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Groups > sci.math > #412942 > unrolled thread

The fundamental theorem of set theory is problematic

Started byDavid Petry <davidlpetry@gmail.com>
First post2018-05-11 11:20 -0700
Last post2018-05-17 12:29 -0700
Articles 20 on this page of 227 — 16 participants

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Contents

  The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-11 11:20 -0700
    Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-11 19:33 +0000
      Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-11 13:16 -0700
        Re: The fundamental theorem of set theory is problematic "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-05-11 16:48 -0700
        Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-11 18:31 -0700
          Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-11 18:46 -0700
            Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-11 18:49 -0700
              Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-12 00:59 -0700
                Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 02:20 -0700
              Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-12 12:43 -0700
                Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 14:09 -0700
          Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-12 12:40 -0700
            Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-12 20:48 +0000
              Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-12 14:50 -0700
                Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-13 01:00 +0000
                  Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-13 15:10 -0700
                    Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-14 17:33 +0000
                      Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-14 21:09 -0700
                        Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-15 19:19 +0000
                          Re: The fundamental theorem of set theory is problematic "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-05-15 13:50 -0700
                          Re: The fundamental theorem of set theory is problematic "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-05-15 21:34 -0500
                            Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-16 09:10 -0700
                            Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-16 09:15 -0700
                      Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-15 05:33 -0700
              Re: The fundamental theorem of set theory is problematic Jim Burns <james.g.burns@att.net> - 2018-05-12 19:02 -0400
                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-13 01:38 -0700
                Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-14 21:40 -0700
                  Re: The fundamental theorem of set theory is problematic Jim Burns <james.g.burns@att.net> - 2018-05-15 05:22 -0400
              Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-13 01:31 -0700
                Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-13 03:51 -0700
                  Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-13 05:18 -0700
                    Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-13 06:59 -0700
                Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-13 11:02 +0000
                  Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-13 05:37 -0700
                    Re: The fundamental theorem of set theory is problematic Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-05-13 21:57 +0100
                      Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-14 04:44 -0700
                        Re: The fundamental theorem of set theory is problematic Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-05-14 13:29 +0100
                          Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-14 07:42 -0700
                            Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-14 09:36 -0700
                              Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-14 09:42 -0700
                              Re: The fundamental theorem of set theory is problematic Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-05-14 18:29 +0100
                                Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-14 12:03 -0700
                                  Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-14 12:06 -0700
                                    Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-14 12:10 -0700
                              Re: The fundamental theorem of set theory is problematic "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-05-15 13:44 -0700
                            Re: The fundamental theorem of set theory is problematic Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-05-14 18:16 +0100
                              Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-15 05:44 -0700
                        Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-14 06:38 -0700
            Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 17:58 -0700
              Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 18:04 -0700
                Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 18:19 -0700
        Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-15 09:14 -0700
          Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-15 10:07 -0700
            Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-16 09:26 -0700
              Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-16 11:18 -0700
                Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-16 12:26 -0700
                  Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-16 14:06 -0700
                    Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-16 15:53 -0700
                      Re: The fundamental theorem of set theory is problematic Jim Burns <james.g.burns@att.net> - 2018-05-16 19:07 -0400
                        Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 01:17 -0700
                          Re: The fundamental theorem of set theory is problematic Jim Burns <james.g.burns@att.net> - 2018-05-17 09:42 -0400
                  Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-16 17:40 -0700
          Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-15 11:06 -0700
      Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-12 01:05 -0700
      Re: The fundamental theorem of set theory is problematic David Petry <davidlpetry@gmail.com> - 2018-05-12 12:57 -0700
        Re: The fundamental theorem of set theory is problematic Alan Mackenzie <acm@muc.de> - 2018-05-13 00:20 +0000
    Re: The fundamental theorem of set theory is problematic "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-05-11 20:03 -0500
      Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-12 00:59 -0700
      Re: The fundamental theorem of set theory is problematic Julio Di Egidio <julio@diegidio.name> - 2018-05-12 01:59 -0700
        Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 02:55 -0700
          Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 03:04 -0700
          Re: The fundamental theorem of set theory is problematic Julio Di Egidio <julio@diegidio.name> - 2018-05-12 03:06 -0700
            Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 03:09 -0700
              Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 03:13 -0700
                Re: The fundamental theorem of set theory is problematic Julio Di Egidio <julio@diegidio.name> - 2018-05-12 03:20 -0700
                  Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 03:28 -0700
                Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-12 03:24 -0700
    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-12 01:14 -0700
      Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-13 09:07 -0700
        Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-13 11:08 -0700
          Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-13 12:05 -0700
            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-13 12:53 -0700
        Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-15 11:02 -0700
          Re: The fundamental theorem of set theory is problematic j4n bur53 <janburse@fastmail.fm> - 2018-05-15 21:13 +0200
            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-16 11:30 -0700
              Re: The fundamental theorem of set theory is problematic Zeit Geist <Tucsondrew@me.com> - 2018-05-16 12:23 -0700
                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-16 14:00 -0700
                  Re: The fundamental theorem of set theory is problematic Zeit Geist <Tucsondrew@me.com> - 2018-05-16 16:18 -0700
                  Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-16 16:27 -0700
                    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 05:01 -0700
                      Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-17 08:34 -0700
                        Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 09:34 -0700
                          Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-17 10:12 -0700
                            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 10:57 -0700
                              Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 11:56 -0700
                                Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 12:00 -0700
                                  Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 12:29 -0700
                              Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-17 13:38 -0700
                                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-18 08:12 -0700
                                  Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-18 12:23 -0700
                                    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-19 04:53 -0700
                                      Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-19 07:21 -0700
                                        Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-19 09:11 -0700
                                        Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-20 03:20 -0700
                                          Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-20 04:48 -0700
                                            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-20 05:19 -0700
                                              Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-20 10:09 -0700
                                                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-20 13:26 -0700
                                                  Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-20 18:10 -0700
                                                    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-21 06:05 -0700
                                                      Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-21 07:24 -0700
                                                        Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-21 08:59 -0700
                                                          Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-21 11:48 -0700
                                                            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-22 05:45 -0700
                                                              Re: The fundamental theorem of set theory is problematic Python <python@python.invalid> - 2018-05-22 14:51 +0200
                                                              Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-22 06:31 -0700
                                                                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-22 13:26 -0700
                                                                  Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-22 14:22 -0700
                                                                    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-23 06:06 -0700
                                                                      Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-23 07:19 -0700
                                                                        Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-23 11:56 -0700
                                                                          Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-23 12:08 -0700
                                                                            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-23 13:22 -0700
                                                                              Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-23 18:11 -0700
                                                                                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-24 02:47 -0700
                                                                                  Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-24 06:00 -0700
                                                                                    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-24 07:43 -0700
                                                                                      Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-24 08:10 -0700
                                                                                        Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-24 09:37 -0700
                                                                                          Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-24 09:45 -0700
                                                                                            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-25 09:05 -0700
                                                                                              Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-25 11:09 -0700
                                                                                                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-25 15:26 -0700
                                                                                                  Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-25 23:14 -0700
                                                                                                  Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-26 03:23 -0700
                                                                                                    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-26 06:37 -0700
                                                                                                      Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-26 06:50 -0700
                                                                                                      Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-26 07:30 -0700
                                                                                                        Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-26 08:39 -0700
                                                                                                          Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-26 09:15 -0700
                                                                                                            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-27 05:37 -0700
                                                                                                              Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-27 08:58 -0700
                                                                                                                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-28 03:53 -0700
                                                                                                                  Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-28 05:04 -0700
                                                                                                                    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-28 05:10 -0700
                                                                                                                      Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-28 05:19 -0700
                                                                                                                        Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-29 04:53 -0700
                                                                                                                          Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-29 06:22 -0700
                                                                                                                            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-29 06:36 -0700
                                                                                                                              Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-29 07:12 -0700
                                                                                                                                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-29 08:35 -0700
                                                                                                                                  Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-29 08:52 -0700
                                                                                                                                    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-30 04:25 -0700
                                                                                                                                      Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-30 04:50 -0700
                                                                                                                                        Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-31 06:17 -0700
                                                                                                                                          Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-31 07:05 -0700
                                                                                                                                            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-31 09:53 -0700
                                                                                                                                              Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-31 11:47 -0700
                                                                                                                                                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-01 03:58 -0700
                                                                                                                                                  Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-06-01 05:07 -0700
                                                                                                                                                    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-01 05:24 -0700
                                                                                                                                                      Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-06-01 06:27 -0700
                                                                                                                                                        Re: The fundamental theorem of set theory is problematic "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-01 10:21 -0700
                                                                                                                                                          Re: The fundamental theorem of set theory is problematic "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-02 14:04 -0700
                                                                                                                                                            Re: The fundamental theorem of set theory is problematic "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-06-02 16:27 -0700
                                                                                                                                                        Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-06-02 07:23 -0700
                                                                                                                                                          Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-06-04 00:11 -0700
                                                                                                              Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-27 23:12 -0700
                                                                          Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-23 12:49 -0700
                                                                            Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-23 12:51 -0700
                                                                            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-23 13:24 -0700
                                                                              Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-24 02:09 -0700
                                                              Re: The fundamental theorem of set theory is problematic Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-05-22 19:09 +0100
                                                                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-22 13:29 -0700
                                                              Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-23 22:32 -0700
                                                                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-24 03:57 -0700
                                                                  Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-24 04:48 -0700
                                                                    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-24 07:29 -0700
                                                                      Re: The fundamental theorem of set theory is problematic Python <python@python.invalid> - 2018-05-24 16:39 +0200
                              Re: The fundamental theorem of set theory is problematic Python <python@python.invalid> - 2018-05-18 01:19 +0200
                                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-18 08:14 -0700
                                  Re: The fundamental theorem of set theory is problematic Python <python@python.invalid> - 2018-05-18 17:31 +0200
                                    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-18 10:09 -0700
                                      Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-18 10:53 -0700
                                      Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-18 13:54 -0700
                                        Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-18 13:55 -0700
                                          Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-18 14:09 -0700
                                            Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-18 14:19 -0700
                                              Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-18 14:23 -0700
                                                Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-18 14:37 -0700
                                      Re: The fundamental theorem of set theory is problematic Zeit Geist <Tucsondrew@me.com> - 2018-05-18 14:33 -0700
                                        Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-19 04:58 -0700
                                          Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-19 05:28 -0700
                                            Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-19 05:34 -0700
                                              Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-19 05:36 -0700
                                                Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-19 05:46 -0700
                                          Re: The fundamental theorem of set theory is problematic Zeit Geist <Tucsondrew@me.com> - 2018-05-19 09:00 -0700
                                            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-20 03:21 -0700
                                      Re: The fundamental theorem of set theory is problematic Python <python@python.invalid> - 2018-05-19 02:01 +0200
                                      Re: The fundamental theorem of set theory is problematic Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-05-21 16:40 +0100
                                        Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-21 09:06 -0700
                                          Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-21 13:52 -0700
                                            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-22 05:45 -0700
                                              Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-22 08:27 -0700
                                                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-22 13:29 -0700
                                                  Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-22 13:43 -0700
                                                    Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-22 13:52 -0700
                                                      Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-23 06:06 -0700
                                                  Re: The fundamental theorem of set theory is problematic Zeit Geist <Tucsondrew@me.com> - 2018-05-22 17:30 -0700
                                                    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-23 06:06 -0700
          Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-15 17:14 -0700
            Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-16 11:26 -0700
              Re: The fundamental theorem of set theory is problematic wpihughes@gmail.com - 2018-05-16 16:35 -0700
                Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 05:03 -0700
                  Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-17 05:33 -0700
                    Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 09:31 -0700
    Re: The fundamental theorem of set theory is problematic Sergio <invalid@invalid.com> - 2018-05-13 12:40 -0500
    Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-13 22:36 -0700
      Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-14 04:49 -0700
        Re: The fundamental theorem of set theory is problematic Zelos Malum <zelos.malum@gmail.com> - 2018-05-17 01:34 -0700
          Re: The fundamental theorem of set theory is problematic WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-17 05:08 -0700
            Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 10:03 -0700
              Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 10:06 -0700
                Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 10:19 -0700
                  Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 10:26 -0700
                    Re: The fundamental theorem of set theory is problematic bursejan@gmail.com - 2018-05-17 10:30 -0700
                  Re: The fundamental theorem of set theory is problematic FredJeffries <fredjeffries@gmail.com> - 2018-05-17 12:29 -0700

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#413523

FromWM <wolfgang.mueckenheim@hs-augsburg.de>
Date2018-05-21 09:06 -0700
Message-ID<b21d12aa-bcf4-4421-a3f0-10664abe585c@googlegroups.com>
In reply to#413521
Am Montag, 21. Mai 2018 17:45:07 UTC+2 schrieb Alan Smaill:
> WM <wolfgang.mueckenheim@hs-augsburg.de> writes:

> > Not necessary to argue about that. Take the set of all definable real
> > numbers which exists according to set theory since every subset of |R
> > exists, even when ZFC is unable to define definability.
> 
> Can WM define definability for us?
> Otherwise I have no idea what a definable real is.

Well, every mathematical object is definable. What does that mean? Every object that can be applied in mathematics must be applied by (one of its) its finite name(s) because an object of mathematics has no other form of existence. This name, wherever defined, is one of perhaps many definitions of the object. A number or finite string of symbols is definable if mathematicians can talk about it.
> 
> Can we at least take it that if a real is definable, then it is
> a consequence of the definition that a digit expansion is uniquely
> defined at each index, for arbitrarily large indices?

Not necessarily. The following reals are defined:
The first prime number discovered after 3000 AC.
The smallest positive fraction.
The first real number Cantor thought of on 20 May 1888.
The antidiagonal of the list of all definable real numbers.

The latter shows a contradiction in case "all such and such" has any meaning for infinite sets.

Regards, WM

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#413539

Frombursejan@gmail.com
Date2018-05-21 13:52 -0700
Message-ID<f7a031d9-4a25-4ac6-8d14-5c648ebcd75a@googlegroups.com>
In reply to#413523
A name is not a definition. A name is only the head of
what is defined. But what is its body?
For example the name "finite sequence", doesn't define
a "finite sequence". How do you know that a black

swan is not a finite sequence? How do you define
your finite sequences, N*, which are a class.
Do you know how to define it? So Volkswagen Omlette
can even not define things. What can the members

of Augsburg Crank institute then do? Say Prayers to 
the order of the bird brain?

Am Montag, 21. Mai 2018 18:06:06 UTC+2 schrieb WM:
> Am Montag, 21. Mai 2018 17:45:07 UTC+2 schrieb Alan Smaill:
> > WM <wolfgang.mueckenheim@hs-augsburg.de> writes:
> 
> > > Not necessary to argue about that. Take the set of all definable real
> > > numbers which exists according to set theory since every subset of |R
> > > exists, even when ZFC is unable to define definability.
> > 
> > Can WM define definability for us?
> > Otherwise I have no idea what a definable real is.
> 
> Well, every mathematical object is definable. What does that mean? Every object that can be applied in mathematics must be applied by (one of its) its finite name(s) because an object of mathematics has no other form of existence. This name, wherever defined, is one of perhaps many definitions of the object. A number or finite string of symbols is definable if mathematicians can talk about it.
> > 
> > Can we at least take it that if a real is definable, then it is
> > a consequence of the definition that a digit expansion is uniquely
> > defined at each index, for arbitrarily large indices?
> 
> Not necessarily. The following reals are defined:
> The first prime number discovered after 3000 AC.
> The smallest positive fraction.
> The first real number Cantor thought of on 20 May 1888.
> The antidiagonal of the list of all definable real numbers.
> 
> The latter shows a contradiction in case "all such and such" has any meaning for infinite sets.
> 
> Regards, WM

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#413575

FromWM <wolfgang.mueckenheim@hs-augsburg.de>
Date2018-05-22 05:45 -0700
Message-ID<36e378fc-92db-4533-a79b-059c0db65988@googlegroups.com>
In reply to#413539
Am Montag, 21. Mai 2018 22:52:44 UTC+2 schrieb burs...@gmail.com:
> A name is not a definition. A name is only the head of
> what is defined.

The meaning of a name is defined in many places: dictionaries, textbooks, etc.

> For example the name "finite sequence", doesn't define
> a "finite sequence".

But a lot of textbooks do.

Regards, WM

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#413582

Frombursejan@gmail.com
Date2018-05-22 08:27 -0700
Message-ID<00ac1850-7c55-4f2c-9549-ab85f4110a23@googlegroups.com>
In reply to#413575
Dictionaries don't qualify as math theories, with
math definitions. You are halucinating and
confused. You still don't understand what math means.

Also if you mean by "textbook", for example
math textbook, a math textbook might contain
a N* definition. But usually math textbooks

use sets. But you seem not to use sets. So what
is your N*, finite sequences. Can you give a 
definition that doesn't use sets?

Can you define N* as a class? My guess is,
that this is possible, see for example Levy,
Basic Set Theory, but this

textbook definition might still not match
the world of Volkswagen Omlette, where there
are more prime numbers tomorrow, than

today. Can you define N* from within Augsburg
Crank institute. If you cannot do it, why do
you talk about them as if you would

know anything about them?

Am Dienstag, 22. Mai 2018 14:46:05 UTC+2 schrieb WM:
> Am Montag, 21. Mai 2018 22:52:44 UTC+2 schrieb burs...@gmail.com:
> > A name is not a definition. A name is only the head of
> > what is defined.
> 
> The meaning of a name is defined in many places: dictionaries, textbooks, etc.
> 
> > For example the name "finite sequence", doesn't define
> > a "finite sequence".
> 
> But a lot of textbooks do.
> 
> Regards, WM

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#413607

FromWM <wolfgang.mueckenheim@hs-augsburg.de>
Date2018-05-22 13:29 -0700
Message-ID<d86169c6-1df3-46a6-a836-3d2ac88ed34a@googlegroups.com>
In reply to#413582
Am Dienstag, 22. Mai 2018 17:27:52 UTC+2 schrieb burs...@gmail.com:
> Dictionaries don't qualify as math theories,

Irrelevant. Every word you use is defined (with very few exceptions).

Regards, WM

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#413609

Frombursejan@gmail.com
Date2018-05-22 13:43 -0700
Message-ID<4b95db84-f705-41ce-bc3d-1db007fb93b2@googlegroups.com>
In reply to#413607
I am not sure whether my words are mathematically
defined. After all I am human with common sense
and my everyday reasoning is not the same 

reasoning than what math requires. You are 
halucinating and confused as usual. I am not
solving an integral when 

cooking some eggs.

Am Dienstag, 22. Mai 2018 22:29:52 UTC+2 schrieb WM:
> Am Dienstag, 22. Mai 2018 17:27:52 UTC+2 schrieb burs...@gmail.com:
> > Dictionaries don't qualify as math theories,
> 
> Irrelevant. Every word you use is defined (with very few exceptions).
> 
> Regards, WM

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#413610

Frombursejan@gmail.com
Date2018-05-22 13:52 -0700
Message-ID<bf61d66f-d876-4117-badd-3c887b1e7b47@googlegroups.com>
In reply to#413609
Here are my common sense definitions
of chicken and egg, that I am using:

egg: What a chicken is laying.

chicken: What is hatching from an egg.

But thats not a mathematical definition,
although its not really wrong.

BTW: You might really find such definitions
in an encyclopedia.

Am Dienstag, 22. Mai 2018 22:45:16 UTC+2 schrieb burs...@gmail.com:
> I am not sure whether my words are mathematically
> defined. After all I am human with common sense
> and my everyday reasoning is not the same 
> 
> reasoning than what math requires. You are 
> halucinating and confused as usual. I am not
> solving an integral when 
> 
> cooking some eggs.
> 
> Am Dienstag, 22. Mai 2018 22:29:52 UTC+2 schrieb WM:
> > Am Dienstag, 22. Mai 2018 17:27:52 UTC+2 schrieb burs...@gmail.com:
> > > Dictionaries don't qualify as math theories,
> > 
> > Irrelevant. Every word you use is defined (with very few exceptions).
> > 
> > Regards, WM

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#413635

FromWM <wolfgang.mueckenheim@hs-augsburg.de>
Date2018-05-23 06:06 -0700
Message-ID<c384d86c-ac89-4eac-bd66-303bf23b4aed@googlegroups.com>
In reply to#413610
Am Dienstag, 22. Mai 2018 22:52:29 UTC+2 schrieb burs...@gmail.com:
> Here are my common sense definitions
> of chicken and egg, that I am using:
> 
> egg: What a chicken is laying.
> 
> chicken: What is hatching from an egg.
> 
> But thats not a mathematical definition,

Mathematical definition have to be defined by common language. It only appears as if mathematics was on a higher level.

The curse of the invasion of mathematics by mathematical logic is that now any proposition can be represented in a mathematical symbolism, and this makes us feel obliged to understand it. Although of course this method of writing is nothing but the translation of vague ordinary prose. (Wittgenstein)

Mathematics is common sense. (Bishop)

Regards, WM

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#413617

FromZeit Geist <Tucsondrew@me.com>
Date2018-05-22 17:30 -0700
Message-ID<b7682c64-77ff-4151-a9dc-0ed71c04f5cc@googlegroups.com>
In reply to#413607
On Tuesday, May 22, 2018 at 1:29:52 PM UTC-7, WM wrote:
> Am Dienstag, 22. Mai 2018 17:27:52 UTC+2 schrieb burs...@gmail.com:
> > Dictionaries don't qualify as math theories,
> 
> Irrelevant. Every word you use is defined (with very few exceptions).

You conflate mathematics with physics, and now you conflate mathematical/logical expressions with natural languages.  This is why you are lost, and why you can’t understand simple concepts.  You are sad.

> Regards, WM

ZG

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#413637

FromWM <wolfgang.mueckenheim@hs-augsburg.de>
Date2018-05-23 06:06 -0700
Message-ID<3ed4cf73-3f86-436d-8798-3535f2fd9785@googlegroups.com>
In reply to#413617
Am Mittwoch, 23. Mai 2018 02:30:48 UTC+2 schrieb Zeit Geist:
> On Tuesday, May 22, 2018 at 1:29:52 PM UTC-7, WM wrote:
> > Am Dienstag, 22. Mai 2018 17:27:52 UTC+2 schrieb burs...@gmail.com:
> > > Dictionaries don't qualify as math theories,
> > 
> > Irrelevant. Every word you use is defined (with very few exceptions).
> 
> You conflate mathematics with physics, and now you conflate mathematical/logical expressions with natural languages.

Mathematical expressions cannot be defined other than by common language. They are only abbreviations which would need longer paragraphs of ordinary prose to obtain the same degree of prescision. 

The curse of the invasion of mathematics by mathematical logic is that now any proposition can be represented in a mathematical symbolism, and this makes us feel obliged to understand it. Although of course this method of writing is nothing but the translation of vague ordinary prose. (Wittgenstein)

Regards, WM

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#413147

Fromwpihughes@gmail.com
Date2018-05-15 17:14 -0700
Message-ID<78458f69-e346-4131-8c1f-3c9884b2e288@googlegroups.com>
In reply to#413125
On Tuesday, May 15, 2018 at 3:02:17 PM UTC-3, WM wrote:
> Am Sonntag, 13. Mai 2018 18:08:04 UTC+2 schrieb wpih...@gmail.com:
> 
> 
> > No problem doing Cantor's proof in a computable setting.
> >  
> > Assume only computable objects exists
> 
> Assume that "computable" has meaning also in ZFC.
> Take the set of all real numbers and choose the subset of computable numbers. 

How are you going to do this?  Recall, only computable operations are allowed.  There is no computable solution to the halting problem.


>It has a well-ordering in ZFC. This well-ordering is a sequence

In ZFC.  There are sequences in ZFC that do not exist in computable mathematics

> since the subset is countable.

In ZFC, i.e. in ZFC there is a list L ...  There are lists in ZFC that do not exist in computable mathematics


Note that in computable mathematics you do not have an arbitrary 0/1 sequences.  Thus, you do not have arbitrary subsets of the naturals. (so a subcollection of naturals may or may not be a subset pf naturals)

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#413187

FromWM <wolfgang.mueckenheim@hs-augsburg.de>
Date2018-05-16 11:26 -0700
Message-ID<a5c7d403-1b35-47ff-9528-0d1555377546@googlegroups.com>
In reply to#413147
Am Mittwoch, 16. Mai 2018 02:14:26 UTC+2 schrieb wpih...@gmail.com:
> On Tuesday, May 15, 2018 at 3:02:17 PM UTC-3, WM wrote:
> > Am Sonntag, 13. Mai 2018 18:08:04 UTC+2 schrieb wpih...@gmail.com:
> > 
> > 
> > > No problem doing Cantor's proof in a computable setting.
> > >  
> > > Assume only computable objects exists
> > 
> > Assume that "computable" has meaning also in ZFC.
> > Take the set of all real numbers and choose the subset of computable numbers. 
> 
> How are you going to do this?  Recall, only computable operations are allowed.  There is no computable solution to the halting problem.

There is everything allowed that is possible in ZFC. The definition of computable is well-known even there.
> 
> 
> >It has a well-ordering in ZFC. This well-ordering is a sequence
> 
> In ZFC.  There are sequences in ZFC that do not exist in computable mathematics

In ZFC there is every subset of |R. One of them is the subset of constructible numbers. Since it is countable, it has a bijection with |N, i.e., it is a sequence.
> 
> > since the subset is countable.
> 
> In ZFC, i.e. in ZFC there is a list L ...  There are lists in ZFC that do not exist in computable mathematics

Just that is my argument. In ZFC there is a list of all computable numbers by AC. Contradiction.
> 
> 
> Note that in computable mathematics you do not have an arbitrary 0/1 sequences.

Irrelevant. Here we discuss was ZF + AC can have.

Regards, WM

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#413205

Fromwpihughes@gmail.com
Date2018-05-16 16:35 -0700
Message-ID<fc27e0e9-3b31-4b07-8267-813539663fb3@googlegroups.com>
In reply to#413187
On Wednesday, May 16, 2018 at 3:26:22 PM UTC-3, WM wrote:
 
> Just that is my argument. In ZFC there is a list of all computable numbers by AC. Contradiction.
> > 


Nope, the list is not computable, therefore the antidiagonal is not computable.  

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#413242

FromWM <wolfgang.mueckenheim@hs-augsburg.de>
Date2018-05-17 05:03 -0700
Message-ID<e3180fb9-febd-4001-8e4e-9eaf9443c789@googlegroups.com>
In reply to#413205
Am Donnerstag, 17. Mai 2018 01:35:29 UTC+2 schrieb wpih...@gmail.com:
> On Wednesday, May 16, 2018 at 3:26:22 PM UTC-3, WM wrote:
>  
> > Just that is my argument. In ZFC there is a list of all computable numbers by AC. Contradiction.
> > > 
> 
> 
> Nope, the list is not computable, therefore the antidiagonal is not computable.

If it is possible to count to omega, to well-order even uncountably many elements, why then is it impossible, in ZFC, to compute all computable numbers and to store the results?

Regards, WM

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#413247

FromZelos Malum <zelos.malum@gmail.com>
Date2018-05-17 05:33 -0700
Message-ID<ee76bbf3-a2ab-4740-a902-65c870988d5b@googlegroups.com>
In reply to#413242
> If it is possible to count to omega, to well-order even uncountably many elements, why then is it impossible, in ZFC, to compute all computable numbers and to store the results?
> 
> Regards, WM

We don't count to omega you moron.

>If there are uncountably many real numbers, then there are uncountably many theorems and proofs. Most of them cannot be formulated. Should they be believed?

Your question boils down "Should we believe that which we cannot prove or disprove?" at which the answer is "no", it is only if its independent we can accept either proposition.

As for your statment of "uncountable theorems and proofs", it depends on how you define them. Considering a theorem is usually a NOL statement, it can be written down finitely and there are various extensions, which is why NOL exists, amongst many that allows the language to capture ever greater deals of objects and with it, your issue vanishes.

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#413256

FromWM <wolfgang.mueckenheim@hs-augsburg.de>
Date2018-05-17 09:31 -0700
Message-ID<fc4a32a3-027e-4f79-a472-d03a5a93259d@googlegroups.com>
In reply to#413247
Am Donnerstag, 17. Mai 2018 14:33:07 UTC+2 schrieb Zelos Malum:
> > If it is possible to count to omega, to well-order even uncountably many elements, why then is it impossible, in ZFC, to compute all computable numbers and to store the results?
> > 
> We don't count to omega

since no omega exists. I know. Nevertheless you claim so (at least those set theorists who understand their theory claim so) because otherwise no equicardinality could be "proved". What ordinal below omega would be left out? Any answer?

Obviously you don't even know the basic requirements of what you think is set theory.

Regards, WM

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#413031

FromSergio <invalid@invalid.com>
Date2018-05-13 12:40 -0500
Message-ID<pd9t9u$t30$1@gioia.aioe.org>
In reply to#412942
On 5/11/2018 1:20 PM, David Petry wrote:
> 
> 
> The essence of mathematics is proof.  The idea behind proof is that if we believe we have proved some assertion, 

wrong.  google axiums

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#413056

FromZelos Malum <zelos.malum@gmail.com>
Date2018-05-13 22:36 -0700
Message-ID<cc832800-5700-4644-8b0a-540d35fe94f8@googlegroups.com>
In reply to#412942
Den fredag 11 maj 2018 kl. 20:20:17 UTC+2 skrev David Petry:
> The essence of mathematics is proof.  The idea behind proof is that if we believe we have proved some assertion, then we must also believe that everyone has no choice but to believe that the assertion is actually true.  And consistent with the idea that the essence of mathematics is proof, is the idea that the domain of discourse for mathematics is the things that are provably well-defined.
> 
> So now let's look at the fundamental theorem of set theory (Cantor's theorem).
> 
> If we have a provably well-defined list of provably well-defined real numbers (so that every digit of every real number in the list can be computed), then the diagonal argument gives us a provably well-defined real number that is not in that list.  So if we start with the premiss that the domain of discourse for mathematics is the things that are provably well-defined, then the diagonal argument most certainly does not prove to us that there must exist anything outside of that domain.  At the same time, the domain of discourse cannot be larger than "countable", since proofs are objects in a language, and languages are countable.  The conclusion being that there is no reason to think we are compelled to believe in the existence of uncountable sets, which contradicts what Cantor's theorem says, and furthermore, there is good reason to say that Cantor's theorem is false.
> 
> Note that I'm not claiming that set theory is inconsistent as a game consisting of symbols and rules for manipulating strings of those symbols, as long as we recognize that the symbols have no meaning, and the strings of symbols have no connection to truth and reality.
> 
> The argument I just presented for not accepting set theory as part of mathematics has been around right from the start of set theory.  I believe that Julius Konig was the first to present that argument (or some variation of it).  The fact that many first rate mathematicians do not believe that Cantor's formal proof proves that his theorem is actually true, should be seen as justification for believing that set theory is not part of mathematics: mathematics is all about things we have no choice but to believe are actually true.
> 
> Mathematics has important connections to real life.  Real life is not just a game.  Set theory is nothing but a game.  It is not mathematics.

The fact that the formal language used can only produce countably many valid sentences does not in anyway make it unable to discuss things beyond countable.

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#413070

FromWM <wolfgang.mueckenheim@hs-augsburg.de>
Date2018-05-14 04:49 -0700
Message-ID<5becd8be-a57b-4c2e-b2ed-71153786e097@googlegroups.com>
In reply to#413056
Am Montag, 14. Mai 2018 07:36:14 UTC+2 schrieb Zelos Malum:
> Den fredag 11 maj 2018 kl. 20:20:17 UTC+2 skrev David Petry:


> > Mathematics has important connections to real life.  Real life is not just a game.  Set theory is nothing but a game.  It is not mathematics.
> 
> The fact that the formal language used can only produce countably many valid sentences does not in anyway make it unable to discuss things beyond countable

and to believe in uncountably more valid sentences. If undefinable numbers are acceptable, why not accept undefinable proofs? We can discuss collections of these things but we cannot read or write them. It is not mathematics. It is matheology.

Regards, WM

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#413219

FromZelos Malum <zelos.malum@gmail.com>
Date2018-05-17 01:34 -0700
Message-ID<cfd6bfc9-ee7c-48fc-8d26-fdc9ccf5060d@googlegroups.com>
In reply to#413070
Den måndag 14 maj 2018 kl. 13:50:03 UTC+2 skrev WM:
> Am Montag, 14. Mai 2018 07:36:14 UTC+2 schrieb Zelos Malum:
> > Den fredag 11 maj 2018 kl. 20:20:17 UTC+2 skrev David Petry:
> 
> 
> > > Mathematics has important connections to real life.  Real life is not just a game.  Set theory is nothing but a game.  It is not mathematics.
> > 
> > The fact that the formal language used can only produce countably many valid sentences does not in anyway make it unable to discuss things beyond countable
> 
> and to believe in uncountably more valid sentences. If undefinable numbers are acceptable, why not accept undefinable proofs? We can discuss collections of these things but we cannot read or write them. It is not mathematics. It is matheology.
> 
> Regards, WM

I never said that the sentences are uncountably many, but that doesn't mean they cannot describe thigns that are uncountable.

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