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November 8th, 2007

Gillies on Wide-Scopism

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.

Posted by Brian Weatherson in Uncategorized

4 Comments »

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4 Responses to “Gillies on Wide-Scopism”

  1. Ralph Wedgwood says:

    Brian —

    Isn’t your argument against the wide-scope view essentially the very same argument as the one that was used by all of those great Scandinavian deontic logicians in the 1960s and 1970s when they were arguing in favour of the dyadic ‘ought’ (i.e. basically the same sort of conditional ‘ought’ that David Lewis advocates in Counterfactuals)?

    See e.g. Lennart Åqvist, “Good Samaritans, Contrary-to-Duty Imperatives, and Epistemic Obligations”, Noûs 1 (1967): 361–379.

  2. Brian Weatherson says:

    Perhaps it’s an old argument, but I didn’t see it in that Aqvist article. Gillies’ argument turns crucially on permission statements in consequents, which Aqvist didn’t seem to be concerned with.

  3. jrgwilliams says:

    Hi Brian,

    In the Gillies paper (unless I’m missing something), the dialectic is a lot more complicated: the mutual entailment between might-conditionals and might-conjunctions is used only to knock out what he calls “egalitarian” wide-scope theories. If I’m reading him right, Stalnaker-style theories of the conditional aren’t in the firing line of this particular style of argument. (The putative equivalence with “must” is used to knock out these).

    Of course, Stalnaker-theories are in the firing line of your argument, and it’s interesting to figure out why there’s this difference in ambition.

    Consider an “epistemicized” version of Stalnaker. Here are two crucial Stalnaker-y assumptions. First, that all else equal, epistemically possible worlds are closer than epistemically impossible worlds; and second, an indicative conditional is defective if its antecedent is epistemically impossible.

    Then “Might(if p, q)” holds iff there’s an epistemically possible world where “if p, q” holds. And that’s either (i) a pq world, or (ii) a world where the closest p world is a q world. If (i) then Might(pq) is true. If (ii), it must be that q is true at the nearest p world; but it follows from the two Stalnaker-y assumptions that the nearest p-world must be epist. poss. So this is the pq-world needed to make true Might(pq).

    The other direction is pretty clear: if Might(pq) then the pq world is one where (for Stalnaker) the conditional is true. So Might(if p, q) is true.

    There’s wriggle room here wrt (ii), but there’s a pretty good case for the equivalence between wide-scoped Might(if p,q) and Might(pq).

    What’s interesting about the case you mention, though, is that the parallel story doesn’t go through for the deontic modals. What was crucial to getting something like the equivalence on the Stalnaker story is the delicate interaction between the closeness-ordering for conditionals and the space of epistemically possible worlds. And absent some similar interaction between the closeness ordering and the space of permissible worlds, we can’t get the same story running.

    So I think the shift to the deontic case isn’t just an innocent reapplication of the same argument: it’s much harder to get traction against Stalnaker in the original setting.

  4. Rachael Briggs says:

    What’s interesting about the case you mention, though, is that the parallel story doesn’t go through for the deontic modals. What was crucial to getting something like the equivalence on the Stalnaker story is the delicate interaction between the closeness-ordering for conditionals and the space of epistemically possible worlds. And absent some similar interaction between the closeness ordering and the space of permissible worlds, we can’t get the same story running.

    Here’s a shot at getting the story running for deontic modals: Plausibly, it’s permissible to bring about F iff it’s permissible to perform a basic action C such that (if C, would F). (This is a little sloppy—I’m using C both for the action and for the proposition that the action occurs—but I don’t think the sloppiness does any harm.) So where O is the obligation operator, A is “Alice dies” and B is “Bob dies”, and the quantifiers range over actions (or the propositions that correspond to them), you might read 1 as follows:

    1*) For all X, (If A, would (if X, would B) —> O(~X))

    And you might read 2 as follows:

    2*) ~(For all X (If X, would (if A, would B) —> O(~X))

    The inequivalence between 1 and 2 could then be explained in terms of the failure of import/export on the Stalnaker semantics. (Or actually, something a bit weaker than import/export; I’m not sure what it’s called. “Associativity”?)

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