There are other ways for experience to be relevant to the justification of a priori beliefs than by enabling the concepts that are part of their contents. It's also standardly allowed that certain experiences would defeat a priori justification -- the experience of lots of misleading but authoritative testimonial evidence, for example, could make it unreasonable to retain some particular a priori belief. If such obtained, then you wouldn't be justified; therefore, your justification depends on such experience not obtaining. Thus does, for example, Marcus Giaquinto distinguish between 'positive' and 'negative' roles for experience:
We could mark the distinction by saying that if a belief is rationally revisable in the light of future experience, its retention is negatively dependent on experience; and if a belief cannot have been justiﬁably acquired unless some experience was used as grounds in the process, its acquisition is positively dependent on experience.
But there is room for a kind of dependence on experience that is neither 'negative dependence' nor 'positive dependence' in Giaquinto's sense. And I think that it, too, is consistent with apriority. We can distinguish between the reasons in favor of some belief, on the one hand, and various conditions that are necessary for those reasons to count in favor of the belief, on the other. And in at least some cases, we should think that experiences can play that latter role in a way consistent with apriority. I'll close with an example, and continue with further thoughts and possible applications in another post.
Consider a moderately complicated proof. Suppose it requires a couple dozen lines, and involves fairly lengthy sentences. In fact, it is valid, and indeed, I have produced it correctly -- every step followed from the previous one in a way that I appreciated while writing it down on my blackboard. I've reached my conclusion, but I do not, at this moment, know it to be true. The reason this is so is that the proof is too complicated for me to know it sound straightaway; the chance of making a mistake is too great. Sometimes I apply rules incorrectly; sometimes I accidentally change variables. I don't do this very often -- no more than most philosophers -- but I do it often enough that it would be unreasonable to be confident in the soundness at this point. Instead, I should go back and check my work. I review each step, looking for mistakes, and find that I made none. Now I know the conclusion.
My experience of checking my proof played a significant role in my knowledge of its conclusion. Certainly, that latter knowledge at least counterfactually depends upon it. But these experiences, of course, weren't necessary for the possession of any concepts in the conclusion; I was perfectly capable of entertaining the thought before I began. And this is a positive dependence on experience; it's not just that I need to lack particular misleading experiences. Nevertheless, this looks like a merely enabling role for experience; my belief in the conclusion is not based on my experience of checking the proof; it is based only on the premises. If those are a priori, then my knowledge of the conclusion is too.
So there are ways for experience to play merely enabling roles beyond the ones articulated above.
Here is how I would describe the case. When you went through the proof for the first time you didn't have knowledge because you had an undercutting defeater - something like: when I go through proofs of this degree of complexity, I am not reliable enough to acquire knowledge on this basis. By going through the proof once again, you defeat this defeater because, say, you know that going through a proof of this degree of complexity twice usually suffices for knowledge. So, the impression that "this looks like a merely enabling role for experience" probably arises because the experience involved when you go through the proof the second time just helps to defeat a defeater, which is - in some sense - not much of a positive epistemic achievement. Still, to help defeating a defeater is more than merely playing an enabling role - at least that's how it looks to me.ReplyDelete
Joachim: two responses. First, it's not clear that the line you suggest is going to be sufficiently general. For there won't always, I think, be the relevant kind of empirical defeater; a special feature of the case that you rely on is that I know these facts about my reliability. But suppose I don't; for all I know, I never make logical or transcription errors. I think the worry still goes through. If in fact I'm not reliable enough, then I don't know until I check my proof, whether or not I had that empirical defeater.ReplyDelete
Second, suppose you're right: the role for experience described is a empirical-defeater defeater. Isn't that just the kind of thing I'm talking about? It's not part of my evidence for believing C; my reasons for believing C don't include having double-checked the proof.
to your first point: it seems like you're going in a Burgean direction here, at least I vaguely remember Burge saying similar things (e.g. in "Content Preservation" or in his paper on the apriority of computer proofs). Anyway, it's not clear to me anymore why you actually need the complication with going through the proof for a second time. After all, when you go through it the first time, experience is already involved when you work out the steps of the proof on the blackboard - and it seems merely enabling here just as well, even though it is probably crucial for reaching the (correct) conclusion. In fact, what the experience & the blackboard are doing in your case seems exactly parallel to the merely preservative use of memory à la Burge.
To your second point: Suppose you're right that the experience involved in checking the proof is not part of my evidence for believing C. Doesn't that just show that there are other ways to play more than a merely enabling role than by being part of one's evidence? For, it just seems undeniable to me that either being a defeater or being a defeater-defeater is more than being something that's merely enabling. Maybe we could call a defeater a "preventing condition" and a defeater-defeater a "restoring condition", and then my claim would be that in your original case experience plays a merely restoring role - still something else than a merely enabling one...