X-Received: by 2002:a37:4055:0:b0:763:a819:286f with SMTP id n82-20020a374055000000b00763a819286fmr805856qka.15.1687360359848; Wed, 21 Jun 2023 08:12:39 -0700 (PDT) X-Received: by 2002:a81:e703:0:b0:568:9e88:6aa4 with SMTP id x3-20020a81e703000000b005689e886aa4mr5777079ywl.6.1687360359615; Wed, 21 Jun 2023 08:12:39 -0700 (PDT) Path: csiph.com!news.mixmin.net!proxad.net!feeder1-2.proxad.net!209.85.160.216.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail Newsgroups: sci.logic Date: Wed, 21 Jun 2023 08:12:39 -0700 (PDT) In-Reply-To: <9538f9ab-a424-4f1f-9254-a30e1776305en@googlegroups.com> Injection-Info: google-groups.googlegroups.com; posting-host=2604:3d09:1771:e900:25ac:37ef:58b6:b21d; posting-account=hsXSVgoAAAAitoRfE-spc_8dYrrq_Iht NNTP-Posting-Host: 2604:3d09:1771:e900:25ac:37ef:58b6:b21d References: <723c735d-8545-4b76-a8dc-38cd58a3a5d2n@googlegroups.com> <9538f9ab-a424-4f1f-9254-a30e1776305en@googlegroups.com> User-Agent: G2/1.0 MIME-Version: 1.0 Message-ID: Subject: Re: What's formal, axiomatic mathematics without the word "infinity"? From: Khong Dong Injection-Date: Wed, 21 Jun 2023 15:12:39 +0000 Content-Type: text/plain; charset="UTF-8" Xref: csiph.com sci.logic:254790 On Tuesday, 20 June 2023 at 17:07:07 UTC-6, Julio Di Egidio wrote: > On Tuesday, 20 June 2023 at 19:19:16 UTC+2, Khong Dong wrote: > > > What's up with formal, axiomatic mathematics > > which is without the word "infinity" being used > > to convey mathematical concepts? > Formal and axiomatic are two distinct levels, as I > have been explaining upthread, and that you keep > asking why apples are not oranges. Ok, then: What's the usefulness, in abstraction, formalism, practicality, of axiomatic mathematics (FOL, SOL, HOL) for which there's _no_ associated semantics? > > Julio