The three papers which make up this dissertation form part of a larger project, which aims to solve the `access problem' for realism about mathematics by providing a clear and plausible example of what a satisfying explanation of human accuracy about objective mathematical facts could look like. They fit into this project as follows. / Philosophy

It is widely accepted, amongst epistemologists, that evidence plays an important role in our epistemic life. Crucially, there is no agreement on what evidence is. Following Silins, we can cash out the disagreement around the notion of evidence in terms of the opposition between Evidential Internalism and Evidential Externalism (Silins, 2005). Evidential internalists claim that evidence supervenes on one's non-factive mental states, such as, beliefs, impressions (BonJour, 1999, Audi, 2001). Evidential Externalists deny that. In this Thesis, first, I contrastively assess the plausibility of two prominent contemporary externalist theories: Duncan Pritchard's Epistemological Disjunctivism, the thesis on which one's evidence in perceptual cases is truth-entailing and reflectively accessible (Pritchard, 2012), and Timothy Williamson's E=K, the thesis on which one's evidence is all and only the propositions one knows (Williamson, 2000). Second, I develop a novel externalist account of evidence that I call Ecumenical Evidentialism. I show how Ecumenical Evidentialism is able to bring together some of the benefits of both Pritchard's Disjunctivism and Williamson's E=K. This Thesis is structured into three sections, each of which addresses the following three questions respectively: Does the Access Problem represent a real threat to Evidential Externalism? Is Evidential Externalism committed to a sceptical variety of Infallibilism? How does Evidential Externalism understand the relation between evidence and epistemic justification? I argue that neither Epistemological Disjunctivism nor E=K are fully satisfying Externalist accounts of evidence. On one hand, I argue that Disjunctivism captures the orthodox intuition on which justification is a matter of being evidence-responsive, but it does so on pain of facing the so-called Access Problem. On the other hand, by rejecting any strong accessibility thesis, Williamson's E=K is better positioned to resist both the Access Problem as well as the Infallibility Problem, but it does not vindicate the orthodox intuition on which justification is a matter of being evidence-responsive. Finally, I show that, while retaining the main commitments of Williamson's theory of evidence, such as, E=K, my Ecumenical Evidentialism is able to capture the orthodox responsiveness intuition about epistemic justification.