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Path: ...!eternal-september.org!feeder3.eternal-september.org!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: Sun, 30 Mar 2025 12:57:43 +0300 Organization: - Lines: 177 Message-ID: <vsb4in$14lqk$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> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 30 Mar 2025 11:57:44 +0200 (CEST) Injection-Info: dont-email.me; posting-host="af6bf321dc250098f0a7fad67f14c49f"; logging-data="1202004"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18op3ZDBNC1ZE/xlFqysOiy" User-Agent: Unison/2.2 Cancel-Lock: sha1:QgJJ77bMQ59DHKUpIY2Nmwt5QiE= Bytes: 8928 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. If you reject the idea that a sentence derived from true sentences with turth preserving transformations is always true then you may disagree. -- Mikko