Tjrnest Adams (1965, 1975) has advanced a probabilistic acL count of conditionals, according to which the probability of a simple English indicative conditional is the conditional probability of the consequent given the antecedent. The theory describes what English speakers assert and accept with unfailing accuracy, yet the theory has won only limited acceptance. A principal reason for this has been that the theory is so limited in its scope. While the theory does a marvelous job of accounting for how we use simple conditionals, it tells us nothing about compound conditionals or about Boolean combinations of conditionals. In view of the Lewis Triviality Theorem (which we shall discuss below), this limitation has been thought to be insuperable, so that Adams's theory has appeared to be a dead end, highly accurate in a narrowly specialized domain, but isolated from the rest of logical theory and unable to overcome that isolation. Adams's theory has also seemed to be isolated from probability theory, since it tells us nothing about the probabilities of Boolean compounds of conditionals, and the laws governing the probabilities of Boolean compounds lie at the very center of classical probability theory. Since the laws of probability cannot be meaningfully applied to the numerical values Adams assigns to conditionals, there has seemed to be little point in referring to these numerical values as "probabilities." The numerical values accurately measure the assertability and acceptability of conditionals, but they are, as Lewis (1976, p. 135) puts it, "probabilities only in name." In the present paper, I shall attempt to meet these difficulties