Path: ...!local-4.nntp.ord.giganews.com!Xl.tags.giganews.com!local-3.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Thu, 06 Feb 2025 06:29:44 +0000 Subject: Re: The set of necessary FISONs (axiomless natural deduction) Newsgroups: sci.math References: <680d4249c9bf1504231a53732ac5096184261495@i2pn2.org> <12a38458-bfb9-4611-9072-eadbb166c0ec@att.net> <908c8431-3d44-496c-8f5c-e33cc9554956@att.net> <23897a18-0c29-411f-973e-c1d206dede54@att.net> <1fb07888-c66d-423e-9b02-dfb328174f3e@att.net> <845d3507-6fc0-4182-acf6-dcb391ab72dc@att.net> From: Ross Finlayson Date: Wed, 5 Feb 2025 22:29:57 -0800 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: Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Message-ID: Lines: 114 X-Usenet-Provider: http://www.giganews.com X-Trace: sv3-7baBD0SOCKmQF5NkhkTeSN4w4DX4BW7pZ+YF2rlxtMhHZExxuS+eFWYwbDcjMqGbHkPlKGEjZvEd6t0!pYUBpH4o+Ny4M90khVPuwjqXCU5s2EAFwOCLYLIK22qmCnbWRfcTfetLW4pObiWk+8xlK4KqLgcT 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: 5981 On 02/05/2025 10:19 PM, Ross Finlayson wrote: > On 02/05/2025 10:25 AM, Jim Burns wrote: >> On 2/5/2025 8:25 AM, Ross Finlayson wrote: >>> On 02/04/2025 08:26 PM, Ross Finlayson wrote: >>>> On 02/04/2025 11:38 AM, Jim Burns wrote: >> >>>>> [...] >>>> >>>> What it's all about is >>>> "The Principle of Sufficient Reason". >> >> ⎛ The principle of sufficient reason states that >> ⎝ everything must have a reason or a cause. >> https://en.wikipedia.org/wiki/Principle_of_sufficient_reason >> >> What causes everything to have a cause? >> Does that have a cause? Is the cause itself? >> >> I think that 'cause' is insufficiently described >> For this discussion. >> >> Judea Pearl and his colleagues have done admirable work >> in this area. >> >>>> There's that >>>> the principle of sufficient reason is satisfying, and, >>>> the principle of sufficient reason is satisfied. >> >> Does making an unsupported claim ("There's that...") >> count as offering a reason? >> May I offer unsupported claims as reasons, too? >> >>>> So, axiomatics, >>>> or modern weak logicist positivism >>>> or the nominalism or fictionalism >>>> all about same, >>>> have unfounded axioms that supposedly >>>> thusly make for both >>>> that anything that can be derived can be derived, >>>> yet also of course >>>> that anything that can be derived must be derived, >>>> here that's model theory, >>>> and a structuralist view, >>>> and it's equi-interpretable with proof theory, >>>> insofar as inter-subjectivity is established, >>>> and equi-interpretability, in language. >> >> "That anything that can be derived can be derived" >> is clearly true. Axiomatic, even. So what? >> >> "That anything that can be derived must be derived" >> is clearly false, >> if you mean what I mean by 'derive': >> among other things, >> a non.empty list of actions by finite beings (me and my ilk) >> >> Those which can be derived >> are infinitely.many. >> The resources available to derive with >> are finite. >> If the rule is >> "That anything that can be derived must be derived", >> then the rulemaker will be disappointed. >> >> "Unfounded axioms" sounds to me like >> a key to making sense of what you mean by >> "axiomless geometry" and its ilk. >> Is it >> not "no axioms", but "no unfounded axioms"? >> >> > > Hm. Have you heard of "first principles" and "final cause"? > > In logicist positivism, it's either/or "an axiom system" > and "science", is the usual idea. > > Anyways it's usually attributed to "idealism" > vis-a-vis "the analytical", and there's quite > a long story about it it's sort of nice to > have ideals. > > Then, something like Hegel's "Being and Nothing", > if you read the Wissenschaft der Logik, is pretty > great, then there's Kant's Sublime, pretty usual, > these being the things that the analytical tradition > does not and cannot say much about, yet, Hegel and > Kant do, because they're idealists. > > Then, "anti-Platos" like Wittgenstein, Nietszsche, > and Heidegger, say, sort of have that Gadamer arrives > for hermeneutics at "amicus Plato", and, the Tractatus > Logico-Philosophicus, which is really sort of a reading > of Leibniz' monadology or about the radical origination > of things, is quite, strongly platonic, and idealistic. > > If you're going to have a theory at all, > it might as well be the good one. > > > Then, here Duns Scotus' super|natural is considered > pretty great, and Chrysippus of course provides the > modal against Plotinus and his fallacies of material > implication, making sure that Aristotle won't be fooled. > > > https://www.youtube.com/watch?v=LKnZUg9jPf0&list=PLb7rLSBiE7F4_E-POURNmVLwp-dyzjYr-&index=11 "Logos 2000: philosophical theory"