Abstract:
Say that an argument is valid if we may be certain of the conclusion if the premises are accepted, that is to say, the conditional probability of the conclusion given the premises is 1. What are the formal properties of this concept of validity? By introducing various concepts from information theory, I relate the question to a problem in measure theory posed by Von Neumann in 1937, and show how Kelly's 1959 solution provides an axiomatisation of the logic of relative certainty.