principle of insufficient reason the principle that if there is no sufficient reason (or explanation) for something’s being (the case), then it will not be (the case). Since the rise of modern probability theory, many have identified the principle of insufficient reason with the principle of indifference (a rule for assigning a probability to an event based on ‘parity of reasons’). The two principles are closely related, but it is illuminating historically and logically to view the principle of insufficient reason as the general principle stated above (which is related to the principle of sufficient reason) and to view the principle of indifference as a special case of the principle of insufficient reason applying to probabilities. As Mach noted, the principle of insufficient reason, thus conceived, was used by Archimedes to argue that a lever with equal weights at equal distances from a central fulcrum would not move, since if there is no sufficient reason why it should move one way or the other, it would not move one way or the other. Philosophers from Anaximander to Leibniz used the same principle to argue for various metaphysical theses. The principle of indifference can be seen to be a special case of this principle of insufficient reason applying to probabilities, if one reads the principle of indifference as follows: when there are N mutually exclusive and exhaustive events and there is no sufficient reason to believe that any one of them is more probable than any other, then no one of them is more probable than any other (they are equiprobable). The idea of ‘parity of reasons’ associated with the principle of indifference is, in such manner, related to the idea that there is no sufficient reason for favoring one outcome over another. This is significant because the principle of insufficient reason is logically equivalent to the more familiar principle of sufficient reason (if something is [the case], then there is a sufficient reason for its being [the case]) – which means that the principle of indifference is a logical consequence of the principle of sufficient reason. If this is so, we can understand why so many were inclined to believe the principle of indifference was an a priori truth about probabilities, since it was an application to probabilities of that most fundamental of all alleged a priori principles of reasoning, the principle of sufficient reason. Nor should it surprise us that the alleged a priori truth of the principle of indifference was as controversial in probability theory as was the alleged a priori truth of the principle of sufficient reason in philosophy generally.
See also PRINCIPLES OF INDIFFERENCE , PROBABILITY. R.H.K.