We mentioned a number of linguistic and philosophical applications of the tools that we'd be helping you learn in the seminar. (We really do mean "helping you learn," not "teaching you." You'll need to aggressively browse and experiment with the material yourself, or nothing we do in a few two-hour sessions will succeed in inducing mastery of it.)

## From linguistics

• Generalized quantifiers are a special case of operating on continuations. Richard Montague analyzed all NPs, including, e.g., proper names, as sets of properties. This gives names and quantificational NPs the same semantic type, which explain why we can coordinate them (John and everyone, Mary or some graduate student). So instead of thinking of a name as refering to an individual, which then serves as the argument to a verb phrase, in the Generalized Quantifier conception, the name denotes a higher-order function that takes the verb phrase (its continuation) as an argument. Montague only continuized one syntactic category (NPs), but a more systematic approach would continuize uniformly throughout the grammar. See a paper by me (CB) for detailed discussion.

• Computing the meanings of expressions involving focus. Consider the difference in meaning between John only drinks Perrier, with main sentence accent on Perrier, versus John only DRINKs Perrier. Mats Rooth, in his 1995 dissertation, showed how to describe these meanings by having the focussed expression contribute a normal denotation and a focus alternative set denotation. The focus alternative sets had to be propagated upwards through the compositional semantics. One way to implement this idea is by means of delimited continuations, making use of operators similar to fcontrol and run proposed for a scheme-like language by Sitaram and other computer scienticsts. See another paper by CB.

• Generalized coordination, as proposed by Partee and Rooth in highly influential papers in the 1980s. The idea is that the way that John saw Mary or Bill comes to mean John saw Mary or John saw Bill is by cloning the context of the direct object, feeding one of the clones Mary, feeding the other clone Bill, and disjoining the resulting propositions. See either of the two papers mentioned in the previous two items for discussion.

• Anaphora, as in Everyone's mother loves him (which says that for every person x, x's mother loves x). A paper by CB and Chung-chieh Shan discusses an implementation in terms of delimited continuations. See also a different implementation in work of Philippe de Groote.

• As suggested in class, it is possible to think of the side effects of expressives such as damn in John read the damn book in terms of control operators such as call/cc in Scheme. At the end of the seminar we gave a demonstration of modeling damn using continuations...see the summary for more explanation and elaboration. In the meantime, you can read a new paper about this idea here---comments welcome.

## From philosophy

• the natural semantics for positive free logic is thought by some to have objectionable ontological commitments; Jim says that thought turns on not understanding the notion of a "union type", and conflating the folk notion of "naming" with the technical notion of semantic value. We'll discuss this in due course.

• those issues may bear on Russell's Gray's Elegy argument in "On Denoting"

• and on discussion of the difference between the meaning of "is beautiful" and "beauty," and the difference between the meaning of "that snow is white" and "the proposition that snow is white."

• the apparatus of monads, and techniques for statically representing the semantics of an imperatival language quite generally, are explicitly or implicitly invoked in dynamic semantics

• the semantics for mutation will enable us to make sense of a difference between numerical and qualitative identity---for purely mathematical objects!

• issues in that same neighborhood will help us better understand proposals like Kit Fine's that semantics is essentially coordinated, and that R a a and R a b can differ in interpretation even when a and b don't