Principle of Epistemic Closure
The principle of epistemic closure (PEC) states that our knowledge is closed under implication. If we know one proposition, then we can know propositions entailed by that proposition. PEC allows for the expansion of our knowledge via cognition.
PEC has been formalized in various ways. The simplest formulation goes like this:
If person S knows p, and p entails q, then S knows q.
This formulation has received a good deal of criticism, since we obviously don't know everything entailed by each bit of knowledge. A better formulation might require mental accessibility:
If S knows p, and believes q by recognizing that p entails q, then S knows q.
Under this formulation, S must believe q and the implication from p to q must be accessible.
The principle of epistemic closure is significant to modern epistemology because it provides the force behind external world skepticism. There is an intuition that if any skeptical scenario is true (e.g. brain in a vat), then our everyday knowledge is false. Since we can't rule out the possibility of skeptical hyopthesis (indiscernability), we can't know things about the external world.
The skeptical paradox is formalized below. Notice the third premise which depends on the principle of epistemic closure:
h = I have two hands
S = subject
b = I am a brain in a vat
1. S knows that h (everyday knowledge).
2. S does not know that ~b (indiscernability).
3. If S does not know that ~b, then S does not know that h (PEC).
External world skepticism finds its ammo in the force of premise two and three against premise one.
Web Resources On Principle of Epistemic Closure
The Epistemic Closure Principle