Glad you asked. I highly recommend Bart Kosko's "Fuzzy Thinking".
(short review: http://public.logica.com/~stepneys/bib/nf/kosko.htm)
If it isn't on the Virus reading list yet, it will be.
While re-reading parts of W.W.Bartley's "The Retreat to Commitment" [1][2]
to research an upcoming message on metacontexts for the Buddhism vs.
Objectism thread, I came across the answer to your question:
Ordinary logic includes both the law of non-contradiction[3] and the
law of the excluded middle[4]. Of the two, our minimal logic would
have to retain the law of non-contradiction as a metalinguistic rule
governing the argument situation: for if contradictions were
permitted, falsity could not be retransmitted and criticism in the
sense intended would be impossible.
So there you have it, a logic that permitted contradictions would be
useless for its intended purpose. (Which isn't to say that it might
not be useful for something else.)
[1] Which is very high on the Virus reading list.
[2] I'm glad I bought the book. In fact I thought it was so important,
I bought a 1st ed. copy I came across at a used bookstore, something
I had never done before.
[3] ~(A and ~A)
[4] if A then ~(~A)
-- David McFadzean david@lucifer.com Memetic Engineer http://www.lucifer.com/~david/ Church of Virus http://www.lucifer.com/virus/