Technical Report TR-ARP-14-95

Automated Reasoning Project
Research School of Information Sciences and Engineering and Centre for Information Science Research
Australian National University

August 10, 1995

PARACONSISTENT LOGICS!

Greg Restall

Abstract In this note I respond to Hartley Slater's argument [12] to the effect that there is no such thing as paraconsistent logic. Slater's argument trades on the notion of contradictoriness in the attempt to show that the negation of paraconsistent logics is merely a subcontrary forming operator and not one which forms contradictories. I will show that Slater's argument fails, for two distinct reasons. Firstly, the argument does not consider the position of non-dialethic paraconsistency (which rejects the possible truth of any contradictions). Against this position Slater's argument has no bite at all. Secondly, while the argument does show that for dialethic paraconsistency (according to which contradictions can be true), certain other contradictions must be true, I show that this need not deter the dialethic paraconsistentist from their position.