In the previous chapter we introduced indexing conventions that expressed our intuitions about the (im)possibility of coreference between two NPs in a given structure. In this chapter I am going to provide a semantic interpretation that cashes out this indexing in semantic terms. It is against this formal, precise interpretation of syntactic indexing that we are going to check the predictions of our theory and its possible modifications later on.

Basics of interpretation

The kind of semantic interpretation we assume here is a truthconditional one. Linguistic expressions are associated with non-linguistic entities, i.e. things in the world (e.g. my left thumb and the Cologne Cathedral), and set-theoretic constructs made out of these (e.g. the set of all my fingers, or the set of all sets that contain that set). The task of the semanticist is to devise basic meanings for the words of the language and systematic ways of combining them so as to arrive at intuitively correct truth conditions for entire sentences.

Since this book is not an introduction to semantics, I will keep the technical apparatus to a minimum. Also, common semantic concepts and techniques will be introduced only very briefly. The formalism introduced and used starting with section 2.3 is for the most part compatible with that laid out in great detail in Heim and Kratzer (1998).

This book presents a comprehensive treatment of the syntax and semantics of binding. It is meant to fill the gap between existing introductory texts, both semantic and syntactic, and the rich primary research literature on the topic. If you work your way through this book, you should be able to read and understand almost any of the works mentioned in the references.

There are at least two reasons why I thought such a book may be useful. First, Binding Theory figures prominently in a vast amount of works, either as the main research topic, or, perhaps even more frequently, as a diagnostic for constituency, derivational history, and other abstract aspects of grammatical analysis. I felt that an accessible survey of some of the more recent insights into the nature of binding would benefit both those who read those studies, as well as those who want to undertake them in the future.

Second, by its very nature, Binding Theory involves an equal amount of syntax and semantics. As such, it recommends itself as the topic for an advanced level textbook. There is, I believe, no insightful syntactic analysis without a solid semantics to access its adequacy; in any event, there certainly can't be any insightful analysis of the syntax of binding without a semantics to accompany it. The present book, therefore, is an introduction to doing syntactic and semantic analysis side by side.

In this chapter we will refine the interpretation procedure developed in chapter 2. An important distinction – that between coreference and binding – will be introduced, motivated, and technically implemented. An early and very lucid explication of the distinction is found in Bach and Partee (1980), so lucid, in fact, that I'll simply quote it:

Let's summarize the places where something like coindexing is used in the literature:

1. (1) The same pronoun appears in several places in a sentence:

2. He said he was OK.

3. (2) A pronoun appears together with a referring NP:

4. John said that he was OK.

5. (3) A pronoun appears together with a quantificational NP:

6. No woman doubts that she is OK.

7. (4) A pronoun occurs in a relative clause:

8. … the woman who said that she had found the answer.

9. (5) A reflexive or other obligatorily bound pronoun appears in a sentence:

10. John loves himself

11. Oscar is out of his head.

Other authors have emphasized this point, too, in particular Tanya Reinhart (Reinhart, 1982, 1983a, b).

The semantics of plural NPs

What is the denotation of a plural NP such as we, they, yourselves, Heidi and Tor or the trombones? We assume that these are referring expressions, and denote pluralities. For example, 〚the trombones〛g is the plurality consisting of all (contextually salient) trombones, and 〚Heidi and Tor〛g denotes the plurality consisting of Heidi and Tor.

Technically, a plurality is an individual, just like the denotation of a singular NP like he or Sidney is; where we need to distinguish them, we call the latter atoms (as opposed to pluralities). So atoms and pluralities together make up the domain of individuals, De.

Being an individual, a plurality like 〚Heidi and Tor〛g is different from a QNP denotation like 〚each of Heidi and Tor〛g (which is a generalized quantifier, cf. chapter 4, sections 4.1 and 4.5.2); note, for example, that you can say Heidi and Tor make a good couple, but not *Each of Heidi and Tor make a good couple. It is also different from the set containing Heidi and Tor (e.g. the denotation of the VP is Heidi or Tor). This is important to keep in mind, since thinking of plural NPs as denoting sets is probably the analytical option that comes to mind first (see e.g. Bennet [1994]).