Re: William T. Parry gets rid of Disjunction introduction

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.

Model theory was created only because keeping semantics
directly within logic at the time was too complicated.
It did make logic easier to work with and it also made
logic diverge from correct reasoning.

Only people having actual psychosis would conclude
that "The Moon is made from green cheese" AND
"The Moon is NOT made from green cheese" SEMANTICALLY
PROVES that Donald Trump is the one and only Lord
and Savior Jesus Christ.

Relevance logic, also called relevant logic, is a
kind of non-classical logic requiring the antecedent
and consequent of implications to be relevantly related.
https://en.wikipedia.org/wiki/Relevance_logic

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


-- 
Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).