Path: csiph.com!fu-berlin.de!uni-berlin.de!individual.net!not-for-mail From: phoenix Newsgroups: sci.logic,sci.math,sci.math.symbolic,comp.theory,comp.ai.philosophy Subject: =?UTF-8?Q?Re:_Within_Proof_Theoretic_Semantics_G=c3=b6del's_G_has_n?= =?UTF-8?Q?o_meaning_in_PA?= Date: Wed, 6 May 2026 13:48:49 -0600 Lines: 43 Message-ID: References: <10s5lu4$sv0r$2@dont-email.me> <10slu2o$1sd53$1@dont-email.me> <10snaci$28k0a$1@dont-email.me> <10snt9d$2f46l$1@dont-email.me> <10t2u7p$1hf24$1@dont-email.me> <_w9JR.81647$kT.59546@fx16.ams4> <10t51ji$26cn4$1@dont-email.me> <10tg5ah$1dvta$1@dont-email.me> Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: individual.net dbr3YIbImTuB1Zauy7PKMQ4nnykrpnGfz6E3MaHS+prmYBy8Eo Cancel-Lock: sha1:hTlRI2xavv/3UZ2lbfTfKz8E+aw= sha256:B9gMCdVa+SKFGJTff9oez8xXtWCGsxx77WezX+roKVI= User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:128.0) Gecko/20100101 Firefox/128.0 SeaMonkey/2.53.23 In-Reply-To: <10tg5ah$1dvta$1@dont-email.me> Xref: csiph.com sci.logic:345840 sci.math:645029 sci.math.symbolic:8824 comp.theory:141154 comp.ai.philosophy:34484 Julio Di Egidio wrote: > On 02/05/2026 20:47, Scott Hoge wrote: > >> In Cantor's theorem, we do not actually construct a diagonal. >> Rather, we presuppose that we can enumerate a set, and then, >> /purely on the grounds of possibility/, conceive a diagonalized >> non-element. > > Nope, as explained and re-explained ad nauseam around here: > just the resident trolls won't get it. > > Cantor's diagonal argument, the one with the binary sequences, > is indeed constructive: a definition of anti-diagonal of *any* > (infinite) list is provided, and the proof that the anti-diagonal > cannot be in the list is quite constructive. > > (Namely, we don't need to say "assume ab abdsurdo that > an enumeration is given", we can just say "for *any* list, > we *construct* an element not in the list".) > > Just look it up.  Here is my own rendition in Rocq: > > >> This links diagonalization to criterion (4) of consciousness. > > Rather, and to sum up, it links diagonalisation to the limits > of physicalism... > > HTH, > > Julio > I guess my question is this: If the diagonal sequence is inadequate, just what exactly is Cantor attempting to represent with the diagonal sequence at all? -- War in the east War in the west War up north War down south War War