A puzzle about conditionals

This paper examines a neglected puzzle about conditionals: namely, the fact that each of a pair of conditionals with incompatible consequents, [A>C] and [B>C*], may be properly affirmable in circumstances when one does not believe, and is not entitled to infer, the denial of the conjunction of the antecedents, i.e. [¬(A & B)]. The puzzle is why this should be so, since the conditionals entail the denial of the conjunction on the popular accounts of conditionals. I present a pragmatic solution which distinguishes between two levels of affirmability.