 First consider classically valid (that is, necessarily truth-preserving) arguments which don’t involve conditionals. We use them in arguing from contingent premises about which we are often less than completely certain. The question arises: how certain can we be of the conclusion of the argument, given that we think, but are not sure, that the premises are true? Call the improbability of a statement one minus its probability. Adams showed this: if (and only if) an argument is valid, then in no probability distribution does the improbability of its conclusion exceed the sum of the improbabilities of its premises. Call this the Probability Preservation Principle (PPP).