ABSTRACT
Probability is usually contrasted with certainty, and both terms apply only either to judgments or to propositions. The term “chances” is sometimes used instead of the expression “probability.” The mathematical treatment of probability is concerned almost exclusively with the measurements of probability. The probability is then expressed by means of a fraction, the denominator of which gives the total number of equally likely alternatives, while the numerator gives the number of alternatives which are favourable to the event in question. Many, and practically the most important, cases of probability cannot be calculated a priori at all; but they can be estimated by the aid of sufficiently numerous observations of the class of events contemplated. Influenced by the empirical tendencies of a scientific age, and contemptuous of the high apriori road favoured of theologians and philosophers, writers on Probability have been tempted to base all calculations of probability on frequencies.
