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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: 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: Wed, 2 Apr 2025 23:27:10 -0500 Organization: A noiseless patient Spider Lines: 75 Message-ID: References: <7e0f966861ff1efd916d8d9c32cc9309fd92fe82@i2pn2.org> <3ab00594a6cdaa3ca8aa32da86b865f3a56d5159@i2pn2.org> <45167877871179050e15837d637c4c8a22e661fd@i2pn2.org> <4c1393a97bc073e455df99e0a2d3a47bfc71d940@i2pn2.org> <7286761fb720294d7a87d883fc82c8f8cf95a460@i2pn2.org> <6edcdf0fa4f6ec503240b27a5801f93c470ed7d6@i2pn2.org> <82f475a36dde2b1f95ea47820f94c20f15f519db@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Thu, 03 Apr 2025 06:27:11 +0200 (CEST) Injection-Info: dont-email.me; posting-host="3670ccff229fdc0c136848dacf82765a"; logging-data="3937906"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18szsym1jKgT8pcNh2XqtOb" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:o7Np4h6Pi9yWxgs6eXMTtZEJdW4= Content-Language: en-US In-Reply-To: <82f475a36dde2b1f95ea47820f94c20f15f519db@i2pn2.org> X-Antivirus: Norton (VPS 250402-4, 4/2/2025), Outbound message X-Antivirus-Status: Clean On 4/2/2025 10:09 PM, Richard Damon wrote: > On 4/2/25 10:51 PM, olcott wrote: >> 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. >> >> Basic facts and expressions semantically entailed >> by the basic facts cannot have undecidability[math]. >> > > Wrong, Godel shows that having the properties of the Natural numbers is > enough. > They are merely an ordered set of finite strings of digits. > Show what property he uses that you can withhold and still have a > reasonably usable mathematics. > > Your problem is you don't understand the power that basic logic gets > from the basic nature of the Natural Numbers. -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer