AbstractOne type of argument to sceptical paradox proceeds by making a case that a certain kind of metaphysically “heavyweight” or “cornerstone” proposition is beyond all possible evidence and hence may not be known or justifiably believed. Crispin Wright has argued that we can concede that our rational acceptance of these propositions is evidentially risky though we still remain rationally entitled to those of our ordinary knowledge claims that are seemingly threatened by that concession. A problem for Wright's proposal is the so‐called Leaching Worry: if we are merely rationally entitled to accept the cornerstones without evidence, how can we achieve evidence‐based knowledge of the multitude of quotidian propositions that we think we know, which require the cornerstones to be true? This paper presents a rigorous, novel explication of this worry within a Bayesian framework, and offers the Epistemic Entitlement theorist two distinct responses.