Jean Paul Van Bendegem (Vrije Universiteit Brussel)The many uses of paraconsistent logic(s)
Paraconsistent logics all share the same feature: they reject one of the fundamental principles of classical logic, namely, the “ex falso sequitur quodlibet” or, in formal terms, the fact that from a contradiction p and not-p anything, q, follows. Broadly speaking, the rejection of this principle creates the possibility to reason with contradictions and inconsistencies.
In the first part of the tutorial the focus will be on the formal systems themselves, ranging from Graham Priest’s “Logic of Paradox” to adaptive logics studied by the Diderik Batens’ group.
In the second part some applications will be looked at: inconsistent truth theories (in brief, the sentence “This sentences is not true” can be interpreted as both true and false), vagueness (or the Sorites paradox), belief revision, and inconsistent mathematics (is it, e.g., possible to rehabilitate infinitesimals in analysis?).