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

On 5/21/2025 11:09 AM, Richard Heathfield wrote:

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>
 

*You aren't paying enough attention*
The counter-example input D to the conventional HP
proofs that actually does the opposite of whatever
H returns cannot possibly exist.
If you think that it can exist then prove that it
exists by encoding it in C.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer