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: All analytic propositions are knowable a prioriand 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. (shrink)

Alberto Casullo ("Necessity, Certainty, and the A Priori", Canadian Journal of Philosophy 18, 1988) argues that arithmetical propositions could be disconfirmed by appeal to an invented scenario, wherein our standard counting procedures indicate that 2 + 2 != 4. Our best response to such a scenario would be, Casullo suggests, to accept the results of the counting procedures, and give up standard arithmetic. While Casullo's scenario avoids arguments against previous "disconfirming" scenarios, it founders on the assumption, common to scenario and (...) response, that arithmetic might be independent of standard counting procedures. Here I show, by attention to tallying as the simplest form of counting, that this assumption is incoherent: given standard counting procedures, then (on pain of irrationality) arithmetical theory follows. (shrink)

ABSTRACT Historical structuralist views have been ontological. They either deny that there are any mathematical objects or they maintain that mathematical objects are structures or positions in them. Non-ontological structuralism offers no account of the nature of mathematical objects. My own structuralism has evolved from an early sui generis version to a non-ontological version that embraces Quine’s doctrine of ontological relativity. In this paper I further develop and explain this view.

In at least some cases of justified perceptual belief, our perceptual experience itself, as opposed to beliefs about it, evidences and thereby justifies our belief. While the phenomenon is common, it is also mysterious. There are good reasons to think that perceptions cannot justify beliefs directly, and there is a significant challenge in explaining how they do. After explaining just how direct perceptual justification is mysterious, I considerMichael Huemers (Skepticism and the Veil of Perception, 2001) and Bill Brewers (Perception and (...) Reason, 1999) recent, but radically different, attempts to eliminate it. I argue that both are unsuccessful, though a consideration of their mistakes deepens our appreciation of the mystery. (shrink)