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Re: A Paradox of Equality?

Newsgroups sci.logic
Date 2023-06-03 11:13 -0700
References <77d5dd37-e474-426f-b536-9ee66b2b7232n@googlegroups.com>
Message-ID <dcef026b-a934-4268-b2d2-ffd75b64b1b8n@googlegroups.com> (permalink)
Subject Re: A Paradox of Equality?
From Mild Shock <bursejan@gmail.com>

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I guess its rather the paradox of irrelevance. 
There are so many theorems that are irrelevant, 
und would never make it into a paper, since 

they use either inconsistent assumptions, 
or then are non-construction and can therefore not be 
applied. Are just some Unicorn dreams. 

Maybe post some math when have outgrown your 
juvenile phase of 1000-th version of Russels paradox 
which is totally irrelevant and useless to mathematics. 

Dan Christensen schrieb am Samstag, 3. Juni 2023 um 19:33:09 UTC+2:
> Using ordinary set theory, we can prove: 
> 
> (1) ALL(a):[a in X & a=a] is FALSE for any set X. 
> 
> Whereas 
> 
> (2) ALL(a):[a in X => a=a]] is TRUE for any set X. 
> 
> ---------------------------------------------------------------------- 
> PROOF (1) 
> 
> Lemma: From Russel's Paradox (Proof: http://dcproof.com/UniversalSet.htm ) 
> 
> 1. ALL(a):[Set(a) => EXIST(b):~b in a] 
> Axiom 
> 
> Let x be a set 
> 
> 2. Set(x) 
> Premise 
> 
> Apply lemma 
> 
> 3. Set(x) => EXIST(b):~b in x 
> U Spec, 1 
> 
> 4. EXIST(b):~b in x 
> Detach, 3, 2 
> 
> 5. ~y in x 
> E Spec, 4 
> 
> 6. ~y in x | ~y=y 
> Arb Or, 5 
> 
> 7. ~[~~y in x & ~~y=y] 
> DeMorgan, 6 
> 
> 8. ~[y in x & ~~y=y] 
> Rem DNeg, 7 
> 
> 9. ~[y in x & y=y] 
> Rem DNeg, 8 
> 
> 10. ALL(x):[Set(x) => EXIST(a):~[a in x & a=a]] 
> Conclusion, 2 
> 
> 11. ALL(x):[Set(x) => ~ALL(a):~~[a in x & a=a]] 
> Quant, 10 
> 
> 12. ALL(x):[Set(x) => ~ALL(a):[a in x & a=a]] 
> Rem DNeg, 11 
> 
> ---------------------------------------------------------------------- 
> PROOF (2) 
> 
> 1. Set(x) 
> Premise 
> 
> 2. y in x 
> Premise 
> 
> 3. y=y 
> Reflex 
> 
> 4. ALL(a):[a in x => a=a] 
> Conclusion, 2 
> 
> 5. ALL(x):[Set(x) => ALL(a):[a in x => a=a]] 
> Conclusion, 1 
> 
> 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? 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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