Three concepts of probability

Abstract

Early probability theorists often spoke of probability in a way that was ambiguous between two different concepts of probability: a subjective concept and an objective concept. Subsequent theorists distinguished these two concepts from another, defining the subjective concept as the “uncertainty of an individual”, and the objective concept as a kind of “uncertainty in the world”. While these two concepts were distinguished from one another, some theorists believed that there was no such thing as “uncertainty in the world”, and that the only type of probability is subjective probability. The advent of quantum mechanics changed this orthodoxy. Here, for the first time—or so it has been argued—a scientific theory described the world as irreducibly probabilistic, using an objective concept of probability. While there have been authors who have levelled serious objections to this view, it has nonetheless been fairly popular. Scientific theories, however, were probabilistic long before quantum mechanics was developed. Perhaps the two most prominent cases in point were the fields of classical statistical mechanics and evolutionary theory. These two fields made use of probability theory in a way that looked objective, but often with the assumptions that the world is not irreducibly probabilistic, and that for there to be genuine “uncertainty in the world”, the world has to be irreducibly probabilistic. This caused many authors to wonder just what the probabilities in these fields could be representing. Proposed solutions to this puzzle have often been in the form of shoe-horning the probabilities of these fields into either the “uncertainty in the world” concept or the “uncertainty of an individual” concept—both with unsatisfactory consequences. In this dissertation, I investigate how we should understand the probabilities of classical statistical mechanics and evolutionary theory. To do this, I engage with arguments in the contemporary literature, and conclude that the probabilities of these two fields should be understood as neither the subjective concept of probability, nor the objective concept—standardly conceived. I argue that in order to develop an adequate account of these probabilities, we need to distinguish a third concept of objective probability that has nothing to do with “uncertainty”, whether it be in the world or of an individual. I then give an analysis of this third concept of probability. Show more