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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Newsgroups | sci.logic |
| Subject | Re: A Paradox of Equality? |
| Date | 2023-06-05 19:47 +0200 |
| Message-ID | <u5l73e$us46$1@solani.org> (permalink) |
| References | (12 earlier) <f9d02454-c11c-4be5-a3ae-46eaa430c557n@googlegroups.com> <a1a04e8d-9223-4a55-8d7d-09f38592dd31n@googlegroups.com> <edec0db3-0f0e-4e78-8267-52548b1dc674n@googlegroups.com> <982abeab-52f1-4942-b877-e7bc822e21f6n@googlegroups.com> <d992cfe4-8e05-4bcc-a62a-5712061bf041n@googlegroups.com> |
Terrence Tao says the contrary: In order to prevent this post from being totally devoid of mathematical content, I’ll mention that I recently came across the phenomenon of nonfirstorderisability in mathematical logic: there are perfectly meaningful and useful statements in mathematics which cannot be phrased within the confines of first order logic (combined with the language of set theory, or any other standard mathematical theory); one must use a more powerful language such as second order logic instead. This phenomenon is very well known among logicians, but I hadn’t learned about it until very recently, and had naively assumed that first order logic sufficed for “everyday” usage of mathematics. https://terrytao.wordpress.com/2007/08/27/printer-friendly-css-and-nonfirstorderizability/#more-172 The Drinker Paradox is also such an instance. Not that you would really need 2nd Order, but set theory breaks it. Dan Christensen schrieb: > On Monday, June 5, 2023 at 5:55:12 AM UTC-4, Mild Shock wrote: >> Using ordinary propositional 2nd order logic, we can prove: >> > > Who uses 2nd order logic? I don't think you will find it any math textbooks. They do tend, however, to use a lot of set theory instead. > > Dan > > Download my DC Proof 2.0 freeware at http://www.dcproof.com > Visit my Math Blog at http://www.dcproof.wordpress.com >
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A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 10:33 -0700
Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-03 11:02 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 11:17 -0700
Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-03 11:47 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:57 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 12:37 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:13 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:20 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:42 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 12:14 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 11:56 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:58 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 12:08 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 12:25 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 11:26 -0700
Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 21:12 +0200
Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 21:20 +0200
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 12:27 -0700
Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 21:41 +0200
Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 21:41 +0200
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 13:02 -0700
Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 22:07 +0200
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 13:27 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 13:49 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 13:56 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 14:12 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 14:24 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 19:24 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 06:46 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 06:47 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 06:51 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 09:33 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 12:22 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 13:48 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 14:38 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 15:29 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 17:20 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 18:23 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 01:31 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 02:55 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 08:22 -0700
Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-05 19:47 +0200
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 11:59 -0700
Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-05 21:49 +0200
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 13:39 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 12:32 -0700
Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 12:39 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 13:03 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 13:09 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 13:14 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 14:34 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:04 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:14 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:26 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 16:33 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 14:22 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:06 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 17:13 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 17:26 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 17:36 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 17:47 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 17:54 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 18:00 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 18:02 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 18:05 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 18:35 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 22:38 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 22:47 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 22:58 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-06 07:35 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-06 09:11 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-06 10:08 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-08 01:25 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 08:09 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-08 11:09 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 11:35 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-08 11:36 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-09 12:51 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-09 13:12 -0700
Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 18:17 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 18:44 -0700
Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 14:09 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 14:32 -0700
Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 17:42 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 18:32 -0700
Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 19:04 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-16 05:53 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-16 16:59 -0700
Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-16 17:07 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-16 21:55 -0700
Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 19:15 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 20:39 -0700
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 08:43 -0700
Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-04 17:55 +0200
Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 09:40 -0700
Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-04 10:42 -0700
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