Physics and Leibnizs Principles

Leibniz’s principles made for an elegant and coherent philosophy. In part metaphysical, in part methodological, they addressed fundamental questions in the treatment of symmetry, in the relationship of physics to mathematics, in logic that are if anything even more pressing today than they were in Leibniz’s time. As I shall read them, they also expressed a distinctive and uncompromising form of realism, a commitment to the adequacy of purely descriptive concepts. This doctrine has been called ‘semantic universalism’by van Fraassen (1991), and the ‘generalist picture’by O’Leary-Hawthorne and Cover (1996): it will become clearer in due course just what it entails. The principles that I shall consider are the Principle of Su¢ cient Reason (PSR) and the Principle of Identity of Indiscernibles (PII). In the …rst instance I shall take them both to be methodological principles. The former I shall read as requiring that the concepts of physics be entirely transparent. Analysis and explanation are to proceed without any limits. The perspective is impersonal: any epistemological limitation, to do with our human situation or perceptual apparatus, is to be viewed as a purely practical matter, re‡ecting no fundamental constraint. This puts in place a part of the generalist picture. The PSR clearly promotes the use of mathematical concepts in physics. The PII, in contrast, depends on a sharp distinction between purely mathematical concepts, and physical ones. Leibniz too made use of this distinction (between ‘real’and ‘notional’or ‘ideal’concepts), but in his hands the principle depended heavily, though often tacitly, on his metaphysical theory of substance (and, with quali…cations, on his philosophical logic). He was led to a restrictive formulation of it in consequence: