When Words Point Backward: The Puzzle of Anaphora

Imagine you’re telling a friend a story: “A woman walked into the room. She sat down.” Your friend understands perfectly that “she” refers to the woman you just mentioned. No problem.

Now try this: “If a woman owns a donkey, she beats it.” You probably understand this as meaning something like: whenever a woman owns a donkey, she beats every donkey she owns. But here’s the strange thing—“a donkey” doesn’t refer to any particular donkey. And “it” somehow talks about all the donkeys she might own, not just one. How does that work?

Or consider this: “Hob thinks a witch blighted Bob’s mare. Nob wonders whether she killed Cob’s sow.” This can be true even if there are no witches at all. So what exactly is “she” pointing at? Nothing real.

These are the puzzles of anaphora—the technical term for when a word (usually a pronoun like “he,” “she,” or “it”) reaches back to an earlier word or phrase for its meaning. Most of the time, anaphora is simple. But philosophers and linguists have discovered cases where it gets deeply weird—and those weird cases have forced them to rethink how language works.

The Simple Cases (That Aren’t the Problem)

Some anaphora is boringly easy. When I say “John left. He said he was ill,” the “he” just picks up the reference to John. John is a specific person; the pronoun refers to the same person. This is like handing someone a photo and saying “this person.”

Also straightforward: “Every male skier loves his mother.” Here “his” acts like a variable in math—it’s bound by “every male skier,” meaning each skier loves their own mother. This works the same way as “for every x, x loves x’s mother.”

These cases aren’t what got philosophers excited. The interesting stuff started when people noticed pronouns that couldn’t work either way.

The Three Puzzles

Puzzle 1: Pronouns That Reach Across Sentences

Consider: “An anthropologist discovered the skeleton called ‘Lucy.’ He named it after a Beatle’s song.”

The first sentence doesn’t point to any particular anthropologist—it just says there was some anthropologist who did the discovering. So when “he” appears in the second sentence, it can’t be referring to a specific person. And “a anthropologist” is inside its own sentence; it can’t reach across to bind “he” as a variable either.

Yet the whole thing makes perfect sense. We understand it as saying: there was some anthropologist who discovered Lucy, and that same person named her after a song.

Or take: “Few professors came to the party. They had a good time.” The “they” can’t mean “few professors” as a bound variable—that would give the wrong meaning. (Try reading it as “few professors are such that they both came and had a good time”—that doesn’t match the original, because the original says few came, and then separately says those who came had fun.)

What’s even stranger: “Few students came to the party. They were busy studying.” Here “they” picks out the students who didn’t come. So the pronoun doesn’t even refer to the same group mentioned in the first sentence. It points to the complement—the ones left out.

Puzzle 2: Talking About Nothing

This is the witch example from the opening: “Hob thinks a witch blighted Bob’s mare. Nob wonders whether she killed Cob’s sow.”

The reading that interests philosophers is the one where there are no witches at all. Hob just thinks there’s a witch who did something. Nob then wonders about “she”—but there’s no actual witch for “she” to refer to. And “a witch” is inside “Hob thinks,” so it can’t reach out to bind the pronoun either.

Yet the sentence clearly has a meaning. We can understand it as: Hob thinks there’s a witch who blighted the mare, and Nob wonders whether that same (non-existent) witch killed the sow. Somehow we’re talking about something that doesn’t exist.

Puzzle 3: The Donkey Sentences

These are the most famous puzzles, named after an example from the philosopher Peter Geach. They come in two flavors:

Conditional version: “If Sarah owns a donkey, she beats it.”

Relative clause version: “Every woman who owns a donkey beats it.”

These sentences aren’t about any particular donkey. But “it” can’t be a bound variable—on any normal understanding, the quantifier “a donkey” can’t reach out of its clause to bind the pronoun. And if “a donkey” were an ordinary “there exists” statement, the conditional would mean something like “if there exists a donkey Sarah owns, then she beats it”—which would be true even if she owned ten donkeys and beat only one. But the sentence clearly means she beats all the donkeys she owns.

So somehow “a donkey” ends up meaning “every donkey” in these sentences. How?

What Philosophers Think

Nobody has fully agreed on the answer. But there are four main approaches, each with strengths and weaknesses.

Approach 1: Discourse Representation Theory

In the 1980s, two philosophers—Irene Heim and Hans Kamp—independently developed a radical idea. Maybe indefinite phrases like “a donkey” aren’t really quantifiers at all. Maybe they’re just labels that introduce new “discourse referents”—like creating a new file folder in your mental filing cabinet.

When you say “A woman walked in,” you create a folder for “woman who walked in” (let’s call it x). When you say “She sat down,” you just add information to folder x. The existential force (“there exists a woman”) comes from a default rule that kicks in at the end, not from the word “a” itself.

This explains donkey sentences nicely. “If Sarah owns a donkey, she beats it” creates a rule: for any folder entry matching “donkey Sarah owns,” add “Sarah beats it” to that entry. This naturally gives the universal reading (every donkey gets beaten).

But problems emerged. Consider: “Most women who own a donkey beat it.” If the sentence is true whenever most pairs of women-and-donkeys satisfy the beating relation, then a woman who owns ten donkeys and beats all ten weighs much more in the count than a woman who owns one donkey. That seems wrong—the sentence seems to be about women, not about donkey-woman pairs.

Approach 2: Dynamic Semantics

This approach keeps the idea that meaning changes as a discourse unfolds, but tries to do it in a more mathematically precise way. Think of it like this: a sentence doesn’t just have a truth value. It also changes the context for the next sentence.

When you say “A man loves Annie,” you don’t just say something true or false. You also set up a “variable” that the next sentence can pick up. “He is rich” then checks whether that same variable satifies “rich.” Even though “he” isn’t inside the original quantifier’s scope, the dynamic nature of the quantifier lets it “reach out” and affect later sentences.

This approach handles the basic puzzles well. But it runs into trouble with sentences like: “A man broke into Sarah’s apartment. Scott believes he came in the window.” This sentence has a reading where Scott just has a general belief (that some man broke in through the window), not a belief about a particular man. Dynamic semantics, like DRT, tends to force a specific individual into the belief—which misses this reading.

Approach 3: The Pronoun is a Secret Description

Maybe pronouns in these tricky cases actually are referring expressions—just not to simple individuals. Instead, they refer to whatever satisfies a description.

So “If Sarah owns a donkey, she beats it” really means: “If Sarah owns a donkey, she beats the donkey she owns.” The pronoun “it” is secretly a definite description like “the donkey Sarah owns.”

This is simpler in some ways. But it has its own problems. For one thing, it predicts a uniqueness requirement: “the donkey” implies there’s exactly one. But “a donkey” doesn’t imply uniqueness—Sarah might own five donkeys. Some versions of this theory try to handle that by saying the description refers within minimal situations (tiny slices of reality containing exactly one donkey). But this gets complicated.

Another problem: consider “A man murdered Smith, but John doesn’t believe that he murdered Smith.” “He” would become “the man who murdered Smith”—but then the sentence becomes contradictory (how can John not believe that the murderer murdered Smith?). Yet the original sentence is perfectly fine. So the description can’t be that specific.

Approach 4: Context-Dependent Quantifiers

Maybe the pronouns themselves are quantifiers—they say “there exists” or “for all” depending on context. The pronoun “it” in “Every woman who owns a donkey beats it” might really mean “some donkey she owns.” The sentence would then be: every woman who owns a donkey beats some donkey she owns.

This gives a weak reading (beating at least one donkey per woman) rather than the strong reading (beating all donkeys). And there’s genuine debate about which reading is correct. Consider: “Every person who had a credit card paid his bill with it.” Surely this doesn’t mean you had to use every credit card you own to pay—just one. So maybe the weak reading is right for some cases.

But then consider: “Every student who borrowed a book from Peter eventually returned it.” This seems to mean they returned every book they borrowed. So maybe both readings exist, and which one we get depends on context, the specific words used, and our background knowledge.

Why This Matters

You might wonder: why do philosophers care so much about pronouns? Two reasons.

First, anaphora reveals something deep about how human language works. Pronouns seem like the simplest words, but they connect to complex mental processes of keeping track of who and what we’re talking about. Understanding anaphora means understanding how our minds build and maintain models of conversations.

Second, these puzzles connect to big philosophical questions. Can we talk meaningfully about things that don’t exist? (The witch example suggests we can.) Do sentences have meanings that go beyond just being true or false? (Dynamic semantics says yes—they also change what can be said next.) How do we represent general beliefs versus beliefs about specific things? (The “Scott believes” example shows this matters.)

The debate continues. New evidence comes from sign languages, which use physical space to mark anaphoric connections—providing a window into how these mental processes work that spoken languages can’t offer. And researchers are still arguing about whether donkey sentences have one reading or two, and whether the differences between human languages reveal something universal about the mind.

Nobody has fully solved these puzzles. But the fact that simple pronouns can generate such deep questions is part of what makes language so fascinating.

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Appendices

Key Terms

Term	What it does in this debate
Anaphora	The relationship between a pronoun and the earlier word or phrase it “looks back” to for its meaning
Antecedent	The word or phrase that a pronoun points back to (e.g., “a woman” is the antecedent of “she”)
Bound variable	A pronoun that acts like a variable in math, linked to a quantifier like “every” or “some”
Discourse anaphora	Cases where a pronoun in one sentence looks back to a quantifier in a previous sentence
Donkey anaphora	Special cases where “a donkey” in “if” or “every” sentences seems to mean “every donkey”
Weak reading	The interpretation where a donkey sentence is true if each person beats some donkey they own
Strong reading	The interpretation where a donkey sentence is true only if each person beats every donkey they own
Dynamic semantics	A theory that sentence meaning includes how it changes what can be said next

Key People

• Peter Geach (1916–2013) – British philosopher who first pointed out the weird behavior of pronouns in “donkey sentences” and “intentional identity” discourses
• Hans Kamp (born 1940) – German philosopher/linguist who co-founded Discourse Representation Theory, arguing that anaphora requires a radical new approach to meaning
• Irene Heim (born 1954) – German-American linguist who independently developed a similar theory to Kamp’s, becoming one of the most influential semanticists of her generation
• Gareth Evans (1946–1980) – British philosopher who argued that pronouns in discourse anaphora function like definite descriptions, not bound variables
• Stephen Neale – British philosopher who developed a detailed D-type theory where pronouns “go proxy for” descriptions (including special “numberless” descriptions)

Things to Think About

1. If you say “A bird flew into the window. It was a sparrow,” does “it” refer to a specific bird? How do you know? What if you didn’t actually see which bird it was?

2. Consider: “No one brought an umbrella. They got wet.” Does “they” refer to everyone? To no one? To the people who didn’t bring umbrellas? How do you decide?

3. Does “Every hacker who found a bug reported it” mean they reported each bug (strong reading) or some bug (weak reading)? What about “Every chef who burned a dish threw it away”? Do different sentences work differently?

4. If sign languages use physical space to mark anaphora (pointing to locations for different people), does that mean spoken languages have invisible “locations” too? What would that say about how our minds work?

Where This Shows Up

• Law and contracts – Legal documents often depend on exactly what a pronoun refers back to. Disputes about “it” in contracts can end up in court.
• Computer programming – Variable binding in programming languages works much like anaphora. The “scope” of variables is a practical version of the same problem philosophers study.
• Everyday disagreements – Arguments like “Someone left their trash here. They should clean it up” involve exactly the same puzzles about referring to unknown people.
• Artificial intelligence – To make chatbots understand stories, AI systems need to solve anaphora problems. Modern language models still sometimes fail at this.