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  • Indefinites and Choice Functions
  • Bart Geurts

1 Introduction

The idea of analyzing indefinites with the help of choice functions is not new; it even has a venerable tradition in mathematical logic (see von Heusinger 1997 for details). What is new is the claim that, with the help of choice functions, specific indefinites can be interpreted without being moved about. That is, choice functions make it possible to construe specific indefinites in situ—or so it is claimed by Reinhart [End Page 731] (1997), Winter (1997), Kratzer (1998), and Matthewson (1999), among others (there are various differences among these proposals, most of which I will ignore). In the following I hope to show that such claims are precipitate.

A choice function is any function that takes a set X as its argument and returns an element of X as its value. The idea is that it is choice functions that carry the existential force typically associated with indefinite expressions. Therefore, it is not the indefinite itself that has existential force. Indefinites merely introduce properties for choice functions to apply to, and choice functions are contributed by extraneous sources, the precise nature of which need not concern us here. Following Reinhart (1997) and Winter (1997), I will assume that a choice function is existentially bound somewhere between the sentence root and the position at which the indefinite occurs. For example, if a German in (1a) is construed specifically, we may obtain a specific reading whose representation in standard predicate logic would be as in (1b). This reading (or, at any rate, something approximating it—see below) may be rendered with the help of quantification over choice functions as shown in (1c).

(1)

  1. a. All bicycles were stolen by a German.

  2. b. ∃y[German(y) ∀x[bicycle(x) → y stole x]]

  3. c. ∃f[CF(f) ∀x[bicycle(x) → f(German) stole x]]

(1c) says that there is a choice function f such that all bicycles were stolen by f(German), which is equivalent to (1b) provided the predicate German denotes a nonempty set. This raises the question of what happens if there are no Germans. Another question that comes to mind is what exactly f's argument is. Is it just the set of individuals that German happens to denote, or is it a richer object, such as the intension of German, for example? These questions will be addressed below.

The main points that I hope to establish are that there is no good reason for believing that choice functions allow us to construe specific indefinites in situ, and that some sort of movement is indispensable if we are to have an adequate account of specificity. It is immaterial to my argument what exactly a movement analysis must look like, although I should note that I do not equate movement with quantifier raising or anything equivalent to that: I prefer to view specificity as a pragmatic phenomenon, to be treated in tandem with presupposition projection, which on my account involves a form of movement (Geurts 1999). This, however, is as it may be, for what I want to show here is that just about any movement theory will do better than a nonmovement choice function account.

2 What Is a Choice Function?

For the time being I will adopt the extensional stance and suppose that a choice function takes as its argument the set of individuals satisfying the descriptive content of an indefinite NP. Now let us first [End Page 732] ask: What exactly is a choice function? This is a rather obvious question, and therefore it may come as a surprise that the answer is not nearly as obvious. Here is a first stab:

(2) CF(f) iff ∀X[X ≠ Ø → f(X) X)]

This says that a choice function picks an element from X provided X is not empty. This definition imposes no restrictions on f if X is empty, and this is what renders it inadequate, because it will generally yield truth conditions that are too weak. For example, if (2) is adopted, then only on the premise that there are Germans will (1a) entail that a German stole all bicycles. It has been suggested by Reinhart (1997) and Winter (1997...

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