| In this interdisciplinary dissertation, I navigate between the disciplines of philosophy and history in an attempt to re-envision the production of mathematical knowledge. I use historical case studies as sites where I can pose epistemological questions about the production of mathematical knowledge and about the construction of mathematics as a discipline. I begin with the assumption that the conceptual categories of argument, explanation, and rationality are neither universal nor ahistorical and throughout my dissertation work to establish what counts as mathematical evidence, mathematical justification, and, ultimately, as mathematical truth, during the time period in question.; Because I understand the production of mathematical knowledge to be a human endeavor, who produces this knowledge is also a key question in my study. Central to my dissertation, then, is an analysis of how the discourses that shaped the conceptual categories of mathematical knowledge production in late-eighteenth century Britain were in turn constituted by the politics of identity formation. My project is of interest to feminists, indeed, requires a feminist analysis, for precisely this reason. In order to trace the complex interplay of mathematical, philosophical, and cultural discourses that played a part in determining standards of justification and proof, as well as standards of mathematical truth, an intersectional analysis of gendered, racial, class-based, and national identity formation is needed.; The British mathematician, Reuben Burrow (1747--1792), serves as an ideal figure for such a project. As both an outsider and an insider within late-eighteenth century communities of British mathematicians and natural philosophers, Burrow was forced to navigate the various discourses that shaped the production of mathematical knowledge at the time. What makes Burrow such a potent figure for the historical epistemologist is his awareness of his status at the fringes of late-eighteenth century British intelligentsia, apparent in a number of his personal and public writings. In what follows I use Burrow, and the work he does in mathematics, to explore a number of epistemological questions around the production of mathematical knowledge during that period. |
