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.
[4] The epistemic closure principle typically takes the form of a modus ponens argument: This epistemic closure principle is central to many versions of skeptical arguments.
[5] The skeptic will then utilize this conditional to form a modus tollens argument.
Ernest Sosa says that there are three possibilities in responding to the skeptic: 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.)[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 the logical conjunction of (1) and (2)): Why doesn't Gettier's principle (PDJ) hold in the evidential situation he has described?
(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 by empirical evidence.
[8] This use of the term was popularized by libertarian blogger and commentator Julian Sanchez in 2010 as an extreme form of confirmation bias.