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Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko <mikko.levanto@iki.fi> Newsgroups: sci.logic Subject: Re: Undecidability based on epistemological antinomies V2 --Mendelson-- Date: Fri, 26 Apr 2024 11:42:20 +0300 Organization: - Lines: 21 Message-ID: <v0fpdc$3j50e$1@dont-email.me> References: <uvq0sg$21m7a$1@dont-email.me> <uvq359$1doq3$4@i2pn2.org> <uvrbvs$2acf7$1@dont-email.me> <uvs70t$1h01f$1@i2pn2.org> <uvsgcl$2i80k$1@dont-email.me> <uvsj4v$1h01e$1@i2pn2.org> <uvsknc$2mq5c$1@dont-email.me> <uvvrj6$3i152$1@dont-email.me> <v00r07$3oqra$1@dont-email.me> <v02ggt$6org$1@dont-email.me> <v03866$bitp$1@dont-email.me> <v056us$rmqi$1@dont-email.me> <v08i2i$1m5hp$2@dont-email.me> <v0akj8$28ghd$1@dont-email.me> <v0bada$2defp$2@dont-email.me> <v0d42v$2tclm$1@dont-email.me> <v0dp8c$31vd9$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 26 Apr 2024 10:42:20 +0200 (CEST) Injection-Info: dont-email.me; posting-host="f0f02d3bf937615601747b28e3f4a69a"; logging-data="3773454"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18Ags0ICNPdYZs7cJHu1kGX" User-Agent: Unison/2.2 Cancel-Lock: sha1:sji5THPnHnYrivJzek9zpxCpujM= Bytes: 2120 On 2024-04-25 14:27:23 +0000, olcott said: > On 4/25/2024 3:26 AM, Mikko wrote: >> epistemological antinomy > > It <is> part of the current (thus incorrect) definition > of undecidability because expressions of language that > are neither true nor false (epistemological antinomies) > do prove undecidability even though these expressions > are not truth bearers thus not propositions. That a definition is current does not mean that is incorrect. An epistemological antinomy can only be an undecidable sentence if it can be a sentence. What epistemological antinomies you can find that can be expressed in, say, first order goup theory or first order arithmetic or first order set tehory? -- Mikko