25. Mill, An Examination of Sir William Hamilton’s Philosophy, 323.
26. This thesis bears a superficial resemblance to the one worked out in Brandom (Making it Explicit, 305–327) and passim. Brandom argues that a reference statement like “The term ‘Leibniz’ refers to Leibniz” can be interpreted as “The one referred to by the term ‘Leibniz’ = Leibniz,” where the indirect description “The one referred to etc.” is anaphorically dependent on some previously occurring token of “Leibniz.” The resemblance is only superficial, in my view. For example, Brandom quotes with apparent approval Chastain’s claim that indefinite descriptions can be straightforwardly referential. See my discussion of this point in chapter 3.
27. This is an old argument. Quine (Methods of Logic, 199) argues that “Parthenon” names the Parthenon and only the Parthenon, whereas “the Parthenon-idea” names the Parthenon-idea. Frege (“On sense and reference,” 31) says that the sentence “The Moon is smaller than the Earth” is not about the idea of the Moon. “If this is what the speaker wanted, he would use the phrase ‘my idea of the Moon’” Earlier than that, Mill (A System of Logic, I.v.i) notes that “fire causes heat” does not mean that my idea of fire causes my idea of heat. “When I mean to assert any thing respecting the ideas, I give them their proper name, I call them ideas: as when I say, that a child’s idea of a battle is unlike the reality, or that the ideas entertained of the Deity have a great effect on the characters of mankind.” In the late thirteenth century, Duns Scotus argued that if “stone” referred to the idea of a stone, then Aristotle’s claim in De anima III “A stone is not in the soul, but the idea of a stone” would be contradictory, because “being in the soul” is first removed from the idea of a stone, which is signified by the name “stone” by the first part of the proposition, “a stone is not in the soul,” and yet in the second part, the same predicate would be attributed to the “same subject” (Duns Scotus On Time and Existence, 31, I have changed the translation from “species” to “idea”).
28. Locke, An Essay Concerning Human Understanding, III. iii. 3.
29. Reid, The Works of Thomas Reid, 389.
30. Sainsbury, “Fregean sense,” 136.
31. It may be objected that in English, as well as in Greek and Latin, a relative may anticipate a pronoun in such a way that the pronoun refers to a preceding or succeeding relative or vice versa. I deal with this objection in chapter 3.
32. Strawson, Individuals, 21.
My first thesis is that co-reference is signified or guaranteed when it is clear from the meaning of two terms that if they have a referent at all, they have a single referent, that is, that if one is true of a thing, the other, if true, is true of the same thing also. Consider pronouns: if the (definite) antecedent refers, the pronoun refers to the same thing. Since we understand this even when the antecedent term is empty (“As soon as the demon smells the odour, it will flee”), it follows that the co-reference is signified without any semantic connection between the terms and some external object. The connection is internal or intralinguistic, and must be determined by some rule of use. There can be co-reference without a co-referent.
I shall argue that the same must be true of proper names and definite descriptions and that, while the rules may be complex and difficult to specify, they must nonetheless exist.
Rules for Reference
The question of what authors wish to convey through their work in general is an old and difficult question,1 but we cannot doubt their specific ability to successfully convey, which individual they are writing about. Our ability to comprehend a narrative involves keeping track of which character is which. There are about 31,000 verses in the whole Bible, and (from Aaron to Zurishaddai) about 2,000 characters. The biblical narrative would make little sense if we were unable to tell whether the same character was the subject of any two of those verses, or not. There are more than 700 occurrences of the proper name “Moses” in the Old Testament, and it is crucial to our ability to comprehend the work that we understand that these are not ambiguous names for 700 different people. Chastain calls such a set of names an anaphoric chain, namely “a sequence of expressions such that if one of them refers to something then all of the others refer to it.”2 The chain does not have to consist solely of proper names, but will normally be a mixture of proper names and other singular expressions.3 The question of how we resolve anaphoric chains is remarkably difficult, but it belongs to the science of computational linguistics, rather than philosophy.
Computational linguists traditionally distinguish co-reference from anaphor. Co-reference is when two terms refer to the same entity “in the world,” anaphora is when “a term (anaphor) refers [sic] to another term (antecedent) and the interpretation of the anaphor is in some way determined by the interpretation of the antecedent.”4 I reject this distinction, for I regard co-reference and anaphora as essentially the same phenomenon. To start with, we understand complete fiction, where all proper names and pronouns are empty, because we are able to bundle up singular terms into different anaphoric chains. Hence co-reference cannot depend on reference to the same entity “in the world.” The claim that an anaphor “refers to” another term is misleading for the same reason, as though the relation between a pronoun and its proper name antecedent were intralinguistic, but the relation between two co-referring proper names were not. As for the interpretation of the anaphor being determined by the interpretation of the antecedent, the idea seems to be that pronouns are essentially ambiguous, their sense (or reference?) determined by the immediate context, whereas proper names have a fixed and context independent reference. One dictionary defines anaphor as “an expression that can refer to virtually any referent, the specific referent being defined by context.”5 But this is not true. Proper names also are essentially ambiguous and require a context. Consider the name “Moses” in a book about the Pentateuch as contrasted with a book about Moses Maimonides. Clearly the rules determining proper name co-reference will be different from the rules determining pronoun co-reference, and I shall come to that, but this does not mean that co-reference is essentially a different phenomenon from anaphora.
Pronoun Resolution
The resolution of pronoun anaphora has received much attention in the literature, although the record is dismal. Hobb’s algorithm in 1978 was an early attempt.6 The algorithm starts at the NP (noun phrase) node immediately dominating the pronoun and searches in a specified order for the first match of the correct gender and number.7 The algorithm is purely syntactic; there has been some progress since the 1970s by using semantic properties of the term. For example, it seems as though a pronoun will not have a distant antecedent, and so entities introduced recently are more salient, and thus more likely to be the antecedent of back-reference, than those introduced earlier. Lappin and Leass have proposed that salience values should be cut in half each time a new sentence is processed,8 and that entities mentioned in subject position are typically more salient than those in object position. Centering theory, developed by Barbara J. Grosz, Aravind K. Joshi, and Scott Weinstein in the 1980s, proposes that discourse has a kind of center, which remains the same for a few sentences, then shifts to a new center. It is this center that is typically pronominalized in that there is a tendency for subsequent pronouns to take it as antecedent. Modern algorithms perform better than Hobb, but state of the art accuracy for general co-reference