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A BOOLEAN APPROACH TO EVALUATIVE ADJECTIVES AND INTENSIONALITY

A BOOLEAN APPROACH TO EVALUATIVE ADJECTIVES AND INTENSIONALITY

Saturday, February 18, 2017

Exhibit Hall (Hynes Convention Center)

A Boolean model of evaluative adjectives and a variety of intensional phenomena inspired by the model given in "Individuals Explained Away" (Keenan, 2015) is developed. An evaluative adjective like 'skillful' is non-extensional in the following sense: it is possible for the 'surgeons' and the 'pool-players' to be the same people in some situation, even though in that situation the 'skillful surgeons' and the 'skillful pool-players' may be different. By comparison, the 'female surgeons' and the 'female pool-players' would have to be the same due to the extensionality of 'female'. Keenan uses a type of non-atomic Boolean algebra to model these adjectives. Keenan's model is not applicable to other intensional contexts, such as propositional attitudes like 'John believes that ...'. If sentences S and T are logically equivalent, 'it is true that S' and 'it is true that T' must also be logically equivalent; however, it does not follow that 'John believes that S' and 'John believes that T' are logically equivalent. A model inspired by but different from Keenan (2015) is developed to handle this case and other commonly discussed examples of intensionality without introducing novel primitives such as possible worlds or propositions. Possible worlds semantics is often used by linguists in these contexts, although it usually cannot distinguish between logically equivalent sentences (such as the S and T above) due to the fact that it is typically implemented as a parameterized version of the standard extensional semantics, where denotations of words are allowed to vary within the domain of their category in a fixed model. The new approach developed here remains steadfastly in the domain of Boolean structures. This is not an arbitrary choice: expressions in most grammatical categories can be meaningfully combined with Boolean operators such as 'and' and 'neither...nor', a fact which is elegantly captured by Boolean structures and whose ubiquity suggests significance. Furthermore, Boolean structures are well-understood, which allows their use to be rigorous and supported by significant mathematical and linguistic literature. A single intensional domain is constructed for the denotations of expressions of all categories using elementary techniques from mathematical logic. Extensional properties such as reference and truth are computed 'virtually' in the newly constructed intensional domain using the mathematical notion of an embedding. It is shown that this new model can handle evaluative adjectives and a range of common intensional phenomena.