1 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.)
6 * Generalized quantifiers are a special case of operating on continuations. [[!wikipedia Richard_Montague]] analyzed all NPs, including, e.g., proper names, as sets of properties.
7 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
8 one syntactic category (NPs), but a more systematic approach would continuize uniformly throughout the grammar.
9 See <http://dx.doi.org/10.1023/A:1022183511876>.
11 * (Chris: fill in other applications...)
13 * expressives -- at the end of the seminar we gave a demonstration of modeling [[damn]] using continuations...see the [summary](/damn) for more explanation and elaboration
18 * 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.
20 * those issues may bear on Russell's Gray's Elegy argument in "On Denoting"
22 * 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."
24 * 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
26 * the semantics for mutation will enable us to make sense of a difference between numerical and qualitative identity---for purely mathematical objects!
28 * 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