Comparativism and the Measurement of Partial Belief
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Comparativism and the Measurement of Partial Belief Edward Elliott1 Received: 7 July 2019 / Accepted: 14 September 2020 © The Author(s) 2020
Abstract According to comparativism, degrees of belief are reducible to a system of purely ordinal comparisons of relative confidence. (For example, being more confident that P than that Q, or being equally confident that P and that Q.) In this paper, I raise several general challenges for comparativism, relating to (1) its capacity to illuminate apparently meaningful claims regarding intervals and ratios of strengths of belief, (2) its capacity to draw enough intuitively meaningful and theoretically relevant distinctions between doxastic states, and (3) its capacity to handle common instances of irrationality.
1 Introduction Meet Sally. Like the rest of us, Sally has beliefs, broadly construed—there’s some way she takes the world to be that’s generally responsive to her evidence, and which along with her desires guides her behaviour. This paper concerns what Sally’s beliefs might be like at the most fundamental level, and the relationship between the different types of beliefs she might be taken to have. To get the ball rolling, I’m going to assume that Sally has at least two kinds of belief: partial and comparative. With respect to the former, Sally is, for instance, quite certain there’s an external world, uncertain about the consequences of global warming, but doubtful they’ll be good. These are attitudes directed towards individual propositions, each coming with some (possibly vague or imprecise) degree of strength that can at least sometimes be represented numerically. Her comparative beliefs, on the other hand, relate pairs of propositions, and do not come in degrees. Sally is, for example, more confident that she’ll find good coffee in Melbourne than she will in Sydney, and indeed just as confident that she’ll find good coffee in Sydney as that she’ll win the lottery next week. If there’s also a sense in which Sally has ‘all-or-nothing’ beliefs, then we’ll assume that these derive in one way or another from the facts about her partial and/or comparative beliefs. * Edward Elliott [email protected] 1
School of Philosophy, Religion and History of Science, University of Leeds, Leeds, UK
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Taking all that for granted, it’s natural to wonder about the relationship between Sally’s partial and comparative beliefs. It’s clear enough they’re closely related: if Sally is x% confident that P and y% confident that Q, then she’s more confident that P than she is that Q just in case x > y ; and in the other direction, if Sally just as confident that P as she is that Q, then she’s x% confident that P just in case she’s x% confident that Q. Moreover, these conditionals have a certain feel of apriority about them, so it’s reasonable to think they’re underwritten by some interesting conceptual or metaphysical connection. According to comparativism, the facts about Sally’s partial beliefs supervene on, and indeed hold in virtue of, the fac
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