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Paul McNamara
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Hi Janice, It's not about wide scope. Sorry about the compression. Consider the classic semantics for iffy oughts in deontic logic (Hanson, Lewis...): ought q if p iff all the best accessible p worlds are q worlds. This does not support factual detachment: FD: ought q if p p so q Given that p is true in the actual world, and all the best p worlds are q worlds it does not follow that q is true in the best worlds per se, since the best worlds may be ~q worlds. So in my kill my aunt example, even though the best worlds where I kill her with a knife are ones where I use a large sharp knife, it does not follow that the best worlds per se are ones where I kill her with a large sharp knife--in those I don't kill her at all, and that's not changed by the fact that in the actual world, rat that I am, I will kill her for the inheritance. (This sort of semantics, blocks using disjunctive dilemma as well on your 2-4 or my 2'-4' for similar, really derivative, reasons.) But now suppose we add that it is *unalterable* for me that I will kill her with a knife? Then not only the actual world, but all accessible worlds are ones where I do so, and so we can detach on this semantics for iffy oughts and conclude that in the best accessible worlds per se, I kill her with a large sharp knife, and so that is what I ought to do. So valid detachment for this sort of semantics look like this: ought q if p *unalterable* that p So ought q (as well as this: ought q if p, ought p, so ought q). In your MINER case, one of the two disjuncts is not only true, but unalterably true (say that the miners are in shaft A). So you can sidestep this issue for your point by adding the unalterability of each disjunct in the MINER example (but not in mine). (Kratzer was briefly on my diss committee at UMass, but then Cresswell instead when she left for a year; in her earlier work at least, I believe she did not endorse factual detachment for iffy oughts.)
Hi Janice, A small point about the argument form as stated. It shares this form: 1') I ought not kill my rich aunt 2') If I kill her with a knife, I ought to do so with a sharp large knife 3') If I kill her with a hatchet, I ought to do so with a sharp large hatchet 4') either I will kill her with a knife or a hatchet 5') So either i ought to kill my rich aunt with a sharp large knife or I ought to do so with a sharp large hatchet. Many would deny this is valid, and classic make-the-best-of-it semantics for iffy "ought"s invalidates this form of argument, along with factual detachment. It is best to side step this issue by just adding unalterability qualifiers in front of each of your disjuncts in 4), since in the MINERS context, one of the disjuncts is unalterably true (unlike perhaps either of those in my 4') even if one of them is true).
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Jan 16, 2010