The aim of this paper is to sketch a theory of justified belief. What I have in mind is an explanatory theory, one that explains in a general way why certain beliefs are counted as justified and others as unjustified. Unlike some traditional approaches, I do not try to prescribe standards for justification that differ from, or improve upon, our ordinary standards. I merely try to explicate the ordinary standards, which are, I believe, quite different from those of many classical, (...) e. g., ‘Cartesian’, accounts. (shrink)

Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...

a priori. Since I ended up defending an unpopular answer to this question—"No"—it’s hardly surprising that people have scrutinized the account, or that many have concluded that I stacked the deck in the first place. Of course, this was not my view of the matter. My own judgment was that I’d uncovered the tacit commitments of mathematical apriorists and that the widespread acceptance of mathematical apriorism rested on failure to ask what was needed for knowledge to be a priori . (...) Nevertheless, my critics have raised important challenges, and have offered rival conceptions that are less demanding. I want to examine their objections to my explication of a priori knowledge, and to explore whether the weaker alternatives succeed in preserving traditional philosophical claims. What follows is a mixture of penitence and intransigence. (shrink)

In his most recent treatment of a priori knowledge, Philip Kitcher argues against what he takes to be the widespread view that our knowledge and warranted belief is 'tradition-independent'. Furthermore, he argues that defeasible conceptions of a priori warrant entail that it is not tradition-independent, a conclusion which he thinks is contrary to what most epistemologists hold. I argue that knowledge is not widely believed to be tradition-independent, and that, while warrant is widely believed to be tradition-independent, Kitcher's arguments show (...) neither that this widespread view is mistaken nor that it conflicts with defeasible a warrant. I conjecture that Kitcher may be misled by a lack of clarity regarding the analysandum designated by 'warrant'. (shrink)

Radical empiricism is the view that experience is the only source of knowledge. Hence, radical empiricism denies the existence of a priori knowledge. Its most famous proponents are John Stuart Mill and W. V. Quine. Although both reject a priori knowledge, they offer different empiricist accounts of the knowledge alleged by their opponents to be a priori. My primary concern in this paper is not with the cogency of their positive accounts. My focus is their arguments against a priori knowledge. (...) My goal is to establish that although they offer very different arguments against the existence of a priori knowledge, each of their arguments suffers from a common defect. They both fail to appreciate the phenomenon of epistemic overdetermination and its role in the theory of knowledge. (shrink)