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Re: Smullyan's Proof of the Drinkers Principle V3

Newsgroups sci.logic
Date 2023-05-21 08:22 -0700
References (15 earlier) <57f74166-4096-4d9a-89c4-46a6fe8da770n@googlegroups.com> <b5a0b313-6e00-456b-a54a-319224932608n@googlegroups.com> <u3l2ve$gb4s$1@solani.org> <7a8f9c8f-3ee8-4ef2-bf30-e4d5e2f383e3n@googlegroups.com> <a05e76db-1b0b-4e9d-90a9-3f09522e169an@googlegroups.com>
Message-ID <e5ccd941-cd2d-4baa-a6d2-0601411e93cen@googlegroups.com> (permalink)
Subject Re: Smullyan's Proof of the Drinkers Principle V3
From Dan Christensen <Dan_Christensen@sympatico.ca>

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On Sunday, May 21, 2023 at 9:59:36 AM UTC-4, Mostowski Collapse wrote:
> What makes you think your nonsense of a generalized 
> drinker paradox has even the slightest relevance to 
> Smullyans Drinker paradox. 

[snip]

Wrong again, Mr. Collapse. Again,  Smullyan informally states his Drinkers' Principle as follows: 

"There exists someone such that whenever he (or she) drinks, everybody drinks."
--Smullyan, "What is the name of this book?" p.209

You can formalize this statement in at least two different ways: 

(1) Using "standard" FOL implicitly that assumes a non-empty domain of discourse. If we make this assumption explicit in DC Proof, we would have something like:

EXIST(a):U(a) => EXIST(a):[U(a)  & [Drinker(a) => ALL(b):[U(b) => Drinker(b)]]]

For any unary predicates U and Drinker. Note that every quantifier here is restricted by U.

(2) Using ordinary set theory, can obtain: EXIST(a):[a in D => ALL(b):b in D]  

For any set D.

Slightly more interesting might be: EXIST(a):[a in D => ALL(b):[Pub(b) => b in D]  

For any set D and unary predicate Pub.

> Ultimately you cannot prove: 
> 
> ALL(U):ALL(s):[Set(s) & Set(U) & Subset(s,U) => EXIST(a):[a e U & ~a e s]] 
> 

Again, what happens if U=s?

> There is no Russell Paradox for the Smullyan Riddle.

The resolution of Russell's Paradox is fundamental to set theory. Deal with it, Mr. Collapse.

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 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 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 06:59 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 07:10 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-21 08:22 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 12:14 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 12:16 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 12:17 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-21 12:50 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 12:56 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-21 15:45 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-21 16:01 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 16:29 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 16:56 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-21 16:59 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-21 17:51 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-22 02:51 +0200
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-26 14:13 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 08:53 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 08:56 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 09:03 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 09:34 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 09:38 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 09:39 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 10:24 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <janburse@fastmail.fm> - 2023-05-29 19:49 +0200
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 11:10 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 13:39 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 13:58 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 15:17 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 15:24 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 17:39 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 18:52 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 19:04 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 19:34 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-30 15:18 -0700

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