Path: ...!feeds.phibee-telecom.net!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: sci.logic Subject: Re: Undecidability based on epistemological antinomies V2 --Tarski Proof-- Date: Tue, 23 Apr 2024 09:31:00 -0500 Organization: A noiseless patient Spider Lines: 104 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 23 Apr 2024 16:31:01 +0200 (CEST) Injection-Info: dont-email.me; posting-host="a7006f3e3637d5c785f9944f8af11529"; logging-data="1763242"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+VBDNbRSHEkC1luObPUTQF" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:oz7GqGYORbP8Lx+D9zCEi4kLEkg= Content-Language: en-US In-Reply-To: Bytes: 6057 On 4/23/2024 3:21 AM, Mikko wrote: > On 2024-04-22 17:37:55 +0000, olcott said: > >> On 4/22/2024 10:27 AM, Mikko wrote: >>> On 2024-04-22 14:10:54 +0000, olcott said: >>> >>>> On 4/22/2024 4:35 AM, Mikko wrote: >>>>> On 2024-04-21 14:44:37 +0000, olcott said: >>>>> >>>>>> On 4/21/2024 2:57 AM, Mikko wrote: >>>>>>> On 2024-04-20 15:20:05 +0000, olcott said: >>>>>>> >>>>>>>> On 4/20/2024 2:54 AM, Mikko wrote: >>>>>>>>> On 2024-04-19 18:04:48 +0000, olcott said: >>>>>>>>> >>>>>>>>>> When we create a three-valued logic system that has these >>>>>>>>>> three values: {True, False, Nonsense} >>>>>>>>>> https://en.wikipedia.org/wiki/Three-valued_logic >>>>>>>>> >>>>>>>>> Such three valued logic has the problem that a tautology of the >>>>>>>>> ordinary propositional logic cannot be trusted to be true. For >>>>>>>>> example, in ordinary logic A ∨ ¬A is always true. This means that >>>>>>>>> some ordinary proofs of ordinary theorems are no longer valid and >>>>>>>>> you need to accept the possibility that a theory that is complete >>>>>>>>> in ordinary logic is incomplete in your logic. >>>>>>>>> >>>>>>>> >>>>>>>> I only used three-valued logic as a teaching device. Whenever an >>>>>>>> expression of language has the value of {Nonsense} then it is >>>>>>>> rejected and not allowed to be used in any logical operations. It >>>>>>>> is basically invalid input. >>>>>>> >>>>>>> You cannot teach because you lack necessary skills. Therefore you >>>>>>> don't need any teaching device. >>>>>>> >>>>>> >>>>>> That is too close to ad homimen. >>>>>> If you think my reasoning is incorrect then point to the error >>>>>> in my reasoning. Saying that in your opinion I am a bad teacher >>>>>> is too close to ad hominem because it refers to your opinion of >>>>>> me and utterly bypasses any of my reasoning. >>>>> >>>>> No, it isn't. You introduced youtself as a topic of discussion so >>>>> you are a legitimate topic of discussion. >>>>> >>>>> I didn't claim that there be any reasoning, incorrect or otherwise. >>>>> >>>> >>>> If you claim I am a bad teacher you must point out what is wrong with >>>> the lesson otherwise your claim that I am a bad teacher is essentially >>>> an as hominem attack. >>> >>> You are not a teacher, bad or otherwise. That you lack skills that >>> happen to be necessary for teaching is obvious from you postings >>> here. A teacher needs to understand human psychology but you don't. >>> >> >> You may be correct that I am a terrible teacher. >> None-the-less Mathematicians might not have very much understanding >> of the link between proof theory and computability. > > Sume mathematicians do have very much understanding of that. But that > link is not needed for understanding and solving problems separately > in the two areas. > >> When I refer to rejecting an invalid input math would seem to construe >> this as nonsense, where as computability theory would totally understand. > > People working on computability theory do not understand "invalid input" > as "impossible input". The proof then shows, for any program f that might determine whether programs halt, that a "pathological" program g, called with some input, can pass its own source and its input to f and then specifically do the opposite of what f predicts g will do. No f can exist that handles this case, thus showing undecidability. https://en.wikipedia.org/wiki/Halting_problem# So then they must believe that there exists an H that does correctly determine the halt status of every input, some inputs are simply more difficult than others, no inputs are impossible. > They understand it as an input that must be > handled differently from ordinary input. Likewise, mathematicians do > understand that some inputs must be considered separately and differently. > But mathematicians don't call those inputs "invalid". > It is so dead obvious that the whole world must be wired with a short circuit in their brains. Formal bivalent mathematical systems of logic must reject every expression that cannot possibly have a value of true or false as a type mismatch error. A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity. https://en.wikipedia.org/wiki/Proposition -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer