John’s defense of closure in the Blackwell Debates volume is, pretty clearly, the best defense available. It’s a nice summary of points found elsewhere in the literature, and also is filled with interesting and important new developments on the subject.
It also contains a really neat passage that presents a problem for critics of closure. Here’s the passage:
I ask S whether she agrees that P. She asserts that she does: “Yes,” she says. I then ask S whether she realizes that Q follows from P. “Yes, ” she says. I then ask her whether she agrees that Q. “Im not agreeing to that,” she says. I ask her whether she now wishes to retract her earlier claims. “Oh no,” she says. “I’m sticking by my claim that P and my claim that P entails Q. I’m just not willing to claim that Q.” Our interlocutor now resembles perfectly Lewis Carroll’s Tortoise, that familiar object of ridicule who was perfectly willing to accept the premises of a modus ponens argument but was unwilling to accept the conclusion…
This is a neat example, but the set up John uses for the problem is a little perplexing. Hawthorne precedes the example by saying that there is an argument for closure deriving from Williamson’s idea that knowledge is the norm of assertion. Then he gives the argument just quoted.
The question is what role the knowledge norm plays in generating the troubling scenario for deniers of closure.
S could be violating that norm in the example if there’s a true closure principle about knowledge and the refusal to assert Q is a sign that S doesn’t know Q. For then S ought to take back one of the earlier assertions as well, but S doesn’t. But the case needn’t go this way, since you don’t violate the norm by refusing to say things that the norm would allow you to say.
It is true that if Dretske is right that closure should be abandoned, then if knowledge is the norm of assertion, there will be cases where you do nothing wrong in asserting P and P entails Q, but refuse to assert Q. But the appeal to knowledge being the norm of assertion here is superfluous–whatever the norms of assertion are, the above case will look funny. Whether the norm is belief, or truth, of justified belief, the example above will leave S in the same predicament John describes for her.
There is, of course, the really interesting question of whether there is a way to describe S’s predicament further to keep her from being the object of ridicule as described, but I’ll leave that for another post. Here I just want to raise the question of what work the appeal to the knowledge norm is adding to the case. As far as I can tell, it doesn’t do any work here.