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Path: ...!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: =?UTF-8?Q?Re=3A_G=C3=B6del=27s_Basic_Logic_Course_at_Notre_Dame_=28?= =?UTF-8?Q?Was=3A_Analytic_Truth-makers=29?= Date: Tue, 23 Jul 2024 19:18:09 -0500 Organization: A noiseless patient Spider Lines: 57 Message-ID: <v7ph81$1dv95$1@dont-email.me> References: <v7m26d$nrr4$1@dont-email.me> <e41a2d324173031e1fe47acc0fd69b94b7aba55e@i2pn2.org> <v7msg0$sepk$1@dont-email.me> <3fb77583036a3c8b0db4b77610fb4bf4214c9c23@i2pn2.org> <v7much$sepk$2@dont-email.me> <9577ce80fd6c8a3d5dc37b880ce35a4d10d12a0e@i2pn2.org> <v7n3ho$t590$1@dont-email.me> <7d9b88425623e1166e358f1bce4c3a2767c36da0@i2pn2.org> <v7naae$120r5$1@dont-email.me> <v7o64d$7r0l$1@solani.org> <v7ogdr$17h8r$9@dont-email.me> <v7p499$8bb2$5@solani.org> <v7p4mt$8bl4$1@solani.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 24 Jul 2024 02:18:10 +0200 (CEST) Injection-Info: dont-email.me; posting-host="16ed067bd5cc70aacf71dd1f4de1f69e"; logging-data="1506597"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX183v71Rozyc5j0T3Oi6I9lz" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:VWebEZHzHkHthIjaWpI0becU7T8= Content-Language: en-US In-Reply-To: <v7p4mt$8bl4$1@solani.org> Bytes: 3241 On 7/23/2024 3:44 PM, Mild Shock wrote: > Of course you can restrict yourself to > only so called "decidable" sentences A, > > i.e. sentences A where: > > True(L,A) v True(L,~A) > > But this doesn't mean that all sentences > are decidable, if the language allows for > example at least one propositional variables p, > > then you have aleady an example of an > undecidable sentences, you even don't > need anything Gödel, Russell, or who knows > > what, all you need is bivalence, which was > already postualated by Aristoteles. > > Principle of bivalence > https://en.wikipedia.org/wiki/Principle_of_bivalence > > if you assume that a propostional variable > is "variably", meaning it can take different truth > values depending on different possible worlds, > > or state of affairs, or valuations, or how ever > you want to call it. Then a propositional variable > is the prime example of an undecided sentence. > The key difference is that we no long use the misnomer "undecidable" sentence and instead call it for what it really is an expression that is not a truth bearer, or proposition in L. > Mild Shock schrieb: >> Thats a little bit odd to abolish incompletness. >> Take p, an arbitrary propositional variable. >> Its neither the case that: >> >> True(L,p) >> >> Nor is ihe case that: >> >> True(L,~p) >> >> Because there are always at least two possible worlds. >> One possible world where p is false, making True(L,p) >> impossible, and one possible world where p is true, >> >> making True(L,~p) impossible. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer