I discuss two questions: (1) would Duhem have accepted the thesis of the continuity of scientific methodology? and ( 2) to what extent is the Oxford tradition of classification/subalternation of sciences continuous with early modern science? I argue that Duhem would have been surprised by the claim that scientific methodology is continuous; he expected at best only a continuity of physical theories, which he was trying to isolate from the perpetual fluctuations of methods and metaphysics. I also argue that the evidence does not support the conclusion that early modern doctrines about mathematics and physics are continuous with the subalternation of sciences from Grosseteste, Bacon, and the theologians of fourteenth-century Oxford. The official and dominant context for early modern scientific methodology seems to have been progressive Thomism, and early modern thinkers seem to have pitted themselves against it.
When considering the various historical doctrines relating science and mathematics, we should keep in mind three important facts. (1) Early modern science considered mathematics as the foundation of physics or natural philosophy -witness Galileo's famous assertion that "the great book of nature is written in the language of mathematics and its characters are triangles, circles, and other geometrical figures" (1960, p. 25). (2) It wasn't always that way. Aristotle in the Physics discussed how the mathematician differs from the physicist (1930, II, chap. 2). He asserted that physicists deal with physical bodies and their essential attributes; physicists treat of surfaces and volumes, lines and points, but as the limits of physical bodies. Mathematicians also treat of surfaces and volumes, points and lines, but not as physical, separating them from their essential attributes and from motion. Geometry investigates physical lines, but not qua physical; the more physical branches of mathematics such as optics, harmonics, and astronomy, investigate mathematical lines, qua physical, not qua mathematical. Instead of mathematics being the foundation of physics, Aristotle conceived of mathematics and physics as different sciences separated by their differ-' ent objects. And (3) the medievals were not univocal in their support of the Aristotelian position. They interpreted' Aristotle's remarks so variously that they can be considered as making up at least two distinct