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Re: Smullyan's Proof of the Drinkers Principle V3

Newsgroups sci.logic
Date 2023-06-05 11:39 -0700
References (20 earlier) <5a63fe01-7e52-46b8-abdf-768d264a2ca1n@googlegroups.com> <9fb38325-1197-4eb8-8ab0-81576941ac5dn@googlegroups.com> <f7567415-7e88-43aa-b51d-277b8d5e8e8cn@googlegroups.com> <59591d0d-ff24-402a-89fb-61d36058f344n@googlegroups.com> <478c25c6-698f-497c-97ed-5e944b14305cn@googlegroups.com>
Message-ID <cce648fc-09ed-438c-8f33-b17fb6baf8fen@googlegroups.com> (permalink)
Subject Re: Smullyan's Proof of the Drinkers Principle V3
From Mild Shock <bursejan@gmail.com>

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In second order logic, one cannot prove your nonsense.
In second order logic one would have capital case variable
names X, Y, ... for "sets" and lower case variable names x, y, ...

for "elements". You cannot prove in second order logic
your nonsense. In second order logic there is no need for
Set(_) since there is the variable casing convention:

/* Not Provable in Second Order Logic */
ALL(X):EXIST(x):~x e X
http://www.dcproof.com/UniversalSet.htm

Why is it not provable in second order logic? Well
if it where provable ALL(X):EXIST(x):~x e X in second
order logic, it would hold for any second order logic

model. But a second order logic has usually X=U
as a possible value for a "set" variable. And we have
ALL(x):x e U. End of demonstration.

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Thread

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
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-05 11:39 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-05 15:56 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 18:53 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-05 22:40 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-05 22:48 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-05 22:57 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-06 07:37 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-06 09:13 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-06 10:13 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-07 13:31 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-07 13:37 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-07 13:42 -0700

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