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Re: Smullyan's Proof of the Drinkers Principle V3

Newsgroups sci.logic
Date 2023-04-30 07:42 -0700
References <c100517c-4b7c-4e83-86ef-02ce3e336698n@googlegroups.com> <ba84dd85-8d6e-4084-b3b1-ff2c094eab36n@googlegroups.com> <0d85cc45-42bf-4802-a0b7-2e4eb078443en@googlegroups.com>
Message-ID <e7a2f6da-4699-4735-8792-b8a3082a225dn@googlegroups.com> (permalink)
Subject Re: Smullyan's Proof of the Drinkers Principle V3
From Mostowski Collapse <bursejan@gmail.com>

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Well its a theorem:

Theorem 1: The Drinker Paradox
∃xPx entails ∃x(Px ∧ (Dx → ∀y(Py → Dy))).
https://www.umsu.de/trees/#~7xPx|=~7x(Px~1(Dx~5~6y(Py~5Dy)))

Theorem 2: The Drinker Paradox Reverse Direction2
∃x(Px ∧ (Dx → ∀y(Py → Dy))) entails ∃xPx.
https://www.umsu.de/trees/#~7x(Px~1(Dx~5~6y(Py~5Dy)))|=~7xPx

So you can. The reverse direction is also mentioned on Wikipedia:
https://en.wikipedia.org/wiki/Drinker_paradox#Non-empty_domain

Can you do the reverse direction in DC Poop?

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Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-04-29 17:16 -0700
  Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-04-29 17:20 -0700
    Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-04-30 07:42 -0700
      Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-04-30 07:45 -0700
        Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-04-30 08:31 -0700
          Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-04-30 10:50 -0700
            Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-04-30 12:35 -0700
              Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-04-30 22:16 +0200
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-04-30 14:34 -0700
              Re: Smullyan's Proof of the Drinkers Principle V3 Jeff Barnett <jbb@notatt.com> - 2023-04-30 16:58 -0600
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-04-30 16:25 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-04-30 17:21 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-04-30 17:24 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-04-30 17:46 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-01 02:15 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-01 02:24 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-01 08:24 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-01 17:00 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-01 17:54 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-02 06:50 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-03 18:07 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-03 23:47 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 07:41 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 08:41 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 10:14 -0700

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