Epistemic closure is a property of some belief systems. It is the principle that if a subject knows , and knows that entails , then can thereby come to know . Most epistemological theories involve a closure principle and many skeptical arguments assume a closure principle.
On the other hand, some epistemologists, including Robert Nozick, have denied closure principles on the basis of reliabilist accounts of knowledge. Nozick, in Philosophical Explanations, advocated that, when considering the Gettier problem, the least counter-intuitive assumption we give up should be epistemic closure. Nozick suggested a "truth tracking" theory of knowledge, in which the x was said to know P if x's belief in P tracked the truth of P through the relevant modal scenarios.
A subject may not actually believe q, for example, regardless of whether he or she is justified or warranted. Thus, one might instead say that knowledge is closed under known deduction: if, while knowing p, S believes q because S knows that p entails q, then S knows q. An even stronger formulation would be as such: If, while knowing various propositions, S believes p because S knows that they entail p, then S knows p. While the principle of epistemic closure is generally regarded as intuitive, philosophers such as Robert Nozick and Fred Dretske have argued against it.
In the seminal 1963 paper, “Is Justified True Belief Knowledge?”, Edmund Gettier gave an assumption (later called the “principle of deducibility for justification” by Irving Thalberg, Jr.) that would serve as a basis for the rest of his piece: “for any proposition P, if S is justified in believing P and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q.” This was seized upon by Thalberg, who rejected the principle in order to demonstrate that one of Gettier's examples fails to support Gettier's main thesis that justified true belief is not knowledge (in the following quotation, (1) refers to “Jones will get the job”, (2) refers to “Jones has ten coins”, and (3) is the logical conjunction of (1) and (2)):
Why doesn't Gettier's principle (PDJ) hold in the evidential situation he has described? You multiply your risks of being wrong when you believe a conjunction. [… T]he most elementary theory of probability indicates that Smith's prospects of being right on both (1) and (2), namely, of being right on (3), are bound to be less favorable than his prospects of being right on either (1) or (2). In fact, Smith's chances of being right on (3) might not come up to the minimum standard of justification which (1) and (2) barely satisfy, and Smith would be unjustified in accepting (3). (Thalberg 1969, p. 798)
- Luper, Steven (31 December 2001). "The Epistemic Closure Principle". Stanford Encyclopedia of Philosophy.
- Philosophical explanations, By Robert Nozick (Harvard 1981), page 204
- Brady, Michael; Pritchard, Duncan (2005). "Epistemological Contextualism: Problems and Prospects". The Philosophical Quarterly 55 (219): 161–171. doi:10.1111/j.0031-8094.2005.00393.x.
- Thalberg Jr., Irving (November 1969). "In Defense of Justified True Belief". Journal of Philosophy 66 (22): 794–803. JSTOR 2024370.
- Gettier, Edmund (June 1963). "Is Justified True Belief Knowledge?". Analysis 23 (6): 121–3. doi:10.1093/analys/23.6.121. JSTOR 3326922.
- The Epistemic Closure Principle entry in the Stanford Encyclopedia of Philosophy
- Epistemic closure at the Indiana Philosophy Ontology Project
- Epistemic closure entry in the Internet Encyclopedia of Philosophy
- Epistemic closure at PhilPapers