I was doing some contextualist bashing over on Crooked Timber when I noticed that I hadn’t realised before. The explanation for this is probably completely obvious, and it’s just revealing my own ignorance that I don’t know the explanation, but I couldn’t figure out why (1) is three-way ambiguous, when by rights it should be four-way ambiguous.

(1) Bill said that he loves his mother. So did Tom.

The three readings I think the second sentence has are

(1a) Tom said that Tom loves Tom’s mother.
(1b) Tom said that Tom loves Bill’s mother.
(1c) Tom said that Bill loves Bill’s mother.

I don’t think the second sentence can mean

(1d) Tom said that Bill loves Tom’s mother.

Now why should this be? I thought the explanation for the original ambiguity was that we can break down the first sentence in (1) the following ways under lambda abstraction. (This will all be in words because I don’t really know how to use the right symbols in HTML.)

(1a’) Bill self-ascribed the property of being a person who loves his mother.
(1b’) Bill self-ascribed the property of being a person who loves Bill’s mother.
(1c’) Bill ascribed to Bill the property of loving Bill’s mother.

But we could equally analyse the first sentence in (1) as (1d’).

(1d’) Bill self-ascribed the property of having a mother loved by Bill.

And if Tom also did that, then ‘So did Tom’ would mean (1d). But that’s blocked somehow? What’s going on?

One explanation is that (1d) is a disambiguation of ‘So did Tom’, but it’s never the salient disambiguation because of pragmatic reasons. But what would the pragmatic reasons be?

Another explanation is that the differences are due to differences in the binding constraints on ‘he’ and ‘his’. I’m not really sure what those constraints could be, since they couldn’t be absolute constraints. When (1) means (1d’), ‘he’ means just what it does in the (1c’) interpretation, and ‘his’ means just what it does in the (1a’) interpretation. (This sentence is rough, but I hope it’s clear enough.)

To complicate matters, it seems (2) is four-way ambiguous.

(2) Bill said that his mother loves him. So did Tom.

I think that with a bit of effor we can get all four readings for this sentence.

(2a) Tom said that Tom’s mother loves Tom.
(2b) Tom said that Tom’s mother loves Bill.
(2c) Tom said that Bill’s mother loves Bill.
(2d) Tom said that Bill’s mother loves Tom.

To get the final interpretation, consider the following dialogue.

Who said that Bill’s mother loves them?
Bill said that his mother loves him.
So did Tom.

And to get the (2b) reading, simply stress ‘his’ in the first sentence of (2). At first I was unsure whether either (2b) or (2d) were available readings, but it seems that both are.

So maybe it’s just a pragmatic blocking on (1d), because it’s hard to see how we could have a semantic or syntactic reason for blocking (1d) as a disambiguation, while keeping all four here. Or maybe I’m just not alert enough to find a context where the (1d) reading is allowed, and if so there isn’t a problem at all. Very confusing.