Re: William T. Parry gets rid of Disjunction introduction

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:
>>>>>>>>>> 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 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.

-- 
Mikko