The Epistemic Closure Principle
Most of us think we can always enlarge our knowledge base by accepting things that are entailed by (or logically implied by) things we know. The set of things we know is closed under entailment (or under deduction or logical implication), which means that we know that a given claim is true upon recognizing, and accepting thereby, that it follows from what we know. However, some theorists deny that knowledge is closed under entailment, and the issue remains controversial. The arguments against closure include the following:
The argument from the analysis of knowledge: given the correct analysis, knowledge is not closed, so it isn't. For example, if the correct analysis includes a tracking condition, then closure fails.
The argument from nonclosure of knowledge modes: since the modes of gaining, preserving or extending knowledge, such as perception, testimony, proof, memory, indication, and information are not individually closed, neither is knowledge.
The argument from unknowable (or not easily knowable) propositions: certain sorts of propositions cannot be known (without special measures); given closure, they could be known (without special measures), by deducing them from mundane claims we known, so knowledge is not closed.
The argument from skepticism: skepticism is false but it would be true if knowledge were closed, so knowledge is not closed.
Edward N. Zalta
Luper, S. (2012) The epistemic closure principle. In E.N. Zalta (Ed.) The Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/archives/fall2012/entries/closure-epistemic.
The Stanford Encyclopedia of Philosphy