Epistemic closure^[1] is aproperty of somebelief systems. It is theprinciple that if a subject${\displaystyle S}$ knows${\displaystyle p}$, and${\displaystyle S}$ knows that${\displaystyle p}$entails${\displaystyle q}$, then${\displaystyle S}$ can thereby come to know${\displaystyle q}$. Mostepistemological theories involve a closure principle and manyskeptical arguments assume a closure principle.

On the other hand, some epistemologists, includingRobert Nozick, have denied closure principles on the basis ofreliabilist accounts of knowledge. Nozick, inPhilosophical Explanations, advocated that, when considering theGettier 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 relevantmodal scenarios.^[2]

A subject may not actually believeq, for example, regardless of whether he or she is justified or warranted. Thus, one might instead say that knowledge is closed underknown deduction: if, while knowingp,S believesq becauseS knows thatp entailsq, thenS knowsq.^[1] An even stronger formulation would be as such: If, while knowing various propositions,S believesp becauseS knows that these propositions entailp, thenS knowsp.^[1] While the principle of epistemic closure is generally regarded as intuitive,^[3] philosophers such as Robert Nozick andFred Dretske have argued against it.^[4]

The epistemic closure principle typically takes the form of amodus ponens argument:

1. S knows p.
2. S knows that p entails q.
3. Therefore, S knows q.

This epistemic closure principle is central to many versions of skeptical arguments. Askeptical argument of this type will involve knowledge of some piece of widely accepted information to be knowledge, which will then be pointed out to entail knowledge of some skeptical scenario, such as thebrain in a vat scenario or theCartesian evil demon scenario. A skeptic might say, for example, that if you know that you have hands, then you know that you are not a handless brain in a vat (because knowledge that you have hands implies that you know you are not handless, and if you know that you are not handless, then you know that you are not a handless brain in a vat).^[5] The skeptic will then utilize this conditional to form amodus tollens argument. For example, the skeptic might make an argument like the following:

1. You do not know that you are not a handless brain in a vat (${\displaystyle \mathrm{\neg }K\mathrm{\neg }h}$)
2. If you know that you have hands, then you know that you are not a handless brain in a vat (${\displaystyle Ko\to K\mathrm{\neg }h}$)
3. Conclusion: Therefore, you do not know that you have hands (${\displaystyle \mathrm{\neg }Ko}$)

Much of the epistemological discussion surrounding this type of skeptical argument involves whether to accept or deny the conclusion, and how to do each.Ernest Sosa says that there are three possibilities in responding to the skeptic:

1. Agree with the skeptic by granting him both premises and the conclusion (1, 2, c)
2. Disagree with the skeptic by denying premise 2 and the conclusion, but maintaining premise 1 (1, ~2, ~c) asNozick andDretske do. This amounts todenying the epistemic closure principle.
3. Disagree with the skeptic by denying premise 1 and the conclusion, but maintaining premise 2 (~1, 2, ~c) asMoore does. This amounts tomaintaining the epistemic closure principle, and holding that knowledge is closed under knownimplication.

In the seminal 1963 paper, “Is Justified True Belief Knowledge?”, Edmund Gettier gave an assumption (later called the “principle of deducibility for justification” byIrving Thalberg, Jr.)^[6] 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.”^[7] 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 thelogical 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)

The term "epistemic closure" has been used in an unrelated sense in American political debate to refer to the claim that political belief systems can be closed systems of deduction, unaffected byempirical evidence.^[8] This use of the term was popularized by libertarian blogger and commentatorJulian Sanchez in 2010 as an extreme form ofconfirmation bias.^[8][9]

• Epistemic logic
• Doxastic logic
• Here is one hand#Objections and replies – Epistemological argument by George Edward Moore

• Zalta, Edward N. (ed.)."The Epistemic Closure Principle".Stanford Encyclopedia of Philosophy.ISSN 1095-5054.OCLC 429049174.
• Epistemic closure at theIndiana Philosophy Ontology Project
• Fieser, James; Dowden, Bradley (eds.)."Epistemic closure".Internet Encyclopedia of Philosophy.ISSN 2161-0002.OCLC 37741658.
• Epistemic closure atPhilPapers

• Concepts in epistemology
• Belief
• Epistemic logic
• Philosophy of Robert Nozick
• Concepts in logic

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• Articles with Internet Encyclopedia of Philosophy links