The paradox of knowability (a.k.a. Fitch’s paradox or the Church-Fitch paradox) is a proof that threatens all too easily to refute various forms of semantic anti-realism and to collapse useful modal epistemic distinctions. The anti-realisms in question are those that advocate an epistemic characterization of truth. They tell us that truth and knowability are necessarily coextensive—or at least that any truth is knowable in principle. We call this the knowability principle (KP), which is naturally expressed by the following formula:

(KP) ¬∀ϕ(ϕ → ◊Kϕ)

(KP) says, “for all propositions ϕ, if ϕ then it is possible that somebody at some time knows that ϕ.” Interesting versions of the thesis focus on moderately idealized human knowability—that is, knowability by subjects whose capacities and resources are only finitely better than our own. Knowability-by-God is too weak of an idealization, since it leaves us with a view that is consistent with realism—namely, the view that truth can outrun the epistemic capacities of subjects like us. Moderate epistemic theories of truth also aim to protect themselves from going in the other direction; the epistemic idealization is meant to distance the theory from naive forms of idealism (NI), which say that something is true only if it is known (by someone at some time):

(NI) ∀ϕ(ϕ → Kϕ)