Re: ex contradictione quodlibet

[John Denker <jsd@MONMOUTH.COM>]

At 01:51 PM 10/28/99 -0500, Richard Grandy wrote:
> There is an important distinction to be marked between  "ex falso
> quodlibet"  and "ex contradiction quodlibet".  The first says that from a
> false statement  anything/everything follows, which is not a principle of
> symbolic logic.  The second says that from a *contradiction*
> anything/everything follows, which is an accepted principle.

Exactly so.  Thanks.

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Also, at 09:28 AM 10/28/99 -0500, Karl Trappe wrote:
> Does anyone know the resource for this ancient premise.

Why not just prove it on the spot?

Note that the implication "A implies B" can be written in Boolean terms as
        B or not(A)             quite generally.

We want to prove:
  "'P and not(P) implies X' is a true statement for all P and all X."

So we calculate:  Let the statement in question (the implication) be called
Z.  It can be written as:
        Z = X or not(P and not(P))
         = X or not(0)
         = X or 1
         = 1

So we conclude Z=1 (i.e. the implication is true) for all X and all P, QED.

==========

Further reference: If your formal logic is too rusty to follow the
foregoing calculation, you can get a refresher from the _Encyclopedia
Britannica_ macropedia article on Logic.

______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com