Path: ...!eternal-september.org!feeder3.eternal-september.org!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 Date: Wed, 2 Apr 2025 22:33:00 -0500 Organization: A noiseless patient Spider Lines: 78 Message-ID: References: <0306c3c2d4a6d05a8bb7441c0b23d325aeac3d7b@i2pn2.org> <04aa9edbe77f4e701297d873264511f820d85526@i2pn2.org> <80b5a3b38362ba5fd57348f78fbdc0d3b5f1c167@i2pn2.org> <27033d4449296dac8c675e73ba2811bdd14385c7@i2pn2.org> <7b2312a71210e65cf978248ff7a9dfaa7c283123@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 03 Apr 2025 05:33:00 +0200 (CEST) Injection-Info: dont-email.me; posting-host="3670ccff229fdc0c136848dacf82765a"; logging-data="3383955"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/SJe28NRMNdBOwSkVgO2Lj" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:FONNFWfWTBY1o9A8He6W0fo0R30= X-Antivirus-Status: Clean Content-Language: en-US X-Antivirus: Norton (VPS 250402-4, 4/2/2025), Outbound message In-Reply-To: <7b2312a71210e65cf978248ff7a9dfaa7c283123@i2pn2.org> Bytes: 4916 On 4/2/2025 10:11 PM, Richard Damon wrote: > On 4/2/25 10:57 PM, olcott wrote: >> On 4/2/2025 8:58 PM, Richard Damon wrote: >>> On 4/2/25 9:33 PM, olcott wrote: >>>> On 4/2/2025 5:07 PM, Richard Damon wrote: >>>>> On 4/2/25 12:03 PM, olcott wrote: >>>>>> On 4/2/2025 4:32 AM, Mikko wrote: >>>>>>> On 2025-04-01 17:56:25 +0000, olcott said: >>>>>>> >>>>>>>> On 4/1/2025 1:33 AM, Mikko wrote: >>>>>>>>> On 2025-03-31 18:33:26 +0000, olcott said: >>>>>>>>> >>>>>>>>>> >>>>>>>>>> Anything the contradicts basic facts or expressions >>>>>>>>>> semantically entailed from these basic facts is proven >>>>>>>>>> false. >>>>>>>>> >>>>>>>>> Anything that follows from true sentences by a truth preserving >>>>>>>>> transformations is true. If you can prove that a true sentence >>>>>>>>> is false your system is unsound. >>>>>>>> >>>>>>>> Ah so we finally agree on something. >>>>>>>> What about the "proof" that detecting inconsistent >>>>>>>> axioms is impossible? (I thought that I remebered this). >>>>>>> >>>>>>> A method that can always determine whether a set of axioms is >>>>>>> inconsistent >>>>>>> does not exist. However, there are methods that can correctly >>>>>>> determine >>>>>>> about some axiom systems that they are inconsistent and fail on >>>>>>> others. >>>>>>> >>>>>>> The proof is just another proof that some function is not Turing >>>>>>> computable. >>>>>>> >>>>>> >>>>>> A finite set of axioms would seem to always be verifiable >>>>>> as consistent or inconsistent.  This may be the same for >>>>>> a finite list of axiom schemas. >>>>>> >>>>> >>>>> Think of how many statements can be constructed from a finite >>>>> alphabet of letters. >>>>> >>>>> Can you "test" every statement to see if it is consistant? >>>>> >>>> >>>> Is "LKNSDFKLWRLKLKNKUKQWEEYIYWQFGFGH" consistent or inconsistent? >>>> Try to come up with a better counter-example. >>> >>> It depends on what each of those letters mean. >>> >> >> So say what they mean to form your counter-example >> showing that consistency across a finite set of axioms >> is undecidable. PUT UP OR SHUT UP. > > No. You are just going off on a Red Herring. > > Show where your system defeats Godel's proof of the inability to prove > consistancy. > > PUT UP OR SHUT UP. > *I am proved categorically correct* A system that begins with A consistent set of basic facts and only derives expressions from this set by semantic logical entailment cannot possibly have inconsistency. If such a system could possibly have inconsistency then at least one valid counter-example could be provided showing this. -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer