Topic: PARACONSISTENCY
previousCOMPLEMENTARITY 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, if alpha and beta are both theses or theorems of a theory (founded on classical logic), then alpha & beta is 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 group Delta1 of axioms of a theory T we deduce gamma, and if from another group Delta2 we deduce non-gamma, then gamma & non-gamma is also deductible in T.
Normally, our group Delta of axioms of T is finite, so that we may talk of the conjunction of its sentences instead of Delta itself. Then, if alpha and beta are respectively the conjunctions associated to Delta1 and Delta2, as above, we are looking for a theory T such that in T we may have alpha |- gamma and beta |- non-gamma, but in which gamma & non-gamma is not a theorem of T.
Therefore, our goal is to describe a way to formally avoid that Delta1 U Delta2 (or alpha&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
