Wednesday, October 17, 2012

Joint-Carving and Projectability

So this weird thing has been happening to me lately where I think about metaphysics. My current symptom is an attempted negotiation of Ted Sider's recent book, Writing the Book of the World. Ted's Big Idea is that there is objective structure to reality, and that this structure is really important for all kinds of reasons; I find the general picture a pretty attractive one, but I'm rather puzzled by some of his remarks on the applicability of structure to induction and confirmation.

Ted writes:
Which observations confirm a generalization 'all Fs are Gs'? A natural answer is the "Nicod principle": observations of Fs that are Gs confirm 'All Fs are Gs'. But suppose that an observation confirms any logical equivalent of any sentence that it confirms. Then, as Hempel pointed out, the observation of red roses confirms 'All ravens are black' (given the Nicod principle it confirms 'All nonblack things are nonravens', which is logically equivalent to 'All ravens are black'.) And as Goodman pointed out, Nicod's principle implies that observations of green emeralds before 3000 AD confirm 'All emeralds are grue' (sice green emeralds observed before 3000 AD are grue.) But anyone who believed that all emeralds are grue would expect emeralds observed after 3000 AD to be blue.
[This conclusion] can be avoided by restricting Nicod's principle in some way -- most crudely, to predicates that carve at the joints. Since 'is nonblack', 'is a nonraven', and 'grue' fail to carve at the joints, the restricted principle does not apply to generalizations containing them. In Goodman's terminology, only terms that carve at the joints are "projectable". (35)
I'm confused about this strategy. Ted says we can avoid the conclusion that nonblack nonravens confirm ravens' blackness because 'nonblack' and 'nonraven' don't carve at the natural joints. But 'nonblack' carves at exactly the same joint as 'black' does -- to push the metaphor only slightly further, it's the very same cut. So if 'nonblack' isn't joint-carving, and is therefore nonprojectable, then it looks like just the same would go for 'black', and mutatis mutandis for ravens and nonravens. So now it looks like I can't confirm that all ravens are black by observing black ravens. This isn't the result Ted wanted, surely.

So I'm worried that one of these things must be true:

  1. The story quoted above about why red roses don't confirm that all ravens are black is wrong;
  2. Black ravens don't confirm that all ravens are black; or 
  3. The 'black' joint is natural, but the 'nonblack' joint isn't.
When I asked Carrie about this, she suggested that Ted might be intending something like (3) here. After all, she pointed out, there might be more of an objective sense in which all black things resemble each other than that in which all non-black things do. I guess the thought would be that the metaphor is breaking down here; 'joint-carving' isn't the right term. Maybe this is right, but I didn't see that Ted could go this way, since he doesn't want to take objective similarity as the most fundamental thing. He wants structure to be most fundamental, and to explain objective similarity in terms of structure.

I feel like I must be missing something obvious here, but I can't see what it is. Somebody help?


  1. I think it's got something to do negation being less simple logically than the simple statement being negated. It's less about the natural joint and more about how complex your statement's logical operators are when speaking of that joint.

  2. Thanks, Jeremy; this looks like a version of the kind of strategy Carrie was suggesting. But can it square with Ted's insistance the relevant structural facts be objective and 'out there in the world'? It's not clear to me how objective considerations like these could depend on how we're able to talk about the relevant properties.

  3. I share your worry. Ted thinks negation is joint carving. Thus, if 'black' is natural, so must 'nonblack' be. But of course, Ted is going to end up saying neither 'black' nor 'nonblack' are perfectly natural - and being natural is an all or nothing affair on his view. So maybe he can say 'black' is more natural (which means it has a simpler reduction to the perfectly natural) than 'nonblack'. And this seems somewhat plausible.