This came up in a discussion thread on facebook (do we have to start citing that now?) and I thought I'd do a quick post. The question was whether there were examples of the contingent apriori that did not involve indexicals or demonstratives. Floated a possibility that I think I discussed with Turri some time ago that I also think figures in his forthcoming PPR paper. Suppose you know that there's a large and fair lottery coming up and you have a ticket for it. If you think you know your ticket will lose, the question is whether you can also know the lottery conditional apriori:
(LC) If I have a ticket in a fair lottery with n tickets, my ticket will lose.
I think that in some ways, this is a poor choice of examples. There are difficult questions about whether you can know lottery propositions and this muddies the waters a bit. Let's try something a bit different.
Suppose you're a fallibilist who thinks that if S has fallible grounds, FG, S can know some contingent proposition p by believing p on FG. Consider the fallibilist conditional:
(FC) If I have FG, p.
I know apriori that if I don't have FG, FC is true. I won't know apriori that FC is true in a world in which I have FG and ~p. But, is there any possible world in which I know FC apriori?
Someone could say that there's a possibility of error that comes with believing FC, but that's true when it comes to believing p on the basis of FG. Assuming that the fallibilist is right, this "possibility" of error is not sufficiently threatening to prevent you from knowing p. So, the question is whether it is sufficiently threatening to prevent you from knowing FC apriori.
Here's an argument for the claim that fallibilists ought to believe in the contingent apriori:
(1) The possibility if being mistaken in believing p when you have FG does not prevent you from knowing p and the same possibilities of error that arise when you believe on FG are the possibilities of error that arise when you believe FC on apriori grounds.
(2) The the threatening possibilities aren't sufficiently threatening to prevent you from having aposteriori knowledge, they aren't sufficiently threatening to prevent you from having apriori knowledge.
(C) You ought to think you can know FC apriori if you think you can know aposteriori that p is true on the basis of FG.
The argument for (2) is basically this: differences between apriori and aposteriori knowledge need to be explained, not brute.
I don't buy the argument, but I think it's interesting. I suspect that (1) is mistaken. ((2) might be as well.) Knowledge-threatening possibilities are not just a function of your evidence or grounds, but also your situation externally characterized. In describing someone has having FG, we might rule out certain knowledge threatening possibilities that don't get ruled out if all we have is someone who can entertain the conditional FC. So, there's no particularly compelling reason (yet) to think that fallibilists ought to embrace the contingent apriori.
So, perhaps the response works if we assume this: the set of knowledge threatening possibilities an individual needs to neutralize differ depending upon whether the individual:
(a) knows that she has FG vs.
(b) knows that FC is true if ~FG or if p.