Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory Subject: Re: The philosophy of logic reformulates existing ideas on a new basis --- Date: Fri, 8 Nov 2024 09:15:29 -0600 Organization: A noiseless patient Spider Lines: 116 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 08 Nov 2024 16:15:30 +0100 (CET) Injection-Info: dont-email.me; posting-host="c2fa6bf0e4c95fa4383978e96b35b7f1"; logging-data="3392616"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX192NtoWo25nqTTf5TmMEniD" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:+IvYhiXioqCfuQbogZ/S2mXKt+I= Content-Language: en-US In-Reply-To: X-Antivirus: Norton (VPS 241108-6, 11/8/2024), Outbound message X-Antivirus-Status: Clean Bytes: 6311 On 11/8/2024 9:05 AM, Alan Mackenzie wrote: > olcott wrote: >> On 11/8/2024 5:58 AM, Alan Mackenzie wrote: >>> In comp.theory olcott wrote: >>>> On 11/6/2024 2:34 PM, Alan Mackenzie wrote: >>>>> In comp.theory olcott wrote: >>>>>> On 11/6/2024 10:45 AM, Alan Mackenzie wrote: > >>> [ .... ] > >>>>>>> There is another sense in which something could be a lie. If, for >>>>>>> example, I emphatically asserted some view about the minutiae of >>>>>>> medical surgery, in opposition to the standard view accepted by >>>>>>> practicing surgeons, no matter how sincere I might be in that >>>>>>> belief, I would be lying. Lying by ignorance. > > >>>>>> That is a lie unless you qualify your statement with X is a >>>>>> lie(unintentional false statement). It is more truthful to >>>>>> say that statement X is rejected as untrue by a consensus of >>>>>> medical opinion. > >>>>> No, as so often, you've missed the nuances. The essence of the >>>>> scenario is making emphatic statements in a topic which requires >>>>> expertise, but that expertise is missing. Such as me laying down the >>>>> law about surgery or you doing the same in mathematical logic. > >>>> It is not at all my lack of expertise on mathematical logic >>>> it is your ignorance of philosophy of logic as shown by you >>>> lack of understanding of the difference between "a priori" >>>> and "a posteriori" knowledge. > >>> Garbage. > >>>> Surgical procedures and mathematical logic are in fundamentally >>>> different classes of knowledge. > >>> But the necessity of expertise is present in both, equally. Emphatically >>> to assert falsehoods when expertise is lacking is a form of lying. That >>> is what you do. > >>>>>> This allows for the possibility that the consensus is not >>>>>> infallible. No one here allows for the possibility that the >>>>>> current received view is not infallible. Textbooks on the >>>>>> theory of computation are NOT the INFALLIBLE word of God. > >>>>> Gods have got nothing to do with it. 2 + 2 = 4, the fact that the >>>>> world is a ball, not flat, Gödel's theorem, and the halting problem, >>>>> have all been demonstrated beyond any doubt whatsoever. > >>>> Regarding the last two they would have said the same thing about >>>> Russell's Paradox and what is now known as naive set theory at the >>>> time. > >>> There's no "would have said" regarding Russell's paradox. Nobody would >>> have asserted the correctness of naive set theory, a part of mathematics >>> then at the forefront of research and still in flux. We've moved beyond >>> that point in the last hundred years. > >>> And you are continually stating that theorems like 2 + 2 = 4 are false. > >> That is a lie. I never said anything like that and you know it. > > Now who's lying? You have frequently denied the truth of proven > mathematical facts like 2 + 2 = 4. Never and you are a damned (going to actual Hell) liar for saying so. > As I have continually made clear in > my posts "like 2 + 2 = 4" includes the halting theorem, Gödel's theorem, > and Tarski's theorem. > Your misconceptions are not my errors. You cannot possibly prove that they are infallible that best that you can show is that you believe they are infallible. >> Here is what I actually said: > >> When the operations are limited to applying truth preserving >> operations to expressions of language that are stipulated to >> be true then >> True(L,x) ≡ (L ⊢ x) and False(L, x) ≡ (L ⊢ ~x) > >> Then >> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))) >> becomes >> (¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))) >> Incompleteness utterly ceases to exist > > Incompleteness is an essential property of logic systems Rejecting what I say out-of-hand on the basis that you don't believe what I say is far far less than no rebuttal at all. What I said about is a semantic tautology just like 2 + 3 = 5. Formal systems are only incomplete when the term "incomplete" is a euphemism for the inability of formal systems to correctly determine the truth value of non-truth-bearers. > which can do > anything at all. If what you assert is true (which I doubt), then your > system would be incapable of doing anything useful. > >> -- >> Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius >> hits a target no one else can see." Arthur Schopenhauer > -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer