In the comments below Dave Chalmers said he’s on the road, so it’s probably wrong to launch into criticisms of his theory at just this time while he’s not ideally placed to respond. But I’m never as motivated to avoid the wrong as I should be, so here’s a brief note on Dave’s concept of positive conceivability. All the references are to Does Conceivability Entail Possibility?.

Dave wants to defend the answer __yes__, at least when conceivability is properly curtailed. There’s a few aspects to the curtailment, but one is the distinction between positive and negative conceivability.

bq. “S is [negatively] conceivable if no contradiction is detectable in the hypothesis expressed by S”

bq. S is positively conceivably if “one can form some sort of positive conception of a situation in which S is the case.”

The initial problem is that neither positive nor negative conceivability entail possibility. If S is just too complex to detect a contradiction in, it will be negative conceivable even if impossible.

And Dave acknowledges that some incoherent situations are positively conceivable.

I think The Restaurant at the End of the Universe, from where diners can watch the universe ending, is such a case. I think (tentatively) that it’s part of the concept of observation that you can’t observe the end of the universe because observation is a causal process and the end of the universe is the end of all causal processes. We’ll come back to my tentativeness on this point very shortly.

In any case, Escher prints such as Waterfall can provide clearer cases of positive conceptions of the impossible.

Note that since neither positive conceivability nor negative conceivability entail possibility, their conjunction cannot entail possibility either. Let P be an impossibility that is positively conceivable, and N an impossibility that is negatively conceivable. Then P v N will be an impossibility that is both negatively and positively conceivable.

Dave wants to mix the two concepts, but not quite in this way. To avoid Escher like cases, he modifies the definition of positive conceivability as follows.

bq. S is positively conceivable when one can __coherently__ modally imagine a situation that verifies S. A situation is coherently imagined when it is possible to fill in arbitrary details in the imagined situation such that no contradiction reveals itself. To coherently imagine a situation that verifies S, one must be able to coherently imagine a situation such that reasoning about the imagined situation reveals it as a situation that verifies S. This notion is our core notion of positive conceivability: I will henceforth say that S is positively conceivable when it is coherently modally imaginable.

I don’t think this is the kind of thing that we can safely take to entail possibility for a couple of reasons, both of them methodological. Basically S is positively conceivable when there’s a fictional world F such that (a) we can positively conceive of F, and (b) F is negatively conceivable. That is, when F is both negatively and positively conceivable. But since we’ve already seen that positive and negative conceivability does not entail possibility, it’s not altogether clear why the positive and negative conceivability of F entails its possibility. It’s possible that for sufficiently detailed hypotheses, positive plus negative conceivabilty is enough for possibility, but I’d like to see a strong argument for why this is true.

Here’s where the Restaurant becomes important. It’s hard for me to tell whether the Restaurant is impossible. (Well, it’s pretty clearly impossible in some respects, but whether it’s impossible to observe the end of the universe.) I think it is, but I didn’t think this when I first heard about the Restaurant. What with my numerous intellectual failings there are sure to be many impossible things I now conceive of without noticing their impossibility. Maybe at the limit of ideal reasoning all these impossibilities would be made clear, or maybe they wouldn’t be. (There’s a reason ideal negative conceivability does not entail possibility after all.) So it seems possible to me that there should be cases like the Restaurant that even an ideal observer will not be able to see are incoherent. In the nature of the case, it’s hard to come up with examples since any example I give will look like a Moorean paradox, but I think there could be such cases.

The other methodological quibble concerns Dave’s argumentitive strategy at this point. Dave notes that there are very few clear examples of this kind of positive conceivability without possibility (assuming we mean ideal conceivability and positive possibility, as I do). But that doesn’t strike me as very good evidence that there are no such examples. We know that positive conceivability is a good inductive guide to possibility. And we know negative conceivability is a good inductive guide to possibility. And we know these guides fail in different ways. So we know that whether their combination (either in the crude form that I gave above or Dave’s more subtle form) will be __really__ good inductive guides to possibility, i.e. that they won’t have many counterexamples, before we even go and look at the counterexample data. So the fact (and I think it is a fact) that all the potential examples of positive conceivability without possibility are contentious is __just what we’d expect__, and hence no evidence that there are no real such examples.