I've been thinking a little about the puzzle about the contingent a priori, and at the moment my basic thought is that there are two ways of looking at the problem. I'll try to explain them here. All I really want to do is just to try to articulate the two different ways of looking at the puzzle. I'd be interested in hearing what people think about them, of course.
Given the factivity of knowledge, and hence of a priori knowledge, it is natural to think that only true sentences could qualify as contingent a priori. As a working characterization, let us understand contingent truth and apriority in the following way:
A sentence S is contingently true if S is true in the actual world and there is at least one accessible possible world at which S is false.
A sentence S is a priori if one may have a belief in S (or some appropriate semantic entity associated with S) the justificational force of which does not rest upon experimental factors, although acquiring the resources for the appropriate belief-formation may do so.
One way to see why, given this sketch of the notions, it might be found puzzling how some sentences could be both contingently true and a priori, is to introduce a notion of triviality, or uninformativeness of the sort which is intuitively associated with sentences like 'John is John'. However, approaching the puzzle of the contingent a priori through a notion of uninformativeness really gives us two ways of looking at the problem.
According the view held by Stalnaker in Inquiry (MIT Press, 1984), passing on information is a matter of distinguishing between possible worlds. On such a view, one could regard a sentence as trivial if acquiring knowledge of its truth does not require distinguishing between worlds. Consequently, since a contingently true sentence is false at some possible world w, finding out whether it is true will always require the nontrivial task of distinguishing the actual world from w.
The upshot of such a train of thought would be that contingency implies non-triviality or informativeness. The puzzle then arises from the further consideration that discovering a posteriori that, say, the sentence ‘Indonesia has over a hundred active volcanoes’ is true seems to involve distinguishing how the actual world is from other ways it might have been, namely those ways such that the sentence would be false. But since finding out that a contingent sentence is true requires exactly that kind of enterprise, this view would describe the puzzle as how we could have a priori knowledge of an informative sentence.
On the other hand, some philosophers seem to think that this way of characterizing the worry is incorrect. Indeed, Evans ('Reference and Contingency' 1979, reprinted in his Collected Papers, Clarendon 1985, p. 198) states that:
"The puzzle is not how we can know a priori something informative, but how something contingent can be uninformative."
We might conclude that what separates Evans’ view from Stalnaker’s is that for Evans, the triviality or informativeness of the sentences in question resides in the apriority, or otherwise, of the sentence.
So, the two ways of looking at the puzzle derive from two ways of looking at uninformativeness. In a framework like Stalnaker's, no contingent proposition could be uninformative, and so the puzzle becomes how we can know a priori something informative. On Evans' view, uninformativeness is tied to apriority in the first place so that the puzzle becomes something we can know a priori, and which is therefore uninformative, could be contingent.
I think this relates to the way Kripke (Naming and Necessity, Blackwell, 1981) himself describes the problem, although I'm not sure exactly how. Kripke seems to think that a proposition is a priori just in case the mere understanding of S implies knowing without relying on evidence about any distinguishing characteristic about the actual world, that S is true in the actual world. And it seems that what he takes himself as having shown is that some propositions are like this even though there is a distinction to be made between worlds in which they are true and worlds in which they are false, i.e. they are contingent.
It is interesting to note in this connection how Kripke characterizes the view he is attacking:
"I guess it’s thought that [...] if something is known a priori it must be necessary, because it was known without looking at the world. If it depends on some contingent feature of the actual world, how could you know it without looking. Maybe the actual world is one of the possible worlds in which it would have been false." (p. 38)
Kripke adds concerning the traditional view:
"This depends on the thesis that there can’t be a way of knowing about the actual world without looking that wouldn’t be a way of knowing the same thing about every possible world." (p. 38)
At the moment, I'm not entirely sure how to link this up with either of the two ways I tried to delineate above. Does this suggest that Kripke is thinking of the puzzle in ways which are more congenial to Evans' than to Stalnaker's, or the other way around, or neither?
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