An Antinomy about Anaphora

Standard theories of so-called donkey anaphora (Kamp 1981, Heim 1982, Groenendijk and Stokhof 1991) predict that sentence (1) is truth-conditionally equivalent to (2).¹

1. 1. Every farmer who owns a donkey beats it.

2. 2. Every farmer who owns a donkey beats every donkey that he owns.

I will refer to the proposition expressed by (2) as the strong reading of (1). A nonstandard theory, defended by King (1993, 2004), predicts that (1) is equivalent to (3).

1. 3. Every farmer who owns a donkey beats a donkey that he owns.

The proposition expressed by (3) is the weak reading of (1).

Although the authors I have referred to disagree about how best to interpret (1), they agree that (1) is not ambiguous; it semantically expresses no more than one reading. Not everyone shares this opinion, though. Schubert and Pelletier (1989), Kanazawa (1994), and Chierchia (1995) suggested that sentences relevantly like (1) are ambiguous. ² Consider, for example, sentences (4)–(6).

1. 4. Everyone who owns an umbrella leaves it at home on a sunny day.

2. 5. Everyone who owns an umbrella uses it on a rainy day.

3. 6. Every farmer who owns a donkey rides it to and from the market on Saturday.

Sentence (4) naturally elicits the strong reading, on which every umbrella is left at home. In contrast, (5) and (6) naturally elicit the weak reading, on which an umbrella is used and at least one donkey is ridden. Very likely, which reading is favored is determined by our knowledge of how people use umbrellas in rainy and sunny conditions, and of how someone typically uses something as a means of transportation. So (4)–(6) do not conclusively support the idea that the ambiguity is semantic in nature, because (it is standardly assumed that) semantic aspects of meaning can be recovered by speakers/listeners without the aid of “world knowledge” (i.e., knowledge that in some way extends beyond what is needed to be linguistically competent).

Aware of examples such as (4)–(6), King (2004) expressed skepticism about there being an ambiguity. His skepticism was based on two considerations. First, he claimed, it is difficult to construct a single sentence that allows for both a strong and a weak reading. Second, sentences relevantly like (1), but which begin with some rather than every, seem always to elicit a weak reading. Consider, for example, Some farmer who owns a donkey beats it. We naturally take this sentence to mean that some farmer who owns a donkey beats at least one of his donkeys. “This makes the view that the sentences actually possess both readings as a matter of their semantics at least somewhat suspect” (King 2004:110).

I think King and others are wrong to be skeptical. Sentence (1) semantically expresses both strong and weak readings. This can be clearly illustrated as follows.

Imagine a world—call it McWorld—where there are exactly two farmers, Old McDonald and Young McDonald.³ And let us say OM owns exactly two donkeys, Daisy and Duke. YM owns exactly one, Duchess. OM beats Duke, but not Daisy. YM beats Duchess. Now, unless we acknowledge that (1) is semantically ambiguous between the strong and weak readings, two equally compelling arguments would force us to say that my description of McWorld is incoherent.

thesis

1. 7. OM owns Daisy and doesn’t beat her.

2. 8. So, OM owns a female donkey and doesn’t beat her.

3. 9. So, OM owns a donkey and doesn’t beat it.

4. 10. So, a farmer owns a donkey and doesn’t beat it.

5. 11. Therefore, not every farmer who owns a donkey beats it.

antithesis

1. 12. OM owns Duke and beats him.

2. 13. So, OM owns a male donkey and beats him.

3. 14. So, OM owns a donkey and beats it.

4. 15. YM owns Duchess and beats her.

5. 16. So, YM owns a female donkey and beats her.

6. 17. So, YM owns a donkey and beats it.

7. 18. OM and YM are the only farmers who own donkeys.

8. 19. Therefore, every farmer who owns a donkey beats it. [From (14), (17), and (18).]

Every inference in both...