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

On 11/3/2024 5:53 AM, Mikko wrote:

On 2024-11-02 11:43:02 +0000, olcott said:
 

On 11/2/2024 4:09 AM, Mikko wrote:

On 2024-11-01 12:19:03 +0000, olcott said:
 

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.

 No, that does not follow. In particular, Russell's paradox is not a
problem, just an element of the proof that the naive set theory is
inconsistent. The problem then is to construct a consistent set
theory. Zermelo proposed one set theory and ZF and ZFC are two other
proposals.

 My view is that the same kind of self-reference issue that
showed naive set theory was inconsistent also shows that the
current notion of a formal system is inconsistent.

 From the proof of the exstence of Russell's set it is easy
to prove that 1 = 2. As long as no proof of 1 = 2 from a
self-reference in a formal system is shown there is no
reason to think that such system is inconsisten.

 In other words you presume yourself to be all knowing about this.