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Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder3.eternal-september.org!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: Sun, 30 Mar 2025 22:22:17 -0500 Organization: A noiseless patient Spider Lines: 313 Message-ID: <vsd1p9$379dn$3@dont-email.me> References: <vrfvbd$256og$2@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> <vs63o2$2nal3$1@dont-email.me> <vs6v2l$39556$17@dont-email.me> <vs8hia$13iam$1@dont-email.me> <vs8uoq$1fccq$2@dont-email.me> <vsb4in$14lqk$1@dont-email.me> <vsb9d5$19ka5$1@dont-email.me> <04aa9edbe77f4e701297d873264511f820d85526@i2pn2.org> <vsbu9j$1vihj$1@dont-email.me> <215f3f8823df394f0cbd307af57a528cb3afc52f@i2pn2.org> <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> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Mon, 31 Mar 2025 05:22:18 +0200 (CEST) Injection-Info: dont-email.me; posting-host="7c3e41e7cd06e5848bcc8c57c53d2c68"; logging-data="3384759"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18Yo1PyITVcR5X5KQe3nfh2" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:NYOinoi8ObwTWFqS5NTC2gCFJps= X-Antivirus: Norton (VPS 250330-6, 3/30/2025), Outbound message Content-Language: en-US X-Antivirus-Status: Clean In-Reply-To: <3ab00594a6cdaa3ca8aa32da86b865f3a56d5159@i2pn2.org> Bytes: 16501 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 <is> 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. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> Reverse-engineer how you could define a set of >>>>>>>>>>>>>>>>>> knowledge that is finite rather than infinite. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> First one should define what the elements of that set >>>>>>>>>>>>>>>>> could be. >>>>>>>>>>>>>>>>> If sentences, and there are not too many of them, a set >>>>>>>>>>>>>>>>> of knowledge >>>>>>>>>>>>>>>>> could be presented as a book that contains those >>>>>>>>>>>>>>>>> sentences and nothing >>>>>>>>>>>>>>>>> else. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> A list of sentences would not make for efficient >>>>>>>>>>>>>>>> processing. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Unless you want to exclude uncertain facts the set of ========== REMAINDER OF ARTICLE TRUNCATED ==========