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Path: ...!weretis.net!feeder8.news.weretis.net!reader5.news.weretis.net!news.solani.org!.POSTED!not-for-mail From: Mild Shock <janburse@fastmail.fm> Newsgroups: comp.theory,sci.logic Subject: =?UTF-8?Q?Re:_G=c3=b6del's_Basic_Logic_Course_at_Notre_Dame_=28Was:?= =?UTF-8?Q?_Analytic_Truth-makers=29?= Date: Tue, 23 Jul 2024 22:44:15 +0200 Message-ID: <v7p4mt$8bl4$1@solani.org> References: <v7m26d$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> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 23 Jul 2024 20:44:13 -0000 (UTC) Injection-Info: solani.org; logging-data="274084"; mail-complaints-to="abuse@news.solani.org" User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101 Firefox/91.0 SeaMonkey/2.53.18.2 Cancel-Lock: sha1:ObaLrG/vFlFo7IETcq6FTr2rySk= In-Reply-To: <v7p499$8bb2$5@solani.org> X-User-ID: eJwNwocRwDAIBLCVDPgp44S2/wjOSRAlLbsKvdhfZp2cEeUtI4eDssPMhD5KHrl7fE/oYGMbHanszDXEhH5ZiRVr Bytes: 2756 Lines: 44 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. 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.