A minimal second order modal logic of natural kinds is formulated. Concepts are distinguished from properties and relations in the conceptual-logistic background of the logic through a distinction between free and bound predicate variables. Not all concepts (as indicated by free predicate variables) need have a property or relation corresponding to them (as values of bound predicate variables). Issues pertaining to identity and existence as impredicative concepts are examined and an analysis of mass terms as nominalized predicates for kinds of (...) stuff is proposed. The minimal logic is extendible through a summum genus, an infima species or a partition principle for natural kinds. (shrink)

Noam Chomsky's book on syntactic structures is a serious attempts on the part of a linguist to construct within the tradition of scientific theory-construction ...

We started from the fact that type theory, in the way it was implemented in IL, makes it costly to deal with nominalization processes. We have also argued that the type hierarchy as such doesn't play any real role in a grammar; the classification it provides for different semantic objects is already contained, in some sense, in the categorial structure of the grammar itself. So, on the basis of a theory of properties (Cocchiarella's HST*) we have tried to build a (...) language (IL*) whose syntax does not contain any explicit typing of expressions. Some of the consequences that this move brings about in the overall organization of the grammar can be summarized as follows:it allows for a simple treatment of infinitives, gerunds, factives and, in general, all those phenomena which might be analyzed as cases of nominalization;it provides a simpler and more constrained semantics than IL, since IL* doesn't go beyond second order, and its non-modal basis is axiomatizable;it suggests that the role of logical form in a theory of grammar could be that of a family of theories of semantic objects;it eliminates the extrinsic limitations of a type hierarchy on the choice of the system of syntactic categories.I think that it is interesting to notice how having an explicit semantic framework helps to provide a sense in which it is legitimate to regard the syntax of a language as ‘autonomous’. (shrink)

Whether or not the particular view of generic sentences articulated above is correct, it is quite clear that the study of generic terms and the truth-conditions of generic sentences touches on the representation of other parts of the grammar, as well as on how the world around us is reflected in language. I would hope that the problems mentioned above will highlight the relevance of semantic analysis to other apparently distinct questions, and focus attention on the relevance of linguistic problems (...) to other already established areas of inquiry. (shrink)

In any survey of recent developments in semantics, the game-theoretic approach to the semantics of both formal and of natural languages which has been developed by Jaakko Hintikka and his associates must loom large. It is indeed well known by this time that the semantics of the usual first-order logic can be spelled out in terms of games. What is not equally generally known is that this game-theoretical semantics can be augmented so as to apply also to natural languages and (...) not only to some of the artificial languages studied by logicians. The results already reached by Hintikka and his associates in this direction nevertheless show that many important phenomena of natural language can be handled in the game-theoretical framework. In this paper I shall first try to outline the basic ideas of the game-theoretical approach to semantics, then discuss briefly some problems which have so far been left untouched and thereby try to provide some new evidence for the naturalness and adequacy of a game-theoretical semantics. (shrink)

The format of this book is unusual, especially for a book about linguistics. The book is meant primarily as a research monograph aimed at linguists who have some background in formal semantics, e. g. Montague Grammar. However, I have two other audiences in mind. Linguists who have little or no experience of formal semantics, but who have worked through a basic mathematics for linguists course (e. g. using Wall, 1972, or Partee, 1978), should, perhaps with the help of a sympathetic (...) Montague gramma rian, be able to discover enough of how I have adapted some of the basic ideas in formal semantics to make the developments that I undertake in the rest of the book accessible. Logicians and computer scientists who know about model theoretic semantics and formal systems should be able to glean enough from Chapters I and II about linguistic concerns and techniques to be able to read the remainder of the book, again possibly with the help of a sympathetic Montague grammarian. However, readers should beware. Chapter II is not meant as a general introduction either to formal semantics or to linguistics and while much of the presentation there is going over ground that is already well covered in the literature, the particular formulation and the emphases are very much oriented to the developments to be undertaken later in the book. (shrink)

A more extensive discussion of certain of the more technical notions appears in my paper "On Binding" (Chomsky,; henceforth, OB). ...