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

On 7/15/25 4:05 PM, 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.

Yes it is, can it ever ESTABLISH something to be true when it isn't
Your problem is you don't understand what Logical Implication actually is.
Since you can't show when it fails, it just shows that you are just a stupid and ingorant liar, and don't understand the meaning of logic.

 ∀x (⊥ ⊢ x) simply ignores
https://en.wikipedia.org/wiki/Law_of_noncontradiction

Which means you didn't read the article. The Law of noncontradiction DERIVES from the Principle of Explsion.

 The necessity operator is typically represented by the symbol □.
(A ∧ ¬A) □ ⊥ (and nothing else)
 

But, that just means you are asserting that the Principle of Explsion can't have its conditions ever met.
But the problem is that (A ∧ ¬A) □ ⊥ doesn't actually prevent the creation of a contradiction, it just says that such a creation is wrong.
This goes back to the fact that you don't understand how logic works.
Just stating "(A ∧ ¬A) □ ⊥" doesn't enforce it.