What does the closure principle say?

Roughly, that if you know one thing and recognise that it logically entails a second thing, then you are in a position to know the second thing as well. Knowledge is supposed to extend, by competent deduction, to the known consequences of what you already know.

Why would denying closure block skepticism?

The skeptical argument uses closure to move from 'you cannot know you are not deceived' to 'you cannot know ordinary facts'. If knowledge does not always transmit across entailment, you can know ordinary facts without thereby having to know the denial of the skeptical hypothesis, breaking the argument.

Closure and Skeptical Arguments

Most modern skeptical arguments turn on a single principle — that if you know something and know it entails another thing, you can know that other thing too — which lets the skeptic transmit your inability to rule out deception into ignorance of even the most ordinary facts.

Definition

Epistemic closure is the principle that knowledge is closed under known logical entailment: if a subject knows that p and competently deduces q from p, knowing that p entails q, then the subject is in a position to know that q.

Scope

This topic covers the epistemic closure principle and the canonical skeletal skeptical argument it underwrites: you do not know you are not a brain in a vat; if you knew you had hands you could know you are not a vat-brain; so you do not know you have hands. It examines formulations of closure, the trade-offs each response faces, and the radical option of denying closure pursued by Dretske and Nozick. The substance of the deception hypotheses and the full range of replies are treated in neighbouring topics.

Core questions

How does the closure principle generate the skeptical argument?
Which premise of the closure-based argument should be rejected?
Is epistemic closure true, and how should it be precisely stated?
What are the costs of denying closure to escape skepticism?

Key theories

The closure-based skeptical argument: The argument combines the claim that one cannot know the denial of a skeptical hypothesis with closure to conclude that one cannot know ordinary propositions that entail that denial, making closure the engine of skepticism.
Denial of closure: Dretske and Nozick respond by rejecting closure: one can know everyday facts without knowing one is not deceived, because knowledge does not always transmit across known entailment, though this concedes a counterintuitive result.

History

Dretske's 1970 paper on epistemic operators argued that knowledge does not penetrate to all the known consequences of what one knows, and Nozick's 1981 tracking theory likewise yielded a denial of closure. These proposals made the closure principle the focal point of the skepticism debate, since accepting it seems to lead to skepticism while denying it carries its own heavy costs.

Debates

Whether denying closure is too high a price: Rejecting closure blocks the skeptical argument but implies one can know one has hands while failing to know one is not a handless brain in a vat, a consequence many find more incredible than skepticism itself, fuelling the search for closure-preserving responses.

Key figures

Fred Dretske
Robert Nozick
Barry Stroud

Seminal works

dretske1970
nozick1981

Frequently asked questions

What does the closure principle say?: Roughly, that if you know one thing and recognise that it logically entails a second thing, then you are in a position to know the second thing as well. Knowledge is supposed to extend, by competent deduction, to the known consequences of what you already know.
Why would denying closure block skepticism?: The skeptical argument uses closure to move from 'you cannot know you are not deceived' to 'you cannot know ordinary facts'. If knowledge does not always transmit across entailment, you can know ordinary facts without thereby having to know the denial of the skeptical hypothesis, breaking the argument.