This dissertation examines some of ways of evaluating beliefs, relevant to epistemology and to metaphysics. Some problems in normative epistemology are solved by properly relating justified belief, rational belief, and knowledge. Chapter 1 uses this strategy to defend externalism about justified belief. Chapters 3 and 4 defend the view that knowledge is the epistemic standard we aim for our beliefs to meet. Chapter 2 investigates which beliefs are improper because formed in an objectionably circular way. The findings support the Moorean (...) response to Brain-In-a-Vat skepticism, by rebutting the objection from ‘easy knowledge’. The theory of justified belief developed in chapter 1 underwrites the Moorean reply. Chapters 5 and 6 make a non-epistemic way of evaluating beliefs central to metaphysics. To understand relativity or vagueness in a subject-matter, we must hold that being true or false is not the metaphysically serious evaluation of how a belief answers to reality. Either verdict on a borderline case is ‘acceptable’ in the metaphysically serious sense. For a matter to be relative is for the ‘acceptability’ of affirming the proposition to vary between judges. Chapters 5 and 6 sketch an approach to metaphysics built from the notion of ‘metaphysically acceptable judgment’, with chapter 6 concentrating on vagueness, and chapter 5 focusing on relativism about knowledge. Chapter 5 argues that the lottery and preface puzzles manifest central features of our concept of knowledge. The proposed version of relativism about knowledge is the only theory to respect those features. The view of knowledge presented in chapter 5 is not an isolated metaphysical extravagance, as the same framework is needed for the right metaphysics of everything that’s vague. It is worth noting that my solution to the lottery puzzle is metaphysical relativism about knowledge, but my rebuttal of Brain-In-a-Vat skepticism concerns epistemic circularity and belongs to normative epistemology. Much recent work incorrectly assumes that the two puzzles receive the same treatment. (shrink)