Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: sci.logic Subject: Re: Why Tarski is wrong Date: Wed, 19 Mar 2025 18:36:52 -0500 Organization: A noiseless patient Spider Lines: 103 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 20 Mar 2025 00:36:53 +0100 (CET) Injection-Info: dont-email.me; posting-host="ca94344bd24a354eba3539b74c3bed05"; logging-data="1972381"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18i3bmtWetWYvPWCe0opbXw" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:BSm6IKG+UYr022WF8SI3zV1HL6o= Content-Language: en-US X-Antivirus-Status: Clean X-Antivirus: Norton (VPS 250319-10, 3/19/2025), Outbound message In-Reply-To: On 3/19/2025 9:09 AM, Mikko wrote: > On 2025-03-18 15:28:31 +0000, olcott said: > >> On 3/18/2025 9:34 AM, Mikko wrote: >>> On 2025-03-17 12:54:53 +0000, olcott said: >>> >>>> On 3/17/2025 3:57 AM, Mikko wrote: >>>>> On 2025-03-17 01:50:24 +0000, olcott said: >>>>> >>>>>> On 3/16/2025 5:50 PM, Richard Damon wrote: >>>>>>> On 3/16/25 11:12 AM, olcott wrote: >>>>>>>> On 3/16/2025 7:36 AM, joes wrote: >>>>>>>>> Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott: >>>>>>>>>> >>>>>>>>>> We can define a correct True(X) predicate that always succeeds >>>>>>>>>> except >>>>>>>>>> for unknowns and untruths, Tarski WAS WRONG !!! >>>>>>>>> That does not disprove Tarski. >>>>>>>>> >>>>>>>> >>>>>>>> He said that this is impossible and no >>>>>>>> counter-examples exists that shows that I am wrong. >>>>>>>> True(GC) == FALSE Cannot be proven true AKA unknown >>>>>>>> True(LP) == FALSE Not a truth-bearer >>>>>>>> >>>>>>> >>>>>>> >>>>>>> But if x is what you are saying is >>>>>> >>>>>> A True(X) predicate can be defined and Tarski never >>>>>> showed that it cannot. >>>>>> >>>>>> True(X) only returns TRUE when a a sequence of truth >>>>>> preserving operations can derive X from the set of basic >>>>>> facts and returns false otherwise. >>>>> >>>>> By this criterion True("There is no truth predicate") is TRUE. >>>>> >>>> >>>> The True(X) predicate only takes formalized Natural Language so that >>>> would  be rejected as false. >>> >>> No, if we interprete "There is no truth predicate" to represent the >>> formalized natural language expression that means that there is no >>> turth predicate. >>> >> >> That is already accounted for by the Liar Paradox. >> Every self-contradictory expression cannot be derived >> from the set of basic facts by applying ONLY truth >> preserving operations. > > That depends on "the set of basic facts". OK if they really are facts > but otherwise anything is possible. > Yes they really are facts thus actual elements of the set of human general knowledge that can be expressed using language. >>>> LP := ~True(LP) would also be rejected >>>> as ~TRUE. The Principle of explosion does not apply truth preserving >>>> operations. >>> >>> The expression LP := ~True(LP) should be rejected as a syntax error. >> >> Formalized natural language must be able to directly >> encode the self-reference of the Liar Paradox >> "This sentence is not true" or it is insufficiently >> expressive. > > Depends on your definition of "sufficiently". The truth of a sentence > depends on interpretation, so it is not determined by the real world. > The ONLY formal language that I know that can directly express self-reference is the Minimal Type Theory that I created for the purpose of directly expressing self-reference. Tarski's Liar Paradox x ∉ True if and only if p where the symbol 'p' represents the whole sentence x https://liarparadox.org/Tarski_275_276.pdf Expressed the self-reference in the English and never formalized it in any formal language. LP := ~True(LP) directly encodes ~True(~True(~True(~True(~True(~True(~True(...))))))) Clocksin and Mellish saying the same thing. ?- equal(foo(Y), Y). Y will stand for foo(Y), which is foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))), and soon. So Y ends up standing for some kind of infinite structure. thus directly encodes foo(foo(foo(foo(foo(foo(...)))))) -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer