Comparative Probability in Language and Action

A number of seminal figures in the history of probability, including Keynes, de Finetti, Savage, and others, held that comparative probability judgments -- as expressed, e.g., by statements of the form 'E is more likely than F' -- might be, in one way or another, more fundamental than quantitative probabilistic judgments. Such comparative judgments have mostly been studied in relation to quantitative notions, viz. representation theorem. After briefly discussing how this older work on representation theorems relates to contemporary questions in linguistic semantics about what locutions like 'E is more likely than F' mean, I will then argue that we need a better understanding of normative considerations concerning comparative probability that is, at least potentially, independent of quantitative representations.

I will present a new result -- analogous to, but weaker than, Dutch book arguments for standard quantitative probability -- characterizing exactly when an agent maintaining given comparative judgments is susceptible to a blatant kind of pragmatic incoherence. It turns out that quantitative representability (or at least 'almost representability') can be motivated in this way, without presupposing quantitative representation on the part of the agent. Finally, I will illustrate how this result might bear on the aforementioned questions in semantics, as well as more general questions about the role of qualitative probability judgments in practical reasoning.

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