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Re: Erroneous conclusions from applying material conditionals?

Newsgroups sci.logic
Date 2023-05-28 13:57 -0700
References <1366dae7-673f-4315-98b1-ce4098000d7dn@googlegroups.com> <e2050cec-44a4-4f20-83f9-9f15ae2c6284n@googlegroups.com> <79c5bbaf-b748-4b90-bcd2-d008c665b509n@googlegroups.com> <c1ac5fdf-bf7a-45da-928f-d5a3429bffe4n@googlegroups.com>
Message-ID <ec7f8e96-24ef-48ec-b875-2218f97bfac2n@googlegroups.com> (permalink)
Subject Re: Erroneous conclusions from applying material conditionals?
From Mild Shock <bursejan@gmail.com>

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Material implication is critizised for obeying two laws,
because it is seen as (A => B) == (~A v B):

Law of noncontradiction (LNC) 
Formally this is expressed as the tautology ¬(p ∧ ¬p).
https://en.wikipedia.org/wiki/Law_of_noncontradiction

Law of excluded middle (LEM)
precise statement of the law of excluded middle, P ∨ ~P
https://en.wikipedia.org/wiki/Law_of_excluded_middle

Intuitionistic Logic accepts LNC, but rejects LEM.
~~A -> A needs both LNC and LEM. But it fails in 
intuitionistic logic, because intuitionistic logic

rejects LEM. But as long as you accept ~~A -> A, 
you are swimming in the pool of material implication.
And this pool is affected by some anomalies due to

LEM, such as the existence of this paradox:

Banach–Tarski paradox
https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

In this case, the issue is that the entire concept of partitions
and equivalence classes, which underlies the usual proof of
he Banach-Tarski paradox, behaves very differently in constructive systems.
https://math.stackexchange.com/questions/175675/intuitionistic-banach-tarski-paradox

Mild Shock schrieb am Sonntag, 28. Mai 2023 um 22:47:33 UTC+2:
> This here uses Rem DNeg a couple of times: 
> http://www.dcproof.com/UniversalSet.htm 
> 
> This here uses Rem DNeg once: 
> http://www.dcproof.com/STGeneralizedDrinkersThm.htm 
> 
> An intuitionistic proof would not use ~~A -> A. 
> But searching for intuitionistic proofs is much harder 
> 
> than searching for classical proofs.
> Dan Christensen schrieb am Sonntag, 28. Mai 2023 um 21:01:54 UTC+2: 
> > On Sunday, May 28, 2023 at 11:39:07 AM UTC-4, Mild Shock wrote: 
> > 
> > > Dan Christensen schrieb am Samstag, 27. Mai 2023 um 21:04:05 UTC+2: 
> > > > What erroneous conclusions might arise from applying material conditionals for logical propositions that are unambiguously either true or false in the present? (Hint: None?) 
> > 
> > > The Generalized Drinker Paradox, like here: 
> > > 
> > > ALL(s):[Set(s) => EXIST(x):[x e s => Q(x,s)]] 
> > > http://www.dcproof.com/STGeneralizedDrinkersThm.htm 
> > > 
> > > Its shows that the material implication can be quite challenging. 
> > "Challenging?" Can you be more specific? Nowhere, for example, is the principle of vacuous truth invoked (the Arbitrary Consequent Rule, Arb Cons: P => (~P => Q)). Likewise the Arbitrary Antecedent Rule (Arb Ant: P => (Q => P)). 
> > 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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Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-27 12:04 -0700
  Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-27 13:25 -0700
    Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-27 19:42 -0700
  Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 08:39 -0700
    Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 11:50 -0700
    Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 12:01 -0700
      Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 13:47 -0700
        Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 13:57 -0700
          Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 14:02 -0700
          Re: Erroneous conclusions from applying material conditionals? olcott <polcott2@gmail.com> - 2023-05-28 16:12 -0500
          Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 15:39 -0700
            Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 15:56 -0700
              Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 16:04 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 16:14 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 16:24 -0700
              Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 16:49 -0700
              Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 16:52 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <janburse@fastmail.fm> - 2023-05-29 02:25 +0200
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <janburse@fastmail.fm> - 2023-05-29 02:31 +0200
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <janburse@fastmail.fm> - 2023-05-29 02:45 +0200
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 17:59 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 17:46 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 17:51 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 18:01 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 18:07 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 18:12 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 18:15 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 18:17 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 18:23 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-28 18:28 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 18:46 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-28 21:51 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-28 22:14 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 22:33 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 22:36 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-29 09:01 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 09:27 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 09:32 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 09:35 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 10:03 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <janburse@fastmail.fm> - 2023-05-29 19:45 +0200
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-30 05:52 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-30 15:16 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-29 11:14 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-29 22:53 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-30 17:45 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-31 08:23 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-31 13:22 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-31 13:31 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-31 13:38 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-31 13:51 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-01 19:56 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-01 21:35 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 21:44 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 18:54 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-01 19:55 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 21:13 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 21:19 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 21:23 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 21:30 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-01 22:02 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 22:28 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 22:31 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 22:34 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 22:39 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 23:29 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-03 14:14 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-03 14:23 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 23:26 -0700
                Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-02 09:42 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 20:41 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 20:58 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 21:24 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 21:28 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 21:31 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-01 21:34 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 22:49 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-03 04:49 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-03 04:51 -0700
        Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-28 15:33 -0700
    Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 02:52 -0700
      Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 02:58 -0700
        Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 03:03 -0700
          Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 07:35 -0700
            Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 08:23 -0700
              Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 08:30 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 08:33 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 09:56 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <janburse@fastmail.fm> - 2023-05-29 19:56 +0200
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 11:40 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 11:43 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 13:32 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 13:38 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 13:59 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 15:19 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 15:21 -0700
                Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-05-29 17:37 -0700
                Re: Erroneous conclusions from applying material conditionals? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 19:00 -0700
  Re: Erroneous conclusions from applying material conditionals? Mild Shock <janburse@fastmail.fm> - 2023-06-02 09:41 +0200
    Re: Erroneous conclusions from applying material conditionals? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-02 09:42 -0700
      Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-02 11:00 -0700
        Re: Erroneous conclusions from applying material conditionals? Mild Shock <bursejan@gmail.com> - 2023-06-02 11:14 -0700

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