Finite and Otherwise. Aristotle and Some Seventeenth Century Views

Abstract

It is unwise to discuss so pervasive a cluster of concepts from 17th century natural philosophy as space, matter, extension, and infinity, without referring to Aristotelian and scholastic doctrine. One may argue far into the night over the question of whether Newton’s words reveal a dependance on Burthogge, rather than Herveus Natalis, and whether Descartes at a particular place was using Anselm or John Damascene; but one thing we must surely accept is that the language used was that of the Aristotelian inheritance. Of course it was changed in many ways; but just as when trees are turned into telegraph poles, the grain of the wood remaining visible, so with the language of Aristotle. Since we are particularly concerned with doctrines of the infinite, I will give the merest outline of those parts of Aristotle which seem to me to have a bearing on the 17th century discussion. I will then place rather more emphasis than Ted McGuire is inclined to do on the common element in the thought of Descartes, Locke, and Newton. In the time available I shall not be able to make more than passing reference to scholastic discussions of the same themes, although I am sure that to do so would show that, whether he liked it or not, 17th century man was a lineal descendent of the scholastics. As it happened, Georg Cantor gave the palm to the seventeenth century for its arguments against the actual infinite — arguments which he judged to be more cogent than Aristotle’s, but arguments which he believed he could refute. He commended Locke, Descartes, Spinoza, and Leibniz, while suggesting Hobbes and Berkeley as additional reading.