For a Non-Explosive Logic of Reason. The Challenges of Contradictions and Tautologies

In the present work I investigate how to formalize the expression ‘being a reason for’, and consider some of the challenges involved. The starting ques- tion is: given two propositions p and q, what do we mean when we say that p is a reason for q? The first chapter addresses this question by providing a classification of different kinds of reasons, and by highlighting the main features of what may be called a reason relation. A binary connective ▷ is adopted to express that ‘p is a reason for q’. The second chapter is devoted to the challenges that logical impossibilities and necessities pose in the de- velopment of a logic of reason. That is, to the extent that a reason relation p ▷ q is based on the possibility of inferring (conclusively or not) q from p, classical principles involving contradictions and tautologies lead to counter- intuitive results, as considering any arbitrary contradiction as a reason for every proposition (principle of Explosion), and considering any proposition to be a reason for any arbitrary tautology. In light of this, the last chapter proposes to study the logic of reason relations in non-classical environments, adopting many-valued logics as K3, and non-explosive logics as FDE and LP, with an advantageous treatment of contradictions and tautologies, as a possible basis for the development of a proper logic of the triangle ▷.