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Path: ...!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: Wed, 26 Mar 2025 20:27:20 -0500 Organization: A noiseless patient Spider Lines: 257 Message-ID: <vs29hq$31ibk$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> <4d1d92cfec76603446fd0015ffe8149390540eb4@i2pn2.org> <vs1eom$296sp$1@dont-email.me> <54782b51129b8514f631ef5d004e91d9560a3684@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Thu, 27 Mar 2025 02:27:23 +0100 (CET) Injection-Info: dont-email.me; posting-host="8fbd84b24c3af7ac080451312d40f885"; logging-data="3197300"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/OUo+U77/u6sSQrj+ubDW6" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:ehXS8XpyS4iOjzc1o0QhO8bFLYA= X-Antivirus: Norton (VPS 250326-16, 3/26/2025), Outbound message Content-Language: en-US In-Reply-To: <54782b51129b8514f631ef5d004e91d9560a3684@i2pn2.org> X-Antivirus-Status: Clean Bytes: 10255 On 3/26/2025 6:01 PM, Richard Damon wrote: > On 3/26/25 1:50 PM, olcott wrote: >> On 3/26/2025 6:12 AM, Richard Damon wrote: >>> On 3/25/25 10:15 PM, olcott wrote: >>>> 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. >>> >>> SO that means that "Cats are Dogs" is part of Knowldedge? >>> >> >> Try re-reading what I said as many times as needed >> until you notice ALL of the words. > > > I have, and you can't explain the difference. >> >>>> >>>>> How do we know what we think to be True is actually True? >>>>> >>>> >>>> Stimulated relations between finite strings are necessarily >>>> true. "cats" <are> "animals" >>> >>> Only if "cats" and "animals" have the appropriate definitions. >>> >> >> Do think that anyone ever wrote these down? >> Then they exist in the body of general knowledge expressed in language. > > So anything written down is true? > > Thus climare change must not be real, since THAT "fact" has been written > down and accepted by a large number of peoplel > >> >>> The trator down the street that is a "cat" isn't an animal, but >>> sometimes the person that operates it can be a bit of one. >>> >> >> General knowledge. > > But "cat" is a term for a type of tractor. > >> >>>> >>>>> In FORMAL systems we can rigorously define what is true in that >>>>> system, as we start with a defined set of given facts (which is why >>>>> you can't change the definitions and stay in the system, as those >>>>> definitions are what made the system). >>>> >>>> Almost the same idea as basic facts. >>> >>> Yes, but more than basic facts. Note, >>> >> >> What formal system has an axiom that defines >> ice cream as a diary product? > > Many, > >> >>>> >>>>> When you talk about "Human Knowledge" for the "Real World" you run >>>>> into the problem that we don't have a listing of the fundamental >>>>> facts that define the system, but are trying to discover our best >>>>> explainations by observation. >>>>> >>>> >>>> Basic facts that cannot be derived from anything else. >>> >>> So what makes them true? >> >> What makes a dairy cow not a kind of rattlesnake. >> Stipulated relations between finite strings that >> provides their semantic meaning. > > No, stipulated relationships between concepts. > OK, I will give you that and qualify my original statement. Stipulated relations between concepts that are labeled by finite strings, thus ultimately stipulated relations between finite strings, the ultimate formalism. >> >>> Note, EVERYTHING we know about the real world starts with >>> observations, and observations are always only approximate. >>> >> ========== REMAINDER OF ARTICLE TRUNCATED ==========