Closure and Skepticism
Acknowledging that luck is not incompatible with knowledge makes it easier to deal with other puzzles as well.
Consider a variation of the barn story. The story begins like the original: George is touring farm country and is charmed by the old barns he is seeing; he pulls his car over to the side of the road to appreciate the latest he has happened across; and, as he looks out the window, he has a true belief that he is looking at a barn. In this version of the story, however, there are no barn facades in the region. During his tour until now, he has been seeing nothing but real barns. Moreover, he correctly believes that he has normal vision, there is nothing obstructing his view, and the light is good. He thus apparently knows that he is seeing a barn.
Suppose he now recalls the brain-in-a-vat hypothesis, according to which his brain is in a vat in a laboratory where it is being stimulated to produce precisely the sorts of experiences he is now having. He realizes the proposition that he is now looking at a barn entails that he is not a brain-in-a-vat. He accordingly believes this latter proposition, but does he know it?
Well, why not? His belief that he is not a brain-in-a-vat, like his belief that he is looking at a barn, is true, and as the story has been told, there are no obviously important gaps in his information about the situation.
On the other hand, to the degree that one regards it as questionable whether George can know that he is not a brain-in-a-vat, one might be inclined to think that the argument here has to be reversed, with the unwelcome inference being that George cannot even know that he is now seeing a barn.
The basis for such an inference is the principle that knowledge, to use the term of art, is closed under known entailment. According to this principle, if S is aware that A entails B, then S knows A only if she knows B. This is sometimes referred to as “single premise closure,” since it applies only to entailments from a single known proposition. A much stronger and correspondingly less plausible principle is that knowledge is closed under multiple premises: if S is aware that (A and B) entails C, then S knows A and knows B only if she knows C. Such a principle, for example, implies that in the preface S cannot know each of individual claims in her book without knowing the conjunction and hence without knowing that she has made no mistakes anywhere in the book. The above argument, however, requires only single premise closure along with the assumption that George does not know that he is not a brain-in-a-vat.1
But why make this latter assumption? George’s belief that he is not a brain-in-a-vat is true, and as far as we can tell there are no important truths about his circumstances of which he is unaware. So, why isn’t his belief an instance of knowledge? One line of argument is that he doesn’t have knowledge because knowing something must exclude the possibility of error. Descartes was notoriously attracted to this view, and some notable contemporary philosophers have been drawn to it as well.2
This merely pushes the question back a level, however. Why should it be assumed that knowledge has to exclude the possibility of error, especially since most of our everyday attributions of knowledge would seem to suggest the opposite? What is it that is supposed to require such a demanding standard?
The lurking presupposition, once again, would seem to be that knowledge is incompatible with having a true belief by luck. There is nothing from George’s perspective that allows him to distinguish a situation in which he is a brain-in-a-vat from one in which he is not. So, even if he correctly believes that he is not a brain-in-a-vat, it is a matter of luck that his belief is true.
But as I have been arguing, not only is knowledge not incompatible with luck, it actually requires it. It requires, in effect, the world to be kind. The inclination to think otherwise derives from a failure to distinguish global from local luck. When one has a true belief as a result of local luck, one usually does lack knowledge, but this is so because the luck is accompanied by local ignorance. In the original barn story, George by happenstance has stopped his car in front of one of the few remaining real barns in the region, and he isn’t aware that there are numerous barn facades in the region. His true belief is thus a case of blind luck, but it is his blindness rather than his luckiness that explains his lack of knowledge.
Still, it might be argued that this way of thinking about brain-in-the-vat stories misses their real power, since it approaches the issues from the viewpoint of an audience hearing a story about someone else, in this case George. To appreciate the force of such stories, one has to entertain them as potentially being about oneself. It has to be treated as a first person problem. What if I, not George, am a brain-in-a-vat? What then?
What then indeed? If contrary to what I believe I am a brain-in-a-vat, then most of my beliefs about my environment are mistaken, and not just in trifling ways but thoroughly and deeply mistaken. I thus know much less than I take myself to know. So much the worse for me, but nothing of great interest follows for the theory of knowledge. To be sure, there are important questions raised by the brain-in-a-vat and other such skeptical hypotheses—in particular, questions about what it is appropriate for me to believe given my perspective—but these are first and foremost questions about justified belief rather than knowledge.
Moreover, among the relevant questions are ones about closure. If I am aware that the proposition that I am now looking at a barn entails that I am not a brain-in-a-vat, am I justified in believing the former only if I am also justified in believing the latter? And if so, can I be justified in believing the latter? Likewise, there are questions about the possibility of error. Can I justifiably believe I am looking at a barn even though I cannot completely exclude the possibility that I am a brain-in-a-vat being stimulated to have experiences of just the sort I would have when looking at a barn?
The answer to each of these questions is yes. Being a brain-in-a-vat would seriously disadvantage me, as would any situation in which I am thoroughly deceived. Allow paranoia free rein in imagining scenarios about hallucinatory drugs, conspiracies, and evil demons. In these scenarios, I am deprived of knowledge, but one of the lessons of such stories is that being thoroughly deceived does not also automatically prevent me from having justified beliefs. Justification is closely associated with what I am entitled to believe, given how things look from my perspective and given that my goal is now to have accurate and comprehensive beliefs. Accuracy is the goal, but not a prerequisite, however. Even in a bubbling vat, it is possible for my beliefs to be justified. I may be a brain-in-a-vat, but I can nonetheless be a brain-in-a-vat with justified beliefs about my environment, including the justified belief that I am not a brain-in-a-vat.3