POV-Ray: Newsgroups: povray.off-topic: Logic and false dichotomies

POV-Ray : Newsgroups : povray.off-topic : Logic and false dichotomies		Server Time 1 Nov 2024 23:16:46 EDT (-0400)

From: Warp
Subject: Logic and false dichotomies
Date: 26 Jan 2011 13:58:36
Message: <4d406edc@news.povray.org>

When talking about logic and the truth value of a statement, one could
hastily think that true/false is a true dichotomy: A statement is either
true or false.

  However, this is a false dichotomy. A statement is either true or not
true (which *is* a true dichotomy), but there are more alternatives to
'true' than 'false'.

  For example, "this statement is false" is neither a true statement nor
a false statement. It's a contradictory one. This is a third option to
the true/false pair.

  (Note that the above realization is not mine, and I'm not taking any
kind of credit for it.)

  I was thinking: Are there any other possibilities in logic than true,
false or self-contradictory?

  I came up with this absolutely marvelous option: "This statement is true."

  The beauty of that statement is that it can be either true or false.
If you consider it to be true, it indeed is (because it's asserting its
own truth). However, if you consider it false, it also indeed is (because
it's making a false statement of its own truth).

  In other words, the statement is *ambiguous*, which would be a fourth
option to the true/false/contradiction triplet.

-- 
                                                          - Warp

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From: Le Forgeron
Subject: Re: Logic and false dichotomies
Date: 26 Jan 2011 15:35:14
Message: <4d408582$1@news.povray.org>

Le 26/01/2011 19:58, Warp nous fit lire :

GEB... as soon as you have a powerful enough system, you have a problem.

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From: andrel
Subject: Re: Logic and false dichotomies
Date: 26 Jan 2011 16:04:32
Message: <4D408C73.5050605@gmail.com>

On 26-1-2011 19:58, Warp wrote:
>    When talking about logic and the truth value of a statement, one could
> hastily think that true/false is a true dichotomy: A statement is either
> true or false.
>
>    However, this is a false dichotomy. A statement is either true or not
> true (which *is* a true dichotomy), but there are more alternatives to
> 'true' than 'false'.
>
>    For example, "this statement is false" is neither a true statement nor
> a false statement. It's a contradictory one. This is a third option to
> the true/false pair.
>
>    (Note that the above realization is not mine, and I'm not taking any
> kind of credit for it.)
>
>    I was thinking: Are there any other possibilities in logic than true,
> false or self-contradictory?

another is undecidable. For some statements you can prove that you can 
not prove that they are true or false. (indeed see Goedel)

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From: Darren New
Subject: Re: Logic and false dichotomies
Date: 26 Jan 2011 18:47:48
Message: <4d40b2a4$1@news.povray.org>

Warp wrote:
>   I was thinking: Are there any other possibilities in logic than true,
> false or self-contradictory?

http://en.wikipedia.org/wiki/Paraconsistent

You also missed "Not a well-formed statement" as well as "valid but false" 
and "invalid but true."

-- 
Darren New, San Diego CA, USA (PST)
  "How did he die?"   "He got shot in the hand."
     "That was fatal?"
          "He was holding a live grenade at the time."

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From: nemesis
Subject: Re: Logic and false dichotomies
Date: 27 Jan 2011 10:19:48
Message: <4d418d14$1@news.povray.org>

This statement is bogus.  As logic is.

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