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My dissertation lies at the philosophical intersection of the American pragmatist tradition and contemporary epistemology. By treating truth, justification, and belief as matters of degree, I develop a measure of knowledge that captures all of our fundamental intuitions while providing answers to the problems of epistemic luck, skepticism, and scientific pessimism. Traditionally, knowledge is understood as justified true belief that is not due to luck. My project follows this general outline. First, I describe the pragmatist understanding of truth first articulated by Charles Sanders Peirce in the late nineteenth century. My first chapter offers Peirce's understanding of truth as the best explanation of our intuitive understanding of what it is for a proposition to be the case and shows how we can understand Peirce's theory as compatible with contemporary theories of truth. In my second chapter, I develop a theory of belief such that an agent believes a proposition when she acts as if that proposition were a rule governing her behavior. On this view, beliefs are theoretical entities posited to make sense of other agents' actions. Following this account of belief, I describe what it is for a belief to be true and argue that sense of truth in which beliefs are true is best understood as an approximation of the full descriptive truth. My third, fourth, and fifth chapters are an account of justification. Chapter 3 is a descriptive account of synchronic justification: we all reject or accept propositions in accordance with maximizing the coherence of our belief-networks. Chapters 4 and 5 articulate and then defend a new measure of diachronic justification, which is a measure of the degree to which a belief is appropriately revisable and therefore embeddable in an ongoing process of fallibilist inquiry. I develop a novel formal quantification of methodological justification and show that it gives plausible results when applied to popular cases. My final chapter brings justification, truth, and belief together into a scalar knowledge measure. I locate my theory in ongoing epistemic inquiry, describing its conceptual advantages over rival theories as well as its ability to replicate their successes.