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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: Mikko <mikko.levanto@iki.fi> Newsgroups: sci.logic Subject: Re: How a True(X) predicate can be defined for the set of analytic knowledge Date: Thu, 3 Apr 2025 10:09:43 +0300 Organization: - Lines: 57 Message-ID: <vslc7n$26a4$2@dont-email.me> References: <vrfvbd$256og$2@dont-email.me> <vsc6lj$27lbo$1@dont-email.me> <ba194532a2343e7068ed57b756a99f48241a94fb@i2pn2.org> <vsce69$2fv3s$1@dont-email.me> <7e0f966861ff1efd916d8d9c32cc9309fd92fe82@i2pn2.org> <vsckdc$2l3cb$1@dont-email.me> <cd467496ff18486f746047b3b1affc4927981c0c@i2pn2.org> <vsct12$2ub5m$1@dont-email.me> <3ab00594a6cdaa3ca8aa32da86b865f3a56d5159@i2pn2.org> <vsd1p9$379dn$3@dont-email.me> <45167877871179050e15837d637c4c8a22e661fd@i2pn2.org> <vsenb0$th5g$7@dont-email.me> <4c1393a97bc073e455df99e0a2d3a47bfc71d940@i2pn2.org> <vsfe66$1m8qr$4@dont-email.me> <7286761fb720294d7a87d883fc82c8f8cf95a460@i2pn2.org> <vsfl7f$1s8b0$3@dont-email.me> <6edcdf0fa4f6ec503240b27a5801f93c470ed7d6@i2pn2.org> <vsh931$3mdkb$1@dont-email.me> <vsivgk$1fjla$1@dont-email.me> <vsjmtj$26s7s$2@dont-email.me> <a4fce1db1fdba9c5eba3e64dc7dba83caff192cf@i2pn2.org> <vskobk$378kj$4@dont-email.me> <ad60872952cbc941149035f6569a7bd4d21766f2@i2pn2.org> <vskt3k$378kj$14@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 03 Apr 2025 09:09:44 +0200 (CEST) Injection-Info: dont-email.me; posting-host="6df5713ce06bce9517b6ce5a28cb5963"; logging-data="72004"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/JGIccgvfGQnkoTqAtB34H" User-Agent: Unison/2.2 Cancel-Lock: sha1:d/IE1I4m0FpAP/89FC6F+/o+K3c= Bytes: 3852 On 2025-04-03 02:51:32 +0000, olcott said: > On 4/2/2025 8:56 PM, Richard Damon wrote: >> On 4/2/25 9:30 PM, olcott wrote: >>> On 4/2/2025 5:05 PM, Richard Damon wrote: >>>> On 4/2/25 11:59 AM, olcott wrote: >>>>> On 4/2/2025 4:20 AM, Mikko wrote: >>>>>> On 2025-04-01 17:51:29 +0000, olcott said: >>>>>> >>>>>>> >>>>>>> All we have to do is make a C program that does this >>>>>>> with pairs of finite strings then it becomes self-evidently >>>>>>> correct needing no proof. >>>>>> >>>>>> There already are programs that check proofs. But you can make your own >>>>>> if you think the logic used by the existing ones is not correct. >>>>>> >>>>>> If the your logic system is sufficiently weak there may also be a way to >>>>>> make a C program that can construct the proof or determine that there is >>>>>> none. >>>>>> >>>>> >>>>> When we define a system that cannot possibly be inconsistent >>>>> then a proof of consistency not needed. >>>> >>>> But you can't do that unless you limit the system to only have a finite >>>> number of statements expressible in it, and thus it can't handle most >>>> real problems >>>> >>>>> >>>>> A system entirely comprised of Basic Facts and Semantic logical >>>>> entailment cannot possibly be inconsistent. >>>>> >>>> >>>> Sure it can. >>>> >>>> The problem is you need to be very careful about what you allow as your >>>> "Basic Facts", and if you allow the system to create the concept of the >>>> Natural Numbers, you can't verify that you don't actually have a >>>> contradition in it. >>>> >>> >>> It never has been that natural numbers have >>> ever actually had any inconsistency themselves >>> they are essentially nothing more than an ordered >>> set of finite strings of digits. >> >> No, but any logic system that can support them > > Can be defined in screwy that has undecidability > or not defined in this screwy way. And you can't define it otherwise. -- Mikko