Sujet : Re: The philosophy of computation reformulates existing ideas on a new basis ---
De : mikko.levanto (at) *nospam* iki.fi (Mikko)
Groupes : comp.theoryDate : 02. Nov 2024, 10:09:59
Autres entêtes
Organisation : -
Message-ID : <vg4q97$3np95$1@dont-email.me>
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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.
The foundation of all these theories is classical logic.
-- Mikko
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