Re: William T. Parry gets rid of Disjunction introduction

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.

Nobody cares what you "allow" as long as you don't specify any
inference rule. Probably nobody will care even if you will specify
but there is no way to really know as long as you don't specify.

-- 
Mikko