Desire-as-belief implies opinionation or indifference

Abstract

Rationalizations of deliberation often make reference to two kinds of mental state, which we call belief and desire. It is worth asking whether these kinds are necessarily distinct, or whether it might be possible to construe desire as belief of a certain sort belief, say, about what would be good. An expected value theory formalizes our notions of belief and desire, treating each as a matter of degree. In this context the thesis that desire is belief might amount to the claim that the degree to which an agent desires any proposition A equals the degree to which the agent believes the proposition that A would be good. We shall write this latter proposition 'A' (pronounced 'A halo'). The Desire-as-Belief Thesis states, then, that to each proposition A there corresponds another proposition A0, where the probability of A0 equals the expected value of A. In 'Desire as Belief', David Lewis presented an argument against this anti-Humean proposal.1 Lewis proved that, on pain of triviality, the Desire-as-Belief Thesis cannot be added to the axioms of expected value theory. Our aim in this paper is to present a simpler proof of Lewis's result. The proof we shall give makes clear that the result is a purely synchronic one that depends in no way on the properties of Jeffrey conditionalization or any other revision method. We shall start by presenting a version of expected value theory like the one developed by Richard Jeffrey [2]. Let X be a Boolean algebra of propositions, with greatest and least elements T and F. An expected value model on X is a set .NM of pairs (P, V), where each P is a probability function over X, and each V is an expected value function defined over X {F}. Each pair (P, V) represents a potential state of belief and desire for the agent. The pairs must satisfy the following four axioms: