Abstract

Bayesians hold a subjective interpretation of probability. To show that rational degrees of belief satisfy the probability axioms, Bayesians often refer to the Dutch Book Argument. Similarly, Bayesians argue that rational preference is transitive. They offer the Money-pump Argument. I show that both arguments fail for the same reason. These arguments employ a consequentialist conception of rationality. However, the basic tenet of Bayesian decision theory employs a decision-theoretic conception. The Bayesian decision-theoretic conception of rationality blocks any move to make irrationality claim on inadmissible set of degrees of belief or non-transitive preferences based upon consequentialist conception. ;Bayesians employ the consequentialist conception of rationality because they hold the dispositional theory of beliefs and desires that beliefs and desires are dispositions to act. Bayesians assume the dispositional theory because they believe that this theory allows them to measure degrees of belief and desirabilities. I show that representation theorem under the dispositional assumption does not allow us to measure the degrees of belief and desirabilities. And I also show that maximum betting quotient method does not allow us to measure degrees of belief either. We also observe that the degrees of belief defined by the dispositional theory are not the degrees of belief we want to use in the context of normative decision theory. ;I offer an operational definition of degrees of belief which is not behavioristic. We define an agent's degrees of belief in a proposition as his fair betting quotient on the proposition. And I show that logical consistency requires that a set of fair betting quotients satisfy the axioms of the probability calculus. Since Bayesians interpret probability as rational degrees of belief, our definition offers a new definition of subjective probability. I show that our definition can explain apparently objective features of probability which subjective probability based on dispositional theory could not adequately explain, such as disagreement of probability assessments. I also explain some inductive claims on unobserved instances from observed instances and the feeling varied sureness on probability assessment using our definition