Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!usenet.network!news.neodome.net!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: sci.logic Subject: Re: How a True(X) predicate can be defined for the set of analytic knowledge Date: Tue, 1 Apr 2025 06:31:13 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <6edcdf0fa4f6ec503240b27a5801f93c470ed7d6@i2pn2.org> References: <04aa9edbe77f4e701297d873264511f820d85526@i2pn2.org> <215f3f8823df394f0cbd307af57a528cb3afc52f@i2pn2.org> <7e0f966861ff1efd916d8d9c32cc9309fd92fe82@i2pn2.org> <3ab00594a6cdaa3ca8aa32da86b865f3a56d5159@i2pn2.org> <45167877871179050e15837d637c4c8a22e661fd@i2pn2.org> <4c1393a97bc073e455df99e0a2d3a47bfc71d940@i2pn2.org> <7286761fb720294d7a87d883fc82c8f8cf95a460@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Tue, 1 Apr 2025 11:06:42 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="2664280"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: Content-Language: en-US X-Spam-Checker-Version: SpamAssassin 4.0.0 On 3/31/25 11:06 PM, olcott wrote: > On 3/31/2025 8:23 PM, Richard Damon wrote: >> On 3/31/25 9:06 PM, olcott wrote: >>> On 3/31/2025 5:27 PM, Richard Damon wrote: >>>> On 3/31/25 2:36 PM, olcott wrote: >>>>> On 3/31/2025 5:59 AM, Richard Damon wrote: >>>>>> On 3/30/25 11:22 PM, olcott wrote: >>>>>>> On 3/30/2025 9:31 PM, Richard Damon wrote: >>>>>>>> On 3/30/25 10:01 PM, olcott wrote: >>>>>>>>> On 3/30/2025 7:25 PM, Richard Damon wrote: >>>>>>>>>> On 3/30/25 7:34 PM, olcott wrote: >>>>>>>>>>> On 3/30/2025 5:47 PM, Richard Damon wrote: >>>>>>>>>>>> On 3/30/25 5:47 PM, olcott wrote: >>>>>>>>>>>>> On 3/30/2025 3:59 PM, Richard Damon wrote: >>>>>>>>>>>>>> On 3/30/25 3:39 PM, olcott wrote: >>>>>>>>>>>>>>> On 3/30/2025 1:53 PM, Richard Damon wrote: >>>>>>>>>>>>>>>> On 3/30/25 1:16 PM, olcott wrote: >>>>>>>>>>>>>>>>> On 3/30/2025 6:24 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>> On 3/30/25 7:20 AM, olcott wrote: >>>>>>>>>>>>>>>>>>> On 3/30/2025 4:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>> On 2025-03-29 14:06:17 +0000, olcott said: >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> On 3/29/2025 5:20 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>> On 2025-03-28 19:59:16 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>> On 3/28/2025 7:12 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-28 01:04:45 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>> On 3/27/2025 5:48 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 17:58:10 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/26/2025 3:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 02:15:26 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/2025 8:08 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/25 10:56 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/2025 5:19 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is stipulated that analytic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge is limited to the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of knowledge that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed using language or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived by applying truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations to elements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of this set. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> A simple example is the first >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> order group theory. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When we begin with a set of basic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> facts and all inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is limited to applying truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> elements of this set then a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> True(X) predicate cannot possibly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be thwarted. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> There is no computable predicate >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that tells whether a sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the first order group theory >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can be proven. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Likewise there currently does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist any finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is true or false >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> error. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> However, it is possible that someone >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finds a proof of the conjecture >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or its negation. Then the predicate >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> True is no longer complete. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The set of all human general >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that can >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be expressed using language gets >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> updated. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When we redefine logic systems such >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that they begin >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with set of basic facts and are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only allowed to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> apply truth preserving operations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to these basic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> facts then every element of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> system is provable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on the basis of these truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> However, it is possible (and, for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sufficiently powerful sysems, certain) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that the provability is not computable. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When we begin with basic facts and >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only apply truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to the giant semantic tautology of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the set of human knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be expressed using language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then every element in this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set is reachable by these same truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The set of human knowledge that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed using language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is not a tautology. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> tautology, in logic, a statement so >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> framed that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it cannot be denied without inconsistency. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> And human knowledge is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What is taken to be knowledge might >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> possibly be false. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What actually knowledge is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> impossibly false by >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> How do you DEFINE what is actually knowledge? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>> *This is a good first guess* >>>>>>>>>>>>>>>>>>>>>>>>>>>>> The set of expressions of language that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> have the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic property of true that are written >>>>>>>>>>>>>>>>>>>>>>>>>>>>> down >>>>>>>>>>>>>>>>>>>>>>>>>>>>> somewhere. >>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>> We already know that many expressions of >>>>>>>>>>>>>>>>>>>>>>>>>>>> language that have the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>> proerty of true are not written down anywhere. >>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>> Only general knowledge >>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>> What is "general" intended to mean here? In >>>>>>>>>>>>>>>>>>>>>>>>>> absense of any definition >>>>>>>>>>>>>>>>>>>>>>>>>> it is too vague to really mean anything. >>>>>>>>>>>>>>>>>>>>>>>>>> ========== REMAINDER OF ARTICLE TRUNCATED ==========