Re: Claude.ai provides reasoning why I may have defeated the conventional HP proof

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.

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Rigth, but only because a side affect of (a) is that the moon must exist.

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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.
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((X & ~X) implies Y) is necessarily true.
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That is not the exact meaning of these words

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What is not the exact meaning of which words?
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*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).
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And what is wrong with the analysis given one that page:
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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.
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Here is the correct paraphrase: ∀x (⊥ ⊢ x).
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And Yes that can be PROVEN
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So you agree that André had this wrong when he used
implies(→) instead of proves(⊢).
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No, The FACT that ((X & ~X) implies Y) is true is provable.
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 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.
The fact that y & ~y should be ⊥ doesn't mean that ⊥ proves anything.
Your problem is you don't actually understand how logic works because you never bothered to actually learn it, just how to parrot things taken out of papers.

 

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