modals as generalized quantifiers
April 11, 2008The Kratzer story about natural language modals is roughly that they make generalized quantifiers, by taking sets of worlds (which may or may not be made explicit) as arguments. On this story, the logical form of a conditional claim of epistemic necessity if p, must q will be given by must(p)(q). The first argument slot of must is the restrictor, the second the scope. Ok.
It seems pretty clear that epistemic modals are conservative, in the sense that they always satisfy the following schema.
δ(p)(q) iff δ(p)(p∩q)
(If p, must q) iff (if p, must p and q)
(If p, might q) iff (if p, might p and q)
But it seems pretty clear that deontic (or otherwise normative) modals are not. Consider (1). (1) seems like good advice, but (2) seems like terrible advice.
(1) If you play Russian roulette, you ought to win.
(2) If you play Russian roulette, you ought to play Russian roulette and win.
I don’t know why there’s this asymmetry, or how it might be accounted for (though I can’t imagine this hasn’t been addressed a long, long while ago, and I have a hunch that adding nested modals, a la von Fintel, might help alleviate things). On the Kratzer semantics, ought means (modulo some other things that aren’t important) all, and all is conservative. Help!
Addendum: thinking some more about this, I’m not really sure where to locate the worry. The Kratzer truth conditions for (1) do seem to be correct — (1)’s true iff in all the deontically best worlds where you play Russian roulette, you win — and that straightforwardly entails that all the deontically best worlds where you play Russian roulette are worlds where you play Russian roulette and win. So what’s going on with (2)?
April 11, 2008 at 8:04 pm
re: your addendum
the conjunction is scoping over the modal