In “Mathematical Truth,” Paul Benacerraf raises an epistemic challenge for mathematical platonists. In this paper, I examine the assumptions that motivate Benacerraf’s original challenge, and use them to construct a new causal challenge for the epistemology of mathematics. This new challenge, which I call ‘Gödel’s Gap’, appeals to intuitive insights into mathematical knowledge. Though it is a causal challenge, it does not rely on any obviously objectionable constraints on knowledge. As a result, it is more compelling than the original challenge. (...) It is also more general; the challenge applies equally to platonistic and non-platonistic accounts of mathematical truth. And it can be generalized beyond the case of mathematical knowledge to pose a challenge for, e.g., moral knowledge. (shrink)

Paul Benacerraf’s argument that mathematical realism is apparently incompatible with mathematical knowledge has been widely thought to also show that a priori knowledge in general is problematic. Although many philosophers have rejected Benacerraf’s argument because it assumes a causal theory of knowledge, some maintain that Benacerraf nevertheless put his finger on a genuine problem, even though he didn’t state the problem in its most challenging form. After diagnosing what went wrong with Benacerraf’s argument, I argue that a new, more challenging, (...) version of Benacerraf’s problem can be constructed. The new version—what I call the Defeater Version—of Benacerraf’s problem makes use of a no-defeater condition on knowledge and justification. I conclude by arguing that the best way to avoid the problem is to construct a theory of how a priori judgments reliably track the facts. I also suggest four different kinds of theories worth pursuing. (shrink)

With respect to the confirmation of mathematical propositions, proof possesses an epistemological authority unmatched by other means of confirmation. This paper is an investigation into why this is the case. I make use of an analysis drawn from an early reliability perspective on knowledge to help make sense of mathematical proofs singular epistemological status.

Commonsense psychology and cognitive science both regularly assume the existence of representational states. I propose a naturalistic theory of representation sufficient to meet the pretheoretical constraints of a "folk theory of representation", constraints including the capacities for accuracy and inaccuracy, selectivity of proper objects of representation, perspective, articulation, and "efficacy" or content-determined functionality. The proposed model states that a representing device is a device which changes state when information is received over multiple information channels originating at a single source. The (...) changed state of a representing device is a representation. The unitary information source which would give rise to the information impinging on the representing device, and hence, give rise to the representation, is the content of the representation. The model meets the pretheoretic constraints, and also conforms to available neurobiological data for two invertebrate species. (shrink)

The aim of the present article is to accomplish two things. The first is to show that given some further plausible assumptions, existing challenges to the indispensability of knowledge in causal explanation of action fail. The second is to elaborate an overlooked and distinct argument in favor of the causal efficacy of knowledge. In short, even if knowledge were dispensable in causal explanation of action, it is still indispensable in causal explanation of other mental attitudes and, in particular, some reactive (...) attitudes and factive emotions. Taking into account this sort of causal efficacy in determining which mental states are genuine mental states opens up new perspectives for defending the view that knowledge is the most general factive and genuine mental state. (shrink)