I was reading some papers by “Gil Harman”:http://www.princeton.edu/~harman/ while doing some research for a class on chapter 9 of _The Concept of Mind_, and I was struck by this passage in a “very insightful article on Knowledge and Lotteries”:http://www.princeton.edu/~harman/Papers/Hawthorne.pdf. (The article is co-authored with Brett Sherman.)
bq. A further consequence of denying strong closure principles, according to Hawthorne, is that one must give up at least one of three more restricted closure principles that he thinks would be intuitive even to one who denies the more general closure principles. One of these restricted principles is the Equivalence Principle, according to which, if you know a priori that the propositions that P and that Q are equivalent and you know that P, then you are in a position to know that Q.
bq. However, once it is acknowledged that knowledge can rest on assumptions, the Equivalence Principle has no more intuitive force than more general closure principles. Alice knows this animal is a zebra, on the assumption that it is not a cleverly disguised mule. And the animals being a zebra is equivalent to its being a zebra and not a cleverly disguised mule. But, just as she cannot know on the basis of her assumption that her assumption is correct, she is not in a position to know on the basis of that assumption that the animal is a zebra and not a cleverly disguised mule.
Even granting the anti-closure position being adopted by Harman and Sherman, I don’t see how this is a counterexample to the Equivalence Principle that Hawthorne defends. The following two propositions may be _necessarily_ equivalent, but they aren’t _a priori_ equivalent I’d have thought.
(1) That is a zebra.
(2) That is a zebra and not a cleverly disguised mule.
I don’t think it is a priori that no zebras are mules. I could imagine some kind of argument for that conclusion, but there isn’t one in the paper. Of course (1) is a priori equivalent to (3).
(3) That is a zebra and not a cleverly disguised non-zebra.
But I don’t see how one could ever be in a position to know (1) and not in a position to know (3).