Two Mathematics, Two Gods: Newton and the Second Law

Abstract

This article continues the discussion, begun in an earlier contribution to Perspectives on Science, of recent arguments over the coherence of Newton’s physics. The arguments turn on his use of the term “force” in two apparently different ways in the second law. This ambiguity remains because Newton conceived of mathematics in two entirely different ways—the first as a way of describing how things are in themselves, the second (more positivistic and hypothetical) as a method of approximation. These two conceptions were, in turn, reflections of how, according to Newton, one stands in relation to two ideas of God—God as pure being and God as will.