that if they have a referent at all, they have a single referent—that co-reference is an equivalence relation: it is reflexive, symmetric, and transitive. Every term clearly co-refers with itself, for if it has a referent, it has a single referent, so the relation is reflexive. It is symmetric—if a co-refers with b, then b co-refers with a. And if a, b, and c have a referent, and if a co-refers with b, and b co-refers with c, then a and b have a single referent x, and b and c have a single referent, which must also be x, hence a and c also have x as a referent, and the co-reference relation is transitive.
It also follows from that definition that if any person S understands the meaning of any two co-referring terms, then he or she understands that they co-refer, for if they understand the terms, they understand their meaning, and their meaning, as co-referring terms, is precisely that if they have a referent, they have a single referent. But it does not necessarily follow that understanding an occurrence of a name requires us to comprehend every past occurrence with which the occurrence co-refers. In order to understand the name “Moses,” we do not necessarily have to understand every one of the 700 occurrences of that name in the Hebrew Bible. Indeed, a text can easily be constructed so that it is clear from the meaning of a very small number of terms that they co-refer. Suppose that a is a proper name, that b is a pronoun referring back to b, and c is another pronoun referring back to b. To verify that c co-refers with a, we first have to check that c refers back to b, then that b refers back to a, so we have to check three terms in all. But pronouns have a local or short range, eventually terminating backward in some long-range term such as a proper name or unique description. If there is a rule that tokens of the same long-range term always co-refer (or if not, that there is explicit disambiguation such as with “Phinehas”), and that different long-range terms never co-refer unless stated otherwise, then it will be easy for a reader to quickly identify co-referring terms, wherever they occur in the narrative, without interpreting all the terms in the narrative. For example, if we find a pronoun in one place, and another pronoun of the same gender in another, then trace back the antecedents of each pronoun until we find two corresponding long-range terms. If the long-range terms are the same, then assume they co-refer, if they are different, assume that they do not co-refer.
Thus, we do not have to be a scholar to understand the name “Moses,” wherever it occurs. To decide whether the “he” in Ex. 2:15 co-refers with “the servant of the Lord” Deut 34:5, we find what “he” refers back to (“Moses”), and what “the servant of the Lord” refers back to (“Moses” again), and we have the answer. Nor do we have to understand the whole of a book previously written in order to construct a new book with fresh anaphorically co-referring chains, some of which link back to chains in the book written earlier. The Bible had many authors, all of whom were probably scholars, but scholarship is not strictly necessary. We merely use the same rules as the readers use. As long as we know which existing character we want to speak of, we can look for their name or unique description, then use that term to continue the chain, followed by suitable pronouns or descriptions.
This is not to say that readers cannot be mistaken about the co-reference of different terms. This can happen in two ways. First, the author may not have used the rules correctly, and created a term that referred back to two or more chains. This error probably occurred in the “Imran” example given earlier, where it is not clear whether the name refers to Moses’ father, or Jesus’ uncle. Co-reference is then strictly impossible. Second, the rules may have been clear enough for many readers, but not clear for all readers, some of whom may assign the wrong co-reference. The possibility of such error does not invalidate my claim that if any person S understands two co-referring terms, then he or she understands that they co-refer, since it is clear that in such cases, the interpreter has failed to follow the rules, thus has failed to understand the terms. Such a possibility has an important application in my resolution of Kripke’s belief puzzle (see chapter 9).
Author and Reader Reference
It is common to distinguish between speaker and hearer reference (and by extension, author and reader reference). Strawson31 says that when two people are talking, the speaker may refer to or mention some particular by means of proper names, pronouns, descriptions, and so on, whose function is to enable the hearer to identify the particular. This is “speaker reference” or “identifying reference.” But the hearer may not in fact identify that particular, according to Strawson, so there can be speaker reference without hearer reference. Kripke discusses a similar example, claiming that the speaker’s referent is the object which the speaker wishes to talk about.
Now, there may be cases of spoken reference where this distinction makes sense, that is, in cases where the speaker communicates their intention by gestures or other forms of demonstrative indication, but such cases have no relevance where the only context is written language. We are concerned with texts, the most recent of which was disclosed around 630 AD, that is, nearly 1,400 years ago, the authors (or transcribers)32 of which are long since dead, so we are unlikely to know what their wishes or intentions were, except from the texts themselves, which either enable us to identify the reference, or do not, as in the case of Exodus 4:24–26, or Quran 3:35, or any other parts of the three scriptures where the interpretation is in doubt. In the case of texts, there is only reader reference, namely, the reference, which a reader competent in the language and with the conventions of the genre, would understand.33 There is writer reference, in a sense, but that necessarily coincides with reader reference. For the same reason, there can be no reference failure, strictly speaking. Reference tells us which individual a proposition is about, so if the language fails to tell us this, there is no reference at all. The “failure” in question is an alienans predicate, like the fool’s in fool’s gold.
The Properness of Proper Names
The anaphoric framework explains the properness of proper names better than Aristotelian or standard semantics, neither of which offers a compelling explanation of why proper names “properly” belong in the same sense to only one individual.
There is a long history of attempts to explain properness within the framework of Aristotelian semantics, of which perhaps the best known is Duns Scotus’s fourteenth-century thesis that a specific nature (e.g., man) has a unity that is less than numerical unity, and that a specific nature is made individual (i.e., this man, Socrates) by the addition of a positive individuating factor, which Scotus calls the individuating difference (differentia individualis), or haecitas—“thisness.”34 The idea has found support more recently from Alvin Plantinga, who has argued that the name “Plato” expresses an individual essence of Plato. The essence is “incommunicable to any other” (explaining its properness); moreover, an individual can have two or more essences, which are logically but not epistemically equivalent, explaining why “Hesperus is the evening star” and “Phosphorus is the evening star” express epistemically different propositions. Haecceity properties explain how negative existential statements could be logically possible, but raise the problem that, if Moses no longer exists, the name “Moses” expresses an unexemplified haecceity,35 which seems implausible. How can the haecceity property exist independently of Moses, floating around in the ether without a bearer? Other philosophers have also found the notion challenging.36
The alternative to the standard theory is to suppose that a proper name expresses some kind of property, or combination of properties.37 But as Mill argued (and Kripke after him), if “Moses” signifies the concept of a certain set of attributes that happen to be uniquely satisfied, one of two things follows. Either, if I meet a person who corresponds exactly to the concept I have formed of Moses, I must suppose that this person actually is Moses, and lived in the second millennium BC, or else I cannot think of Moses as Moses, but only as a Moses; and all those that are mistakenly called proper names are common names. “Either theory seems to be sufficiently refuted by stating it.”38
Moreover, if the name expressed some non-singular property, or set of such properties, we could coherently deny, using that name, that its
