Saturday, July 12, 2008
Hawthorne on Closure
According to interest-relative invariantism, in contrast, the interpretation of ‘knows’ and its relatives is invariant across different contexts. Nonetheless its extension can shift in more or less the manner suggested by contextualism because whether one’s true belief counts as knowledge is not determined entirely by truth-conducive factors—such as whether it was formed by a reliable mechanism—but also by factors concerning the subject’s practical interests; the direness of the consequences of the her being mistaken, for instance. We can see how this kind of account of knowledge might help save closure by briefly examining John Hawthorne’s preferred treatment of the lottery paradox. When one needs to consider whether one’s lottery ticket (or a ticket someone is offering you) will win for one’s present practical purposes—one is contemplating whether to sell the ticket for a cent, to take Hawthorne’s favorite example—one does not know what one’s spending power will be after the draw has been announced. However, when the outcome of the lottery isn’t an issue, given one’s practical interests, one can know where the ceiling on one’s spending power after the draw will lie.
So far all that has been suggested is that whether one knows the minor premise of the lottery paradox is sensitive to one's practical environment. We now need to consider three kinds of cases to establish whether such an account of knowledge respects closure. The first kind of case is one in which a subject S knows p, and knows that p entails q, but does not draw the consequences of these pieces of knowledge. Such cases are fully compatible with closure. The closure principle we are working with requires that one actually have made the inference in question, and so there can be no failure of closure when one simply doesn’t make the inference. The second kind of case is one in which a subject knows p, knows that p entails q, and has competently deduced q from p at some point in the past. So suppose again that S is in the bookstore, and the outcome of the draw is the last thing on S’s mind. However, S deduced yesterday that her ticket is a loser from her inability to afford to visit
The third kind of case, in which one starts off in a practical environment such that one knows that p and then competently deduces q, is a little trickier. Suppose once more that S's practical interests are such that whether her lottery ticket wins or loses is not of practical relevance to S, and so she knows that she will not be able to afford to visit