On the characterization of alternatives

We present an argument for revising the theory of alternatives for Scalar Implicatures and for Association with Focus. We argue that in both cases the alternatives are determined in the same way, as a contextual restriction of the focus value of the sentence, which, in turn, is defined in structure-sensitive terms. We provide evidence that contextual restriction is subject to a constraint that prevents it from discriminating between alternatives when they stand in a particular logical relationship with the assertion or the prejacent, a relationship that we refer to as symmetry. Due to this constraint on contextual restriction, discriminating between alternatives in cases of symmetry becomes the task of focus values. This conclusion is incompatible with standard type-theoretic definitions of focus values, motivating our structure-sensitive definition instead.