 The antecedent of the conditional is indeed treated as an assumption. On this conception of validity, the premises are not, primarily, treated as assumptions. We also make inferences from beliefs, including beliefs which are less than certain. Indeed, it is not immediately clear what it would be to treat a conditional, construed according to Supp, as an assumption: to assume something, as ordinarily understood, is to assume that it is true; and conditionals are not being construed as ordinary statement of fact. But we could approximate the idea of taking the premises as assumptions, by treating them, hypothetically, as certainties. Treating the premises thus would be to require of a valid argument that it preserve certainty: that there must be no probability distributions in which all the premises (conditional or otherwise) are assigned probability 1 and the conclusion is assigned probability less than 1. Call this the certainty-preservation principle (CPP).