How many meanings for ‘may’? The case for modal polysemy

The standard Kratzerian analysis of modal auxiliaries, such as ‘may’ and ‘can’, takes them to be univocal and context-sensitive. Our first aim is to argue for an alternative view, on which such expressions are polysemous. Our second aim is to thereby shed light on the distinction between semantic context-sensitivity and polysemy. To achieve these aims, we examine the mechanisms of polysemy and context-sensitivity and provide criteria with which they can be held apart. We apply the criteria to modal auxiliaries and show that the default hypothesis should be that they are polysemous, and not merely context-sensitive. We then respond to arguments against modal ambiguity (and thus against polysemy). Finally, we show why modal polysemy has significant philosophical implications.

Updating on the Credences of Others: Disagreement, Agreement, and Synergy

We introduce a family of rules for adjusting one’s credences in response to learning the credences of others. These rules have a number of desirable features. 1. They yield the posterior credences that would result from updating by standard Bayesian conditionalization on one’s peers’ reported credences if one’s likelihood function takes a particular simple form. 2. In the simplest form, they are symmetric among the agents in the group. 3. They map neatly onto the familiar Condorcet voting results. 4. They preserve shared agreement about independence in a wide range of cases. 5. They commute with conditionalization and with multiple peer updates. Importantly, these rules have a surprising property that we call synergy — peer testimony of credences can provide mutually supporting evidence raising an individual’s credence higher than any peer’s initial prior report. At first, this may seem to be a strike against them. We argue, however, that synergy is actually a desirable feature and the failure of other updating rules to yield synergy is a strike against them.

Counting as a Type of Measuring

There may be two and a half bagels on the table. When there are two and a half, it is false that there are exactly two. As obvious as these claims are, they can’t be accounted for on the most straightforward and familiar views of counting and the semantics of number words. I develop a view on which counting is a type of measuring. In particular, counting involves a specific measure function. I then analyze that function and show how it can account for the cases in which counting is sensitive to partiality, e.g. partial bagels.