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Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott <polcott333@gmail.com> Newsgroups: sci.logic Subject: Re: How a True(X) predicate can be defined for the set of analytic knowledge Date: Sat, 29 Mar 2025 16:51:02 -0500 Organization: A noiseless patient Spider Lines: 40 Message-ID: <vs9q06$27rl4$11@dont-email.me> References: <vrfvbd$256og$2@dont-email.me> <vrh432$39r47$1@dont-email.me> <vrhami$3fbja$2@dont-email.me> <vrj9lu$1791p$1@dont-email.me> <vrjn82$1ilbe$2@dont-email.me> <vrmpc1$bnp3$1@dont-email.me> <vrmteo$cvat$6@dont-email.me> <vru000$33rof$1@dont-email.me> <vrug71$3gia2$6@dont-email.me> <0306c3c2d4a6d05a8bb7441c0b23d325aeac3d7b@i2pn2.org> <vrvnvv$ke3p$1@dont-email.me> <vs0egm$1cl6q$1@dont-email.me> <vs1f7j$296sp$2@dont-email.me> <vs3ad6$2o1a$1@dont-email.me> <vs4sjd$1c1ja$8@dont-email.me> <a17b6d8379479958b80a757258e7378a5a6107e7@i2pn2.org> <vs50t9$1c1ja$16@dont-email.me> <f47aac71a3e5fd0573f734e182916e5636afb644@i2pn2.org> <vs6vhq$39556$19@dont-email.me> <a68d324e7a257930a20d187e323736caaf1e3db8@i2pn2.org> <vs8u01$1fccq$1@dont-email.me> <2235385edf766f66cd1261b54db6573b0d8f691c@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 29 Mar 2025 22:51:03 +0100 (CET) Injection-Info: dont-email.me; posting-host="25098614a506fec9a884b9c00c7b5ec8"; logging-data="2354852"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+l/XihusXFplGtZQmhdhAc" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:9TS8aL937GWSjT9Ror33fv8zGgs= X-Antivirus: Norton (VPS 250329-4, 3/29/2025), Outbound message X-Antivirus-Status: Clean Content-Language: en-US In-Reply-To: <2235385edf766f66cd1261b54db6573b0d8f691c@i2pn2.org> On 3/29/2025 1:18 PM, Richard Damon wrote: > On 3/29/25 9:53 AM, olcott wrote: >> On 3/29/2025 4:51 AM, joes wrote: >>> Am Fri, 28 Mar 2025 15:07:22 -0500 schrieb olcott: >>>> On 3/28/2025 8:46 AM, Richard Damon wrote: >>> >>>>> Ok, so therefore it includes all the "laws of mathematics" and the >>>>> "rules of inference" and thus, the system is capable of creating the >>>>> rules and properties of the Natural Numbers, so it supports the proofs >>>>> of Godel and Tarski, and thus there are statements in that sytstem >>>>> that >>>>> are True but unprovable and no definition of the Truth Predicate can >>>>> handle those, >>>> >>>> Yes it will showed the formal system can be defined that have all kinds >>>> of issues because they were defined incoherently. >>> >>> How is arithmetic (which is all it takes for Gödel's proof) incoherent? >>> >> >> To the best of my knowledge arithmetic itself cannot >> be incomplete unless it can be shown that the sum of >> two finite strings of digits cannot be derived. >> > > Depends on what you consider "Arithmetic". If you just mean "sums" and > the like, then maybe it can't be incomplete, because it can't ask > questions that ask for proofs. > It never could. > Once you include first order logic with things like There exist a number > such that ..., then you can perform Godel's proof and find that there is > at least one statement that is true but can not be proven in the system. -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer