Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: sci.logic Subject: Re: How a True(X) predicate can be defined for the set of analytic knowledge Date: Sat, 5 Apr 2025 15:58:17 -0500 Organization: A noiseless patient Spider Lines: 85 Message-ID: References: <7e0f966861ff1efd916d8d9c32cc9309fd92fe82@i2pn2.org> <3ab00594a6cdaa3ca8aa32da86b865f3a56d5159@i2pn2.org> <45167877871179050e15837d637c4c8a22e661fd@i2pn2.org> <4c1393a97bc073e455df99e0a2d3a47bfc71d940@i2pn2.org> <7286761fb720294d7a87d883fc82c8f8cf95a460@i2pn2.org> <6edcdf0fa4f6ec503240b27a5801f93c470ed7d6@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Sat, 05 Apr 2025 22:58:18 +0200 (CEST) Injection-Info: dont-email.me; posting-host="553bf603fba0ab686689915e3400961c"; logging-data="3380670"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18gQEg1vrwbe8RZl/JHAzhR" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:PEn+DJm0xO+osHNnyumMusG0050= X-Antivirus-Status: Clean Content-Language: en-US In-Reply-To: X-Antivirus: Norton (VPS 250405-6, 4/5/2025), Outbound message On 4/5/2025 2:20 AM, Mikko wrote: > On 2025-04-03 19:33:41 +0000, olcott said: > >> On 4/3/2025 2:09 AM, Mikko wrote: >>> 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. >>> >> >> Yes it free to keeps its screwy definition just like >> set theory until a superior alternative comes along, >> then it may be renamed naive formal systems. >> >> A consistent set of stipulated axioms combined with >> semantic logical entailment as the only inference step >> makes undecidability impossible. > > If semantic logical entaillment is allowed as an inference rule > the system is not formal. In order to be formal the system must > define "proof" as any string that satiisfies the syntactic rules > that the system specifies for proofs. > This "baffled" Richard https://en.wikipedia.org/wiki/Montague_grammar https://plato.stanford.edu/entries/montague-semantics/ Semantics as rich as natural language fully formalized syntactically. -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer