Professor Roeper adresses a large question, whether probabilistic semantics is a kind of semantics at all. Happily, he does this via an exploration of a specific issue on which he and Professor Leblanc have done important work. That is the issue of how the relationship of logical consequence can be characterized as a relation denned in terms of probability. Let us follow him in calling a relevant relationship of the latter sort the degree of implication, and follow Professor Roeper on his quest for a satisfactory one.