Abstract

Carnap and Reichenbach made extraordinary contributions to our understanding of the foundations of probability.1 Each of them provided a precise logical and mathematical analysis of probability that satisfied the formal calculus of probability. Reichenbach’s theory of probability analysed probability as the limit of relative frequency, while Carnap’s theory of probability explicated probability as a degree of logical connection. Carnap articulated his account of the foundations of probability by insisting that there were two concepts of probability, his own, probability one, and the other, including Reichenbach’s, probability two. Probability one is a logical conception, and the truth of the probability statements is a consequence of the definition of a measure function. Probability two is a factual conception, and the truth of the probability statements is a consequence of the existence of limits of relative frequencies. Explained in this way, the two accounts are not competitive. In fact, there is no inconsistency between the two accounts. They offer us two different interpretations of the calculus of probability