Re: William T. Parry gets rid of Disjunction introduction

On 01/07/2026 18:04, olcott wrote:
> 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:
>>>>>>>>>>>>>>>>>>>>> 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.
>>>>
>>>> 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.

No, it is not. It is a matter of definition. Because you have not
defined "correct semantic entailment" as an inference rule my
statement cannot contradict your definition.

 > POE is misconstrued as truth preserving.

Who has said that POE preserves truth? And what does it even mean
if one says that POE preserves or does not preserve truth?

> Every element of logic is utterly discarded and only the underlying
> semantics is preserved.
If you reject inferences (wich are central elements of logic) then
you can't infer anyting from anything.

A part of natural language semantics is logical inference. If you
reject logic you must also reject the logical part of natural
language semantics.

-- 
Mikko