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Re: A Paradox of Equality?

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Subject Re: A Paradox of Equality?
From Dan Christensen <Dan_Christensen@sympatico.ca>
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On Monday, June 5, 2023 at 8:26:41 PM UTC-4, Mild Shock wrote:
> You made an error when you translated the Drinker 
> Paradox from second order logic.

I made no error. I used ordinary math textbook logic and set theory, not second order logic, i.e. no quantifying over logical propositions.

 Second order 
> logic is two sorted. It is a multi sorted logic. 
> 
> It has these two sorts: 
> 
> x, y, z, etc..: Elements or individuals (the 1st order objects) 
> X, Y, Z, etc..: Sets or predications. (the 2nd order objects) 
> 
> Using the native membership between the two, you 
> are only allowed to form: 
> 
> x e X 
> 

Use the rules of syntax of statements in ZFC, show that x in x is not a wff

See the rules of syntax here: https://encyclopediaofmath.org/wiki/ZFC (2nd paragraph)

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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A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 10:33 -0700
  Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-03 11:02 -0700
    Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 11:17 -0700
      Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-03 11:47 -0700
        Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:57 -0700
        Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 12:37 -0700
  Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:13 -0700
    Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:20 -0700
      Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:42 -0700
        Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 12:14 -0700
      Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 11:56 -0700
        Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:58 -0700
          Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 12:08 -0700
            Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 12:25 -0700
    Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 11:26 -0700
      Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 21:12 +0200
        Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 21:20 +0200
        Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 12:27 -0700
          Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 21:41 +0200
          Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 21:41 +0200
            Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 13:02 -0700
              Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 22:07 +0200
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 13:27 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 13:49 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 13:56 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 14:12 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 14:24 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 19:24 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 06:46 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 06:47 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 06:51 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 09:33 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 12:22 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 13:48 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 14:38 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 15:29 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 17:20 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 18:23 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 01:31 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 02:55 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 08:22 -0700
                Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-05 19:47 +0200
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 11:59 -0700
                Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-05 21:49 +0200
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 13:39 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 12:32 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 12:39 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 13:03 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 13:09 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 13:14 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 14:34 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:04 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:14 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:26 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 16:33 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 14:22 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:06 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 17:13 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 17:26 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 17:36 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 17:47 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 17:54 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 18:00 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 18:02 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 18:05 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 18:35 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 22:38 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 22:47 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 22:58 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-06 07:35 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-06 09:11 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-06 10:08 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-08 01:25 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 08:09 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-08 11:09 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 11:35 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-08 11:36 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-09 12:51 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-09 13:12 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 18:17 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 18:44 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 14:09 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 14:32 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 17:42 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 18:32 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 19:04 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-16 05:53 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-16 16:59 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-16 17:07 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-16 21:55 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 19:15 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 20:39 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 08:43 -0700
                Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-04 17:55 +0200
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 09:40 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-04 10:42 -0700

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