In two recent articles, Mark Kaplan has offered a new theory of rational acceptance within the framework of Bayesian epistemology. In one of them (1981a), he discusses some of the foundational difficulties which confront both analyses of the concept of acceptance and normative theories of acceptance, and he offers an analysis of the concept. In the other (1981b), he reviews some of those considerations and also offers a normative theory of acceptance, a sophisticated elaboration and modification of the confidencethreshold theory of acceptance that is designed to adjudicate correctly between the desiderata of truth and comprehensiveness and also to be immune to the lottery paradox problem - a problem, first discussed by Henry Kyburg (1961) and Cad Hempel (1962), that seems fatal to the naive confidencethreshold view. Here, after a brief discussion of Kaplan's analysis of the concept of acceptance, I shall show that, in fact, Kaplan's revision of the confidence-threshold view is not immune to the lottery paradox problem. Central to Bayesian epistemology is the idea that a rational person's beliefs come in degrees that conform to the probability axioms. Within this framework, therefore, it is natural either to try to explicate 'accepting proposition P' as 'having a "high enough" degree of confidence in P' or to reject the idea of acceptance altogether, supposing that the relevant epistemological phenomena (e.g., confirmation of scientific hypotheses) may be better understood in terms of degrees of confidence. Richard Jeffrey (1956, 1968, 1970) has elaborated the second alternative by defending the "probabilistic theory of science," according to which scientists neither accept nor reject hypotheses, but only assign probabilities to them. Kaplan rejects the first Bayesian alternative, but, of course, does not endorse the second. One of the reasons Kaplan gives for rejecting the first alternative involves the lottery paradox. Since I shall later show that the lottery paradox presents difficulties for Kaplan's normative theory, it will be worthwhile to see here how the paradox figures