closure principle

Definition
The closure principle posits that
If I know one proposition, and I know that this proposition entails a second proposition, then I know the second proposition as well.”

“...what the sceptic’s use of the closure principle does is make knowledge of normal ‘everyday’ propositions (i.e. the sort of propositions which we would usually regard ourselves as unproblematically knowing) contingent upon knowledge of the denials of sceptical hypothesis. ”

(From Chappie) Pritchard is explaining that the sceptic uses the closure principle to argue that our ability to know ordinary, everyday propositions depends on already knowing that radical sceptical scenarios are false, thereby putting pressure on our intuitive claims to everyday knowledge.

“One way in which some have gone about rejecting the closure principle is by appeal to the fallibilism intuition that in knowing something I only need to be able to rule out all relevant possibilities of error, and don’t have to rule out all possibilities of error. Taking ‘rule out’ here to mean ‘know to be false’, this means that in order to know something I only need to know that a restricted range of error possibilities are false, not that all of them are (that would be infallibilism). The complaint raised by fallibilists against the closure principle, however, is that it demands that we know the falsity of even far-fetched – and thus, intuitively, irrelevant – error possibilities, such as sceptical hypothesis, and hence that there is something deeply suspect about it.”

“Notice that the closure principle is entirely compatible with fallibilism. This principle does not demand that you know that all error possibilities are false, but only those error possibilities which are known to be incompatible with what you know, which is a much weaker claim. One cannot therefore reject the closure principle solely on fallibilist grounds.”