Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko Newsgroups: comp.theory Subject: Re: The philosophy of computation reformulates existing ideas on a new basis --- Date: Sat, 2 Nov 2024 11:09:59 +0200 Organization: - Lines: 25 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 02 Nov 2024 10:10:00 +0100 (CET) Injection-Info: dont-email.me; posting-host="ac2ed10f994a6b2c09b09e40230988bc"; logging-data="3925285"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18NUOQWVH91FjVb3jV4DQBP" User-Agent: Unison/2.2 Cancel-Lock: sha1:OEPm4CPsmXVMxCm16YTmWCzkRRY= Bytes: 2314 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