A priori knowledge and naturalized epistemology

The focus of this dissertation is the relationship between a priori knowledge and naturalized epistemology. I consider, by way of Paul Benacerraf's essay entitled "Mathematical Truth," the incompatibility between a priori knowledge and a causal theory of knowledge. The ideas in this essay are often invoked to support mathematical empiricism. I show that Benacerraf's own argument offers no conclusive reason to accept mathematical empiricism (and thereby reject that mathematical knowledge is a priori.); The argument given in Benacerraf's essay presupposes a causal theory of knowledge. A priori knowledge is incompatible with a causal theory of knowledge. We must either reject one of these or fit a priori knowledge into some other epistemic framework. I argue that we can accommodate a priori knowledge within a reliabilist framework. One matter that appears to prevent including a priori knowledge into a reliabilist framework is the subjunctive conditional invoked by Fred Dretske and Robert Nozick. What would (subject) S believe if (proposition) p were false? If S would believe p anyway, then S does not know that p. This conditional is met trivially in the case of necessary truths. And necessary truths, as a class of propositions, are alleged to be knowable a priori. So it appears that a priori knowledge meets this important conditional trivially. I argue that with suitable modification, we can construct an acceptable reliabilist framework that accommodates both necessary and contingent truths.; I provide a definition of a priori knowledge that fits into a reliabilist and "externalist" theory of knowledge. However, it could be argued that this is inadequate, that one only knows p if one has internal or "cognitive justification" for p in addition to objective justification for p. Therefore, one knows a priori only if one's objective and cognitive justification is a priori. I argue that S knows a priori if S's objective justification is a priori. More than objective justification may be required for knowledge, but no more than one's objective justification being a priori is required for that knowledge to be a priori.