When I started to read this book I was excited because I knew that a study of quantifiers may throw light on our linguistic and cognitive abilities, cf. (Brooks & Braine 1996). Thus, I thought, I'll learn not only about a specialized subject of semantics but a more general subject which has something to do with our "mental spaces." Perhaps not surprisingly, the book proved itself to be decidedly on the technical (logical) side. Unlike another book which I quite liked (Bach et al. 1995), this one did not really care much about the linguistic or cognitive motivations. (Fortunately, there are a number of exceptions to this generalization, to be noted below.) In (Bach et al. 1995) a majority of the papers elucidate assorted questions of language typology and syntactic/morphological variation. (The languages discussed include English, Dutch, Italian, Hindi, etc.) The present volume is not for the weak-kneed; it requires close familiarity with the worst of mathematical logic.
The predecessor of this book is a workshop on "Generalized Quantifiers" at the Institute for Logic, Language and Computation (ILLC), Amsterdam, circa 1990. The list of contributions (reproduced below) clearly demonstrates that Dutch authors are in clear majority, perhaps substantiating B.H. Partee's well-known observation, found in (Gamut 1991), that "the Dutch not only have what must be the greatest number of linguists per capita in the world, they also have a very long and rich tradition of combining linguistics, logic, and philosophy of language."
1. Basic quantifier theory, J. van der Does & J. van EijckAs usual with such edited volumes, the contributions are of differing quality and relevance. For instance, Westerstahl's paper (Chap. 16) is a technical note on finite model theory and requires familiarity with his review paper (Westerstahl 1989). Doets' proof of a variant of the Lyndon interpolation theorem in Chap. 4 is clearly of a technical character too. Van Lambalgen studies natural deduction for generalized quantifiers in Chap. 9, another short contribution. Lapierre's work (Chap. 10) pertains to the logic of conditionals, analyzing conditional sentences from the perspective of generalized quantifiers.
2. Quantifiers in the world of types, J. van Benthem
3. Dynamic generalized quantifiers, M. van den Berg
4. Monotone quantifiers: Interpolation and preservation, K. Doets
5. Quantifiers and partiality, J. van Eijck
6. The semantics of exception phrases, J. Hoeksema
7. Further beyond the Frege boundary, E.L. Keenan
8. Configurational expression of negation, W.A. Ladusaw
9. Natural deduction for generalized quantifiers, M. van Lambalgen
10. Conditionals and quantifiers, S. Lapierre
11. Branching quantification and scope independence, F.-H. Liu
12. Generalized quantifier theory and the semantics of focus, S. de Mey
13. Parallel quantification, M. Spaan
14. Quantification over time, H. de Swart
15. The semantics of plural noun phrases, H. Verkuyl & J. van der Does
16. Relativization of quantifiers in finite models, D. Westerstahl
17. Facets of negation, F. Zwarts
Similarly, van Benthem's paper (Chap. 2) touches on various bases and cannot be comprehended without an appreciation of the frontiers in quantification research. On the other hand, van der Does & van Eijk do a reasonably good job of covering the essentials of Basic Quantifier Theory. Still, their paper (Chap. 1) suffers from heavy and occasionally unwarranted formalism, and a general lack of motivation. (Could this be another Dutch tradition that Partee forgot to tell us?) In my view, Keenan & Westerstahl (1997) do a better job in terms of giving a balanced review of quantifiers.
Here is a brief appraisal of some good papers (viz. papers which try to inform the reader of their linguistic motivations before they jump into formal analysis) that I have found just to my liking. Van den Berg's paper (Chap. 3) attempts to connect the theory of generalized quantifiers and dynamic logic. In Chap. 5, van Eijck deals with partiality, putting generalized quantifiers in a 3-valued framework where they can introduce truth value gaps. Hoeksema's investigation of the semantics of exception phrases (e.g., "The lady was anything but polite") makes Chap. 6 a lucid and readable one. Keenan's paper (Chap. 7) is an augmented version of his thought-provoking 1992 article, published in Linguistics and Philosophy, where he shows that English presents a large variety of non-Fregean quantifiers. (Fregean quantifiers can in principle be expressed by the iterated application of unary quantifiers.) Ladusaw's concern in Chap. 8 is negative concord, as exemplified in the following widely understood but nonstandard sentence: "The lady didn't say nothing to nobody." De Mey's short paper (Chap. 12) on generalized quantifier theory and the semantics of focus is intriguing, and includes a valuable discussion of the most plausible semantics for only. De Swart's fine paper (Chap. 14) delves into the extensions of Generalized Quantifier Theory to cover expressions of temporal quantification (e.g., "The lady mostly drinks white wine"). Verkuyl and van der Does' goal in Chap. 15 is to reduce the number of readings for plural noun phrases of the sort "Two ladies ate three croissants." (In a related paper, Liu presents simple cases of branching quantification in English in Chap. 11.) Zwarts' work in Chap. 17 is concerned with an accurate description of the connections between sentence negation and predicate negation.
Overall, this collection could have easily been a major reference for "quantifier" researchers. Unfortunately, it fails in this endeavor badly. While the preface states that the book is a cleaned up and substantially revised version of the early proceedings (of the workshop mentioned in the beginning of this review), I have found out that this is not the case at all! In fact, it would not be wrong to assert that this is one of the poorest volumes in the CSLI Lecture Notes Series in terms of the abundance of typos, omissions, and further errors. While I sympathize with the Series' aim to make new ideas in logic, language, and information available as quickly as possible, it looks like in this particular case the output was prepared just too quickly and carelessly. There is a limit to laxness; with this volume, CSLI Publications is really swimming in the waters of negligence and imprudence. (Witness Spaan's bankrupt contribution, Chap. 13, which, due to some silly blunder, omits in the body of the paper all the citations to the references listed at the end. The references are badly incomplete anyway...) All this is unfortunate because technically speaking, most of the papers promise to be quality -- yet occasionally speculative -- contributions to the literature. It is a pity that the editors did not do their homework to prepare a coherent and complete volume. As a matter of fact, I am glad that I did not have to pay for the present bound volume, which is most certainly in need of an emended version if it is going to be of any use.
I would like to mention another (two-volume) recent study on quantifiers, (Krynicky et al. 1995), because it seems to be relevant, at least at first sight. (Its title, on the other hand, indicates that it may well be similar in nature to the book under review, e.g., lots of mathematics, so beware...) And on a related note, in this rather homogeneous and rapidly developing field, time is probably right to write a lucid, luminous textbook rather than putting together papers of unequal importance and quality.
In the words of Charles Olson, "I'm running out of appetite. Let this swirl -- a bit like Crab Nebula -- do for now."
Bach, E., Jelinek, E., Kratzer, A. & Partee, B.H. (eds.) (1995). Quantification in Natural Languages. Dordrecht: Kluwer.
Brooks, P.J. & Braine, M.D.S. (1996). What do children know about the universal quantifiers all and each? Cognition 60(3): 235-68.
Gamut, L.T.F. (1991). Logic, Language, and Meaning, vol. I, p. ix. Chicago: University of Chicago Press.
Keenan, E.L. & Westerstahl, D. (1997). Generalized quantifiers in linguistics and logic. In van Benthem, J. & ter Meulen, A. (eds.) Handbook of Logic and Language. pp. 837-93. Amsterdam: Elsevier.
Krynicky, M., Mostowski, M. & Szczerba, L.W. (eds.) (1995). Quantifiers: Logic, Models and Computation (two vols.). Dordrecht: Kluwer.
Westerstahl, D. (1989). Quantifiers in formal and natural languages. In Gabbay, D. & Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. IV, pp. 1-131. Dordrecht: Reidel.