Empiricist theories of knowledge are attractive for they offer the prospect of a unitary theory of knowledge based on relatively well understood physiological and cognitive processes. Mathematical knowledge, however, has been a traditional stumbling block for such theories. There are three primary features of mathematical knowledge which have led epistemologists to the conclusion that it cannot be accommodated within an empiricist framework: 1) mathematical propositions appear to be immune from empirical disconfirmation; 2) mathematical propositions appear to be known with certainty; and 3) mathematical propositions are necessary. Epistemologists who believe that some nonmathematical propositions, such as logical or ethical propositions, cannot be known a posteriori also typically appeal to the three factors cited above in defending their position. The primary purpose of this paper is to examine whether any of these alleged features of mathematical propositions establishes that knowledge of such propositions cannot be a posteriori.

Edward Erwin has recently argued against the thesis that the concepts a priori truth’ and ‘necessary truth’ are extensionally equivalent. (Following Erwin, I shall refer to this thesis as the ‘Extensional Equivalence Hypothesis’ or, for short, E. E. H.) This thesis consists of two logically independent claims: (1) all a priori truths are necessary; and (2) all necessary truths are a priori. Erwin leaves the first claim unchallenged and elects to devote his efforts exclusively to undermining the second. The brunt of his attack on the second claim rests on alleged unclarities in the concept of an a priori truth. He attempts to show that the E.E.H. cannot be defended upon any plausible interpretation of this concept. Although I agree that the E.E.H., as stated above, is open to Erwin's objections, I shall argue that a slightly revised version of it can be defended against these objections.

Tyler Burge offers a theory of testimony that allows for the possibility of both testimonial a priori warrant and testimonial a priori knowledge. I uncover a tension in his account of the relationship between the two, and locate its source in the analogy that Burge draws between testimonial warrant and preservative memory. I contend that this analogy should be rejected, and offer a revision of Burge's theory that eliminates the tension. I conclude by assessing the impact of the revised theory on the scope of a priori knowledge.

The analytic/synthetic distinction has played a central role in discussions of a priori knowledge throughout the twentieth century. One of the primary reasons for the prominence of this distinction is the widespread influence of the tradition of logical empiricism which endorsed the following principles:

(LEl) All analytic propositions are knowable a priori

and

(LE2) All propositions knowable a priori are analytic.

Hence, proponents of the a priori often argue in support of the contention that the propositions of a particular discipline, say mathematics or logic, are knowable a priori by arguing that it consists solely of analytic propositions. On the other hand, detractors of the a priori often reject such knowledge on the grounds that the analytic/synthetic distinction is not cogent. My primary goal in this paper is to challenge the prevalent acceptance of (LE1).

This paper examines the view that ordinary particulars are complexes of universals. Russell's attempt to develop such a theory is articulated and defended against some common misinterpretations and unfounded criticisms in Section I. The next two sections address an argument which is standardly cited as the primary problem confronting the theory: (1) it is committed to the necessary truth of the principle of the identity of indiscernibles; (2) the principle is not necessarily true. It is argued in Section II that a proponent of the theory need not accept (1) and an argument against (2) is presented in Section III. The final section attempts to show that Russell's theory ultimately fails because of inadequacies in its treatment of space and time. The paper closes with a suggestion for remedying this difficulty.