Drawing on aspects of logic, classical rhetoric, psycholinguistics, social psychology, and probability theory, this article develops the proposition-probability model (PPM) of argument structure and message acceptance in which verbal arguments are decomposed into arrays of three types of propositions: (a) product claims, (b) data supporting those claims, and (c) conditional rules specifying the relationship between the data and the claims. The propositions making up a given argument can be stated, entailed, presupposed, conversationally implicated, and/or linguistically signaled. Message acceptance is based on the formation and/or modification of beliefs corresponding to the propositions in a given argument. For purposes of making precise predictions regarding the effectiveness of various argument structures, these beliefs are represented in terms of probabilities associated with each proposition. Several postulates are derived from the PPM, and directions for future research on communication and persuasion are discussed.