Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA

From	phoenix <j63840576@gmail.com>
Newsgroups	sci.logic, sci.math, sci.math.symbolic, comp.theory, comp.ai.philosophy
Subject	Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA
Date	2026-05-06 13:48 -0600
Message-ID	<n61k90Fh012U1@mid.individual.net> (permalink)
References	(6 earlier) <10t2u7p$1hf24$1@dont-email.me> <_w9JR.81647$kT.59546@fx16.ams4> <10t51ji$26cn4$1@dont-email.me> <cFrJR.53508$qu9.44050@fx08.ams4> <10tg5ah$1dvta$1@dont-email.me>

Cross-posted to 5 groups.

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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:
> <https://gist.github.com/jp-diegidio/eb05f6265c38b35c85853514ed46ab47>
> 
>> 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?

-- 
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Thread

Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-20 11:57 -0500
  Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-21 09:41 +0300
    Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-21 08:33 -0500
      Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 10:19 +0300
        Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 02:48 -0500
          Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 11:19 +0300
            Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 08:17 -0500
              Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-23 10:06 +0300
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-23 08:49 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-24 09:33 +0300
          Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-22 17:06 -0600
            Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 20:21 -0500
              Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-24 00:19 -0600
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:12 -0700
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:14 -0700
            Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:25 -0700
              Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:29 -0700
            Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-20 17:50 +0100
              Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-20 12:32 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-27 07:53 +0100
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-27 07:19 -0700
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 08:29 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 11:05 -0600
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 13:16 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 12:29 -0600
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:08 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 13:33 -0600
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:47 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:02 -0600
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 15:06 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:58 -0600
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:10 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 15:18 -0600
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:39 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 16:25 -0600
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 17:38 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:03 -0600
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 18:36 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:45 -0600
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 19:37 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:01 -0600
                The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 20:19 -0500
                Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:54 -0600
                Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:17 -0500
                Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:31 -0600
                Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:42 -0500
                Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:49 -0600
                Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 22:06 -0500
                Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:26 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-30 11:18 +0300
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-30 08:58 -0500
  Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-26 20:01 +0000
    Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-26 15:54 -0500
      Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Richard Damon <Richard@Damon-Family.org> - 2026-04-26 20:16 -0400
      Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-27 12:30 +0300
        Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 09:53 -0500
          Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 19:15 +0000
            Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 15:10 -0500
            Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-27 21:03 +0000
              Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 16:57 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 10:34 +0300
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:18 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 09:37 +0300
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-29 09:17 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-30 10:55 +0300
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 09:54 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 10:47 -0700
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 11:01 -0700
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 14:35 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 12:54 -0700
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 15:36 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 13:14 +0100
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 15:41 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 19:47 -0700
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-02 11:04 +0300
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-02 07:36 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-03 10:56 +0300
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 10:22 +0000
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 06:14 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 12:04 +0000
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:14 -0500
              Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 22:01 +0000
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 17:22 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 11:10 +0300
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:30 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 10:11 +0300
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 10:35 +0000
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-29 14:27 +0000
            Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-01 21:17 +0200
              Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 12:34 -0700
              Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 14:38 -0500
              Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-01 22:10 +0000
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-02 16:26 +0200
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-02 09:54 -0500
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-02 18:47 +0000
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dart200 <user7160@newsgrouper.org.invalid> - 2026-05-02 12:06 -0700
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-06 21:37 +0200
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA phoenix <j63840576@gmail.com> - 2026-05-06 13:48 -0600
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-06 12:59 -0700
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 16:10 +0100
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-07 01:12 +0000
                Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-02 20:56 -0700
    Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 06:54 +0100

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