Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: sci.logic Subject: Re: How a True(X) predicate can be defined for the set of analytic knowledge ---ZFC Date: Wed, 26 Mar 2025 17:04:14 -0500 Organization: A noiseless patient Spider Lines: 151 Message-ID: References: <3cf0a34d9382774fd8275a118d1af8b0841c8eb1@i2pn2.org> <7d0164a6001fc519a244b7ed4930d757b9bd7ac1@i2pn2.org> <8c4ea7f74348f8becac017bb33d6cab1b30f5e01@i2pn2.org> <4702eef1b0ace44f2a334894a27ead737d674fe6@i2pn2.org> <4d728cda161b629a6fa645a938580551566fda78@i2pn2.org> <0b09ece8b64c4c2f9cd572fe5f5e4a2ae5937348@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 26 Mar 2025 23:04:15 +0100 (CET) Injection-Info: dont-email.me; posting-host="61544cd49926c0716809366eec9fc285"; logging-data="2842321"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19L6UYL6Ee+uvMNxwMeu3n8" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:EgiyBMHzW4hzl+wArUN6odSRA2E= X-Antivirus: Norton (VPS 250326-16, 3/26/2025), Outbound message X-Antivirus-Status: Clean Content-Language: en-US In-Reply-To: On 3/26/2025 2:58 AM, Mikko wrote: > On 2025-03-25 14:28:49 +0000, olcott said: > >> On 3/25/2025 4:50 AM, Mikko wrote: >>> On 2025-03-23 04:24:51 +0000, olcott said: >>> >>>> On 3/22/2025 9:53 PM, Richard Damon wrote: >>>>> On 3/22/25 2:33 PM, olcott wrote: >>>>>> On 3/22/2025 12:34 PM, Richard Damon wrote: >>>>>>> On 3/22/25 11:13 AM, olcott wrote: >>>>>>>> On 3/22/2025 5:11 AM, joes wrote: >>>>>>>>> Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott: >>>>>>>>>> On 3/21/2025 9:31 PM, Richard Damon wrote: >>>>>>>>>>> On 3/21/25 9:24 PM, olcott wrote: >>>>>>>>>>>> On 3/21/2025 7:50 PM, Richard Damon wrote: >>>>>>>>>>>>> On 3/21/25 8:40 PM, olcott wrote: >>>>>>>>>>>>>> On 3/21/2025 6:49 PM, Richard Damon wrote: >>>>>>>>>>>>>>> On 3/21/25 8:43 AM, olcott wrote: >>>>>>>>>>>>>>>> On 3/21/2025 3:41 AM, Mikko wrote: >>>>>>>>>>>>>>>>> On 2025-03-20 14:57:16 +0000, olcott said: >>>>>>>>>>>>>>>>>> On 3/20/2025 6:00 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>> On 3/19/25 10:42 PM, olcott wrote: >>>>>>>>> >>>>>>>>>>>>>>>>>>>> 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. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> Which just means that you have stipulated yourself >>>>>>>>>>>>>>>>>>> out of all >>>>>>>>>>>>>>>>>>> classical logic, since Truth is different than >>>>>>>>>>>>>>>>>>> Knowledge. In a >>>>>>>>>>>>>>>>>>> good logic system, Knowledge will be a subset of >>>>>>>>>>>>>>>>>>> Truth, but you >>>>>>>>>>>>>>>>>>> have defined that in your system, Truth is a subset of >>>>>>>>>>>>>>>>>>> Knowledge, so you have it backwards. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> True(X) always returns TRUE for every element in the >>>>>>>>>>>>>>>>>> set of >>>>>>>>>>>>>>>>>> general knowledge that can be expressed using language. >>>>>>>>>>>>>>>>>> It never gets confused by paradoxes. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Not useful unless it returns TRUE for no X that >>>>>>>>>>>>>>>>> contradicts >>>>>>>>>>>>>>>>> anything that can be inferred from the set of general >>>>>>>>>>>>>>>>> knowledge. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> I can't parse that. >>>>>>>>>>>>>>>>   > (a) Not useful unless (b) it returns TRUE for (c) no >>>>>>>>>>>>>>>> X that >>>>>>>>>>>>>>>>   > contradicts anything (d) that can be inferred from >>>>>>>>>>>>>>>> the set of >>>>>>>>>>>>>>>>   > general knowledge. >>>>>>>>>>>>>>>>   > >>>>>>>>>>>>>>>> Because my system begins with basic facts and actual >>>>>>>>>>>>>>>> facts can't >>>>>>>>>>>>>>>> contradict each other and no contradiction can be formed by >>>>>>>>>>>>>>>> applying only truth preserving operations to these basic >>>>>>>>>>>>>>>> facts >>>>>>>>>>>>>>>> there are no contradictions in the system. >>>>>>>>> The liar sentence is contradictory. >>>>>>>>> >>>>>>>>>>>>>>> No, you system doesn't because you don't actually >>>>>>>>>>>>>>> understand what >>>>>>>>>>>>>>> you are trying to define. >>>>>>>>>>>>>>> "Human Knowledge" is full of contradictions and incorrect >>>>>>>>>>>>>>> statements. >>>>>>>>>>>>>>> Adittedly, most of them can be resolved by properly >>>>>>>>>>>>>>> putting the >>>>>>>>>>>>>>> statements into context, but the problem is that for some >>>>>>>>>>>>>>> statement, the context isn't precisely known or the >>>>>>>>>>>>>>> statement is >>>>>>>>>>>>>>> known to be an approximation of unknown accuracy, so doesn't >>>>>>>>>>>>>>> actually specify a "fact". >>>>>>>>>>>>>> >>>>>>>>>>>>>> It is self evidence that for every element of the set of >>>>>>>>>>>>>> human >>>>>>>>>>>>>> knowledge that can be expressed using language that >>>>>>>>>>>>>> undecidability >>>>>>>>>>>>>> cannot possibly exist. >>>>>>>>> Not self-evident was Gödel's disproof of that. >>>>>>>>> >>>>>>>>>>>>> SO, you admit you don't know what it means to prove something. >>>>>>>>>>>>> >>>>>>>>>>>> When the proof is only syntactic then it isn't directly >>>>>>>>>>>> connected to >>>>>>>>>>>> any meaning. >>>>>>>>>>> >>>>>>>>>>> But Formal Logic proofs ARE just "syntactic" >>>>>>>>> >>>>>>>>> >>>>>>>>>>>> When the body of human general knowledge has all of its >>>>>>>>>>>> semantics >>>>>>>>>>>> encoded syntactically AKA Montague Grammar of Semantics then >>>>>>>>>>>> a proof >>>>>>>>>>>> means validation of truth. >>>>>>>>>>> Yes, proof is a validatation of truth, but truth does not >>>>>>>>>>> need to be >>>>>>>>>>> able to be validated. >>>>>>>>>> True(X) ONLY validates that X is true and does nothing else. >>>>>>>>> Not if X is unknown (but still true). >>>>>>>>> >>>>>>>> >>>>>>>> You must pay complete attention to ALL of my words >>>>>>>> or you get the meaning that I specify incorrectly. >>>>>>>> >>>>>>> >>>>>>> The problem is that statement, you don't get to change the >>>>>>> meaning of the core terms and stay in the system, so you are just >>>>>>> admitting that all your work is based on strawmen, and thus frauds. >>>>>>> >>>>>> >>>>>> >>>>>>    In the exact same way that ZFC totally screwed up >>>>>>    and never resolved Russell's Paradox because they >>>>>>    were forbidden to limit how sets are defined. >>>>>> >>>>>>    When the definition of a set allowed pathological >>>>>>    self-reference they should have construed this >>>>>>    as infallible and immutable. >>>>>> >>>>>> >>>>> >>>>> IN other words, you admit that you can't refute what I said, so you >>>>> just go off beat. >>>>> >>>> >>>> By the freaking concrete example that I provided >>>> YES YOU DO GET TO CHANGE THE MEANING OF THE TERMS. >>> >>> No, you can't. The nearest you can is to create a new term that >>> is homonymous to an old one. But you can't use two homonymous >>> terms in the same opus. >> >> Original set theory became "naive set theory". >> ZFC set theory corrected its shortcomings. > > The original one is Cantor's. But that his presentation was too informal > to determine whether Russell's set is expressible. But he did show that > one can construct from nothing enough sets for natural number arithmetic. > Russell's set cannot be constructed. > My whole point is that a broken system was fixed by redefining it. -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer