Epistemic closure is the idea that if you know a set of propositions, then you also know all of the logical implications of those propositions.

The principle of epistemic closure states that if you know something, then you also know all of the logical implications of that thing.

There are a number of arguments for epistemic closure, including the argument from logical consequence, the argument from coherence, and the argument from simplicity.

There are a number of objections to epistemic closure, including the objection from skepticism, the objection from vagueness, and the objection from circularity.

Whether or not epistemic closure is a necessary condition for knowledge depends on the definition of knowledge that one adopts.

Epistemic closure is not a sufficient condition for knowledge because it is possible to know something without knowing all of its logical implications.

Epistemic closure has a number of implications, including the problem of induction, the paradox of knowability, and the impossibility of skepticism.

Epistemic closure is related to a number of other concepts in epistemology, including justification, evidence, and truth.

There are a number of open questions about epistemic closure, including the relationship between epistemic closure and skepticism, vagueness, and circularity.

The future of research on epistemic closure is bright, with many promising avenues for exploration.