 But suppose, nevertheless, there did in fact exist a correspondence between our concepts and the world, indeed, a deeply reliable, counterfactual-supporting correspondence whereby it was in fact metaphysically impossible for certain claims constitutive of those concepts not to be true. This is, of course, not implausible in the case of logic and arithmetic, and is entirely compatible with, e.g., Boolos’ reasonable doubts about them (after all, it’s always possible to doubt what is in fact a necessary truth). Such necessary correspondences between thought and the world might then serve as a basis for claims to a priori knowledge in at least a reliabilist epistemology, where what’s important is not believers’ abilities to justify their claims, but merely the reliability of the processes by which they arrive at them (see Reliabilist Epistemology). Indeed, in the case of logic and arithmetic, the beliefs might be arrived at by steps that were not only necessarily reliable, but might also be taken to be so by believers, in ways that might in fact depend in no way upon experience, but only on their competence with the relevant words and concepts (Kitcher 1980; Rey 1998; and Goldman 1999 explore this strategy).