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: Sat, 29 Mar 2025 18:06:26 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <58019fb7503574b0b23a3b5b514dee009f14aa48@i2pn2.org> References: <0306c3c2d4a6d05a8bb7441c0b23d325aeac3d7b@i2pn2.org> <39c8eb10924e5aff7b2e2455b1fb8441571a85a9@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Sat, 29 Mar 2025 22:31:41 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="2313829"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US Bytes: 6093 Lines: 90 On 3/29/25 4:53 PM, olcott wrote: > On 3/29/2025 3:19 PM, joes wrote: >> Am Sat, 29 Mar 2025 09:14:36 -0500 schrieb olcott: >>> On 3/29/2025 5:52 AM, Richard Damon wrote: >>>> On 3/28/25 11:19 PM, olcott wrote: >>>>> On 3/28/2025 4:18 PM, Richard Damon wrote: >>>>>> On 3/28/25 4:07 PM, olcott wrote: >>>>>>> On 3/28/2025 8:46 AM, Richard Damon wrote: >>>>>>>> On 3/27/25 10:18 PM, olcott wrote: >>>>>>>>> On 3/27/2025 8:54 PM, Richard Damon wrote: >>>>>>>>>> On 3/27/25 9:04 PM, olcott wrote: >>>>>>>>>>> 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: >> >>>>>>>>>>>>>>>>>>>>>>>>> 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. >> No, it is either true or not. >> >>>>>>>>>>>>>>>>>>>>>> However, it is possible (and, for sufficiently >>>>>>>>>>>>>>>>>>>>>> powerful sysems, certain) >>>>>>>>>>>>>>>>>>>>>> that the provability is not computable. >> >>>>>>>> Ok, so therefore it includes all the "laws of mathematics" and the >>>>>>>> "rules of inference" and thus, the system is capable of creating >>>>>>>> the rules and properties of the Natural Numbers, so it supports the >>>>>>>> proofs of Godel and Tarski, and thus there are statements in that >>>>>>>> sytstem that are True but unprovable and no definition of the Truth >>>>>>>> Predicate can handle those, >>>>>>>> >>>>>>> Yes it will showed the formal system can be defined that have all >>>>>>> kinds of issues because they were defined incoherently. >> Where is there an incoherent definition? >> >>>>> When any formal logic system begins with stipulated set of basic facts >>>>> and is only allowed to apply truth preserving operations to these >>>>> facts and expressions derived from these facts then undecidability >>>>> cannot possibly occur. >>>> >>>> Sure it can, as Godel and Turing Proved. >>>> >>> When full semantics is directly integrated into the formal system, the >>> system begins with an list of basic facts, the only inference step is >>> semantic logical entailment applying truth preserving operations >>> Tarski's proof fails. > >> Where, at which step, how, why? >> > > True(X) and ~Provable(X) cannot possibly exist > in my system because Provable(X) means truth > preserving operations are applied to basic facts > thus deriving True(X). Then you system MUST be "finite" in available scope, as Truth can otherwise exist via a INFINITE sequence of truth preserving operations, while a proof can not, since we can not "see" all of an infinite list. Sorry, you are just proving your stupidity and ignorance. > >>> We are no longer seeking mere provability we are seeking provably true >>> at the semantic level. At the semantic level incoherent nonsense such as >>> "This sentence is not true" is screened out. > >> How? >> > > As I said above and repeated dozens of times. >