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Re: Smullyan's Proof of the Drinkers Principle V3

Newsgroups sci.logic
Date 2023-05-04 17:09 -0700
References (3 earlier) <u30te8$5ba5$1@solani.org> <u30tof$5bhg$1@solani.org> <635396aa-8b27-4b46-92d1-042f120c334en@googlegroups.com> <34b4964f-ebac-41bc-908b-1860d362b799n@googlegroups.com> <c5f1d123-0e61-4bfb-b78c-bd4c57eeb00bn@googlegroups.com>
Message-ID <72b264af-ab22-4faf-8c99-be729e4b95a2n@googlegroups.com> (permalink)
Subject Re: Smullyan's Proof of the Drinkers Principle V3
From Mostowski Collapse <bursejan@gmail.com>

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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] 

Dan Christensen schrieb am Freitag, 5. Mai 2023 um 01:54:54 UTC+2:
> On Thursday, May 4, 2023 at 7:33:21 PM UTC-4, Mostowski Collapse wrote: 
> > Undeniable and possibly a little bit accidentatial you used a 
> > lemma based on Russell Paradox in your proof. 
> > 
> > Does the lemma also work for the dual Drinker Paradox: 
> > 
> > /* There is a guest if some guest drinks then this guest drinks */ 
> > 16 ∃x:(∃y:d(y) ⊃ d(x)) 
> > ▲ Conclusion 1,15 
> > 
> > Or in DC Proof notation: 
> > 
> > EXIST(x):[EXIST(a):[a in drinkers] => x in drinkers]
> Only if x previously introduced in an axiom or premise. 
> 
> 1. P(x) 
> Axiom 
> 
> 2. Set(drinkers) 
> Axiom 
> 
> Lemma (see Russell's Paradox): 
> 
> 3. ALL(a):[Set(a) => EXIST(b):~b in a] 
> Axiom 
> 
> 4. Set(drinkers) => EXIST(b):~b in drinkers 
> U Spec, 3 
> 
> 5. EXIST(b):~b in drinkers 
> Detach, 4, 2 
> 
> 6. ~y in drinkers 
> E Spec, 5 
> 
> 7. ~y in drinkers | x in drinkers 
> Arb Or, 6 
> 
> 8. ~~y in drinkers => x in drinkers 
> Imply-Or, 7 
> 
> 9. y in drinkers => x in drinkers 
> Rem DNeg, 8 
> 
> 10. EXIST(a):[a in drinkers => x in drinkers] 
> E Gen, 9 
> 
> 11. EXIST(x):EXIST(a):[a in drinkers => x in drinkers] 
> E Gen, 10
> 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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