This second horn is sharpened by White (2006), who formalizes it in probabilistic terms. Let \(A(D)\) be the proposition that there appears to be a door before you, and \(D\) the proposition that there really is a door there. The conjunction \(A(D) \wedge \neg D\) represents the possibility that appearances are misleading in this case. It says there appears to be a door but isn’t really. Using the probability axioms, we can prove that \(p(D\mid A(D)) \leq p(\neg (A(D) \wedge \neg D))\) (see tec