Epistemic Closure and Its Denial

You know you have hands. You know that having hands entails not being a handless brain in a vat. Do you therefore know you are not a handless brain in a vat?

Almost everyone's first answer is yes, and almost everyone's second answer, arrived at a moment later, is that this cannot be how one comes to know such a thing. The gap between the two answers is where the sceptical argument lives, and the principle joining them is the most contested in epistemology.

The principle

The careful statement is deliberately hedged. Crude versions, such as the claim that anyone who knows something knows all its consequences, are false for obvious reasons, since consequences can be unrecognised and deduction can be long. The refinement due to Fred Dretske and sharpened by John Hawthorne requires competent deduction and retained knowledge of the premise, and it is this version that the dispute concerns.

What makes the principle look undeniable is that deduction is the least controversial way of extending knowledge. If you may not add to what you know by drawing out what it entails, it is hard to see what inference is for. Mathematics would be in trouble, and so would the ordinary practice of working out consequences.

The sceptical argument

The principle's respectability is the problem, because scepticism uses it.

The argument is valid and its premises are individually attractive, which is the definition of a paradox. Three responses exhaust the space.

Accept the conclusion, which is scepticism. Deny the second premise, which is what G. E. Moore did when he turned the argument around and reasoned from his hands to the falsity of scepticism, and what contemporary dogmatists do more carefully. Or deny the first premise, which means denying closure.

The denial

Dretske argued for this in 1970 and Nozick's tracking account entails it independently, which is the strongest evidence that the position is not merely convenient.

Recall why. Sensitivity requires that had the proposition been false, you would not have believed it. Your belief that you have hands is sensitive: had you lacked hands, you would have noticed. Your belief that you are not a brain in a vat is not sensitive: had you been one, you would have believed you were not, because that is what the hypothesis specifies. So on Nozick's account you know the first and not the second, and closure fails. Nozick did not adopt the denial in order to defeat scepticism. It fell out of a condition he had adopted for other reasons, and he accepted the consequence.

Dretske's route is different and more intuitive. He asks what a knowledge claim is doing. To know that the animal in the pen is a zebra is to have ruled out the alternatives that matter in that setting: that it is a horse, a donkey, a mule. It is not to have ruled out that it is a mule cleverly painted, because that is not an alternative anyone in a zoo needs to eliminate. But being a zebra entails not being a painted mule, and you have not ruled that out, so closure fails.

The relevant alternatives framework is what makes closure denial a position rather than a stipulation. Knowledge is not the elimination of all error, which nothing could achieve, but the elimination of a contextually bounded set. Sceptical hypotheses fall outside that set in ordinary contexts, and the entailments of ordinary knowledge can therefore include things not known.

What the denial costs

The costs are serious and are the main reason the position is a minority one.

The first is abominable conjunctions, Keith DeRose's phrase. The denier must accept sentences of the form: I know I have hands, but I do not know I am not a handless brain in a vat. Stated aloud, these sound not merely surprising but defective, in a way that ordinary counterintuitive philosophical results do not.

The second is the practical role of deduction. If closure fails, then working out the consequences of what you know is no longer a reliable way to extend knowledge, and a believer who reasons carefully from known premises to a validly derived conclusion may end up with something they do not know. This is hard to square with the point of reasoning.

The third is that the denial appears to be selective. Closure is denied for precisely the inferences that make trouble for the theory, and holds everywhere else. Unless the relevant alternatives framework independently predicts where it fails, the denial looks like a repair rather than a discovery.

Dretske's defenders reply that the framework does make the prediction: closure fails exactly where the entailed proposition rules out an alternative that was never relevant, and holds where the entailed proposition stays within the relevant set. Whether that is principled or merely systematic is what the dispute has come down to.

Taking stock

Closure denial buys a response to scepticism that leaves ordinary knowledge intact, and buys it at the price of a principle that governs the most basic way of extending knowledge. Whether the trade is good depends on how bad the abominable conjunctions really are, and that is a judgement about which reasonable people have not converged.

The broader lesson is about method. The sceptical argument is valid and its premises are attractive, so something attractive has to go. Scepticism, dogmatism, closure denial, and contextualism are the four ways of paying, and each of the last three has a constituency because each cost is genuinely lower than the others from some point of view.

Next

A distinction that cuts across everything so far: knowledge whose justification does not depend on experience at all, and the long argument about whether there is any.