Interpretations of probability

Abstract

Probability is a concept that plays a fundamental role in numerous scientific, social, and philosophical fields. However, the nature and meaning of probability remain a subject of ongoing debate. This entry delves into the various interpretations of probability, exploring their strengths and weaknesses. Beginning with Kolmogorov’s axiomatization of probability theory, the entry examines classical, logical, frequency, propensity, and subjective interpretations. Each interpretation is evaluated according to criteria such as admissibility, ascertainability, and applicability. Classical probability is seen as a powerful tool for dealing with finite sample spaces, but it faces challenges when dealing with infinite spaces and the problem of equiprobability. Logical probability, developed by Carnap, attempts to generalize classical probability by assigning unequal weights to possibilities and allowing probabilities to be computed based on evidence. However, the choice of language and confirmation function in logical probability is seen as arbitrary. Frequency interpretations identify probability with the limiting relative frequency of events in either finite or infinite reference classes. However, this interpretation faces the problems of the single case and reference class dependence. Propensity interpretations view probability as a physical disposition or tendency of a system to produce certain outcomes. This interpretation faces difficulties in defining and measuring propensities, as well as in reconciling the concept of propensity with the axioms of probability. Subjective probability equates probability with the degree of belief or credence of a rational agent. The article explores the betting interpretation, the Dutch book argument, and the derivation of probabilities from preferences. It also discusses different versions of subjectivism, including orthodox Bayesianism, regularity, and the concept of expert probabilities. The article concludes by considering future prospects for the interpretation of probability, suggesting that a synthesis of different approaches may be necessary to provide a comprehensive account of the concept. – AI-generated abstract.