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Path: ...!Xl.tags.giganews.com!local-1.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Wed, 17 Apr 2024 20:07:26 +0000 Subject: Re: Undecidability based on epistemological antinomies Newsgroups: sci.logic,comp.theory References: <uvp7rs$1p34r$1@dont-email.me> From: Ross Finlayson <ross.a.finlayson@gmail.com> Date: Wed, 17 Apr 2024 13:07:31 -0700 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101 Thunderbird/38.6.0 MIME-Version: 1.0 In-Reply-To: <uvp7rs$1p34r$1@dont-email.me> Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Message-ID: <UGadnc9UCLFjtr37nZ2dnZfqn_WdnZ2d@giganews.com> Lines: 50 X-Usenet-Provider: http://www.giganews.com X-Trace: sv3-8KarkYMSSbWeTcUVz7HywukoF2HKDCsR2u7CBdjhWSNt4jCoyMe1Fec9qHrb3Xglry4nP/kFBDLDuMN!lWeCsHZziX64ytKN1nZUMhWACrz0nSccyYnUpDq+6qPgkHmQjL6cYl7t1cfNZES2LRHmNYJVDeU= X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.3.40 Bytes: 3061 On 04/17/2024 12:27 PM, olcott wrote: > ...14 Every epistemological antinomy can likewise be used for a similar > undecidability proof...(Gödel 1931:43-44) > > *I will paraphrase his quote using the simplest terms* > > Every expression X that cannot possibly be true or false proves that > there is something wrong with a formal system that cannot correctly > determine whether X is true or false. > > I like to read it more as Mirimanoff and the extra-ordinary. In the early 20'th century, Mirimanoff was very influential in what became set theory. He was very well-known in the small circle that is the usual introduction, and should be more, today. Regularity, a usual ruliality, as Well-Foundedness, has a delicate interplay and contraposition with Well-Orderedness, both regular and rulial, yet in the infinite, that the antinomies sort of make for that for arithmetic, that both increment is an operator, and division is an operator, and while they join as they come together in the field, in the modular, they represent yet opposite concerns. So, Mirimanoff's extra-ordinary, is another way to look at Goedel's incompleteness, that the truths about the objects, i.e. their proofs or models, do have an extra-ordinary existence, arising from the resolution of what would otherwise be the contradiction, the paradox, making for why Goedel's result is as well that there _is_ an extra-ordinary infinity, plainly courtesy the mind, and simple ponderance of alternatives in quantifiers and the basis of fundamental logic. So, it's not "wrong", instead, it's "better". I like to think of it this way as I am entirely pleased about it and it very well follows from what I've studied of the development of the canon of logic as it was and is, and, will be. Warm regards, E.S., bonjour, -- https://www.youtube.com/@rossfinlayson