An understanding of the relationship between metaphysics and natural philosophy - or, as we might now say, between philosophy and science - is fundamental to understanding the rise of the "new science" of the seventeenth century. Twentieth-century scholarship on this relationship has been dominated by the thoughbt of Ernst Cassirer, E. A. Burtt, A. N. Whitehead, and Alexandre Koyre. These authors found a common core in the mathematization of nature, which they ascribed to a common Platonic or Pythagorean metaphysical presupposition, (...) on the part of Copernicus, Kepler, Galileo, and Descartes, that the book of nature is written in mathematical characters. Taking Burtt as its primary stalking horse, this chapter challenges this view by finding significant differences in the relations to metaphysics of major actors such as those just named. It does this in part by recognizing that, in the seventeenth century, metaphysics was an intellectual practice that one engaged in wittingly. By contrast, Burtt adopted a historiographical approach in which metaphysics consists of the nonempirical presupposition of an age (a position advanced by R. G. Collingwood). That approach, although valid within its limits, distorts or omits from consideration the witting practice of metaphysics by figures such as Kepler and Descartes. And it makes metaphysicians of Copernicus and Galileo, who are better classified as a mathematical astronomer and a mathematical natural philosopher and writer on astronomy. The chapter ends with some reflections on purportedly aphilosophical history of science. (shrink)