Chalmers on Scrutability
Here's a little question about David Chalmers' paper "Does Conceivability entail Possibility?". I'm interested in the relation between what Chalmers calls strong scrutability and what he just calls scrutability. In particular, I wonder if strong scrutability is really stronger than mere scrutability. This depends on a claim Chalmers makes in sections 10 and 11: that if there are inscrutable truths, it follows that some statements are epistemically possible (not ruled out a priori) but yet not really (primarily) possible. My question is: why does that follow?
An inscrutable truth is a statement S such that for some truth D,
i) D is positively conceivable.
ii) Whenever (D & F) is positively conceivable, then (D -> F) is a prioti.
iii) (D -> S) is not a priori.
It follows that for the relevant D, neither (D & S) nor (D & -S) is positively conceivable, and neither (D -> S) nor (D -> -S) is a priori.
It's important that at this stage we mustn't assume that whatever is possible is positively conceivable. If we could use this assumption, the alleged gap between epistemic possibility and real (primary) possibility is not hard to find: Since (D & S) is actually true, it can't be ruled out a priori; but it is not positively conceivable, and hence -- using the assumption -- also not really possible. Clearly, if we could use the assumption, every inscrutability would imply that some truths (like (D & S)) are not really possible. That's silly. (Moreover Chalmers can't make the assumption in the mentioned sections because otherwise the contrast he there draws between inscrutablilities and open inconceivabilities would vanish.)
Chalmers explains how inscrutable truths create a gap between epistemic possibility (he calls it "negative conceivability" here) and possibility as follows (that's in section 11 inside some brackets):
if S is a generalized inscrutability, then both D => S and D => -S will be negatively conceivable for a relevant D, but both cannot be possible.
"A => B" means that the material conditional (A -> B) is knowable a priori. So the first part of the consequens, I'll call it (1), says that neither the apriority of (D -> S) nor the a priority of (D -> -S) can be ruled out a priori. I think the second part, (2), is supposed to mean that it is neither possible that (D -> S) is a priori nor that (D -> -S) is a priori. It might also mean that it is impossible that (D -> S) and (D -> -S) are both a priori. But then the argument would be invalid unless we also reformulate (1).
At any rate, (2) doesn't sound too far-fetched. All it requires is that if a statement S is not a priori then it can't possibly be a priori. For by the inscrutability of S, we already know that neither (D -> S) nor (D -> -S) is a priori.
But how on earth do we get (1)?
Maybe it helps to have an example. Remember that we don't assume that all possibilities are positively conceivable. In fact, let's assume that modal imagination is a very poor faculty, so that "x is positively conceivable" is true iff x is one of the following three sentences:
1. Some cubes are blue.
2. Some roses are red.
3. Nothing is green.
Then every sentence S that is not itself knowable a priori is inscrutable. For example, "Some cubes are blue" is inscrutable because "Some roses are red" is true and i) positively conceivable and ii) no conjunction of it with anything else is conceivable, and yet iii) "if some roses are red then some cubes are blue" is not a priori.
By the inscrutability of S, we know that neither "if some roses are red then some cubes are blue" nor "if some roses are red then it is not the case that some cubes are blue" is a priori. That sounds right. But now (1) claims that even though these statements aren't a priori, we can't rule out their apriority on a priori grounds. But why not? Do I need empirical information to find out that "if some roses are red then some cubes are blue" is not the kind of thing that can be known a priori? Certainly not. So (1) is false. And I don't see how it could become true by dropping the simplification about our imaginative capacities. In fact, it seems to me that whenever anything is not a priori then it is a priori that it is not a priori.
I have the impression that I must have overlooked something very obvious.