**Topic:**

**PARACONSISTENCY**

previous## COMPLEMENTARITY AND

PARACONSISTENCY

da Costa & Krause

(excerpt, page 5)

It should be remarked that in the `classical world', which at first glance can be described by using standard logic and mathematics, ifalphaandbetaare both theses or theorems of a theory (founded on classical logic), thenalpha&betais also a thesis of that theory. This is what we intuitively mean when we say that on the grounds of classical logic, a true proposition cannot `exclude' another true proposition.

In classical logic, if from some groupDelta1 of axioms of a theoryTwe deducegamma, and if from another groupDelta2 we deduce non-gamma, thengamma& non-gammais also deductible in T.

Normally, our groupDeltaof axioms of T is finite, so that we may talk of the conjunction of its sentences instead ofDeltaitself. Then, ifalphaandbetaare respectively the conjunctions associated toDelta1 andDelta2, as above, we are looking for a theoryTsuch that in T we may havealpha|-gammaandbeta|- non-gamma, but in whichgamma& non-gammais not a theorem of T.

Therefore, our goal is to describe a way to formally avoid thatDelta1 UDelta2 (oralpha&beta) entails a contradiction, since we do not intend to rule out `complementary situations'.

Posted by Tony Marmo
at 01:53 BST

Updated: Thursday, 9 September 2004 01:57 BST