Re: Kurt Godel: Unpublished Philosophical Essays, by F. A. Rodriquez-Consuegra and Kurt Godel

From: Torkel Franzen (torkel_at_sm.luth.se)
Date: 05/07/04 

Date: 07 May 2004 11:43:33 +0200

the_great_nathan@my-deja.com (Nathan the Great) writes:

> Unless I am mistaken, the "Law of Excluded Middle" is not a
> required axiom of formal systems in general. Systems lacking
> LEM don't use "proof by contradiction," and they are capable
> of being both incomplete and inconsistent.

  It is not the law of excluded middle, but that of ex falso
quodlibet, which is also valid in constructive logic, that is
presupposed in the observation that no formula is undecidable in an
inconsistent theory. If we use, say, minimal logic we can have an
inconsistent and incomplete theory.

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