This could go on all day, but I have serious work to do, so let’s finish with one of my favourite topics. It’s also from Laura’s 2D paper.

In that case, it may make best sense to say that your word is ambiguous and to assign two distinct semantic values. In Hartry Field’s terminology, your word partially refers to H2O and it partially refers to XYZ. This is quite different from saying that it refers to the disjunctive kind H2O-or-XYZ. Clearly, deciding which of these competing interpretations is correct will be neither easy nor automatic.

(Bonus nitpick: I rather doubt that Field’s partial reference is anything at all much like ambiguity. When a word (or, better, a sequence of letters) is ambiguous the inactive meanings are irrelevant to the truth conditions of sentences it contains. When a word has multiple partial referents, they are all relevant to the truth conditions of sentences it appears in.)

Actually this is usually fairly easy. I don’t know whether it’s automatic. These days nothing is automatic, not even taxes. (You still have to make an effort to pay them – that’s why they are late sometimes.) But it’s easy. I’ve probably harped on this a few times before, but since I got some things wrong last time I did, I’ll do it slowly this time.

I used to think cousin was an unambiguous term. Then I realised it was, at best, the disjunction of male cousin and female cousin. Maybe it isn’t disjunctive though. Or maybe it’s ambiguous between those two meanings. If I read Kripke on descriptions, it seems the way to tell whether a term that applies to Xs and Ys is ambiguous between X and Y is to check whether there are usually different terms for X and Y in other languages, and no term for their disjunction. Well I checked a handful of Western European languages (making sure the sample was small and not random) and found there are different terms for male cousin and female cousin, and no term for their disjunction. I was in a panic.

Fortunately I read Zwicky and Saddock’s “Ambiguity Tests and How to Fail Them” and came to my senses. Here’s a few ways that ‘cousin’ behaves that an ambiguous term, say ‘bat’ does not. (Assume Jack is a male cousin of mine, Jill is a female cousin of mine, Ron is my pet bat, and Rosie is my baseball bat. Assume that it’s not abnormal to name a baseball bat.)

(1) Jack and Jill are my cousins.
(2) *Ron and Rosie are my bats.

(3) Jack is my cousin, and so is Jill.
(4) *Ron is a bat, and so is Rosie.

There’s a few other tests that are (marginally) more subtle, but the general principle is sound. If a term t applies to both the Xs and the Ys, then it is ambiguous only if (5) is bad, where a is an X that isn’t a Y, and b is a Y that isn’t an X.

(5) a and b are t

If that reads badly for some reason, you can always use

(6) a is a t, and so is b.

If t is unambiguous, each of these is fairly natural, unless there is some other defect in the sentence. I’m inclined to think this part of the program really is easy. Whether determining the A and B is easy may be another matter, but there isn’t much of a problem at the ambiguity vs disjunction threshold.