Antônio Mesquita

This paper aims at clarifying the procedure of proofs by _reductio ad impossibile_ in Aristotle’s _Prior Analytics_, especially elucidating what can be taken as impossibility in such proofs. Traditional interpretation has it that the impossibility in Aristotle’s _reductio_ proofs must be a contradiction. I argue for an alternative interpretation according to which both contrarieties and contradictions are suitable as the impossibility required by the proofs in question. I also present a definition of proof by _reductio ad impossibile_ in accordance with the alternative interpretation.

This article discusses the definition of paraconsistency understood as the property of a consequence relation that does not trivialize inconsistent theories. Some logicians have argued that standard paraconsistency, the requirement of a non-explosive consequence relation, is insufficient for that purpose. In this article, we have a twofold goal. First, we offer an exposition of some attempts to strengthen standard paraconsistency in the literature. After discussing the shortcomings of those attempts, we examine the concepts of triviality in relation to which those concepts of paraconsistency are defined. Then, as our second goal, we propose an alternative definition of paraconsistency that aims to avoid the trivialization of inconsistent theories in a stricter sense.