This extended collection of papers is the result of putting recent ideas on quantification to work on a wide variety of languages.

This is a collection of papers that helped shape the field of formal semantics in linguistics.

The problem discussed here is to find a basis for a uniform treatment of the relation between pronouns and their antecedents, taking into account both linguists' and philosophers' approaches. The two main candidates would appear to be the linguists' notion of coreference and the philosophers' notion of pronouns as variables. The notion of coreference can be extended to many but not all cases where the antecedent is non-referential. The pronouns-as-variables approach appears to come closer to full generality, but there are (...) some examples of pronouns of laziness which appear to resist either of the two approaches. (shrink)

Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics (...) includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language. (shrink)

Formal semantics is an approach to SEMANTICS1, the study of meaning, with roots in logic, the philosophy of language, and linguistics, and since the 1980’s a core area of linguistic theory. Characteristics of formal semantics to be treated in this article include the following: Formal semanticists treat meaning as mind-independent (though abstract), contrasting with the view of meanings as concepts “in the head” (see I-LANGUAGE AND E-LANGUAGE and MEANING EXTERNALISM AND INTERNALISM); formal semanticists distinguish semantics from knowledge of semantics (Lewis (...) 1975, Cresswell 1978), which has consequences for the notion of semantic COMPETENCE. A central part of the meaning of a sentence on this approach is its TRUTH CONDITIONS, and most although not all formal semantics is model-theoretic, relating linguistic expressions to model-theoretically constructed semantic values cast in terms of truth, REFERENCE, and possible worlds. This sets formal semantics apart from approaches which view semantics as relating a sentence just to a representation on another linguistic “level” (LOGICAL FORM) or a representation in an innate LANGUAGE OF THOUGHT. The formal semanticist could accept such representations as an aspect of semantics but would insist on asking what the model-theoretic semantic interpretation of the given representationlanguage is (Lewis 1970). Formal semantics is centrally concerned with COMPOSITIONALITY at the SYNTAX-SEMANTICS INTERFACE, how the meanings of larger constituents are built up from the meanings of their parts on the basis of their syntactic structure, and with the relation between compositional SENTENCE MEANING and meaning in discourse. (shrink)

Formal semantics and pragmatics as they have developed since the late 1960's have been shaped by fruitful interdisciplinary collaboration among linguists, philosophers, and logicians, among others, and in turn have had noticeable effects on developments in syntax, philosophy of language, computational linguistics, and cognitive science.In this paper I describe the environment in which formal semantics was born and took root, highlighting the differences in ways of thinking about natural language semantics in linguistics and in philosophy and logic. With Montague as (...) a central but not solo player in the story, I reflect on crucial developments in the 1960's and 70's in linguistics and philosophy, and the growth of formal semantics and formal pragmatics from there. I discuss innovations, key players, and leading ideas that shaped the development of formal semantics and its relation to syntax, to pragmatics, and to the philosophy of language in its early years, and some central aspects of its early impact on those fields. (shrink)

The goal of this paper is to argue for the fruitfulness for linguistic theory of an approach to semantics that has been developed primarily by logicians and philosophers. That the theory of possible worlds semantics has been extremely fruitful for logic and philosophy is widely if not universally accepted, and I will not try to convince remaining skeptics on that score. But the goals of linguistics are sufficiently different from those of philosophy and logic that there are independent and highly (...) reasonable grounds for skepticism about the appropriateness of such a theory for linguistics, and I will address what seem to me the most important of these in addition to offering positive evidence in favor of such an approach to semantics. (shrink)

In a provocative book, Andrew Carstairs- McCarthy argues that the apparently universal distinction in human languages between sentences and noun phrases cannot be assumed to be inevitable for languages with the expressive power of human languages, but needs explaining. His work suggests, but does not explicitly state, that there is also no conceptual necessity for the distinction between basic types e and t, a distinction argued for by Frege and carried into formal semantics through the work of Montague. Pragmatic distinctions (...) among various kinds of speech acts, including asserting, questioning, commanding, and pointing things out are assumed in Carstairs- McCarthy ’s work, as are expressions of functional types; what is questioned is whether a syntacticized sentence-NP distinction is essential. (shrink)

“Symmetrical predicates” have distinctive linguistic properties in many languages. But the concept of “symmetry” merits closer examination. Consider the surprising claim by the psychologist Amos Tversky (1977) that the concept ‘similar’, a standard example of a symmetrical predicate, is in fact not symmetrical. Tversky’s evidence includes the fact that experimental subjects generally rate (1a) as holding to a higher degree than (1b). (1) a. North Korea is similar to Red China. b. Red China is similar to North Korea.

Yang (2004) observes that in Mandarin, an initial possessor phrase (PossessorP) may be followed by a bare noun as in (1), or by a possessee phrase that can be headed by a numeral and classifier, [Numeral + CL + N], as in (2) or by a demonstrative, [Dem + (Numeral) + CL + N] as in (3). (In all the examples in this section, we begin with Yang’s own initial glosses and translations3. The interpretation of the examples will be probed (...) after they have been presented.). (shrink)

For me the adventure began just 50 years ago, here at MIT in 1961. The Chomskian revolution had just begun, and Noam Chomsky and Morris Halle had just opened up a PhD program in Linguistics, and I came in the first class. I want to start by thanking Chomsky and Halle for building that program, and I thank MIT and the Research Laboratory of Electronics for supporting it. I’m indebted to Chomsky for revolutionizing the field of linguistics and making it (...) into a field whose excitement has never waned. Chomsky redefined linguistics as the study of human linguistic competence, making linguistics one of the early pillars of cognitive science. (shrink)

Does context and context-dependence belong to the research agenda of semantics - and, specifically, of formal semantics? Not so long ago many linguists and philosophers would probably have given a negative answer to the question. However, recent developments in formal semantics have indicated that analyzing natural language semantics without a thorough accommodation of context-dependence is next to impossible. The classification of the ways in which context and context-dependence enter semantic analysis, though, is still a matter of much controversy and some (...) of these disputes are ventilated in the present collection. This book is not only a collection of papers addressing context-dependence and methods for dealing with it: it also records comments to the papers and the authors' replies to the comments. In this way, the contributions themselves are contextually dependent. In view of the fact that the contributors to the volume are such key figures in contemporary formal semantics as Hans Kamp, Barbara Partee, Reinhard Muskens, Nicholas Asher, Manfred Krifka, Jaroslav Peregrin and many others, the book represents a quite unique inquiry into the current activities on the semantics side of the semantics/pragmatics boundary. (shrink)

In the history of formal semantics, the successful joining of linguistic and philosophical work brought with it some difficult foundational questions concerning the nature of meaning and the nature of knowledge of language in the domain of semantics: questions in part about “what’s in the head” of a competent language-user. This paper, part of a project on the history of formal semantics, revisits the central issues of (Partee, 1979) in a historical context, as a clash between two traditions, Fregean and (...) Chomskyan, a clash that accompanied early work combining Montague’s semantics with Chomskyan syntax. Recent advances in philosophy of mind (from, e.g., Stalnaker and Burge) go a long way towards changing the framework of arguments about “psychological reality” and “competence”, challenging the suppositions on which the original dichotomy rested, thus largely defusing the tension. (shrink)

David K. Lewis was a central player in the golden age of linguistics‐philosophy interaction, and he and his work were important parts of what made that age golden. This chapter discusses some of Lewis's ideas that have been most important for linguists, especially but not only for formal semanticists, and some of the influence his ideas have had. It provides Lewis's distinction between a language as an abstract object and the use of a language by a community, and its importance (...) for defending the non‐psychologistic foundations of formal semantics. The chapter discusses some issues of importance to linguists connected with Lewis's work on possible worlds, modal realism, conditionals, and counterpart theory in brief. It highlights a number of specific ideas that have influenced linguists. The chapter presents David's important role in helping linguists and philosophers understand each other and cooperate in working on the syntax and semantics of natural languages. (shrink)

Montague was born September 20, 1930 in Stockton, California and died March 7, 1971 in Los Angeles. At St. Mary’s High School in Stockton he studied Latin and Ancient Greek. After a year at Stockton Junior College studying journalism, he entered the University of California, Berkeley in 1948, and studied mathematics, philosophy, and Semitic languages, graduating with an A.B. in Philosophy in 1950. He continued graduate work at Berkeley in all three areas, especially with Walter Joseph Fischel in Arabic, with (...) Paul Marhenke and Benson Mates in philosophy, and with Alfred Tarski in mathematics and philosophy, receiving an M.A. in mathematics in 1953 and his Ph.D. in Philosophy in 1957. Alfred Tarski, one of the pioneers, with Frege and Carnap, in the model-theoretic semantics of logic, was Montague’s main influence and directed his dissertation (Montague 1957). Montague taught in the UCLA Philosophy Department from 1955 until his death. (shrink)

Williams (1983) andPartee(1986a) argued that specificational sentences like (2) result from “inversion around the copula”: that NP1 is a predicate (type ) and NP2 is the subject, a referential expression of type e. Partee(1999) argued that such an analysis is right for Russian, citing arguments from Padučeva & Uspenskij (1979) that NP2 is the subject of sentence (1). But in that paper I argued that differences between Russian and English suggest that in English there is no such inversion, contra Williams (...) (1983) and Partee (1986a): the subject of (2) is NP1, and both NPs are of type e, but with NP1 less referential than NP2, perhaps “attributive”. (shrink)

The Russian Genitive of Negation construction (Gen Neg) involves case alternation between Genitive and the two structural cases, Nominative and Accusative.1 The factors governing the alternation have been a matter of debate for many decades, and there is a huge literature. Here we focus on one central issue and its theoretical ramifications. The theoretical issue is the following. The same truth-conditional content can often be structured in more than one way; we believe that there is a distinction between choices in (...) how to structure a situation to be described, and choices in how to structure a sentence describing the (already structured) situation. The distinction may not always be sharp, and the term Information Structure may perhaps cover both, but we believe that the distinction is important and needs closer attention. Babby (1980), in a masterful work on the Russian Genitive of Negation, argued that the choice depended principally on Theme-Rheme structure; after initially following Babby (Borschev & Partee 1998), we later argued (Borschev & Partee 2002a,b) that the choice reflects not Theme-Rheme structure but a structuring of the described situation which we call Perspectival Structure. Here we briefly review the phenomenon, Babby’s Theme-Rheme-based analysis, and our arguments for a different analysis. We then consider Hanging Topics, partitive Genitives, and broader licensing conditions of Genitive case, raising the possibility that our counterexamples to Babby’s use of Theme-Rheme structure might be explained away as examples involving Hanging Topics rather than (Praguian) Themes. We argue against that idea as well, but leave open the possibility that our Perspectival Structure may eventually be construable as a kind of information structure itself, if that notion can include some kinds of structuring of the situation as well as of the discourse. (shrink)

Plurals had a slow start in the history of formal semantics; a significant explosion of innovations didn’t come until the 1980s. In this paper, I offer a picture of developments by noting not only important achievements but also reflecting on the state of thinking about plurals at various periods—what issues or phenomena were not even noticed, what puzzles had started to get attention, and what innovations made the biggest changes in how people thought about plurals. I divide the epochs roughly (...) into decades: before formal semantics ; the first decade of formal semantics—the 1970s, with early work by Montague and Bennett and landmark work on bare plurals by Carlson; the 1980s, when work by Link, Scha, Krifka, Landman, Roberts, and others significantly changed the landscape; and the 1990s, where I mention some key work by Lasersohn and Schwarzschild and stop there, although there was much more work in the 1990s. I don’t discuss the twenty-first century at all because it’s not very historical yet. (shrink)