1. That part of our knowledge which we obtain directly, supplies the premisses of that part which we obtain by argument. From these premisses we seek to justify some degree of rational belief about all sorts of conclusions. We do this by perceiving certain logical relations between the premisses and the conclusions. The kind of rational belief which we infer in this manner is termed probable (or in the limit certain), and the logical relations, by the perception of which it is obtained, we term relations of probability.

The probability of a conclusion a derived from premisses h we write a/h; and this symbol is of fundamental importance.

2. The object of the theory or logic of probability is to systematise such processes of inference. In particular it aims at elucidating rules by means of which the probabilities of different arguments can be compared. It is of great practical importance to determine which of two conclusions is on the evidence the more probable.

The most important of these rules is the principle of indifference. According to this principle we must rely upon direct judgment for discriminating between the relevant and the irrelevant parts of the evidence. We can only discard those parts of the evidence which are irrelevant by seeing that they have no logical bearing on the conclusion. The irrelevant evidence being thus discarded, the principle lays it down that if the evidence for either conclusion is the same (i.e. symmetrical), then their probabilities also are the same (i.e. equal).