A critical study of logical theories of probability

Abstract

Two things are surprising about the foundations of probability theory - the number and variety of those built and their shakiness. Someone has said that the number of theories is somewhere between two and the number of authors, and probably nearer the latter number. Every theory has been severely criticized by someone and is often criticized by different people for different reasons. As disagreement concerning the foundations has spread the superstructure has grown rapidly. Probabilistic ideas are given a theoretical role in quantum mechanics, statistical mechanics and genetics. Statistical methods have come to be used widely in many areas, for example, psychology, agriculture, economics, sociology and zoology, and have proved to be a powerful tool. The theory is used with a confidence hardly justified by the present state of the foundations for theoreticians do not agree even on the meaning of the word which they discuss.