Skepticism and the Closure of Knowledge
Here, I asked: “Are you a brain in a vat?”
One might think: “Of course not! What a silly question! The question is interesting only in movies and other forms of storytelling. Otherwise, it’s totally impractical and unrealistic.”
Well, you might be surprised to hear how practical the question is, for it raises reasonable doubts concerning the human capacity for knowledge (at least in some areas), and such matters are quite practical, notwithstanding their cinematic appeal.
Consider the following propositions:
A. The sprinklers in the front lawn are running.
B. If the sprinklers in the front lawn are running, then the lawn is wet.
The principle of the closure of knowledge under known logical entailment holds that a person knows whatever proposition he knows to be entailed by some other proposition he knows, as long as he understands how entailment works and competently draws the relevant conclusion. In other words, if one knows that p and knows that p entails q, then one knows that q, assuming that one understands how entailment works, and wittingly and adeptly deduces q from p. Call this the principle of knowledge closure (PKC) for short. PKC is hard to deny: it’s intuitive and it makes sense of the practical assumption that we can use deductive logic to add to what we know. A valid deductive argument is truth-preserving, and if we know the premises of a valid argument, then it seems clear that we know the conclusion too, i.e., it seems that a valid deductive argument is also knowledge-preserving in appropriate circumstances.
Suppose that Jones knows that (A). He also knows that (B), and he understands what entailment is and how to draw conclusions. Given the PKC, Jones knows that the lawn is wet. Or suppose that Smith knows that his shirt is on the table, and he knows that ‘the shirt is on the table’ entails that ‘the shirt exists.’ Hence, he knows that ‘the shirt exists’ given that he comprehends how entailment works.
But now consider the proposition ‘I am sitting now.’ Call this proposition S. Note this argument:
If I know that S and that S entails that I am not a brain-in-a-vat (BIV), then I know that I’m not a BIV.*
I don’t know that I’m not a BIV. (I can’t absolutely rule out this possibility. I might be like Neo.)
Thus, I don’t know that S and that S entails that I am not a BIV.
Hence, either I don’t know that S, or I don’t know that S entails that I am not a BIV, or I don’t know either disjunct.
I know that S entails that I am not a BIV.
Therefore, I don’t know that S.
This is a common type of argument for epistemic skepticism about the external world. Some epistemologists try to avoid the skeptical conclusion in (6) by denying the PKC. But to my mind, the PKC (in some fitting formulation) is a principle that we should not give up and that we should affirm if at all feasible. One might well be inclined to bite the bullet, accept (6), and maintain the PKC rather than deny the PKC in order to deny (6).
*If you’re not familiar with the philosophical literature about brains-in-vats, think of Neo in the Matrix before he takes the red pill and realizes that his body is trapped in a big vat of fluid while his brain is connected to a computerized matrix which is stimulating the experiences he is having. Prior to his discovery, he falsely assumes that his experiences are of a real external world. For instance, Neo believes that he is sitting in his chair at his desk reading information on his computer screen. But he’s not. He’s a brain (and body) in a vat. There is no desk, there is no chair, and he not sitting in a chair. There is no computer screen. He’s having non-veridical experiences of sitting, etc. It is only after meeting Morpheus, taking the red pill, and getting acquainted with the evidence that he was (before Morpheus removed him from the vat) actually a brain-in-a-vat that he comes to regard his desk-related experiences as non-veridical.