B. R. George

The notions of finite and infinite second-order characterizability of cardinal and ordinal numbers are developed. Several known results for the case of finite characterizability are extended to infinite characterizability, and investigations of the second-order theory of ordinals lead to some observations about the Fraenkel-Carnap question for well-orders and about the relationship between ordinal characterizability and ordinal arithmetic. The broader significance of cardinal characterizability and the relationships between different notions of characterizability are also discussed.

This paper considers two of the most prominent kinds of evidence that have been used to argue that certain embedded questions receive weakly exhaustive interpretations. The first kind is exemplified by judgments of consistency for declarative sentences that attribute knowledge of a wh-question and ignorance of the negation of that question to the same person, and the second concerns asymmetries between the role of positive and negative information in validating question-embedding surprise ascriptions, and similar judgments for other attitudes. I argue that neither type suffices to show weak exhaustivity. The first can be analyzed in terms of strong exhaustivity in combination with domain restriction effects, while the second can be analyzed in terms of a mention-some interpretation. These kinds of evidence have served as the empirical basis for many claims about weakly exhaustive readings, so the observation that they are unreliable calls into questions a large body of established work on the semantics of question embedding

This paper discusses some formal properties of trivalent approaches to presupposition projection, and in particular of the middle Kleene system of Peters (1977) and Krahmer (1998). After exploring the relationship between trivalent truth-functional accounts and dynamic accounts in the tradition of Heim (1983), I show how the middle Kleene trivalent account can be formulated in a way which shows that it meets the explanatory challenge of Schlenker (2006, 2008a,b), and provide some results relating to the application of the middle Kleene approach to generalised quantifiers