Galileo on the Mathematical Physics of Terrestrial Extrusion

Abstract

We have seen that the empirical astronomical objections and the scriptural theological objections were not the only arguments against the Copernican system. Equally important, strong, and consequential were the mechanical physical objections, involving such phenomena as falling bodies, the motion of projectiles, and the extruding power of whirling. They presupposed Aristotelian physics, based on the principles that rest is the natural state and motion requires a force; and their refutation required a new physics, based on the principles of inertia or conservation of motion and the composition of motion into independent components. Galileo took the physical objections as seriously as the astronomical ones, although he conceived the refutation of the former earlier than the refutation of the latter, since the answers to the physical difficulties were implied by his earlier research into a new physics, whereas the astronomical answers were the result of the telescope.

This chapter will examine how Galileo defended Copernicus from the extremely powerful objection based on the extruding power of whirling. We will see that Galileo criticized the extrusion objection in several distinct ways, but that his major criticism was that the objection was quantitatively invalid. Now, this quantitative invalidity turns out to be a flaw that is partly mathematical, partly physical, and essentially physical-mathematical. That is, the correct understanding of the phenomenon to which the objection appeals requires the proper combination of physical and mathematical principles, namely the skill of physical-mathematical reasoning. Thus, the structure of this chapter will be that of an inquiry into the nature of mathematical reasoning by means of a Galilean case study suggesting a definition of physical-mathematical reasoning.