Carroll's (1895) short piece “What the Tortoise said to Achilles” in many ways anticipates issues that arise in a number of contemporary controversies. One might argue, for example, that initially plausible attempts to deal with the problem of easy knowledge will land one in the unfortunate position of Achilles who followed the Tortoise down a road that leads to vicious infinite regress. Or consider the conditions required for inferential justification. For idealized inferential justification, I have defended (1995, 2004, 2006) the view that to be justified in believing P on the basis of E one needs to be not only justified in believing E, but justified in believing that E makes probable P (where entailment is the upper limit of making probable). And again, critics have argued that such a strong requirement fails to learn the lesson that Achilles should have been taught by the Tortoise. Even more generally, one might well argue that strong access internalists will need to deal with a variation of Carroll's puzzle even for their accounts of non-inferential justification. In this paper I'll examine these controversies with a mind to reaching a conclusion about just exactly how one can accept intellectually demanding conditions on justified belief without encountering vicious regress.
The bifurcated conception of perceptual knowledge: a new solution to the basis problem for epistemological disjunctivism