Abstract

In this work, five different interpretations of "probability" are analyzed: the classical, logical, subjective, relative frequency, and propensity interpretations. The objective is to determine which of these interpretations is most suitable for probability applications in the physical and biological sciences. The first state of this analysis involves evaluating the different interpretations with respect to the probability calculus. The objective at this point is not to reject any interpretations outright, but rather to keep in mind any difficulties in adherence to the calculus when evaluating these interpretations in later chapters. The second stage involves defending the need for an "objectivity criterion" and evaluating the various interpretations of "probability" with respect to this criterion. This "objectivity criterion" states that an adequate analysis of "probability" should result in probability statements that are true or false in virtue of the way the world is, independently of anyone's state of knowledge or beliefs about the probabilities in question. Based on this criterion, the classical, logical, and subjective interpretations are rejected. The third stage involves evaluating the relative frequency interpretation in greater detail. Both the actual relative frequency interpretation and the hypothetical relative frequency interpretation are evaluated. The actual relative frequency interpretation is found to be a promising candidate for providing an adequate analysis of "probability" for the physical and biological sciences. The fourth stage involves a detailed evaluation of the propensity interpretation. The propensity interpretation is shown to be in a weaker epistemological position than the relative frequency interpretation and to stem largely from misguided motivations concerning the importance of the single case in scientific applications and the nature of scientific explanation. Ultimately, it is concluded that the traditional actual relative frequency interpretation provides the best analysis of "probability" for applications in the physical and biological sciences