I’ve been meaning to write up something on this excellent post by Robbie Williams on this excellent paper by Thony Gillies. But that post was getting long, so instead I thought I’d note one point from Thony’s paper that he doesn’t make as explicit as perhaps it should be. The point is that “wide-scope” interpretations of weak modals in the consequents of conditionals are massively implausible.
This is quite relevant to a debate in ethics about the interpretation of conditionals like “If p, you ought to do q”. One view, sometimes called “the wide-scope view” is that the deontic modal has wide scope, so the structure of that conditional is something like Ought (If p, you do q). There is a long thread on this over at PEA Soup. It seems to me that Gillies has shown that this view is untenable.
Gillies is mostly interested in epistemic modals, but it is pretty trivial to transpose his arguments to the ethical case. Here is one way to do this. Given reasonable background assumptions, e.g. that Alice and Bill are two normal human beings, (1) is false.
(1) If you kill Alice, you may kill Bill.
But (2) will be true despite the intuitive falsity of (1).
(2) You may make it the case that: if you kill Alice, you kill Bill.
That will certainly be true if the inner conditional in (2) is a material conditional. Since you may refrain from killing Alice, you may make the material conditional true. But, and this is the interesting point, it is also true on views that make the conditional much stronger.
For example, imagine that you, as a favour to Alice an Bill, drive them to the airport. You are a careful driver, and you stay out of accidents. But accidents happen on roads. Assuming you are (properly) free of homicidal tendencies, it may be that the only conceivable sate in which you kill Alice is one where you are part of a horrific accident that kills everyone in the car. So in the nearest world in which you kill Alice, you kill Bill. Indeed in all salient worlds in which you kill Alice, you kill Bill. But nothing wrong with this, provided you take all appropriate precautions that such a world is not actualised.
So the wide-scope interpretation of (1) is implausible. And it is implausible on general grounds that the ‘may’ in (1) takes narrow scope with respect to the conditional, but a strong modal like ‘ought’ should take wide scope. So the wide scope view is wrong.
Of course, there were reasons that people were pushed to the wide-scope view. Happily, I think Gillies’s positive view about how to interpret context-sensitive terms in the consequent of conditionals can explain (away) those motivations. But that’s for another post. For now I just wanted to publicise this neat argument against the wide-scope view.