Abstract

My dissertation is a reexamination of a crucial question in the history of early modern mathematical science: What was the basis for the adoption of mathematics as the primary mode of discourse for describing natural events by a large segment of the natural philosophical community during the 17 th century? In answering this question, I argue that in order to properly understand the adoption of mathematics as the 'language' of nature by early modern practitioners, it is important to examine contemporary positions concerning both the nature of language and mathematics. This involves exploring the relationship between the philosophies of mathematics and linguistic meaning held by several prominent natural philosophers associated with the nominalist tradition in scientific epistemology. This group, which included Pierre Gassendi, Thomas Hobbes, and George Berkeley, shared a belief that there is no necessary correspondence between external reality and objects of human understanding, which they held to include the objects of linguistic and mathematical discourse. I trace the development of a 'constructivist' approach to language and mathematics among these and other natural philosophers , which contributed to a tension in seventeenth-century mathematical philosophy that influenced later mathematical practitioners. The unifying theme in this nominalist tradition was a concern, not simply with the rules of mathematical practice, but with a general epistemological account of representation that saw objects of human knowledge---both in mathematics and language---as 'constructed' out of distinct experiences, rather than as innately-perceived archetypes in a divine order. At the heart of this problem is the question of how natural philosophers justified claims about knowledge of the physical world. I argue that this nominalist tradition explicitly informed the mathematical philosophy of John Wallis and Isaac Barrow, and I contend that nominalist constructivism played an important role in defining the use and status of mathematical demonstrations in early modern science