Sujet : Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --logically impossible--
De : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : comp.theory sci.logicDate : 12. Mar 2024, 21:33:55
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <usqan4$1l201$30@i2pn2.org>
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On 3/12/24 11:16 AM, olcott wrote:
On 3/12/2024 1:04 PM, Richard Damon wrote:
But SHOWING that something is logically impossible reveals the limitations that were already there.
>
Yes, the Halting Theorem doesn't MAKE the problem impossible, it shows that it always was, and gives us knowledge of that.
>
The halting problem does not derive a limit to computation
any more than the inability of CAD systems to draw square
circles places a limit on computation.
>
But shows the limitation that already existed in compuations.
You don't seem to understand that.
Computation can only do what Computation do.
One of the LIMITS of Computations, is they can not determine is the halting state us any and all algoritms + data.
They may be able to determine it for a subset of all possible,
but not for all possible.
That IS a limit of Computations REVEALED by the Halting Theorem.