Important to Kuhn's account of scientific change is the observation that when paradigms are in competition with one another, there is a curious breakdown of rational argument and communication between adherents of competing programs. He attributed this to the fact that competing paradigms are incommensurable. The incommensurability thesis centrally involves the claim that there is a deep conceptual gap between competing paradigms in science. In this paper I argue that in one important case of competing paradigms, the Aristotelian explanation of the properties of bodies in terms of matter and form as opposed to the Cartesian mechanist paradigm, where the properties of bodies are explained on the model of machines, there was no such conceptual gap: the notion of a machine was as fully intelligible on the Aristotelian paradigm as it was on the Cartesian. But this does not mean that the debate between the two sides was conducted on purely rational terms. Rational argument breaks down not because of Kuhnian incommensurability, I argue, but because of other cultural factors separating the two camps.