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From: =?UTF-8?B?QW5kcsOpIEcuIElzYWFr?= <agisaak@gm.invalid>
Newsgroups: comp.theory
Subject: Re: Claude.ai provides reasoning why I may have defeated the
 conventional HP proof
Date: Tue, 15 Jul 2025 17:45:06 -0600
Organization: Christians and Atheists United Against Creeping Agnosticism
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On 2025-07-15 17:35, olcott wrote:
> 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
>>
> 
> You still make the same mistake with the implication operator.
> That has always been the wrong operator for PROVES.

You're being an idiot. The principle of explosion can be stated either 
in terms of implication or proof. I prefer implication. I'm not 
mistaking one symbol for another. I'm saying exactly what I intend to say.

André

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