The Meaning of Probability Statements

Abstract

Though the computational aspects of probability theory are well-developed, the foundations of probability theory have not been well articulated. It is unclear what sense is to be made of numeric probability. Every report of numeric probability hangs on a notion of ‘equal possibility’. Probability statements represent some knowledge of objective relations, rather than knowledge of lawful connection. There are notions which do not capture what we mean by probability in numbers: inductive conclusion by analogy is one. There is no measure of probability as psychological expectation, just as there is no measure of the intensity of sensation. Also, numeric probability cannot be based on the Principle of indifference (here called the Principle of insufficient reason). Two examples are given to reinforce these claims: the probability of a meteor striking the earth’s surface, and the probability that terrestrial elements exist on a distant star.