Unary Probabilistic Semantics

Writers in Popper’s debt generally use binary probability functions when doing probabilistic semantics. I recount here results lately obtained when unary functions are used instead. I first describe the formal language (call it L) that I work with, provide a probabilistic semantics for it, and attend to such matters as strong soundness and strong completeness. This done I consider the relationship between unary probability functions and truth-value ones, and I demonstrate that and why unary probability theory is but a generalization of truth-value-theory. Lastly I study what Charles G. Morgan and I call assumption sets, here the assumption sets of unary probability functions. The unary probability functions in this text are in good standing: they are the probability functions in Chapter I of Kolmogorov (1933), with statements substituting for sets and provision made for the probabilities of quantifications.