‘Can’ and Reference

I would like to make an observation about the semantics of ‘can’ (and, I believe, of agentive modals generally) that has not been noted, to my knowledge, in the previous literature. This observation appears to tell against a theory of ‘can’ of the kind proposed by Kratzer in her great essays on this topic.

Quine says that a context is ‘referentially opaque’ just in case the substitution of co-referring names may induce a change in truth value. Thus:

(1) Lois is unaware that Clark was born on Krypton

(2) Lois is unaware that Superman was born on Krypton

We can imagine that (1) is true and (2) false (perhaps this was true in the comic books). So ‘is unaware that’ is referentially opaque.

By contrast, a context is ‘referentially transparent’ just in case the substitution of co-referring names does not induce a change in truth value.

It will be helpful to define up an additional notion. Let us say that a context is strongly referentially transparent just in case the substitution of co-referring names OR definite descriptions does not induce a change in truth value. (Maybe this notion already has a name in the previous literature, and I think some people may already be using transparency in this broader sense, or even more broadly to range over demonstratives etc. Anyhow, this is how I will be using the term).

I now wish to make two claims: (i) ‘can’ is strongly referentially transparent and (ii) this is difficult to accommodate within the standard Kratzer framework for ‘can’.

Here is the argument for (i). Let us say that Smith is in fact the most popular man in town. Consider:

(3) Jones can have dinner with Smith

(4) Jones can have dinner with the most popular man in town

Given that Smith is in fact the most popular man in town, the truth of (3) ensures the truth of (4), and conversely. There is no way for the one to be true and the other false.

Crucially, this is the case even under unusual circumstances. Let us say that Smith would in fact have dinner with Jones only if his popularity declined – since he is so popular, he is very busy, but were he less popular, his calendar would free up. So – now speaking a bit more semantically – the scenario in which Jones in fact has dinner with Smith is one in which Smith is _not_ the most popular man in town. Nonetheless, that scenario suffices for the truth of (4), since we describe the scenario in terms of how things actually are – and, actually, Smith is the most popular man in town. So we might sensibly say: “Jones can have dinner with the most popular man in town, Smith, though, if they really did have dinner, Smith would not be so popular.”

Here is the argument for (ii), that it is difficult to accommodate this observation within the Kratzer semantics. On the Kratzer semantics, (3) is true only if there is a world w meeting certain conditions (roughly, that it is in the set of worlds W that are compatible with the modal base and that are most highly-ranked according to the ordering source) such that Jones has dinner with Smith at that world. Let us say that there is some such world – call it w1 – and so that (3) is true.

Now, by our argument above, (4) must be true as well. Is it? Well, (4) is true only if there is a world w meeting certain conditions (roughly, that it is in the set of worlds W that are compatible with the modal base and that are most highly-ranked according to the ordering source) such that Jones has dinner with the most popular man in town at that world. Is there? Well, there may or may not be. Since all that is ensured by the truth of (3) is the existence and accessibility of w1, the truth of (4) is ensured only if w1 is a world such that Jones has dinner with the most popular man in town at that world. And this may not be the case, as in the scenario described above.

So it is difficult to explain the strong referential transparency of ‘can’ on the Kratzer account. I do not say that it is impossible to do so, and I’m open to the idea that some mechanism could give an explanation of this phenomenon. That said, I think this little argument suggests two broader points.

First, there’s an extensive philosophical literature on reference and modality, including the Quine essay mentioned above and a few lectures. To some extent these issues have been taken up in the excellent recent literature on epistemic modals. To my knowledge, they are less studied in the literature on ‘root modals,’ which include agentive modals but also include circumstantial modals more generally as well as deontic modals. I’d be interested in seeing more discussion of how issues of reference and modality play out in thinking about root modals.

Second, I’m sympathetic with the thought that agentive modals don’t quantify over worlds but instead quantify over intra-worldly entities – what I call options. Options are not themselves modal, though they do have modal entailments. On my view, (3) is true because Jones has, at this world, a certain option. That very option is, at this world, an option of meeting the most popular man in town. So (4) is true as well. So this is a phenomenon that can be explained quite simply when we take options as fundamental.