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Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon <richard@damon-family.org> 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 22:15:43 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <2e363c4050872820bdebbbb513fcb54596211440@i2pn2.org> 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> <v7p4m6$1btr0$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 24 Jul 2024 02:15:43 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="142535"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: <v7p4m6$1btr0$1@dont-email.me> X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US Bytes: 3387 Lines: 66 On 7/23/24 4:43 PM, olcott wrote: > On 7/23/2024 3:36 PM, Mild Shock wrote: >> 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. >> > > We are not using propositional logic we are using an extension > of Montague Semantics such that every natural language meaning > can be formalized. Then you aren't in the same system as Tarski, and prove yourself to be a liar. > > L is an actual language and p is a specific static constant > finite string expression of that language. > > There is no possible world where the living animal > of a puppy is a 15 story office building. Are you SURE about that? > > There is no possible world where this sentence or its > negation are true: "This sentence is not true". How do you know that? > >> olcott schrieb: >>> On 7/23/2024 7:02 AM, Mild Shock wrote: >>>> Little bit odd reference to mathematical logic for 2024. >>>> >>>> olcott schrieb: >>>>>>> Curry, Harkell B. 1977. Foundations of Mathematical Logic. Page:45 >>> >>> https://www.liarparadox.org/Haskell_Curry_45.pdf >>> >>> *It sustains this idea* >>> >>> L is the language of a formal mathematical system. >>> x is an expression of that language. >>> >>> When we understand that True(L,x) means that there is a finite >>> sequence of truth preserving operations in L from the semantic >>> meaning of x to x in L, then mathematical incompleteness is abolished. >>> >>> ~True(L,x) ∧ ~True(L,~x) >>> means that x is not a truth-bearer in L. >>> It does not mean that L is incomplete >>> >> >