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From: olcott <polcott333@gmail.com>
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 20:47:22 -0500
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On 7/15/2025 5:39 PM, Richard Damon wrote:
> On 7/15/25 8:40 AM, olcott wrote:
>> On 7/15/2025 6:44 AM, Richard Damon wrote:
>>> 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.
>>>
>>
>> Yet is not an accurate paraphrase of: ∀x (⊥ ⊢ x)
>> so André was wrong in his paraphrase.
> 
> But ∀x (⊥ ⊢ x) isn't a correct statement of the Principle of Explosion.
> 
> Because it doesn't say a Falsestate proves all, it says that a 
> contradiction proves all.
> 

Here's why falsum is important in logic
Represents contradiction: Falsum is equivalent to a contradiction like P 
∧ ¬P (a statement and its negation simultaneously being true), which is 
always false. (Always except for nitwits that accept POE's disagreement
with the law of non-contradiction).


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