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Exactly one donkey

posted Sep 16, 2013, 6:19 PM by Ezra Keshet   [ updated Sep 16, 2013, 6:40 PM ]
The E-type theory of donkey anaphora requires each pronoun be unique (within a situation).  To this end, Heim follows Berman in claiming that (1) means (2):
  1. If a man owns a donkey, he beats it.
  2. Every minimal situation such that a man owns a donkey can be extended to a minimal situation such that the unique man in the situation beats the unique donkey in the situation.
Now, imagine that Farmer Joe owns three donkeys (total).  According to the definitions Heim assumes, then, there are three minimal situations such that Joe owns a donkey; and each of these situations contains exactly one man and exactly one donkey. This allows the pronouns "he" and "it" to refer to a man unique to the situation and a donkey unique to the situation. So far, so good.

Consider Heim's (presumed) meaning for (3), given in (4), though:
  1. If a man owns exactly one donkey, he beats it.
  2. Every minimal situation such that a man owns exactly one donkey can be extended to a minimal situation such that the unique man in the situation beats the unique donkey in the situation.
Notice that (4) means exactly the same thing as (2), since every minimal situation where a man owns a donkey is a minimal situation where a man owns exactly one donkey.  If this is right, however, then (1) and (3) should be synonymous.  But they aren't.  Comments?

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