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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Claude.ai provides reasoning why I may have defeated the
 conventional HP proof
Date: Tue, 15 Jul 2025 18:07:15 -0500
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In-Reply-To: <1056hhq$a36q$1@dont-email.me>

On 7/15/2025 4:34 PM, André G. Isaak wrote:
> On 2025-07-15 14:05, olcott wrote:
>> On 7/15/2025 2:28 PM, André G. Isaak wrote:
>>> On 2025-07-15 06:40, olcott wrote:
>>>
>>>>>>>>> And what is wrong with the analysis given one that page:
>>>>>>>>>
>>>>>>>> André G. Isaak's paraphrase of this:
>>>>>>>> "any statement can be proven from a contradiction"
>>>>>>>> to this:
>>>>>>>> ((X & ~X) implies Y) is necessarily true.
>>>>>>>> Is incorrect.
>>>
>>> I wasn't attempting to paraphrase anything. I was simply providing a 
>>> formula which is true.
>>>
>>
>> https://en.wikipedia.org/wiki/Truth_table#Logical_implication
>> is a not truth preserving operation.
>>
>> ∀x (⊥ ⊢ x) simply ignores
>> https://en.wikipedia.org/wiki/Law_of_noncontradiction
>>
>> The necessity operator is typically represented by the symbol □.
>> (A ∧ ¬A) □ ⊥ (and nothing else)
> 
> You really need to review your basic logic. (A ∧ ¬A) □ ⊥ doesn't mean 
> anything. What you (might) be trying to claim is □((A ∧ ¬A) → ⊥), though 
> that statement would be false.
> 
> André
> 

It is necessarily true that only ⊥ can be derived from a contradiction.

When logic discarded being anchored in a semantic basis
like the syllogism it went astray of truth.

(A ∧ ¬A) ⊢ "Donald Trump is the Christ"

When we plug semantics into POE and give A the value "The Moon exists"
then we can know that there is no semantic basis for concluding that
that (A ∧ ¬A) ⊢ "Donald Trump is the Christ", yet POE disagrees.

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