Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko Newsgroups: sci.logic Subject: Re: Undecidability based on epistemological antinomies V2 --Mendelson-- Date: Thu, 25 Apr 2024 11:26:07 +0300 Organization: - Lines: 72 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 25 Apr 2024 10:26:07 +0200 (CEST) Injection-Info: dont-email.me; posting-host="cc7791d62a6d3eaec3a9ae09cded4cbc"; logging-data="3060406"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+MN4bhbUdG/+3iWCH563J9" User-Agent: Unison/2.2 Cancel-Lock: sha1:bSh52Q68tMsJUwqxHAXA5ChtdgU= Bytes: 4124 On 2024-04-24 16:01:46 +0000, olcott said: > On 4/24/2024 4:49 AM, Mikko wrote: >> On 2024-04-23 14:54:09 +0000, olcott said: >> >>> On 4/22/2024 3:26 AM, Mikko wrote: >>>> On 2024-04-21 14:34:44 +0000, olcott said: >>>> >>>>> On 4/21/2024 2:50 AM, Mikko wrote: >>>>>> On 2024-04-20 16:37:27 +0000, olcott said: >>>>>> >>>>>>> On 4/20/2024 2:41 AM, Mikko wrote: >>>>>>>> On 2024-04-19 02:25:48 +0000, olcott said: >>>>>>>> >>>>>>>>> On 4/18/2024 8:58 PM, Richard Damon wrote: >>>>>>>> >>>>>>>>>> Godel's proof you are quoting from had NOTHING to do with undecidability, >>>>>>>>> >>>>>>>>> *Mendelson (and everyone that knows these things) disagrees* >>>>>>>>> >>>>>>>>> https://sistemas.fciencias.unam.mx/~lokylog/images/Notas/la_aldea_de_la_logica/Libros_notas_varios/L_02_MENDELSON,%20E%20-%20Introduction%20to%20Mathematical%20Logic,%206th%20Ed%20-%20CRC%20Press%20(2015).pdf >>>>>>>>> >>>>>>>> >>>>>>>> On questions whether Gödel said something or not the sumpreme authority >>>>>>>> is not Mendelson but Gödel. >>>>>>>> >>>>>>> >>>>>>> When some authors affirm that undecidability and incompleteness >>>>>>> are the exact same thing then whenever Gödel uses the term >>>>>>> incompleteness then he is also referring to the term undecidability. >>>>>> >>>>>> That does not follow. Besides, a reference to the term "undecidability" >>>>>> is not a reference to the concept 'undecidability'. >>>>>> >>>>> >>>>> In other words you deny the identity principle thus X=X is false. >>>> >>>> It is not a good idea to lie where the truth can be seen. >>>> >>> >>> It is not a good idea to say gibberish nonsense and >>> expect it to be understood. >>>  >>> a reference to the term "undecidability" >>>  >>> is not a reference to the concept 'undecidability'. >> >> That is how a sentence must be quoted. The proof that the quoted >> sentence can be understood is that Richard Damon undesstood it. >> >>>>> An undecidable sentence of a theory K is a closed wf ℬ of K such that >>>>> neither ℬ nor ¬ℬ is a theorem of K, that is, such that not-⊢K ℬ and >>>>> not-⊢K ¬ℬ. (Mendelson: 2015:208) >>>> >>>> So that is what "undecideble" means in Mendelson: 2015. Elsewhere it may >>>> mean something else. >> >>> It usually means one cannot make up one's mind. >>> In math it means an epistemological antinomy expression >>> is not a proposition thus a type mismatch error for every >>> bivalent system of logic. >> >> No, it doesn't. There is no reference to an epistemological >> anitnomy in "undecidable". >> > > ...14 Every epistemological antinomy can likewise be used for a similar > undecidability proof...(Gödel 1931:43-44) That is not a part of the definition of "undecidable". -- Mikko