Re: Analysis of Flibble’s Latest: Detecting vs. Simulating Infinite Recursion ZFC

On 21/05/2025 16:54, olcott wrote:

On 5/21/2025 12:56 AM, Richard Heathfield wrote:

On 21/05/2025 06:23, olcott wrote:

<snip>

Do you mean like how ZFC resolved Russell's
Paradox thus converting "set theory" into "naive set theory"?

>
No, because there is no paradox in the Halting Problem. A proof by contradiction is not a paradox.
>

 A self-contradictory input and a proof by contradiction
are not the same thing.

Agreed.

A proof by contradiction would
conclude that "this sentence is not true" is true because
it cannot be proved false.

A proof by contradiction would conclude that 'by assuming A was possible we have derived a contradiction. We conclude that A is not possible'.
There is no self-contradictory input because such an input is impossible.

ZFC shows how a whole way of examining a problem can be
tossed out as incorrect and replaced with a whole new way.

The Halting Problem shows how there are some problems that cannot be computed by a finite algorithm.

The HP proofs are based on defining a D that can
actually do the opposite of whatever value that H returns.
No such D can actually exist.

That an algorithm for ascertaining whether an arbitrary program with arbitrary input halts cannot actually exist is precisely what the Halting Problem proves.
<snip>
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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