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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Claude.ai provides reasoning why I may have defeated the
 conventional HP proof
Date: Tue, 15 Jul 2025 07:44:44 -0400
Organization: i2pn2 (i2pn.org)
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On 7/14/25 11:03 PM, olcott wrote:
> On 7/14/2025 9:21 PM, Richard Damon wrote:
>> On 7/14/25 3:15 PM, olcott wrote:
>>> On 7/12/2025 6:03 PM, Richard Damon wrote:
>>>> On 7/11/25 1:12 AM, olcott wrote:
>>>>> On 7/10/2025 11:42 PM, André G. Isaak wrote:
>>>>>> On 2025-07-10 22:29, 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:
>>>>>>>>
>>>>>>>>>> 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
>>>>>>
>>>>>> What is not the exact meaning of which words?
>>>>>>
>>>>>
>>>>> *This Wikipedia quote*
>>>>> On 7/10/2025 11:29 PM, olcott wrote:
>>>>>  >    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
>>>>>
>>>>> Here is the exact meaning of:
>>>>> *any statement can be proven from a contradiction*
>>>>> ∀x (⊥ ⊢ x).
>>>>>
>>>>>
>>>>>
>>>>
>>>> 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.
>>>
>>> Here is the correct paraphrase: ∀x (⊥ ⊢ x).
>>>
>>
>> And Yes that can be PROVEN
>>
> 
> So you agree that André had this wrong when he used
> implies(→) instead of proves(⊢).
> 
> 

No, The FACT that ((X & ~X) implies Y) is true is provable.

Now, it is also true that (X & ~X) is enough to PROVE any statement, 
which is actually a stronger statement.