Title

Interpretations of probability

Date of Completion

January 2003

Keywords

Philosophy|Statistics

Degree

Ph.D.

Abstract

In this dissertation I aim to clarify the concept of probability. There are three kinds of interpretation of probability: the objective interpretation, the logical interpretation, and the subjective interpretation. The objective interpretation understands probability as a natural property that exists independently of our minds. I will clarify and defend one version of objective probability—the propensity interpretation of probability. I reject the logical interpretation of probability that treats probability as a logical relation between evidence and hypothesis, and maintain that probability is an empirical relation. The subjective interpretation of probability, which is quite influential in recent literature, understands probability as the subject's degree of confidence (“partial belief”) that is only concerned with the states of one's mind. There are two arguments to support the claim that partial beliefs satisfy the probability measure, the Dutch Book Argument (from Ramsey and de Finetti) and the Representation Theorem (from Ramsey, Savage and Jeffrey). I argue that the subjective probability derived from both arguments is in fact the subjective estimate of objective chance, rather than subjective uncertainty of the mind assumed by subjective interpretation. The clarification of the concept of probability, I think, is of crucial importance to the studies in the philosophy of science, epistemology, and statistics. ^