Towards a logic for ‘because’

Abstract

This paper explores the connective ‘because’, based on the idea that ‘C because A’ implies the acceptance/truth of the antecedent A as well as of the consequent C, and additionally that the antecedent makes a difference for the consequent. To capture this idea of difference-making a ‘relevantized’ version of the Ramsey Test for conditionals is employed that takes the antecedent to be relevant to the consequent in the following sense: a conditional is true/accepted in a state $$\sigma $$ σ just in case (i) the consequent is true/accepted when $$\sigma $$ σ is revised by the antecedent and (ii) the consequent fails to be true/accepted when $$\sigma $$ σ is revised by the antecedent’s negation. To extend this to a semantics for ‘because’, we add that (iii) the antecedent and (iv) the consequent are accepted/true in the state $$\sigma $$ σ . We get metaphysical or doxastic interpretations of these clauses, depending on what we mean by a model and a state. We introduce several semantics known from suppositional conditionals, which we reinterpret for difference-making conditionals and ‘because’. We present a minimal logic for ‘because’ sentences and show how it can be extended in ways that parallel the hierarchy of extensions of the logic of suppositional conditionals. We establish correspondence results between axioms for ‘because’ and properties of states, and prove that the specified logics are sound with respect to the semantics.