May 112017

Eriksson, Lina, and Alan Hájek. What are Degrees of Belief?

2007, Studia Logica 86(2): 185-215.

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, the authors 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.

Comment: This paper is accessible to an advanced undergraduate audience in a formal philosophy course, since it provides an overview of the different accounts of the notion of degrees of belief. However, it's most adequate for graduate level, where it could be used in a formal epistemology course or in a course on the philosophy of probability.

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