Discourse, Diversity, and Free Choice
This paper began as a couple of blog posts in January 2007, here and here. At the time, I was thinking about why counterfactuals with unspecific antecedents appear to imply counterfactuals with more specific antecedents. I noticed that a similar puzzle arises for possibility modals in general. My hunch was that this is a special kind of scalar implicature: if you say of a group of things (say, rooms) that they satisfy an unspecific predicate (like, having a size between 10 and 20 sqm), you implicate that different, more specific predicates, apply to different memebers of the group.
At the time, Kai von Fintel pointed out to me that the puzzle is discussed under the heading of "free choice". I couldn't find my suggestion in the literature, most of which seemed to concentrate on a far too narrow range of cases (involving 'or' and deontic modals). Later, Paolo Santorio pointed out that my explanation resembles Nathan Klinedinst's proposoal in his (2007) dissertation. Klinedinst suggests that free choice effects are "diversity implicatures" of just the kind I thought they are. What I didn't originally appreciate is that the implicature can't be derived along standard Gricean lines. Klinedinst instead invokes a grammatical mechanism. I wasn't convinced by that, because it seemed (and still seems) to me that there is a fairly straightforward, pragmatic explanation.
Consider "The rooms are between 10 and 20 sqm". This implicates that the rooms are not all the same size. Why? Because if they all had a size of, say, 16 sqm, it would have been simpler and more informative to say so.
Next, consider "Some rooms are between 10 and 20 sqm". This also implicates that the relevant rooms are not all the same size. And for the same reason: if they all had a size of 16 sqm, it would have been simpler and more informative to say so.
But here's the problem for the Gricean model. Suppose there are rooms of size 10, 12, 15, 16, 20, and 40 sqm. So it's true that some rooms are between 10 and 20 sqm. My suggestion is that the implicature arises because if those rooms (the ones between 10 and 20 sqm) all had the same size, it would have been simpler and more informative to describe them as having that particular size. But what, exactly, is the stronger Gricean alternative that would have been available if all relevant rooms were the same size? "Some rooms are 16 sqm"? That's true even in the scenario I've described.
To derive the implicature, we have to hold fixed the original plurality. The formal mechanism is easy to describe with the help of discourse referents. Suppose we analyse "Some rooms are between 10 and 20 sqm" as introducing a plural variable X that can be re-used in subsequent assertions about the relevant rooms. We can then derive the implicature by assuming that the Gricean alternatives contain the same variable.
There are independent reasons to allow for such "dynamic implicatures". In the paper, I consider this example: "A gambler lost some of his savings. Another lost all of his." There's an implicature that the first gambler didn't lose all his savings. But the classical Gricean derivation doesn't work, because the alternative "A gambler lost all of his savings" is true -- it is verified by the second gambler. To derive the implicature, we have to hold fixed the relevant gambler.
In linguistics, it looks like most people have given up the neo-Gricean, pragmatic account of scalar implicatures. The most popular alternative postulates a lexical exhaustification operator which enriches the content of an embedded sentence by the negation of (some of) its scalar alternatives. This approach has been fruitfully applied to many puzzles beyond those I consider. I have no strong arguments against it. So I'm no longer convinced my explanation is correct. But I think it's worth considering.
I'm glad the paper has finally come out. I first submitted it to Linguistics & Philosophy in 2016, but withdrew it after three years, since it didn't seem to get any closer to publication. I hear turnaround times have since improved.