Re: William T. Parry gets rid of Disjunction introduction

On 6/29/2026 9:55 AM, 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:
>>>>>>>> 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.
>>
>> 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 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.

It does follow from the semantics, as you have admitted on the record 
(see below):

On 6/28/2026 11:56 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:
 >>>>>>>>> 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.