principle is simply whenever X cannot be proven
in F then X is ungrounded in the atomic base F. Even
diagonalization makes to attempt at actual proof.
I can't make heads or tails of that.
The actual proof in meta-math that G cannot be
proved in PA is itself not any sequence of inference
steps. It simply uses a version of the proof that
Cantor use to show that reals are not countable.
???
Cantor's proof absolutely contained inference steps, as did Gödels. >>>>> I don't think you actually know what you're talking about.
If you can't illustrate your alleged system with a simple proof, >>>>>>> then I have no choice but to conclude that it is as ill-defined >>>>>>> to you as it is to me.
André
2 + 3 = 4 in PA cannot be proven because
s(s(0)) + s(s(s(0))) != s(s(s(s(0))))
I asked you to provide an example of a proof which illustrates what >>>>> you mean by "semantic entailments encoded syntactically in the
language". I didn't ask for an example of something which cannot be >>>>> proven.
André
PTS simply declares by fiat that syntactic inference steps
are semantic steps. I actually mean natural language semantic
inference in the CycL programming language. This is the place
where nothing follows form a contradiction is most easily seen.
So basically you're saying that you are incapable of constructing
even a simple mathematical proof. Gödel is about theories of
arithmetic. CycL is not. If you can't construct proofs in an
arithmetic framework you really have no business talking about Gödel.
André
So basically you are totally not interested in understanding me.
As far as proofs go I always think in terms of syllogisms and
their extensions. Every other proof is utterly irrelevant to my
work.
If your interest is limited to syllogisms then both Gödel and the
halting problem are utterly irrelevant to your work, so you probably
should stop making claims about them.
On 6/30/2026 2:55 AM, Mikko wrote:
On 29/06/2026 16:23, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
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:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural language >>>>>>>>>>>>>>>>> statement:
On 6/27/2026 7:22 PM, olcott wrote:1) P ∧ ¬P // Premise
On 6/27/2026 5:52 PM, dbush wrote:
On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus forHe also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of PAI >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this principle >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication— >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even know >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced from a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> statement where eachstatement either is a >>>>>>>>>>>>>>>>>>>>>>>>>>>>> premis or follows from one or more earlier >>>>>>>>>>>>>>>>>>>>>>>>>>>>> statements
Except with Disjunction introduction, that >>>>>>>>>>>>>>>>>>>>>>>>>>>> is its problem.
So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving operations, >>>>>>>>>>>>>>>>>>>>>>> when a contradiction is given as true, any >>>>>>>>>>>>>>>>>>>>>>> statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration of >>>>>>>>>>>>>>>>>>>>>>> *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid of >>>>>>>>>>>>>>>>>>>>>>> the principle of explosion is to be able to use a >>>>>>>>>>>>>>>>>>>>>>> system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the >>>>>>>>>>>>>>>>>>>>> law of non- contradiction goes away as it looses >>>>>>>>>>>>>>>>>>>>> its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the
propositional variables it is as obvious
as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>> - Earth is the third planet from the sun.
- <X>
--------------------------------------
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>> exists a statement X such that the condition "At least >>>>>>>>>>>>>>>>> one of the following statements is true" is false. >>>>>>>>>>>>>>>>>
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>
Let me spell it out more explicitly then.
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>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>>>> exist a statement X such that the condition "At least one >>>>>>>>>>>>>>> of the following statements is true" is false?
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>> true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so it >>>>>>>>>>> can't be used in logic. I didn't think I had to make that >>>>>>>>>>> explicit.
However, let's go with it anyway because it still illustrates >>>>>>>>>>> the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" true? >>>>>>>>>>>
On second though, let's back up as that might confuse you. >>>>>>>>>>
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.
That you did so well on the other things
so I will not block you.
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.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different
rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
One can construct a system where a truth-preserving operation is not
valid, and must if one wants to construct a paraconsistent system,
where some but not every sentence can be both PTS-true and PTS-false.
Current semantic entailment is the only inference step allowed.
On 7/1/2026 1:50 AM, Mikko wrote:
On 30/06/2026 16:45, olcott wrote:
On 6/30/2026 2:55 AM, Mikko wrote:
On 29/06/2026 16:23, dbush wrote:
On 6/29/2026 9:17 AM, polcott wrote:
On 6/29/2026 7:08 AM, dbush wrote:
On 6/29/2026 12:13 AM, olcott wrote:
On 6/28/2026 10:56 PM, dbush wrote:
On 6/27/2026 11:34 PM, dbush wrote:
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:
On 6/27/2026 9:24 PM, olcott wrote:
On 6/27/2026 8:08 PM, dbush wrote:
On 6/27/2026 7:56 PM, olcott wrote:
On 6/27/2026 6:30 PM, dbush wrote:So you're saying that in the following natural >>>>>>>>>>>>>>>>>>> language statement:
On 6/27/2026 7:22 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 5:52 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 6:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:34 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:29 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:24 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 12:54 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:11 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:08 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 15:49, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 04:32, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> William T. Parry, Entailment Logics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets rid of Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to prevent the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>1) P ∧ ¬P // Premise
Explain in detail how the below which you >>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic. >>>>>>>>>>>>>>>>>>>>>>>>>>>As I recently showed in another post. I >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> figuredA simple logical matrix and sequent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> calculus for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Parry’s logic of Analytic Implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>He also gets rid of an efficient way to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> convince people who don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand much of logic. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The main and distinctive feature of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PAI (and of the many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems of analytic implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> belonging to its ilk) is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the rejection of the classically valid >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle of Addition, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sometimes also referred to as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Disjunction Introduction. In >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> other words, the principle leading >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> from a formula ϕ to a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> disjunction of the form ϕ ∨ ψ, where ψ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula. Parry blamed on this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> principle the derivability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the paradoxes of strict implication >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> — given that it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> famously featured in Lewis’ derivation >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of an arbitrary >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> formula ψ from a contradiction of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> form ϕ ∧ ¬ϕ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
https://philarchive.org/archive/SZMASL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
all this out on my own. I didn't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> know that
anyone else ever did this. I just knew >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that when
trying to find out what is deduced from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a set of
premises that you cannot pop in another >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence
from out of nowhere and get a correct >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conclusion.
By popping in another sentence from out >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of nowhere
(as it shows above) the principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explosion is
derived.
The usual meaning of proof is a sequence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of statement where eachstatement either >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is a premis or follows from one or more >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> earlier
statements
Except with Disjunction introduction, that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is its problem.
So you're saying that in the following >>>>>>>>>>>>>>>>>>>>>>>>>>>>> natural language statement: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is a key issue in that it creates the >>>>>>>>>>>>>>>>>>>>>>>>>>>> psychotic break from reality known as the >>>>>>>>>>>>>>>>>>>>>>>>>>>> Principle of Explosion, otherwise it may >>>>>>>>>>>>>>>>>>>>>>>>>>>> make no difference at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stay on topic or I will block you. >>>>>>>>>>>>>>>>>>>>>>>>>>>
The topic is how Disjunction introduction >>>>>>>>>>>>>>>>>>>>>>>>>> enables the
Principle of Explosion.
Rejected, as you not liking the result doesn't >>>>>>>>>>>>>>>>>>>>>>>>> make it invalid.
Through a series of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>> operations, when a contradiction is given as >>>>>>>>>>>>>>>>>>>>>>>>> true, any statement can be proven as true. >>>>>>>>>>>>>>>>>>>>>>>>>
The principle of explosion is a demonstration >>>>>>>>>>>>>>>>>>>>>>>>> of *why* a formal system whose axioms lead to a >>>>>>>>>>>>>>>>>>>>>>>>> contradiction is useless.
The only reason someone would want to get rid >>>>>>>>>>>>>>>>>>>>>>>>> of the principle of explosion is to be able to >>>>>>>>>>>>>>>>>>>>>>>>> use a system that has a contradiction. >>>>>>>>>>>>>>>>>>>>>>>>>
My reason to get rid of the principle of explosion >>>>>>>>>>>>>>>>>>>>>>>> it to get rid of anything and everything that >>>>>>>>>>>>>>>>>>>>>>>> prevents
infallibly correct reasoning.
If you get rid of the principle of explosion, the >>>>>>>>>>>>>>>>>>>>>>> law of non- contradiction goes away as it looses >>>>>>>>>>>>>>>>>>>>>>> its basis.
You keep failing to pay close enough attention. >>>>>>>>>>>>>>>>>>>>>> I only get rid of the POE by getting rid of >>>>>>>>>>>>>>>>>>>>>> Disjunction introduction.
Which you can't do because it's a truth-preserving >>>>>>>>>>>>>>>>>>>>> operation.
2) P // Conjunction elimination >>>>>>>>>>>>>>>>>>>> 3) ¬P // Conjunction elimination >>>>>>>>>>>>>>>>>>>> 4) P ∨ Q // Disjunction introduction >>>>>>>>>>>>>>>>>>>> 5) Q // Disjunctive syllogism >>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/
Principle_of_explosion#Proof
When you insert English meanings into the >>>>>>>>>>>>>>>>>>>> propositional variables it is as obvious >>>>>>>>>>>>>>>>>>>> as a pie in the fact the DI IS NOT TRUTH PRESERVING. >>>>>>>>>>>>>>>>>>>
--------------------------------------
At least one of the following statements is true: >>>>>>>>>>>>>>>>>>> - Earth is the third planet from the sun. >>>>>>>>>>>>>>>>>>> - <X>
--------------------------------------
Where <X> is any natural language statement, there >>>>>>>>>>>>>>>>>>> exists a statement X such that the condition "At >>>>>>>>>>>>>>>>>>> least one of the following statements is true" is false. >>>>>>>>>>>>>>>>>>>
Name it.
That is not Disjunction introduction combined with >>>>>>>>>>>>>>>>>> Disjunctive syllogism, it is bare Disjunction. >>>>>>>>>>>>>>>>>>
Let me spell it out more explicitly then.
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>
--------------------------------------
Where <X> is any natural language statement, does there >>>>>>>>>>>>>>>>> exist a statement X such that the condition "At least >>>>>>>>>>>>>>>>> one of the following statements is true" is false? >>>>>>>>>>>>>>>>>
Where X is "What time is it?"
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>>>> true?
We have a type mismatch error.
The statement you gave isn't a truth-bearing statement, so >>>>>>>>>>>>> it can't be used in logic. I didn't think I had to make >>>>>>>>>>>>> that explicit.
However, let's go with it anyway because it still
illustrates the point.
So I'll ask again:
Is the statement "Earth is the third planet from the sun" >>>>>>>>>>>>> true?
On second though, let's back up as that might confuse you. >>>>>>>>>>>>
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.
That you did so well on the other things
so I will not block you.
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.
William T. Parry, Entailment Logics
gets rid of Disjunction introduction
to prevent the principle of explosion
A simple logical matrix and sequent calculus for
Parry’s logic of Analytic Implication
The main and distinctive feature of PAI (and of the many
systems of analytic implication belonging to its ilk) is
the rejection of the classically valid principle of Addition,
sometimes also referred to as Disjunction Introduction. In
other words, the principle leading from a formula ϕ to a
disjunction of the form ϕ ∨ ψ, where ψ is an arbitrary
formula. Parry blamed on this principle the derivability
of the paradoxes of strict implication—given that it is
famously featured in Lewis’ derivation of an arbitrary
formula ψ from a contradiction of the form ϕ ∧ ¬ϕ.
https://philarchive.org/archive/SZMASL
So someone came up with a different system that has different
rules. That has no bearing on existing systems.
The bearing that it has on existing systems is
None, as you can't remove a truth-preserving operation.
One can construct a system where a truth-preserving operation is not
valid, and must if one wants to construct a paraconsistent system,
where some but not every sentence can be both PTS-true and PTS-false.
Current semantic entailment is the only inference step allowed.
Every truth-prserving transformation is a correct semantic entailment.
In particular, disjunction introduction is.
That is counter-factual.
POE is misconstrued as truth preserving.
Every element of logic is utterly discarded and only the underlyingIf you reject inferences (wich are central elements of logic) then
semantics is preserved.
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