Sujet : Re: Claude.ai provides reasoning why I may have defeated the conventional HP proof
De : agisaak (at) *nospam* gm.invalid (André G. Isaak)
Groupes : comp.theoryDate : 15. Jul 2025, 22:34:50
Autres entêtes
Organisation : Christians and Atheists United Against Creeping Agnosticism
Message-ID : <1056hhq$a36q$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
User-Agent : Mozilla Thunderbird
On 2025-07-15 14:05, 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.
∀x (⊥ ⊢ x) simply ignores
https://en.wikipedia.org/wiki/Law_of_noncontradiction
The necessity operator is typically represented by the symbol □.
(A ∧ ¬A) □ ⊥ (and nothing else)
You really need to review your basic logic. (A ∧ ¬A) □ ⊥ doesn't mean anything. What you (might) be trying to claim is □((A ∧ ¬A) → ⊥), though that statement would be false.
André
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