Leibniz's principles made for an elegant and coherent philosophy. In part meta-physical, 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 Sufficient Reason (PSR) and the Principle of the Identity of Indiscernibles (PII). In the first 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, reflecting 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.