Abstract: The logical probability of a proposition on another proposition is the true measure of how probable the latter makes the former. The central case of this concerns how likely some evidence makes some hypothesis postulated to explain it. This depends on how probable it is, given the hypothesis that we would find the observed evidence, whether the hypothesis fits with background evidence, how simple it is, and how narrow is its scope. (The scope of a hypothesis depends on how many big and detailed claims it makes.) The latter two a priori criteria give to every proposition an intrinsic probability (a probability on no evidence). These criteria are captured by Bayes's Theorem. A detailed analysis is provided of what it is for a hypothesis to be simple. This account of the probability of a hypothesis on evidence is extended to deal generally with the probability of one proposition on another; and in particular with our grounds for believing testimony.

Keywords: Bayes's Theorem, evidence, hypothesis, David Lewis, logical probability, Popper, simplicity, Sober, testimony,