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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko <mikko.levanto@iki.fi> Newsgroups: sci.logic Subject: Re: Undecidability based on epistemological antinomies Date: Fri, 3 May 2024 11:27:35 +0300 Organization: - Lines: 101 Message-ID: <v1275n$eg4b$1@dont-email.me> References: <uvq0sg$21m7a$1@dont-email.me> <uvvsap$3i5q8$1@dont-email.me> <v00mf6$3nu0r$1@dont-email.me> <v02gu5$6quf$1@dont-email.me> <v038om$bitp$2@dont-email.me> <v05b0k$sivu$1@dont-email.me> <v05r5e$vvml$2@dont-email.me> <v05vl4$1165d$1@dont-email.me> <v0679k$12sq2$1@dont-email.me> <v07r2j$1h57l$1@dont-email.me> <v08gn4$1lpta$2@dont-email.me> <v0ag7u$27jkb$1@dont-email.me> <v0b8np$2d4ja$1@dont-email.me> <v0d372$2t7ec$1@dont-email.me> <v0do5i$31mkn$1@dont-email.me> <v0frdr$3jhng$1@dont-email.me> <v0gka2$3pm6f$1@dont-email.me> <v0idnn$91b6$1@dont-email.me> <v0ivqh$d40l$1@dont-email.me> <v0l3a0$vanr$1@dont-email.me> <v0lin5$12ip9$1@dont-email.me> <v0np15$1llt9$1@dont-email.me> <v0ob1e$1pbn5$7@dont-email.me> <v0ocuq$1qcqi$1@dont-email.me> <v0odv3$1qgpk$1@dont-email.me> <v0qmi5$2eont$1@dont-email.me> <v0r4tg$2hb7o$8@dont-email.me> <v0t0n4$32utt$1@dont-email.me> <v0tmiq$37lgj$2@dont-email.me> <v0vhr7$3o5tp$1@dont-email.me> <v103p6$3s7vi$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 03 May 2024 10:27:36 +0200 (CEST) Injection-Info: dont-email.me; posting-host="12c1b288cba0d9e035ffa5a10b12ab63"; logging-data="475275"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/uLBiaEYmTbFeGcf8IPYP0" User-Agent: Unison/2.2 Cancel-Lock: sha1:jUrwoWzPFY36/zO3FxlLwXv0fIk= Bytes: 5305 On 2024-05-02 13:17:24 +0000, olcott said: > On 5/2/2024 3:11 AM, Mikko wrote: >> On 2024-05-01 15:19:54 +0000, olcott said: >> >>> On 5/1/2024 4:06 AM, Mikko wrote: >>>> On 2024-04-30 16:06:08 +0000, olcott said: >>>> >>>>> On 4/30/2024 7:01 AM, Mikko wrote: >>>>>> On 2024-04-29 15:22:11 +0000, olcott said: >>>>>> >>>>>>> On 4/29/2024 10:04 AM, Mikko wrote: >>>>>>>> On 2024-04-29 14:32:13 +0000, olcott said: >>>>>>>> >>>>>>>>> On 4/29/2024 4:24 AM, Mikko wrote: >>>>>>>>>> On 2024-04-28 13:24:52 +0000, olcott said: >>>>>>>>>> >>>>>>>>>>> Translated into a syllogism: >>>>>>>>>>> >>>>>>>>>>> All A are True >>>>>>>>>>> No A are True >>>>>>>>>>> Therefore B >>>>>>>>>> >>>>>>>>>> Which inference rule of syllogistic logic permits that inference? >>>>>>>>>> >>>>>>>>> >>>>>>>>> (1) That is a correct translation from this POE argument: >>>>>>>>> Proposition A is True. >>>>>>>>> Proposition A is False. >>>>>>>>> Therefore B >>>>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion >>>>>>>>> >>>>>>>>> (2) That as a syllogism it is the non-sequitur error proves >>>>>>>>> that the POE was the non-sequitur error all along. >>>>>>>> >>>>>>>> What you call a "syllogism" isn't one as it has none of the forms >>>>>>>> of valid syllogism as listed by Aristotle. >>>>>>>> >>>>>>> >>>>>>> https://en.wikipedia.org/wiki/Categorical_proposition >>>>>> >>>>>> That page does not tell what a syllogism is. Instead, the page >>>>>> https://en.wikipedia.org/wiki/Syllogism >>>>>> does. >>>>>> >>>>> >>>>> This is the part of the page on syllogism that links to that link >>>>> https://en.wikipedia.org/wiki/Syllogism#Basic_structure >>>> >>>> THat's right. That section says what the form of a syllogism is. >>>> Your "syllogism" has not that form. >>>> >>> >>> *This part is correct* >>> Each part is a categorical proposition, and each categorical >>> proposition contains two categorical terms. >>> >>> *This part is incorrect only because the POE expression is incorrect* >>> "Each of the premises has one term in common with the conclusion:" >> >> There is nothing incorrect in that. In every syllogism each of the >> premises has one term in common with the conclusion. That this is >> not true about yor "syllogism" > > Only because this error already exists in the POE argument, > thus the same error is transferred to the syllogism when the POE > argument is accurately translated into the syllogism. > >> simply means that your "syllogism" >> is not true. (Etymologically the term "syllogism" is reference to >> the common words.) >> >>> By retaining the same lack of a common term as the POE expression we >>> see that the POE expression has the non-sequitur error. >> >> No, but we do see that your "syllogism" is not a syllogism. >> > > It is the exact same invalid syllogism with the non-sequitur > as the POE argument that it was translated from. It is an ivanlid syllogism as the conclusion does not follow by any valid inference rule of syllogistic logic. However, the conclusion follows by classical logic. One can prove about every inferences of the form Premise1 Premise2 ---------- Conclusion that it is a valid inrerence of ordinary logic if ¬Premise1 ∨ ¬Premise1 ∨ Conclusion is a tautology of propositional logic then. From this theorem follows that your invalid "syllogism" is a valid inference of ordinary logic. -- Mikko