What Are Degrees of Belief?

Abstract

Probabilism is committed to two theses: 1) Opinion comes in degrees-call them degrees of belief, or credences.2) The degrees of belief of a rational agent obey the probability calculus.Correspondingly, a natural way to argue for probabilism is: i) to give an account of what degrees of belief are, and then ii) to show that those things should be probabilities, on pain of irrationality.Most of the action in the literature concerns stage ii). Assuming that stage i) has been adequately discharged, various authors move on to stage ii) with varied and ingenious arguments. But an unsatisfactory response at stage i) clearly undermines any gains that might be accrued at stage ii) as far as probabilism is concerned: if those things are not degrees of belief, then it is irrelevant to probabilism whether they should be probabilities or not.In this paper we scrutinize the state of play regarding stage i). We critically examine several of the leading accounts of degrees of belief: reducing them to corresponding betting behavior (de Finetti); measuring them by that behavior (Jeffrey); and analyzing them in terms of preferences and their role in decision-making more generally (Ramsey, Lewis, Maher). We argue that the accounts fail, and so they are unfit to subserve arguments for probabilism. We conclude more positively: 'degree of belief' should be taken as a primitive concept that forms the basis of our best theory of rational belief and decision: probabilism.Probabilism is committed to two theses: 1) Opinion comes in degrees-call them degrees of belief, or credences.2) The degrees of belief of a rational agent obey the probability calculus.Correspondingly, a natural way to argue for probabilism is: i) to give an account of what degrees of belief are, and then ii) to show that those things should be probabilities, on pain of irrationality. Special Issue Formal Epistemology I. Edited by Branden Fitelson

Belief and Degrees of Belief

“…In section 3.1 primitivism seemed to be the only plausible game in town. In the present case "going hypothetical" (Eriksson & Hájek 2007) is more promising: the agent's degree of disbelief in A is the number of information sources saying A that it would take for her to give up her disbelief that A, if those sources were independent and minimally positively reliable. Now we are in the position to say why degrees of disbelief should obey the ranking calculus.…”

“…The latter are operationally defined and observable. The former are unobservable, theoretical entities that, following Eriksson & Hájek (2007), we should take as primitive.…”

A scoping inquiry into the potential contribution of Subjective Probability Theory, Dempster–Shafer Theory and Possibility Theory in accommodating degrees of belief in traveller behaviour research

“…The concept of subjective probability was originally proposed by Ramsay (1931) and further developed by Savage (1954). The entire theory of subjective probability is established around the notion of 'degree of belief' (Eriksson and Hάjek 2007). The operational explanation of subjective probability is "the probability of an uncertain event is the quantified measure of one's belief or confidence in the outcome, according to their state of knowledge at the time it is assessed" (Vick 2002, p.3).…”

Don’t Know, Don’t Kill: Moral Ignorance, Culpability, and Caution

“…27 Except insofar as we struggle to come up with a compelling account of what talk of degrees of beliefs amounts to. See, for example, Eriksson and Hájek (2007). Don't Know, Don't Kill: moral ignorance, culpability, and caution 79…”