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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory Subject: Re: The philosophy of computation reformulates existing ideas on a new basis --- Date: Sun, 3 Nov 2024 08:16:33 -0600 Organization: A noiseless patient Spider Lines: 87 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Sun, 03 Nov 2024 15:16:34 +0100 (CET) Injection-Info: dont-email.me; posting-host="78d696b0e880e7e96a4aa9625f760657"; logging-data="426305"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18Jn6VZ7HGEoq6Y735ymV9k" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:YsKNrqPnBFa4X3H1maf7T+cBw8g= In-Reply-To: X-Antivirus: Norton (VPS 241102-0, 11/1/2024), Outbound message X-Antivirus-Status: Clean Content-Language: en-US Bytes: 4984 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. > And the > existence of insonstent formal systems does not mean that > the notion of a formal system is inconsistent. > The notion of formal systems is incoherent because they rule that self-contradictory expressions prove that the system is incomplete rather than the expression is incorrect. >> 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. >> You can't ignore this. The above is the essence of my whole system of thought. >>> 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. When modern logic divides the formal system from the underlying semantics there is no direct path to True(L,x) within the system, thus no way to reject self-contradictory expressions on the basis that they have no path to true or false. > 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. > -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer