Re: Claude.ai provides reasoning why I may have defeated the conventional HP proof

On 7/11/25 12:29 AM, olcott wrote:

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:

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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.

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Rigth, but only because a side affect of (a) is that the moon must exist.

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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.
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((X & ~X) implies Y) is necessarily true.
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 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

SUre it does.

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

Only because

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

But "semanitcs" in formal logic is symbolic, based on the axioms and operations of the system.

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

And greatly limits what the logic can handle.

 

Whether Y is true is a completely independent question.
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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.
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 You are addressing this different issue:
https://en.wikipedia.org/wiki/Paradoxes_of_material_implication

No, you are the one that doesn't know what you are talking about.
That article is about the "translation" of Formal Logic into Natural Language and how it can make some statements that are absolutely true in the Formal Logic not make sense in Natural Language, in part because the ttanslation misses that words of implication have term-of-art meaning in the formal language that doesn't fully hold in Natural Language.
This is why the use of Natural Language when talking about Formal Logic is dangerous, as you can easily misuse a word.
This is likely why you don't understand the Principle of Explosion, because Natural Language version of the statements don't actually mean the same thing.

 

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.
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André
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