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Abstract: In my talk I will present a new semantics for conditionals according to which “if A then B“ is true in case (i) the corresponding Stalnaker-Lewis conditional is true, and (ii) the antecedent A makes a difference to the consequent B. The novely of the semantics consists in the analysis of (ii), which is made precise as: the distance between the closest B-worlds and the closest non-B-worlds is smaller than the distance between the closest A&B-worlds and the closest A&non-B-worlds. I will explain how the required ordering of distances between worlds can be captured in non-numerical terms, what the logic is like that is sound and complete with respect to the semantics, what a probabilistic version of the semantics looks like, and why the system is to be preferred over other recent semantics and logics of conditionals that analyse (ii) above differently.

(This is joint work with Hans Rott.)