One issue raised by the tracking theory of knowledge discussed in yesterday's post is "epistemic closure."
Epistemic closure is a property of belief systems that is generally considered a good thing. Specifically, a belief system is said to be "closed" if and only if we can say that whenever a subject (S) knows a proposition (p), and S also knows that P implies q, then S knows q.
If I know that today is Sunday, and I know that this implies that yesterday was Saturday, then I know that yesterday was Saturday.
In examples like yesterday-was-Saturday, closure is strongly intuitive. But the standard view of the consequences of the tracking theory is that accepting it entails the abandonment of closure as a premise.
Consider the "fake barns" scenario. I'm driving through a neighborhood where some of the locals delight in creating fake paper mache barns that look quite realistic from the road. I don't know about the local custom and, when I see a red barn in front of me, I adopt the belief that "there is a red barn here." In fact (we further suppose) this IS a red barn, not a fake. In this case, though, the tracking theory will NOT say that I know that it is a red barn. I would have believed it to be a red barn even if it weren't, so my belief isn't tracking the fact.
Fine, you say, but not really relevant to closure. Okay, let's go further. Suppose that the neighborhood custom applies only to paper mache BLUE barns. I've included here a photo of what appears to be a blue barn (but hey, who knows?). The fake barns are always blue, never red. I clearly see a red barn. Now, even though we're still supposing that I'm ignorant of the local customs, we're in a situation where an observer can say that my belief that "the object in front of me is a red barn" is not just true, but something I KNOW. If it weren't a red barn, I wouldn't believe it to be a red barn.
Fine, you say, tapping your foot with impatience, but weren't we discussing closure? Yes! And here is the nub of the gist. My belief that p, "this object in front of me is a red barn," is an instance of knowledge, and I know p to imply q, that this object in front of me is a barn. The category "red barn" fits entirely inside the category "barn," after all. Yet the inference does not close, because I do not KNOW that this is a barn. If it weren't a barn (if it were, in particular, a blue pretend barn) still I would nonetheless believe it to be a barn, and then I would be wrong. So my belief isn't tracking in the proper counterfactual way with the truth of the matter.
Thus, I know p, "this is a red barn" but I don't know q, "this is a barn," or (what is the same) my system of beliefs is not closed as to knowledge.
Nozick accepted this because he believed that we have to get rid of some strong intuitive belief in order to banish Gettier problems from epistemology, He had another reason for accepting this part of the tracking theory too, it helped him banish global skepticism -- the hypothesis that I might be a brain in a vat, or deluded by an evil demon. For this reason, non-closure wasn't a bug in the tracking theory, it was a feature.
I hope to come back to these points next week.
Suppose that a vast conspiracy existed to trick me into believing that today was Monday rather than Sunday. Everyone to whom I might speak today would greet me with, "How are you this Monday, Henry?" A fake calendar would be printed, and my wife would substitute it for my present calendar. She'd also reset the date on my watch. Newspapers and websites would all have a false date on them. My point, of course, is that perhaps no system of beliefs can ever be closed as to knowledge.
ReplyDeleteIf you find my hypothetical unlikely, then consider the Italian Renaissance tale, "The Fat Woodcarver" or "The Fat Woodworker," by Antonio Manetti. Here is a description I found online: "The Fat Woodworker" is a delightful story in the tradition of the Italian Renaissance beffe, stories of practical, often cruel jokes. It is the tale of a prank engineered by the great Renaissance architect, Filippo Brunelleschi (1377-1446), played upon an unsuspecting (and perhaps less-than-brilliant) friend and woodworker named Manetto, in reprisal for the woodworker's social slight. While the prank is indeed cruel, it is so ingenious, and the victim is so comical, that the reader soon forgets the architect's - and the author's - malice and settles in for a delightful turn as part of the unfolding conspiracy set in motion by Brunelleschi's circle of friends."
DeleteThe prank is a vast conspiracy, as in my hypothetical, to trick Manetto to believe that he is someone else. I read it in "An Italian Renaissance Sextet: Six Tales in Historical Context," in which historian Lauro Martines provides the commentary placing the tales in their historical context.
Henry, I don't think you've quite caught onto what "closed" means in this context. It doesn't mean "certain." It is a transitive property. I have a bit more discussion of it in a post I plan for tomorrow, but in the meantime, this exposition might be better than mine. https://plato.stanford.edu/entries/closure-epistemic/
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