In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it (...) is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. (shrink)

There are two broad approaches to theorizing about ontological categories. Quineans use first-order quantifiers to generalize over entities of each category, whereas type theorists use quantification on variables of different semantic types to generalize over different categories. Does anything of import turn on the difference between these approaches? If so, are there good reasons to go type-theoretic? I argue for positive answers to both questions concerning the category of propositions. I also discuss two prominent arguments for a Quinean conception of (...) propositions, concerning their role in natural language semantics and apparent quantification over propositions within natural language. It will emerge that even if these arguments are sound, there need be no deep question about Quinean propositions’ true nature, contrary to much recent work on the metaphysics of propositions. (shrink)

Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in terms of relations (using the definite description operator). We argue that there is a reason to prefer Whitehead & Russell's reduction of functions to relations over Frege's reduction of relations to functions. There is an interesting (...) system having a logic that can be properly characterized in relational but not in functional type theory. This shows that relational type theory is more general than functional type theory. The simplification offered by Church in his functional type theory is an over-simplification: one can't assimilate predication to functional application.<br>. (shrink)

The popular interpretation of token‐reflexivism states that at the level of logical form, indexicals and demonstratives are disguised descriptions that employ complex demonstratives or special quotation‐mark names involving particular tokens of the appropriate expression‐types. In this article I first demonstrate that this interpretation of token‐reflexivism is only one of many, and that it is better to think of token‐reflexivism as denoting a family of distinct theoretical frameworks. Second, I contrast two interpretations of the idea of the token‐reflexive paraphrase of an (...) indexical sentence. The utterance approach claims that token‐reflexive paraphrases involve tokens of entire utterances. The sub‐utterance approach maintains that token‐reflexive paraphrases involve tokens of the particular indexical words used in the utterance. Next, I pose a problem that shows that neither of the two approaches is correct. The problem shows that the only viable version of the token‐reflexive proposition must somehow take into account the referential intentions of the speaker of the context. Therefore I conclude the article by sketching the framework of restricted intentional token‐reflexivism. I argue that it is an attractive semantic theory of distributed utterances that, among other things, enables automatic and intentional indexicals to be distinguished. (shrink)