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Chapter 2

Rules for Reference

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 resolution is sadly quite low, in the range of 60 percent.

This is a puzzle, for it means we do not understand something that humans do easily, namely reading a simple story. Children soon learn to do this, yet the most advanced computational techniques fail. Does this mean there are no rules? Surely not. Either co-reference (1) is enabled by a sort of telepathy between author and reader, whereby the author telepathically communicates the intended reference to the reader, (2) involves some semantic relation between language and reality that a computer could not possibly emulate, or (3) is a property of the text, in which case, there must exist some method of decoding it. I rule out the first on the assumption that telepathy is impossible, particularly between an author who probably died in the second millennium BC and a reader in the third millennium AD. I rule out the second both as implausible, and because it is the principle target of this book. That leaves the third. I summarize the reasons supporting it here.

First evidence: rules exist. Ordinary grammar books talk about the error of faulty or vague pronoun reference, and specify a rule like “A pronoun should refer back to a single unmistakable antecedent noun.” To be sure, it is difficult to give a criterion or an algorithm for “unmistakable,” but as I said earlier, human readers clearly have the ability to keep track of which individual is which, without making mistakes, also human writers have the ability to enable this by clearly expressing their meaning. When mistakes occur, this is the fault of the writer, not the reader. Humans would not make rules if humans were unable to apply them.

Second, the difficulty that computers have with some exception cases is not that there is no rule, but rather that the rule requires knowledge of human affairs and customs. For example:

Gen 4:20 Adah gave birth to Jabal; he was the father of those who live in tents and raise livestock.

Gen 4:26 Seth also had a son, and he named him Enosh.⁹

Gen 12:18 So Pharaoh summoned Abram. “What have you done to me?” he said.

The first example requires knowledge that “Adah” is the name of a woman, not a man, which is provided in 4:19 (“Lamech married two women, one named Adah and the other Zillah”). This knowledge could be given to the computer through a list of all proper names classified by gender, but in any case, there is a further clue given by “gave birth to.” The computer would have to understand that only women can give birth. There is another difficulty: the verse could easily have been written “Lamech had a son, Jabal; he was the father of those who live in tents and raise livestock,” with no clue given by pronoun gender. To understand why “he” still refers back to “Jabal,” we would have to understand the purpose of 4:19–22, which is to tell us which occupations the descendants Lameth followed. Jabal was the ancestor of tent dwellers, Jubal of musicians, Tubal Cain of blacksmiths. This, in Chastain’s words, is a convention “relevant to the genre.”

Gen 4:26 is an example of a double pronoun use: “he named him Enosh.” The assumption is that the verb is not reflexive, otherwise the reflexive pronoun “himself” would have been used.¹⁰ We also know that human biology generally precludes children naming their parents. Gen 12:18 requires understanding of speech conventions. If “he” refers to Pharoah, and Pharoah uttered “What have you done to me?,” then “you” refers to Abram and “me” to Pharaoh. To understand that “he” refers to Pharoah, we have to understand what Abram is doing, which is explained by 12:17. God is inflicting plagues because Pharaoh has taken Sarai, Abram’s wife.

Third, the knowledge required is likely to be timeless and universal (or at least relatively stable over time, and across languages). We can generally understand texts written in ancient languages and by authors from very different cultures. Mark wrote, “Herod feared John, knowing that he was a just man” with the intention that “he” (αὐτὸν) should refer back to “John.” His intention was realized even though he wrote in Greek, and his English translators have followed him by using the appropriate English pronoun, as do Latin translators (“Herodes enim metuebat Iohannem sciens eum virum iustum”), French (“Hérode craignait Jean, le connaissant pour un homme juste”), German (“Herodes aber fürchtete Johannes; denn er wußte, daß er ein frommer und heiliger Mann war”), and so on. They are able to translate the reference because they understand the rules of the language they were translating into, and Mark would have understood the rules of the original Greek in exactly the same way. Imagine he was working from some lost text in Aramaic, which used the same pronominal reference, or that he had some mental sentence which he wanted to translate into Greek. Thus, the rules cannot be arbitrary if the knowledge required to apply them is knowledge of human nature itself, including the nature that drives people to construct such stories.

Fourth, the cases where resolution is impossible are where no appropriate rule exists.

On the way, at a place where they spent the night, the LORD met him₁ and tried to kill him₂. But Zipporah took a flint and cut off her son’s foreskin, and touched his₃ feet with it, and said, “Truly you are a bridegroom of blood to me!” So he₄ let him₅ alone. [Exodus 4:24-26]¹¹

Rabbinical interpreters have offered a wide range of meanings for this text.¹² The first “him” could refer to Moses, or to his son, either of whom has been struck down by some illness caused by God. The second clearly co-refers with the first. But whether “his feet” refers to Moses’ feet, his son’s feet or God’s feet, is difficult to say. As for the fourth and fifth, logic suggests that the subjects are different, and also that the fifth “he” co-refers with the first and second (the attempt on his life is dropped). But whether it is Moses or his son is not clear. One translation has “it” for the fourth pronoun, meaning the illness that struck down Moses (or his son). The text is most likely corrupt, but that confirms the point that no appropriate rule exists.

Of course, a complete theory governing pronoun resolution is likely to be complex and difficult, and is a problem for computational linguistics, but it is not my purpose to offer a precise theory of co-reference resolution, or any general theory of how people signify and understand co-reference. My assumption is such a theory must be possible. There have to be certain well understood rules of communication, which allow both authors and translators to communicate reference by written or spoken signs, in whatever language they choose.

Proper Names

While pronoun resolution is difficult, proper names and definite descriptions are somewhat easier. For proper names, the rule is that tokens of the same name always co-refer, except when they have been disambiguated in some way. If there are two or more people called “Mary,” the rule is that the name should be further qualified by means of a patronymic or description. For example, Mary Magdalene is qualified as Magdalene, as is Mary the mother of James and Joseph, who is also called the other Mary (Matthew 27:61, 28:1).¹³ Likewise, where the reader might think that different individuals had the same name, or where it is not clear, a description may be added. Thus, John 11:2 states, “It was that Mary [the sister of Martha] who anointed the Lord with ointment,” in case we think she is a different Mary, although Luke does not say whether they are the same or different. Likewise, Acts 13:14 tells us that the Apostles came to Antioch in Pisidia, to distinguish it from the Antioch in Syria.

The ambiguity can also be resolved by the passage of time. There are two people called “Herod” in the gospels. The first, the infant boy slayer of Matthew 2, was Herod the Great (74 BC – 4 BC), whereas the person to whom Jesus was sent before his crucifixion (and the one who had John the Baptist murdered) was Herod the Great’s son Herod Antipas (Matthew 14:1; Luke 3:1). There is no overt disambiguation in Luke. Luke 1:5 says, “In the time of Herod king of Judea,” and Luke 3:1 says, “In the fifteenth year of the reign of Tiberius Caesar—when Pontius Pilate was governor of Judea, Herod tetrarch of Galilee.” However, the infant killing episode took place at Jesus’ birth, whereas Luke 3 explicitly states that Jesus was about thirty.

The convention that non-disambiguated tokens of the same name co-refer gives rise to the following puzzle, Quran 3:33-35:

3:33 Indeed, Allah chose Adam and Noah and the family of Abraham and the family of Imran over the worlds—

3:34 Descendants, some of them from others. And Allah is Hearing and Knowing.

3:35 [Mention, O Muhammad], when the wife of Imran said, “My Lord, indeed I have pledged to You what is in my womb, consecrated [for Your service], so accept this from me.”

The context makes it clear that the “wife of Imran” is the mother of Mary and grandmother of Jesus. But the list in 3:33 implies that Imran is the father of Moses, meaning that Moses is Jesus’ uncle! This apparent inconsistency was noticed by John of Damascus as well as Niketas Byzantios,¹⁴ who thought Muhammad had confused Jesus’ mother with Moses’ sister Miriam the prophetess, who “took a timbrel in her hand, and all the women followed her, with timbrels and dancing.”¹⁵

The fact that there is a natural reading at all, that is, reading both tokens of “Imran” as having the same reference, and reading “wife” as meaning a woman who has undergone a legal marriage ceremony with the person she is wife of, suggests some sort of rule or heuristic for determining reference, and the logical difficulty of the natural reading implies, as Spinoza argues in another context, that the author of the scripture made an error in doctrine, or that he did not know how to express himself properly, both of which undermine the authority of scripture.¹⁶ Perhaps the natural reading is not the correct reading, but this requires defining what “correct” means here. For example, the traditional reading, probably following the commentary of Al-Baidawi,¹⁷ avoids the problem of Moses being the uncle of Jesus on the assumption that the first occurrence of “Imran” refers to the father of Moses, the second to the father of Mary. Dawood follows this in an explanatory footnote to his translation.¹⁸ Others have suggested that both tokens of “Imran” do refer to the father of Moses, but since “wife” in Arabic also means “woman,” “wife of Imran” must be read as “woman of Imran,” that is, a descendant of Imran, just as Luke 1 says that Elizabeth was “of the daughters of Aaron,” meaning a descendant of Moses’ brother Aaron.¹⁹A third interpretation is that both tokens of “Imran” refer to the father of Mary.²⁰

The difficulty with any alternative reading, as Spinoza persuasively suggests,²¹ is it that it implies a correct interpretation, that is, a method or rule of interpretation, which we could systematically apply to every passage of the scripture, which other writers could emulate without going astray. Otherwise there is no method or rule for interpreting scripture, and “anyone could make up anything [i.e., any interpretation] he liked.” This is the precisely the difficulty with the interpretation of Quran 3.33–35. The first interpretation implies the rule that we may use the same proper name, without qualification or warning, to refer to different individuals. But if this rule were systematically employed, we would everywhere find sudden jumps like the one from Imran the father of Moses in 3:33 to the grandfather of Jesus in 3:35, which we generally don’t find, and the principle would hardly be recommended in manuals of style, or courses in clear speaking. The whole point of a proper name is for consistency of reference: unless indicated otherwise, repeated tokens of the same name have the same reference. The second interpretation implies that “sister of” is systematically ambiguous between a living relation and a descendant, yet there is no evidence of the term “sister” being used in this way in any other part of the Quran.²² The third, namely that “Imran” in 3:33 refers to the father of Mary, leads to the difficulty that the list does not include the grandfather or father of Noah, so why should it include the grandfather of Jesus? The point of the list is to mention all those individuals (Adam, Noah, Abraham, Imran) as chosen above all others by God. Also, why does the list not include Moses, who the Quran mentions more than any other prophet, if not because the Imran of the list is Moses’ father? Sale²³ mentions a further interpretation by some Muhammadan writers who “have imagined that the same individual Mary, the sister of Moses, was miraculously preserved alive from his time till that of Jesus Christ, purposely to become the mother of the latter.” Hermeneutically, this is the least problematic reading, although it conflicts with the principle that names of people from wildly different time periods do not co-refer (unless it is explicitly stated that the person had lived to be 1,000 years old).

The fact that different authors can write a single large and complex work is further evidence for a uniform or natural method of interpretation. The author of Psalm 106 who says that Phinehas “stayed the plague,” is almost certainly different from the author of Numbers 25:7, who says that Phinehas, “son of Eleazar,” kills an Israelite man and the Midianite woman who he brought into the camp “before the eyes of Moses.” But the author of the Psalm is presumably aware that there is a Phinehas “the son of Eli” mentioned in 1 Samuel 1:3, and so adds a description and a background to distinguish them, so that the meaning is not “Phinehas, son of Eli,” but rather, “Phinehas, plague stopper.” Likewise, the author of Deuteronomy²⁴ would be aware that it is the fifth book in the series, and that Genesis, Exodus, Leviticus, and Numbers precede it. Even if the books were authored separately, the editor would have been aware of this. Thus, Joshua begins “After the death of Moses,” Judges begins “after the death of Joshua,” and so on. The author of that sentence is glancing over his shoulder back to the text that ends Deuteronomy 34, assuming the reader will have it available also. Each successive chapter or book could thus have different authors without impacting the unity of the narrative, so long as they wrote as if they were the same author.²⁵ There is no reason why multiple authors cannot achieve the same effect as a single author, so long as each author understands the text or texts that will be available to the final audience. They (or the editors) have complete control over which characters are introduced, and over the order in which this happens. It does not matter whether they are different, so long as each author is aware of the background information available to the audience, and the multiple authors act as though they were a single author. Think of the different people who write the different episodes of a television soap series. Nothing in the story-relative account requires that the same proper name always signifies co-reference, any more than use of the same pronoun signifies this. The “standard” use of a proper name in the same text is one which conforms to unstated but commonly understood rules for resolving ambiguity.

In some exceptional cases, the ambiguity is resolved on the assumption that co-reference would lead to internal contradictions. For example, Acts 1, where the name “Judas” occurs twice.

Acts 1:13 Coming in, they went up into the upper room where they dwelt, Peter and John, James and Andrew, Philip and Thomas, Bartholomew and Matthew, James the son of Alphaeus and Simon the Zealot, and Judas the brother of James.

[..]

Acts 1:16 Brethren, he [Peter] said, there is a prophecy in scripture that must needs be fulfilled; that which the Holy Spirit made, by the lips of David, about Judas, who shewed the way to the men that arrested Jesus.

This appears to break the rule that successive tokens of the same proper name always co-refer. Clearly in this case they do not. But this is signaled in two ways. First, by a sort of description. One person called “Judas” is described as the brother of James, the other as the betrayer of Christ, just as one person called “Mary” is qualified as Magdalene, another person so-called as the mother of James and Joseph (see earlier). Second, it is signalled from the context that the first person called “Judas” is still alive, being present at the meeting of the brethren, whereas the second is now dead, as Peter explains in verse 18.

Descriptions

The rule for descriptions seems to be that terms involving the same definite description always co-refer, and that an indefinite description can refers forward to some definite description, but (as will be discussed in the next chapter) never backward. Ezekiel 10:7 says that one of the cherubim took a burning coal “and put it into the hands of the man in linen.” Who is the man in linen? Refer back to 9:2:

I saw six men coming from the direction of the upper gate, which faces north, each with a deadly weapon in his hand. With them was a man clothed in linen who had a writing kit at his side.

The indefinite description “a man clothed in linen” in 9:2 refers forward to 10:7, so to speak, although it cannot refer further back. There might have been another man in linen mentioned prior to 9:2, but it would not be signified that he was the same (or different) from the one in 9:2. By contrast, it is part of the meaning of the text that the man in 9:2 and the man in 10:7 are the same person.

The definite article plus a description generally requires prior mention of an individual fitting that description.²⁶ There should be no definite article in the first verse of the Odyssey.²⁷ Note that no individual in reality need satisfy the description in order for the definite description to identify its verbal antecedent (“a demon”). It is enough that some individual is said to satisfy the description.

Although proper demonstratives²⁸ cannot occur in a historical narrative, they can occur in a relative context, for example, in direct speech, such as Matthew 12:49: “Pointing to his disciples, he said, ‘Here are my mother and my brothers.’” The rule is that when the person making the speech says “I,” the pronoun co-refers with “he,” when he says “you,” the pronoun co-refers with “he,” referring to the person who is being addressed. I shall discuss such cases in the chapter in demonstratives.

Objectivity

That there is a natural interpretation of the reference of any part of a text, and that it is difficult to define alternative ways of interpreting that part in a way that would work systematically across the whole text, suggests that co-reference is a real and objective property of a text, rather than a product of unmediated authorial intention, for the author’s intention is necessarily unknown unless the author is able to express it unambiguously in writing, and such expression is only possible if there is some method or rule of interpretation understood by both author and reader. We must distinguish what an author or editor wants the text to signify, from what the text itself signifies. The text may have some private significance to the author that it has to no one else, but semantic reference is not private in this sense. Perhaps Mark wrote, “Herod feared John, knowing that he was a just man” intending that “he” should refer to Herod, rather than John. But this intention is irrelevant, given that, as expressed, it refers to John. Finis sermonis est intellectum constituere ²⁹: the purpose of language is to establish understanding, which is only possible when there is a systemic method of doing so. If it were possible to divine the correct meaning from the author’s intention alone, spoken and written language would not be necessary at all.³⁰

Thus, co-reference is a real property of the text. By “real” I mean objective, observable or determinable by others. The letter “A” is objective in that anyone who understands the roman alphabet can recognize a token of the type “A,” which is the whole purpose of having an alphabet. There are even mechanical systems for recognizing text, which would not work unless being a token of the letter “A” were not some mental or psychical feature, but rather an objective property that many different people, and some machines, could recognize. It is true that some tokens of the letter are harder to recognize, and that machines have more difficulty with handwritten tokens than printed ones, but that is a matter of economics. We have a system for producing well-written tokens of the letter “A” that allows us to produce tokens that everybody, including machines, can recognize, but it may take time to write neatly. Or we can save time and scribble. Similarly, we can make a precise reference to a character by using a proper name rather than a pronoun, by analogy with writing the letter “A” neatly, or we can use a pronoun, by analogy with scribbling. Passages such as the one about Zipporah, where pronoun resolution is impossible, are actually rare.

Meaning and Understanding

It follows from my definition of co-reference—a semantic relation such that it is clear from the meaning of two terms 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 bearer possessed it. It is not, as Wettstein puts it, that a description like “being the man who led the Israelites out of Egypt,” or “being the man who was found as a baby by Pharaoh’s daughter” and so on, searches the world, finds its satisfier, and attaches the name to it. For the referent itself, the man who really did lead the Israelites from Egypt might well have done something else.³⁹ Moses might have chosen to stay in Egypt working for Pharaoh, and might not have led the Israelites out of Egypt. His mother might have decided to keep him, and so on. Kripke:

He might never have gone into either politics or religion at all; and in that case maybe no one would have done any of the things that the Bible relates of Moses.⁴⁰

This doesn’t mean that in such a possible world, he wouldn’t have existed, he just wouldn’t have done those things. Hence, the existence of Moses cannot be reduced to the existence of a man with such attributes.

For similar reasons, Mill argued that a proper name signifies no attributes as belonging to its bearer, that it is more like a mark placed directly on the bearer and so, strictly speaking, has no meaning at all.⁴¹ It merely “answers the purpose of showing what thing it is we are talking about, but not of telling anything about it” (System I. ii. 5). This idea did not originate with him—elsewhere Mill cites Reid’s claim that a proper name “signifies nothing but the individual whose name it is,” and that when we apply it to an individual “we neither affirm nor deny anything concerning him”—which Reid himself probably got from the Greek grammarian Apollonius Dyscolus.⁴² But as I noted in the previous chapter, Mill does not explain how a mark can be meaningless, yet be connected in our mind with the idea of an object, nor does he explain what the idea of an individual object is.

The standard theory is a development of Mill’s theory, and is attended by the same difficulties. It explains properness by a semantic connection between proper name and bearer whereby the name can only signify that thing, but this leads to all the well-known difficulties mentioned in the last chapter, for example (i) how a large planetary body like Jupiter could be a part of a meaning or a thought, (ii) how identity statements involving different names for the same thing, such as “Hesperus is Phosphorus” can sometimes be informative, and (iii) how negative existential statements, which apparently deny a meaning for the name, are possible at all.

By contrast, the anaphoric hypothesis offers a simpler explanation of properness. On the anaphoric thesis, the semantic function of a proper name is to associate the proposition, which contains it with an antecedent anaphoric chain, such that any two terms in the chain, including the proper name in question, signify that if they have a referent at all, they have a single referent. Other singular terms such as definite descriptions and pronouns have a similar function, but a proper name has no other function, being simply a tag for its chain of antecedent terms. We can clearly see this if we express the content of the following single proposition:

A hobbit called “Bilbo” lives in a hole

by means of two separate “that” clauses, namely, (i) a hobbit is called “Bilbo” and (ii) Bilbo (or “he” or “this hobbit”) lives in a hole. It would be ridiculous to suppose that the proper name, when used, signifies some individual essence of a hobbit, or that it directly signifies the hobbit himself. If the single proposition does not express Bilbo-ness, which it cannot because it is an indefinite proposition, and if the propositions signified by the two “that” clauses express the same thing as the single proposition, then the two propositions cannot express Bilbo-ness either, despite the use of the proper name in the second “that” clause. But there is no need to run into the sorts of philosophical difficulties generated by individuating differences or direct reference, so long as we see the proper name as a mere tag that allows us to join two propositions into one, as above.

Hence, a proper name cannot have a plural. Or suppose it had. Then we could use the name to signify both that the same thing is such-and-such, and that a different thing is such-and-such. But a proper name cannot signify identity and difference at the same time, so it cannot have a plural. A common name, by contrast, can be used to signify both “the same F” and “another F,” because its purpose is not to continue an anaphoric chain. The anaphoric account has no philosophical difficulties at all. We run into such difficulties only if we suppose that a name signifies some essential property of an individual, or the individual itself, rather than a property of the language alone.

Summary

I have argued that co-reference is rule governed, and that it in no way depends upon any semantic relation between a text and extratextual items. The difficulty faced by computers in comprehending human texts does not conflict with this principle. The ability to understand a text like the Hebrew Bible presupposes the ability to keep track of which individual is which by assigning the right token of a singular term to the right subject. This requires not just knowledge of the syntax and semantics of the language, but knowledge of the genre, or of human nature itself. Such knowledge determines the “natural” reading of the text, deviation from which can only be justified if it justifies the same reading systematically across every passage of the scripture, and which other writers could emulate without going astray. For this reason, the proper names “Noah,” “Abraham,” and “Moses” have the same reference, that is, co-reference, in all the parts of the Hebrew Bible, even when the parts are written by different authors. Co-reference is objective in the sense that there are systematic rules or heuristics that determine sameness of reference. Otherwise there could be no “natural” reading of the scriptures.

The existence of such rules is crucial to determining the truth conditions for reference statements, which I shall discuss in the next chapter. I shall argue that a reference statement is true if and only if the term that is mentioned in the statement co-refers with the term that is used, hence if co-reference is an objective property of the text, the truth of a reference statement depends on properties of the text, rather than some extralinguistic relation between language and reality.

NOTES

1. Readers interested in the more general question of scriptural interpretation should consult Gracia 1995 and 2001, although Gracia’s work is reliant on an outmoded theory of reference derived from Searle.

2. Chastain 1975, 205. Sommers (1982) also proposed the idea that proper names and indeed all definitely referring expressions are anaphors, but the idea precedes both writers. A similar idea was mooted by Prior, “Oratio Obliqua,” originally published 1963, and Geach discusses something similar in Mental Acts. Strawson introduced the closely connected idea of story-relative reference in 1959, which he may have borrowed from W. E. Johnson (Logic, 1921), who distinguishes between what he calls the “Alternative indefinite” article, as in “A man must have been in this room,” which should really be interpreted as “Some or other man must have been in this room” from what he calls the “Introductory indefinite,” which occurs at the beginning of a narrative, for example, “Once upon a time there was a boy who bought a beanstalk.” Johnson then supposes the narrative to continue: “This boy was very lazy,” where the phrase “this boy” means “the boy just mentioned,” that is, “the same boy as was introduced to us by means of the indefinite article.” The affinity with Strawson’s idea should be obvious. Johnson’s work includes an early use of the term “reference” that is close to its contemporary sense. For example, he says “Here the article ‘this,’ or the analogous article ‘the,’ is used in what may be called its referential sense” (my emphasis). Johnson, Logic, I. vi. §4 (p. 85).

3. Chastain (“Reference and context,” 216) rightly observes that “the ability to comprehend a novel, a biography, or even a single paragraph presupposes the ability to keep track of who’s who by assigning a given singular expression to the right anaphoric chain, where the latter will normally be a mixture of proper names and other singular expressions. This means, for example, knowing when an occurrence of ‘she’ in Lolita belongs with the occurrences of ‘Lolita’ and when it belongs with the occurrences of the names of the other female characters in the book. The ability to identify anaphoric chains of this sort is obviously very complex: we employ our knowledge of the syntax and semantics of the language, plus our knowledge of how discourses are constructed, plus our knowledge of whatever special literary or scholarly or other conventions pertain to the genre in question, plus our knowledge of what the writer is likely to have meant, and so on.”

4. From a presentation by Christopher Manning, https://web.stanford.edu/class/archive/cs/cs224n/cs224n.1162/handouts/cs224n-lecture10-coreference.pdf.

5. Wiktionary.

6. Hobbs, “Resolving pronoun references.”

7. Dominance is a primitive of syntactic analysis, which interprets sentence structure in terms of “trees,” with dominant nodes higher up in the structure than dominated ones.

8. Lappin and Leass, “An algorithm for pronominal anaphora resolution.”

9. I checked the first two of these examples with a user of Stanford CoreNLP tagger, a state of the art neural system, who told me it got them both wrong. However, the Hobb algorithm gets the “Seth” one right.

10. For example, Latin sibi, Greek ἑαυτοῦ. Hebrew uses a different way of expressing the reflexive.

11. I have used a translation consistent with the Hebrew, which uses pronouns only. Some translations resolve the difficulty of interpretation by use of the proper name, for example, NIV “At a lodging place on the way, the LORD met Moses and was about to kill him.”

12. Silverman, From Abraham to America: A History of Jewish Circumcision, 86.

13. Other than Mary Magdalene, of course, since there were only two Marys at the tomb. Mary, mother of Jesus, was not present at that point, although confusingly she also had sons called James and Joseph, common names in first-century Galilee.

14. John of Damascus, De Haeresibus, 766, Niketas of Byzantium, Confutatio dogmatum Mahomedis, 790.

15. Exodus 15:20. If the “Imran” mentioned in Surah 3 is not the father of Moses, how did Muhammad discover the name? The father of Mary is not named in the New Testament, although Christian tradition knows him as “Joachim.” If the author was using a name familiar to his readers, they would associate it with Imran the father of Moses. Otherwise it would be meaningless, unless there was a tradition in the Near East about Mary’s father, but history is so far silent about that.

16. The Quran (3:7) says that some of its verses are specific, others ambiguous, whose meaning is known only to God. “Those whose hearts are infected with disbelief observe the ambiguous part.”

17. Hughes, Dictionary of Islam, 206.

18. See also Esposito, The Oxford Dictionary of Islam, 136, on the tradition that Mary’s father was also called Imran.

19. Sahih Muslim (transl. Siddiqi) Book 25, Hadith 5326 “When I came to Najran, they (the Christians of Najran) asked me: You read ‘Sister of Harun’, (i.e. Mary), in the Qur’an, whereas Moses was born well before Jesus. When I came back to Allah’s Messenger I asked him about that, and he said: ‘The (people of the old age) used to give names (to their persons) after the names of Apostle and pious persons who had gone before them.’”

20. Ibn Kathir, Tafsir Ibn Kathir, Vol. 2, 29–30, “Allah also chose the household of Imran, the father of Maryam bint Imran, the mother of `Isa [Jesus], peace be upon them. So `Isa [Jesus] is from the offspring of Ibrahim, as we will mention in the Tafsir of Surah Al-An`am, Allah willing, and our trust is in Him.”

21. Spinoza, Theological-Political Treatise (trans. Michael Silverthorne, Jonathan Israel), 7, 136.

22. A further difficulty is that in 19:28, Mary is called the sister of Aaron, who was the brother of Moses. Dawood says “sister” here means a virtuous woman. According to Hughes (Dictionary of Islam, 328), Al-Baidawi says she was called “sister of Aaron” because she was of Levitical race; but Husain says that the Aaron mentioned in the verse is not the same person as the brother of Moses.

23. Sale, The Koran, Commonly Called the Alcoran of Mohammed, 56.

24. Strictly speaking, the author or authors, or editors.

25. This basic assumption is occasionally violated. Moses is supposed to be the author of the whole of the Pentateuch. But as Spinoza points out (Theological-Political Treatise, 8.3, trans. Michael Silverthorne, Jonathan Israel, 119), the words of Deuteronomy 31.9 “and Moses wrote the Law” cannot be the words of Moses, but rather of another writer who has temporarily forgotten that he is writing as if he were Moses. The author of Genesis 12.6 says “the Canaanite at that time was in the land,” forgetting that if he had been writing at that time, rather than later, the Canaanite would still be in the land.

26. An exception being the phenomenon of “bridging”: I saw a house. The roof had a hole in it.

27. Basset, “Apollonius between Homeric and Hellenistic Greek: The case of the ‘Pre-positive Article’” in Matthaios, ed., 260. A cold opening (or: in medias res) is a literary device that deliberately flouts this rule. For example, “It was just noon that Sunday morning when the sheriff reached the jail with Lucas Beauchamp” (William Faulkner, Intruder in the Dust, 1948); “He was born with a gift of laughter and a sense that the world was mad” (Raphael Sabatini, Scaramouche, 1921); “She might have been waiting for her lover” (Graham Greene, England Made Me, 1935). Strawson (“On referring,” 331) calls it the “spurious” use of the definite article, claiming that sophisticated fiction depends on it, as opposed to the “unsophisticated kind” which begins “once upon a time there was . . .” The technique suggests the earlier part of a text has been lost, as though a page or two is missing, and hence the co-reference is missing. The use of a definite article in the first verse of a work of fiction implies a semantic dependence on some antecedent that is simply not available. The same is true of complete definite descriptions like “tallest girl in the class,” or indeed “son of God.”

28. That is, demonstratives that involve pointing or gestures or other actions external to the text.

29. Intellectum constituere: literally to create or establish understanding.

30. Essentially the same point is made in Kripke “Speaker’s reference and semantic reference” (262), who distinguishes what a speaker’s words mean, in a specific context, and what he actually meant, or intended, on that occasion.

31. Strawson, Individuals, 15–16.

32. Both the Hebrew Bible and the New Testament have human narrators. However, the central narrator of the Quran purports to be Allah himself.

33. Kripke calls this semantic reference (“Speaker’s reference and semantic reference,” passim).

34. Scotus used the term haecitas only twice: see Quaestiones super libros Metaphysicorum Aristotelis, Libri VI–IX, 7.13 n61, p. 240 and 7.13 n176, p. 278, but his followers popularised it under the spelling “haecceitas.”

35. Plantinga, “A Boethian compromise,” 137.

36. See Vallicella, A Paradigm Theory of Existence, 97–104 for other compelling arguments against Plantinga-style haecceity properties.

37. E.g. Searle, “Proper names.”

38. Mill, An Examination of Sir William Hamilton’s Philosophy (1979), 322–3. Mill’s example is “Caesar.”

39. Wettstein, “On referents and reference fixing,” 112, see also Kripke, Naming and Necessity, 31, 61.

40. Kripke, Naming and Necessity, 58.

41. Mill, A System of Logic, I.ii.5.

42. See Mill, An Examination of Sir William Hamilton’s Philosophy, 1979, 323, citing Reid, The Works of Thomas Reid, 412. See also Reid, ibid., 219–20, where he says that a definition is the explication of the meaning of a word in terms of words whose meaning is already known, for which reason there can be no logical definition of individual things, such as London and Paris. Reid’s source was James Harris’s book Hermes, published in 1773, an outline of Dyscolus’ work on grammar. The idea can also be found in Aristotle, who points out in the Metaphysics (7.15, 1040 a27) that even when a term, such as “night hidden” denotes only one thing, namely the sun, it is still common because there could be two such objects. He contrasts this with a proper name like “Cleon,” which can denote only Cleon.