On the thorny question of impossible antecedents

There are essentially three ways to treat conditionals with impossible antecedents in a formal framework that employs classical truth values: one can hold that such conditionals are all true, that they are all false, or that some are true while others are false. These three options will be examined under the background hypothesis that a conditional is true when its antecedent is incompatible with the negation of its consequent. It will be argued that the third option can be coherently developed by defining a suitable notion of compatibility.