According to the Laplacian definition, the probability of an event is the ratio of “favorable” cases to possible cases. It is obvious that the definition presupposes the equal probability of the possible cases; and to make the definition of probability depend upon the conception of equal probability has the appearance, at least, of a vicious circle. Moreover it is hard to see how we can assure ourselves that each possible case is really no more and no less probable than any other. But even if we define probability as the relative frequency of occurrence of events under a given set of conditions, or of true conclusions from premises of a given type, we still require the conception of equal probability, unless indeed we choose to renounce entirely the mathematical expression and calculation of probabilities.