Re: William T. Parry gets rid of Disjunction introduction

On 02/07/2026 17:37, olcott wrote:
> 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:
>>>>>>>>> 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
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 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.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 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.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Explain in detail how the below which you 
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> dishonestly trimmed is off- topic.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 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.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> 1) P ∧ ¬P    // Premise
>>>>>>>>>>>>>>>>>>>>>>> 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.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> So you're saying that 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, 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.
>>>>>>>>
>>>>>>> Only people having actual psychosis would conclude
>>>>>>> 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.

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.

-- 
Mikko