Re: The philosophy of computation reformulates existing ideas on a new basis ---

On 11/1/2024 5:42 AM, Mikko wrote:

On 2024-10-30 12:46:25 +0000, olcott said:
 

ZFC only resolved Russell's Paradox because it tossed out
the incoherent foundation of https://en.wikipedia.org/wiki/ Naive_set_theory

 Actually Zermelo did it. The F and C are simply minor improvements on
other aspects of the theory.
 

Thus establishing the precedent that replacing the foundational
basis of a problem is a valid way to resolve that problem.
Russell's Paradox was resolved by replacing its foundation.
The Halting Problem Proof result <is> resolved by replacing
its foundation.
void DDD()
{
   HHH(DDD);
   return;
}
_DDD()
[00002172] 55         push ebp      ; housekeeping
[00002173] 8bec       mov ebp,esp   ; housekeeping
[00002175] 6872210000 push 00002172 ; push DDD
[0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
[0000217f] 83c404     add esp,+04
[00002182] 5d         pop ebp
[00002183] c3         ret
Size in bytes:(0018) [00002183]
DDD emulated by HHH according to the semantics of the x86
language cannot possibly reach its own "return" instruction
whether or not any HHH ever aborts its emulation of DDD.
This does provide a basis for HHH to reject DDD as non-halting
even if this basis is unconventional. We simply change the
conventional basis. ZFC established the precedent that this
can be done.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer