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| Date | 2023-05-05 03:35 -0700 |
| References | (5 earlier) <635396aa-8b27-4b46-92d1-042f120c334en@googlegroups.com> <34b4964f-ebac-41bc-908b-1860d362b799n@googlegroups.com> <c5f1d123-0e61-4bfb-b78c-bd4c57eeb00bn@googlegroups.com> <72b264af-ab22-4faf-8c99-be729e4b95a2n@googlegroups.com> <2263c253-068a-4fc7-b57c-3912efeb9e89n@googlegroups.com> |
| Message-ID | <c6812ac7-1760-4457-908f-5a52a2c67fbfn@googlegroups.com> (permalink) |
| Subject | Re: Smullyan's Proof of the Drinkers Principle V3 |
| From | Mostowski Collapse <bursejan@gmail.com> |
Where Russells Paradox used? In a proof of this: /* dual Drinker Paradox */ EXIST(x):[EXIST(a):[a in drinkers] => x in drinkers] Hint: The dual of Russells Paradox would be: Lemma (see dual Russell's Paradox): 3. ALL(a):[Set(a) => EXIST(b):b in a] Axiom Unless your set theory is inconsistent, it shouldn't be provable. Since a counter example is the empty set. So I guess your "More to follow" should say "Nothing to follow" if you are honest and clever. Dan Christensen schrieb am Freitag, 5. Mai 2023 um 07:34:36 UTC+2: > On Thursday, May 4, 2023 at 8:09:16 PM UTC-4, Mostowski Collapse wrote: > > Wrong placing of second EXIST, you proved: > > EXIST(x):EXIST(a):[a in drinkers => x in drinkers] > > But the dual Drinker Paradox is: > > EXIST(x):[EXIST(a):[a in drinkers] => x in drinkers] > Translated Smullyan's proof of the dual Drinker Principle (26 lines in DC Proof): > > EXIST(a):U(a) > => EXIST(a):[U(a) & [EXIST(b):[U(b) & Drinker(b)] => Drinker(a)]] > > Where U is the implicit "domain of discourse" in FOL. > > More to follow. > 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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Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-03 16:16 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-04 20:19 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-04 20:27 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-04 20:32 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 12:15 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 16:33 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 16:50 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 16:54 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 17:09 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 17:12 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 22:34 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-05 03:35 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-05 14:37 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-06 03:09 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-06 03:43 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-06 10:29 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-07 02:41 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-07 06:59 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-07 08:31 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-07 11:19 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-07 20:34 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-07 20:41 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-07 20:47 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-07 20:48 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-07 11:51 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-08 05:36 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-08 07:22 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-11 14:34 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-11 16:10 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-11 17:00 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-12 12:04 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-12 03:13 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-12 07:12 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 11:40 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 11:43 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 11:49 -0700
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