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Path: ...!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott <polcott333@gmail.com> Newsgroups: comp.theory,sci.logic Subject: Re: ""self contradictory"" (Was: Analytic Truth-makers) Date: Mon, 22 Jul 2024 16:42:17 -0500 Organization: A noiseless patient Spider Lines: 85 Message-ID: <v7mjnq$qr0g$2@dont-email.me> References: <v7m26d$nrr4$1@dont-email.me> <v7meqk$6uld$2@solani.org> <v7mfkc$q90s$1@dont-email.me> <v7mgff$6vd3$1@solani.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 22 Jul 2024 23:42:18 +0200 (CEST) Injection-Info: dont-email.me; posting-host="9aaf30c8a38b34dfe54399611020f1ec"; logging-data="879632"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19g9wy5mH4+/j4dFgd5VLZD" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:busyq5uYkz9zOhWkdes/o2eWUtY= Content-Language: en-US In-Reply-To: <v7mgff$6vd3$1@solani.org> Bytes: 3717 On 7/22/2024 3:46 PM, Mild Shock wrote: > And why is there no sequence of > logical transformations that leads to: > > p > > and no sequence of logical > transformations that leads to: > > ~p > > Is p self contradictory? > You have it backwards. x ∉ True if and only if p where the symbol 'p' represents the whole sentence x The above is a very clumsy way of saying that x is only true if x is not true. We can know this because Tarski said the was using the Liar Paradox as his model: It would then be possible to reconstruct the antinomy of the liar in the metalanguage, by forming in the language itself a sentence x such that the sentence of the metalanguage which is correlated with x asserts that x is not a true sentence. > olcott schrieb: >> On 7/22/2024 3:18 PM, Mild Shock wrote: >>> >>> What do you mean by self contradictory. >>> Why is there no sequencce to: >>> >>> p >>> >>> or to >>> >>> ~p >>> >>> Is p self contradictory? >>> >> >> This sentence is not true is *self* contradictory. >> When it is formalized in Tarski formal system it >> becomes the basis for his undefinability theorem. >> >> Tarski's Liar Paradox from page 248 >> It would then be possible to reconstruct the antinomy of the liar >> in the metalanguage, by forming in the language itself a sentence >> x such that the sentence of the metalanguage which is correlated >> with x asserts that x is not a true sentence. >> https://liarparadox.org/Tarski_247_248.pdf >> >> Formalized as: >> x ∉ True if and only if p >> where the symbol 'p' represents the whole sentence x >> https://liarparadox.org/Tarski_275_276.pdf >> >> >>> olcott schrieb: >>>> I have focused on analytic truth-makers where an expression of >>>> language x is shown to be true in language L by a sequence of truth >>>> preserving operations from the semantic meaning of x in L to x in L. >>>> >>>> In rare cases such as the Goldbach conjecture this may require an >>>> infinite sequence of truth preserving operations thus making >>>> analytic knowledge a subset of analytic truth. >>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture >>>> >>>> There are cases where there is no finite or infinite sequence of >>>> truth preserving operations to x or ~x in L because x is self- >>>> contradictory in L. In this case x is not a truth-bearer in L. >>>> >>>> >>>> >>> >> > -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer