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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: Claude.ai provides reasoning why I may have defeated the
 conventional HP proof
Date: Fri, 11 Jul 2025 15:50:50 -0000 (UTC)
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Am Fri, 11 Jul 2025 10:30:35 -0500 schrieb olcott:
> On 7/11/2025 3:43 AM, Mikko wrote:
>> On 2025-07-10 14:09:55 +0000, olcott said:
>>> On 7/10/2025 4:05 AM, Mikko wrote:
>>>> On 2025-07-09 14:16:44 +0000, olcott said:
>>>>> On 7/9/2025 9:04 AM, joes wrote:
>>>>>> Am Wed, 09 Jul 2025 07:31:59 -0500 schrieb olcott:
>>>>>>> On 7/9/2025 3:29 AM, Mikko wrote:
>>>>>>>> On 2025-07-08 14:18:32 +0000, olcott said:
>>>>>>>>> On 7/8/2025 2:41 AM, Mikko wrote:
>>>>>>
>>>>>>>>>> True conclusion from false premeises is fairly common. But that
>>>>>>>>>> is not relevant.
>>>>>>>>> It proves that logic is fundamentally incorrect on this point.
>>>>>>>>> Logic must be a sequence of truth preserving operations or it is
>>>>>>>>> wrong.
>>>>>> Should only false conclusions be derivable from false premises?
>>>>>
>>>>> False premises must be immediately rejected.
>>>>
>>>> Often one must work with sentences that are not known to be true but
>>>> not known to be false, either.
>>>>
>>> Then contradiction proves falsehood.
>> 
>> That's right: if a contradiction is inferred then at least one of the
>> preimises is false. But that does not tell which premise is false.
>> 
>> 
> *This Wikipedia quote*
>  >    the principle of explosion is the law according to which *any
>  >    statement can be proven from a contradiction*
> 
> Here is the exact meaning of:
> *any statement can be proven from a contradiction*
> ∀x (⊥ ⊢ x).
> 
> Is proven to be incorrect in that it diverges from truth preserving
> operations.

How so? If A and ~A are both true, B also is.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.