What is a Conditional?

Abstract This paper examines the nature of conditionals in thought, natural language, and logic. It argues that conditionals are fundamentally concerned with possibilities rather than merely with truth values, and distinguishes several types of conditional according to the relation between antecedent and consequent. Particular attention is given to implicative and concessive conditionals. An implicative conditional is characterized as one in which the antecedent is taken to imply the consequent, whereas in a concessive conditional the consequent holds despite the antecedent providing a reason for its falsity. A modal definition of the implicative conditional is proposed according to which the conjunction of the antecedent with the negation of the consequent is impossible, while the contingency of both antecedent and consequent is treated as a presupposition. This account is compared with material implication, C. I. Lewis’s strict implication, and Pizzi’s consequential implication. A logical definition is also proposed for the concessive conditional according to which the antecedent is contingent, the consequent necessary, and a new operator symbolizes the antecedent as a reason for the falsity of the consequent. The paper also examines the negation of conditionals and squares of opposition generated by relations among implicative and concessive conditionals and their negation. Finally, it briefly discusses three further types of non-implicative natural-language conditionals and argues that logical systems should be assessed partly by how adequately their conditional operators capture the relations of implication and consequence found in natural reasoning.