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Path: 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: Mon, 31 Mar 2025 12:04:08 +0300 Organization: - Lines: 191 Message-ID: <vsdlq8$3shbn$1@dont-email.me> References: <vrfvbd$256og$2@dont-email.me> <vrh432$39r47$1@dont-email.me> <vrhami$3fbja$2@dont-email.me> <vrj9lu$1791p$1@dont-email.me> <vrjn82$1ilbe$2@dont-email.me> <vrmpc1$bnp3$1@dont-email.me> <vrmteo$cvat$6@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> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 31 Mar 2025 11:04:09 +0200 (CEST) Injection-Info: dont-email.me; posting-host="9db5ebc22b0a66665dc12d47e37818b7"; logging-data="4081015"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/N2Gfj9ZqoJh3apze5EEL8" User-Agent: Unison/2.2 Cancel-Lock: sha1:y8dlLra5rsIpoffFuaxMltvxPRA= On 2025-03-30 11:20:05 +0000, olcott said: > 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 know facts is >>>> small, probably empty. If you include many uncertain facts then >>>> almost certainly your True(X) is true for some false X. >>>> >>> >>> Yes of course there are no known facts it might be the case >>> that feline kittens have always been 15 story office buildings >>> and we have been deluded into thinking differently. >>> >>>>> A knowledge ontology inheritance hierarchy is most efficient. >>>>> >>>>>> However, there could be no uncertain sentences as they are not known >>>>>> (sensu Olcotti). >>>>> >>>>> Scientific theories would be uncertain truth. >>>>> It is a known fact that X evidence seems to make Y >>>>> a reasonably plausible possibility. >>>> >>>> A good example is Newtonial mchanics, which is known to be wrong but is >>>> useful and used for practical purposes. How should your True(X) handle >>>> that? >>>> >>>>>>> The set of everything that anyone ever wrote >>>>>>> down would be finite. >>>>>> >>>>>> But not knowable. >>>>>> >>>>>>> Most of this would be >>>>>>> specific knowledge Pete's dog was named Bella. >>>>>>> Some is general dogs are animals. >>>>>>> >>>>>>>>>> Ae also know that many expressions of language that are written down >>>>>>>>>> somewhere lack the semantic property of true. >>>>>>>>> >>>>>>>>> False statements do not count as knowledge. >>>>>>>> >>>>>>>> No, but your "the set of expressions of language that have the semantic >>>>>>>> property of true that are written down somewhere" is not useful because >>>>>>>> there is no way to know that set. >>>>>>> >>>>>>> We can know that the set of general knowledge that can >>>>>>> possibly be written down (formerly the analytic aspect >>>>>>> of the analytic/synthetic distinction) exists without >>>>>>> enumerating its elements. >>>>>> >>>>>> But we can't use it. >>>>> >>>>> We can use it right now to understand that Tarski >>>>> has been refuted and that True(X) does exist for >>>>> a specific and crucially relevant domain. >>>> >>>> Understanding that Tarski has been refuted hardly counts as understanding >>>> as Tarstki has not been refuted. >>>> >>> >>> When Tarski said True(X) cannot be defined, he is proved wrong. >> >> He didn't say that True(X) cannot be defined. He proved that no definition >> defines a predicate that tells whether a sentence is true. > > Mere more verbose way of saying the same thing. > >> If you reject >> the idea that a sentence derived from true sentences with turth preserving >> transformations is always true then you may disagree. > > Since this <is> my own design, I do not reject it. ========== REMAINDER OF ARTICLE TRUNCATED ==========