In 1703 Leibniz told Bernoulli that Witt had computed annuities by the ‘usual method of equally possible cases’. Leibniz was wrong about de Witt, but his remark shows he was familiar with equipossibility. It is commonly supposed that this concept originated with Laplace around the end of the eighteenth century, but in fact it was commonplace at the beginning. Laplace did define probability as the ratio of favourable cases to the total number of equally possible cases, but so did Leibniz in 1678. The definition was in full vigour a century after Laplace and is still not dead. Here is an historical problem. How could so monstrous a definition have been so viable? Its inadequacy seems evident to us. I could quote any of a score of eminent critics. Here, for example, is Hans Reichenbach discussing a ‘principle of indifference’ in the foundation of probability:

Even workers who in our century have defended equipossibility have done so because they have philosophical views about the impossibility of producing non-circular definitions. Thus Émile Borel, to whom all probabilists owe so much, maintained that such circles were not vicious. It is an error of logicians, he thought, to try to produce a non-circular definition of probability [1909, p. 16].