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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Claude.ai provides reasoning why I may have defeated the
 conventional HP proof
Date: Thu, 10 Jul 2025 23:29:38 -0500
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On 7/10/2025 10:58 PM, André G. Isaak wrote:
> On 2025-07-10 19:58, Richard Damon wrote:
>> On 7/10/25 10:09 AM, olcott wrote:
> 
>>> According to the POE:
>>> (a) The Moon is made of green cheese and
>>> (b) the Moon does not exist
>>> proves that
>>> (c) Donald Trump is the Christ.
>>
>> Rigth, but only because a side affect of (a) is that the moon must exist.
> 
> Really, the problem here is that Olcott fails to distinguish between the 
> truth of a conditional statement and the truth of the consequent of a 
> conditional statement. They are not the same thing.
> 
> ((X & ~X) implies Y) is necessarily true.
> 

That is not the exact meaning of these words

   the principle of explosion is the law
   according to which any statement can be
   proven from a contradiction.
https://en.wikipedia.org/wiki/Principle_of_explosion

∀x (⊥ ⊢ x). When we look at that in terms of the
syllogism it is horribly incorrect.

That logic does not require semantic relevance is
its key mistake.

https://en.wikipedia.org/wiki/Relevance_logic
Fixes some aspects of the problem.

> Whether Y is true is a completely independent question.
> 
> But Olcott seems to think that the truth of ((X & ~X) -> Y) somehow 
> proves that Y is true. That's simply not how logic works.
> 

You are addressing this different issue:
https://en.wikipedia.org/wiki/Paradoxes_of_material_implication

> I raise this point purely as a clarification. I'm well aware that this 
> will have no impact on Olcott's (mis)understanding of logic.
> 
> André
> 


-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer