The study of anaphora (from Greek, "carry back") is the study of the ways in which occurrences of certain expressions, particularly pronouns, depend for their interpretations upon the interpretations of occurrences of other expressions. Problems of anaphora are of interest to philosophy and logic because of their intersection with problems of ontology, quantification, and logical form.
Pronouns understood as anaphoric on referential noun phrases are plausibly viewed as referring to the same things as their antecedents. Sentences (1)–(3) permit such readings (coindexing will be used to indicate an intentional anaphoric connection):
- Jim1 respects students who argue with him1.
- Jim1 loves his1 mother.
- Jim1 is here. He1 arrived yesterday. I think he1's asleep right now.
We might call these pronouns "referential anaphors."
It is sometimes suggested (see, e.g., Soames 1994) that anaphoric pronouns in such constructions can be understood in a second way. For example, although (2) might be understood as equivalent to "Jim loves Jim's mother," it might seem to admit of another interpretation that makes it equivalent to "Jim is a self's-mother-lover," the logical form of which is given by (2′):
- (2′) λx(x loves x's mother)Jim.
The contrast between the two readings emerges when (2) is embedded, as in
- (4) Mary believes that Jim1 loves his1 mother.
Certainly, many of the traditional problems involved in interpreting proper names recur for pronouns anaphoric on names.
Pronouns anaphoric on quantified noun phrases cannot be treated as straightforwardly referential. Consider the following:
- (5) Every man1 thinks he would be a good president1.
- (6) No man1 respects his1 brothers' friends.
There is no point inquiring into the referents of the pronouns in examples like these. Following W. V. Quine (1960) and P. Geach (1962), philosophers have tended to treat such pronouns as the natural-language analogs of the variables of quantification theory. Certainly, the logical forms of quantified sentences of the form "every F is G" and "some Fs and Gs" can be captured using the standard first-order quantifiers "∀" and "∃." But a comprehensive semantic theory must treat sentences containing noun phrases formed using "no," "the," "exactly one," "most," "few," and so on. This fact highlights two problems. Using the identity sign "=" and the negation sign "¬," it is possible to use "∀" and "∃" to represent sentences containing "no," "the," "exactly one," "exactly two," and so forth, but the resulting formulae obscure the relationship between the surface syntax of a sentence and its logical form. For example, if Bertrand Russell is right that "the F is G" is true if and only if every F is G and there is exactly one F, then the logical form of this sentence is as follows:
- (7) (∃x)((∀y)(Fy ≡ y = x) & Gx).
A more serious problem is that there are sentences that cannot be dealt with in first-order logic—for instance, sentences of the form "most Fs are Gs."
Both of these problems are solved if quantification in natural language is viewed as restricted. The basic idea here is that determiners combine with their complements (noun complexes) to form restricted quantifiers. So, for example, "every," "some," "most," "the," and so on combine with simple nouns such as "pig" (or "pigs"), "man" (or "men"), and so forth (or complex nouns such as "man who owns a pig," etc.) to form restricted quantifiers such as "some man," "most men," "every man who owns a pig," and so forth. We can represent a restricted quantifier "every man" as "[every x: man x]." This quantifier may combine with a predicate phrase such as "is mortal" (which we can represent as "x is mortal") to form the sentence "every man is mortal," which we can represent as
- (8) [every x: man x]x is mortal.
Now consider sentences (5) and (6) again. If we treat the anaphoric pronouns in these examples as bound variables, their logical forms will be (abstracting somewhat):
- (5′) [every x: man x](x thinks x would be a good president).
- (6′) [no x: man x](x respects x's brothers' friends).
Variable Binding and Scope
G. Evans (1977) has argued that not all pronouns anaphoric on quantified noun phrases are bound variables. Consider the following examples.
- (9) Jim bought some pigs and Harry vaccinated them.
- (10) Just one man ate haggis and he was ill afterward.
A bound-variable treatment of the occurrence of "them" in (9) yields the wrong result. On such an account, the logical form of the sentence will be
- (9′) [some x: pigs x](Jim bought x & Harry vaccinated x).
But (9′) can be true even if Harry did not vaccinate all of the pigs Jim bought, whereas (9) cannot. (If Jim bought ten pigs and Harry vaccinated only two of them, (9′) would be true whereas (9) would not.) And if the pronoun "he" in (10) is treated as a bound variable, the logical form of the sentence will be
- (10′) [just one x: man x](x ate haggis and x was ill afterward).
This is also incorrect; if two men ate haggis and only one was ill afterward, (10′) will be true whereas (10) will be false.
There is a plausible syntactic explanation of these facts. In both (9) and (10), the pronoun is located outside the smallest sentence containing the quantifier upon which it is anaphoric and hence lies outside its scope, according to the most promising syntactic characterization of this notion. The scope of an expression α in a sentence of a natural language appears to correspond to the first branching node dominating α at the syntactic level relevant to semantic interpretation. If this is correct, and contemporary syntactic theory suggests it is, then syntactic theory explains why the pronouns in (9) and (10) are not understood as bound variables. There seem to be, therefore, anaphoric pronouns that are neither bound nor straightforwardly referential.
A plausible paraphrase of (9) is (9″):
- (9″) Jim bought some pigs and Harry vaccinated the pigs Jim bought.
In view of this, Evans (1977) suggests that the pronoun "them" in (9) is understood in terms of the plural description "the pigs Jim bought," as what he calls an "E-type" pronoun. An E-type pronoun has its reference fixed by description (in Saul Kripke's sense) and is therefore a rigid designator. On this account, in (9) the pronoun "them" is taken to refer to those objects satisfying "pigs Jim bought."
Similarly where the antecedent is singular. A plausible paraphrase of (11) is (11′):
- (11) Jim bought a pig and Harry vaccinated it.
- (11′) Jim bought a pig and Harry vaccinated the pig Jim bought.
According to Evans, the pronoun "it" in (11) refers to the unique object satisfying "pig Jim bought."
This idea forms the basis of Evans's general account of the semantic content of unbound anaphors. The pronoun "he" in (10) has its reference fixed by "the man who ate haggis"; and in (12) "they" has its reference fixed by "the philosophers who came":
- (12) A few philosophers came. They drank far too much.
Evans's proposal can be summarized thus: if P is an unbound pronoun anaphoric on a quantified noun phrase "[DET x: ϕ]" occurring in a sentence "[DET x: ϕ]ψ," then the referent of P is fixed by the description "[the x: ϕ & ψ]."
Examination of more complex cases reveals weaknesses in Evans's theory (see below). The problems uncovered have tended to steer semanticists in one of two directions. First, there have been attempts to modify or refine Evans's framework (Davies 1981, Neale 1990). Second, there have been attempts to replace the entire framework with a uniform, discourse-based approach (Kamp 1981, Heim 1982). Both approaches will now be examined.
Evans rejected the view that unbound anaphors go proxy for descriptions (in favor of the view that they have their referents fixed by description) on the grounds that such pronouns, unlike overt descriptions, do not give rise to ambiguities of scope. But consider the following:
- (14) A man murdered Smith, but Jim doesn't think he did it.
- (15) A man murdered Smith. The police have reason to think he injured himself in the process.
If "he" goes proxy for "the man who murdered Smith," there will be two readings for each of the anaphor clauses in these examples—the so-called de re and de dicto readings—according as the description for which the pronoun goes proxy is given large or small scope:
- (14a) [the x: man x & x murdered Smith] (Jim doesn't believe that x murdered Smith)
- (14b) Jim doesn't believe that [the x: man x & x murdered Smith](x murdered Smith)
It is natural to interpret (14) as attributing to Jim a noncontradictory belief concerning the murderer to the effect that he is not the murderer. On the proxy view this is captured by the de re reading of the second conjunct. The de dicto reading is technically available to the proxy theorist but is obviously not the preferred interpretation. But with (15) the de dicto reading of the second sentence is actually the more natural; yet Evans's theory explicitly precludes its existence.
Further support for the proxy rather than reference-fixing approach comes from examples containing modal expressions:
- (16) Mary wants to marry a rich man. He must be a banker.
The first sentence in (16) may be read either de re or de dicto. Moreover, the pronoun "he" can be anaphoric on "a rich man" on either reading. But as L. Karttunen (1976) points out, the modal expression has to be there for the anaphora to work if the antecedent sentence is to be interpreted de dicto. That is, in
- (17) Mary wants to marry a rich man. He is a banker.
it is not possible to get the de dicto reading for the antecedent clause if "he" is anaphoric on "a rich man." This contrast between (16) and (17) is explicable on the assumption that the anaphoric pronoun in (16) goes proxy for the description "the man Mary marries" and may therefore take large or small scope with respect to the modal expression. On the de dicto reading of the antecedent clause, the de re reading of the anaphor clause is infelicitous because an implication of existence results from giving the description large scope. But the de dicto reading of the anaphor clause is fine because on such a reading the description is within the scope of the modal expression. In (17), on the other hand, since there is no modal operator with respect to which the pronoun can be understood with small scope, the sentence has no felicitous reading when the antecedent clause is read de dicto.
H. Kamp (1981) and I. Heim (1982) have explored alternative approaches that aim to treat all anaphoric pronouns in a unitary fashion. One motivation is the problem of so called donkey anaphora, typified by sentences such as (18) and (19), originally discussed by Geach (1962):
- (18) If a man buys a donkey he vaccinates it.
- (19) Every man who buys a donkey vaccinates it.
Both Evans's theory and the simple proxy theory seem to fail here. For example, if the pronoun "it" in (19) is analyzed in terms of the singular description "the donkey he buys" (with "he" bound by "every man who buys a donkey") the sentence will be true just in case every man who buys a donkey vaccinates the unique donkey he buys. Consequently, it will be false if any man buys more than one donkey. But this is incorrect; the truth of (19) is quite compatible with some men owning more than one donkey, as long as every man who buys a donkey vaccinates every donkey he buys. It would appear, then, that the indefinite description "a donkey"—which can normally be treated as an existentially quantified phrase—has the force of a universally quantified phrase in (19). And in (18) both "man" and "a donkey" appear to have universal force.
A common explanation of the "universalization" of the indefinite descriptions in such examples has been proposed by Kamp. The idea (roughly) is that noun phrases introduce variables to which common nouns and predicates supply "conditions" within a "discourse representation" (DR). Typically, the variable is bound by an existential quantifier taking scope over the entire discourse. On this account, an indefinite description is not inherently quantificational; rather, it introduces a variable with conditions on it imposed by, among other things, the predicative material it contains. The DR for (18) might be represented as:
- (18′) [Man(x) & Donkey(y) & Buys(x, x)] ifthen [Vaccinates(x, y)].
Kamp proposes that (18′) is true if and only if every assignment of values to x and y that makes the antecedent true also makes the consequent true. The apparent universalization of the indefinite descriptions "a man" and "a donkey" is thus explained as a consequence of a general analysis of conditionals.
In the light of the equivalence of (18) and (19), Kamp suggests that, although (18) is not actually a conditional, because the subject quantifier is universal we get a DR in which the indefinite "a donkey" has universal force. That is, the DR for (19) is given by
- (19′) [Man(x) & Donkey(y) & Buys(x, y)] every [Vaccinates(x, y)].
Like (18′), (19′) is true if and only if every assignment of values to x and y that makes "[man(x) & donkey(y) & buys(x, y)]" true, also makes "[vaccinates(x, y)]" true.
One problem with this proposal is that it does not predict that indefinite descriptions "universalize" when they are embedded in other quantifiers and thus leads to the so-called proportion problem. Consider
- (20) Most men who buy a donkey vaccinate it.
By analogy with (18′) and (19′), the DR for (20) will be
- (20′) [man(x) & donkey(y) & buys(x, y)] most [vaccinates(x, y)]
which is true just in case most assignments of values to x and y that make "[man(x) & donkey(y) & buys(x, y)]" true also make "[vaccinates(x, y)]" true. But on its most natural reading, the truth of (20) requires that most men who buy a donkey vaccinate every donkey they buy, whereas (20′) can be true as long as most of the donkeys that are bought by men are vaccinated by their respective buyers. Suppose Alan buys five donkeys, Bill buys one donkey, Clive buys one donkey, and no other man buys any donkeys. Sentence (20′) will come out true if Alan vaccinates at least four of his donkeys, even if Bill and Clive do not vaccinate their respective donkeys; but in such a situation (20) would be false. (It has been suggested that there is another reading of (20), which requires that most men who buy at least one donkey vaccinate most of the donkeys they buy; but (20′) does not capture this reading either.)
From this brief overview it should be clear that both the simple descriptive theory and the simple DR theory need to be refined if they are to do justice to the full range of antecedent/anaphor relations in natural language. For example, the descriptive approach needs to be modified if it is to handle donkey anaphora, perhaps allowing for the possibility of interpreting some donkey pronouns in terms of "all of the" rather than "the" (Davies 1981, Neale 1990). And the DR approach needs to be modified to avoid the proportion problem and also permit pronouns to be understood with various scopes. At the time of writing, more sophisticated versions of these theories are being developed, as are alternatives to both.
Davies, M. Meaning, Quantification, Necessity. London: Routledge and Kegan Paul, 1981.
Evans, G. The Collected Papers. Oxford: Clarendon Press, 1985.
Evans, G. "Pronouns." Linguistic Inquiry 11 (1980): 337–362. (Reprinted in Evans , 214–248.)
Evans, G. "Pronouns, Quantifiers, and Relative Clauses (I)." Canadian Journal of Philosophy 7 (1977): 467–536. (Reprinted in Evans , 76–152.)
Geach, P. Reference and Generality. Ithaca, NY: Cornell University Press, 1962.
Heim, I. The Semantics of Definite and Indefinite Noun Phrases. Ph.D diss. University of Massachusetts, Amherst, 1982.
Kamp, H. "A Theory of Truth and Semantic Interpretation." In Formal Methods in the Study of Natural Language, edited by J. Groenendijk et al. Amsterdam Centre, 1981.
Karttunen, L. "Discourse Referents." In Syntax and Semantics 7, Notes from the Linguistic Underground, edited by J. McCawley. New York: Academic Press, 1976.
Kripke, S. "Naming and Necessity." In Semantics of Natural Language, edited by D. Davidson and G. Harman. Dordrecht: Reidel, 1972.
Neale, S. Descriptions. Cambridge, MA: MIT Press, 1990.
Quine, W. V. O. Word and Object. Cambridge, MA: MIT Press, 1960.
Soames, S. "Attitudes and Anaphora." Philosophical Perspectives 8 (1994): 251–272.
Stephen Neale (1996)
1. A term in GRAMMAR and LINGUISTICS for referring back in a stretch of language, as with it in: ‘Although the aircraft had been damaged, it could still fly.’ Here, the pronoun it substitutes for its antecedent the aircraft. In the next example, the definite article the in the conference is anaphoric, referring back to a conference: ‘The EC leaders agreed to hold a conference on economic and monetary union, and have now fixed a date for the conference.’ Anaphoric reference may be achieved through ellipsis, as in ‘We asked them to join us, but they wouldn't’, where they wouldn't means they wouldn't join us. The term is sometimes extended to include CATAPHORA (forward reference to a following part of the text).
2. Also epanaphora. A term in rhetoric for the repetition of the same word or phrase at the beginning of successive phrases, clauses, sentences, and stanzas: ‘He shows us a country where a man can be denied the right to know of what and by whom he is accused. A country where some police shoot first and ask questions later’ (Christian Science Monitor, international edition, 11 Apr. 1988). Compare ANADIPLOSIS.
a·naph·o·ra / əˈnafərə/ • n. 1. Gram. the use of a word referring to or replacing a word used earlier in a sentence, to avoid repetition, such as do in I like it and so do they. 2. Rhetoric the repetition of a word or phrase at the beginning of successive clauses. DERIVATIVES: an·a·phor·ic / ˌanəˈfôrik/ adj.