Generalized Scrutability
I'm back. Here's a question that occurred to me while I was listening to Dave Chalmers's talk on scrutability.
First some background. One might think that for every world w there is a complete description D true at w such that all and only the sentences true at w follow a priori from D: simply let D contain all sentences true at w. Then all sentences true at w will be a priori entailed by D. However, if "true at" is read counterfactually, sometimes sentences false at w will also be so entailed. Consider Twin World where XYZ occupies the water role. "Water doesn't occupy the water role" is true at Twin World. But "water occupies the water role" is a priori, and hence a priori entailed by everything1. Thus every complete description of Twin World a priori entails a contradiction (and every sentence whatever).
It's better to read "true at" counteractually: S is counteractually true at w if w is in the primary intension of S; which it is roughly iff S is true given that it turns out that w is the actual world. "Water doesn't occupy the water role" is not counteractually true at Twin World. Moreover, on the counteractual reading, "water" never needs to occur in the vocabulary of D. For the primary extension of "water" at every world is whatever plays the water role at that world. If that is knowable a priori, the true "water" sentences are therefore a priori entailed by the sentences describing the stuff that occupies the water role.
Suppose at some world w nothing occupies the water role: there are no seas or rivers or taps in our surroundings at w, nor is there any stuff suitably causally linked to our use of the term "water". Then the primary extension of "water" at w is empty, and "there is no water" is counteractually true at w.
Dave Chalmers and Frank Jackson have argued that all macrophysical truths are a priori entailed by microphysical and phenomenal truths. The phenomenal truths are crucial since, as I understand the argument, the primary extension of macrophysical terms is largely determined by phenomenal facts.
Now consider a world w without consciousness, where there are no (relevant) phenomenal truths. w might be Zombie World, or a world containing nothing but yellow rubber balls. If the primary extension of macrophysical terms at w is whatever occupies a certain largely phenomenal role at w, all our macrophysical terms will end up empty at w. So "there are no planets, no tables, no trees, etc." will be counteractually true at Zombie World, and "there are no rubber balls" at Rubber Ball World.
My question is: is that so?
I don't have a good argument why it shouldn't, but it seems odd to me. For one, it doesn't pass the usual heuristics: If it turns out that there are no phenomenal states, will it turn out that there are no planets? I don't think so. More importantly, I would have thought that at least for some macrophysical terms, primary and secondary intension coincide. But if the primary extension of all macrophysical terms is empty at Zombie World this can't be true. For surely there are planets and tables and trees at zombie world, so the secondary extension of those terms isn't empty there.
(A similar problem arises for terms whose primary intension is largely deferential, as it is on some 'theories' of direct reference: If "Neptune" denotes whatever Leverrier called "Neptune", then "Neptune doesn't exist" will be counteractually true at every world where Leverrier doesn't exist. Similarly, if "elm" denotes whatever the experts call "elm", "elms don't exist" will be counteractually true at every world where there are no experts. However, this problem can easily be avoided by conceding that those terms are not in fact largely deferential.)
[1] Update: Actually, "water occupies the water role" isn't a priori. But "if anything occupies the water role then water occupies the water role" is. So still "water occupies the water role" is a priori entailed by "something occupies the water role" which is true at w.