Re: William T. Parry gets rid of Disjunction introduction

On 01/07/2026 18:06, olcott wrote:
> On 7/1/2026 1:53 AM, Mikko wrote:
>> 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
>>>
>>> Relevance Logic
>>> https://plato.stanford.edu/entries/logic-relevance/
>>>
>>>>> 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.
>>>>
>>>> No, it is not. The principle of explosion is about consequencies
>>>> of a false premise, which already is a break from reality even
>>>> when no consequence is inferred.
>>>
>>> Only because semantics is ignored.
>>
>> A break from reality is a break from reality, no matter whether
>> the semantics is ignored or considered. Though if there is no
>> semantics, even any ignored one, there is no connection to
>> reality to break.
>>
> 
> Ignoring semantics is always a break from reality.

So is any semantics other than real world semantics.

-- 
Mikko