Some epistemologists deny closure for knowledge. Dretske is the representative example. (Mark Kaplan was at Brown last week with an anti-closure view, too.) Dretske thinks that I may know that p, and know that p entails q, and believe q on that basis, and yet my belief that q may fail to be knowledge. It's nice to be able to take this line in certain skeptical arguments. After all, something is going to have to go in Dretske's case here:
- I know it's a zebra.
- I know that its being a zebra entails its not being a painted mule.
- Closure
- I don't know it's not a painted mule.
We can't deny (1) because we don't want to be skeptics, and we can't deny (2) because it's clearly right. And shouldn't deny (4) because we just have no way to tell whether it's a painted mule. So, Dretske says, reject (3). We can know that it's a zebra, even though we don't know it's not a painted mule, because that latter is not a relevant alternative.
But I don't think this can work. Here's a simple argument; I'd be surprised if it's original, but I don't know the literature in this area as thoroughly as I might. Let me stipulate a new term zebra*, which means: zebra that is not a mule. Zebra* builds in more relevant alternatives than zebra; that creature's being a mule is definitely a relevant alternative if I want to know whether it's a zebra*. This means that on the relevant alternatives view, in some contexts, such as the ordinary going-to-the-zoo context, if I see an animal, it might be pretty easy to know that it's a zebra, but much more difficult to know it's a zebra*. All the while, of course, I know that necessarily, all and only zebras are zebra*s. This, I take it, is unacceptable. If it is easy to know that necessarily, all and only As are Bs, then it cannot be easy to know that something is an A if it is hard to know that it's a B.
What do you think?