Mathematical method and Newtonian science in the philosophy of Christian Wolff

This paper aims to illuminate Christian Wolff’s view of mathematical reasoning, and its use in metaphysics, by comparing his and Leibniz’s responses to Newton’s work. Both Wolff and Leibniz object that Newton’s metaphysics is based on ideas of sense and imagination that are suitable only for mathematics. Yet Wolff expresses more regard (than Leibniz) for Newton’s scientific achievement. Wolff’s approval of the use of imaginative ideas in Newtonian mathematical science seems to commit him to an inconsistent triad. For he rejects their use in metaphysics, and also holds that every scientific discipline must follow mathematics’ method. A facile resolution would be to suppose Wolff identifies the method of mathematics with the order in which propositions are deduced, or with “analysis” that reveals the structure of concepts. This would be to assimilate Wolff’s view to Leibniz’s (on which all mathematical propositions are ultimately derived from definitions, and definitions are justified by conceptual analysis). On this construal, mathematical reasoning involves only the understanding. But Wolff conceives mathematics’ method more broadly, to include processes of concept-formation which involve perception and imagination. Thus my way of resolving the tension is to find roles for perception and imagination in the formation of metaphysical concepts.