 Non-triviality: an interpretation should make non-extreme probabilities at least a conceptual possibility. For example, suppose that we interpret ‘\(P\)’ as the truth function: it assigns the value 1 to all true sentences, and 0 to all false sentences. Then trivially, all the axioms come out true, so this interpretation is admissible. We would hardly count it as an adequate interpretation of probability, however, and so we need to exclude it. It is essential to probability that, at least in principle, it can take intermediate values. All of the interpretations that we will present meet this criterion, so we will discuss it no more.