Yet another idea that arose from a converssation with John Hawthorne. This one seems relevant given the “Syracuse Workshop on the A Priori”:http://philosophy.syr.edu/swap/index.html starts later this week.

Timothy Williamson has argued that there are no substantial luminous conditions. That is, there is no condition such that whenever you are in it, you are in a position to know you are in it. There is an exception perhaps for necessary conditions such as being such that 2+2=4. Is there also an exception for a priori knowledge, or does his argument work there too? I suspect his argument (or more likely the variant on it that you can get from “my response to Williamson”:http://brian.weatherson.org/lummarg.htm) does work in that domain.

There’s two relevant questions here.

bq. (1) If p is a priori knowable, is it knowable that p is a priori knowable?
(2) If p is a priori knowable, is it a priori knowable that p is a priori knowable?

I think in general the answer to each question is _no_. I’ll just argue that the answer to (1) is _no_ (at least if it’s taken to quantify over all p), from which it follows that the answer to (2) is _no_. The examples are a little controversial, and to some extent they track my epistemological biases, but I think they can probably be modified to fit _your_ epistemologial biases provided you aren’t too, er, biased.

(Note that to motivate the safety principle I’ll use below it would be much easier to use what I call in the paper belief-safety rather than content-safety in the above argument. I think the fact that this anti-luminosity argument requires belief-safety rather than content-safety is actually a consideration in favour of taking belief-safety to be the central notion.)

Assume we have a transparent description of the (past-directed) evidence I actually have about Ithaca’s climate. Let E be shorthand for this description. I think (3₃₆₅) is a priori knowable, and knowably a priori knowable at that.

bq. (3₃₆₅) Anyone with evidence E is justified in believing it will snow in Ithaca sometime in the next 365 days.

But (3₁) is clearly not a priori knowable, indeed it is knowably false.

bq. (3₁) Anyone with evidence E is justified in believing it will snow in Ithaca sometime in the next 1 day.

Now the following safety principle, though a bit of a mouthful, seems true to me for all n.

bq. (S) If it is knowable that (3_n) is a priori knowable, then (3_n-1) is a priori knowable.

By familiar means we can get a contradiction from the knowability of (3₃₆₅) being knowable a priori, the falsity of (3₁), and the truth of (S) and (1). Hence (1) is false.

If you like the contingent a priori, you can re-run this argument with contingent a priori conditionals like (4₃₆₅). (I don’t think (4₃₆₅) is actually contingent a priori, because the antecedent probably needs to be more complicated, but it’s close enough, and the complications are irrelevant here.)

bq. (4₃₆₅) If E is true, then it will snow in Ithaca in the next 365 days.
(4₁) If E is true, then it will snow in Ithaca in the next 1 day.
(S*) If it is knowable that (4_n) is knowable a priori, then (4_n-1) is knowable a priori.

From (1), the knowability of (4₃₆₅) being knowable a priori, the falsity of (4₁), and (S*) we get a contradiction. So again (1) is false.

John had a lot of other examples, but I’ll leave them for his blog – if he ever starts one. As it stands I think there are lots of slippery slope arguments against a specialised version of the KK principle applied to a priori knowledge.