Abstract
Closure is the principle that a person, who knows a proposition p and knows that p entails q, also knows q. Closure is usually regarded as expressing the commonplace assumption that persons can increase their
knowledge through inference from propositions they already know. In this
paper, I will not discuss whether closure as a general principle is true. The aim of this paper is to explore the various relations between closure and knowledge through inference. I will show that closure can hold for two
propositions p and q for numerous different reasons. The standard reason
that S knows q through inference from p, if S knows p and knows that p
entails q, is only one of them. Therefore, the relations between closure and inferential knowledge are more complex than one might suspect.