Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!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: Wed, 26 Mar 2025 23:29:03 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <36140e2ae3411293bc9bf113181dfd63842fa89c@i2pn2.org> References: <0306c3c2d4a6d05a8bb7441c0b23d325aeac3d7b@i2pn2.org> <4d1d92cfec76603446fd0015ffe8149390540eb4@i2pn2.org> <54782b51129b8514f631ef5d004e91d9560a3684@i2pn2.org> <04f073d03e6f8ad8438ea5962ae9d49d6375705a@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 03:31:15 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="1919647"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US In-Reply-To: Bytes: 8951 Lines: 194 On 3/26/25 10:46 PM, olcott wrote: > On 3/26/2025 9:32 PM, Richard Damon wrote: >> On 3/26/25 9:27 PM, olcott wrote: >>> 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 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" "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. >>>> ========== REMAINDER OF ARTICLE TRUNCATED ==========