Deutsch English Français Italiano |
<vg7o86$bk5f$1@dont-email.me> View for Bookmarking (what is this?) Look up another Usenet article |
Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko <mikko.levanto@iki.fi> Newsgroups: comp.theory Subject: Re: The philosophy of computation reformulates existing ideas on a new basis --- Date: Sun, 3 Nov 2024 13:53:42 +0200 Organization: - Lines: 62 Message-ID: <vg7o86$bk5f$1@dont-email.me> References: <vfli1h$fj8s$1@dont-email.me> <vflue8$3nvp8$2@i2pn2.org> <vfmd8m$k2m7$1@dont-email.me> <bcd82d9f8a987d3884220c0df7b8f7204cb9de3e@i2pn2.org> <vfmueh$mqn9$1@dont-email.me> <ff039b922cabbb6d44f90aa71a52d8c2f446b6ab@i2pn2.org> <vfo95k$11qs1$1@dont-email.me> <vfp8c0$3tobi$2@i2pn2.org> <vfpbtq$1837o$2@dont-email.me> <vfq4h9$1fo1n$1@dont-email.me> <vfqpi3$1iaob$4@dont-email.me> <vfqvjs$3v4c4$15@i2pn2.org> <vfr091$1k8im$1@dont-email.me> <vft4or$44tc$5@i2pn2.org> <vft9r1$25aio$9@dont-email.me> <vg2ban$37555$1@dont-email.me> <vg2gvo$37lpn$6@dont-email.me> <vg4q97$3np95$1@dont-email.me> <vg5386$3or7a$6@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 03 Nov 2024 12:53:43 +0100 (CET) Injection-Info: dont-email.me; posting-host="3647495eaf712b89b1330d180c69f26b"; logging-data="381103"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+BCIDJXwvJjTKGRVT52tkB" User-Agent: Unison/2.2 Cancel-Lock: sha1:EgKY69tt2WQbr/merEdj+i1a1H0= Bytes: 3901 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. And the existence of insonstent formal systems does not mean that the notion of a formal system is inconsistent. > When we handle this self-reference differently then this issue > is resolved. No proof ot that, either. > When a formal system is ONLY a sequence of truth preserving > operations applied to a consistent set of expressions that > have been stipulated to be true then expressions that would > otherwise show incompleteness are rejected because they have > no path to true or false. > >> The foundation of all these theories is classical logic. >> > > The key error of classical logic is that it diverged from the > model of the syllogism where there is always a path to true or > false or the syllogism is ill-formed. Classical logic does not substantially diverge from the model of syllogism. It iextends it for situations that cannot be covered with syllogistic logic. Presentational differences follow mainly from the needs of the additional coverage. No error has been shown in classical logic. -- Mikko