More than any other aspect of the Second Scientific Revolution, the remarkable revitalization or British mathematics and mathematical physics during the first half of the nineteenth century is perhaps the most deserving of the name. While the newly constituted sciences of biology and geology were undergoing their first revolution, as it were, the reform of British mathematics was truly and self-consciously the story of a second coming of age. ‘Discovered by Fermat, cocinnated and rendered analytical by Newton, and enriched by (...) Leibniz with a powerful and comprehensive notation’, wrote the young John Herschel and Charles Babbage of the calculus in 1813, ‘as if the soil of this country [was] unfavourable to its cultivation, it soon drooped and almost faded into neglect; and we now have to re-import the exotic, with nearly a century of foreign improvement, and to render it once more indigenous among us’. (shrink)

I have always been a philosopher at heart. I write history of science and history of its philosophy primarily as a philosopher wary of his abstractions and broad conceptualizations. But that has not always been the case. Lakatos famously portrayed history of science as the testing ground for theories of scientific rationality. But he did so along the crudest Hegelian lines that did injury both to Hegel and to the history and methodology of science. Since science is ultimately rational, he (...) argued, rival methodologies can prove their mettle by competing for whose tendentiously reconstructed account of the history of science renders more of it rational! My own approach to the relationship between history and philosophy of science started out perhaps a little more open-mindedly than Lakatos’s, but in a manner no less crude. Over the years the relationship between the history I wrote and the philosophy to which I was committed took on a firmer and more reciprocal shape. It did so in the course of a process that I now realize exemplified the philosophical position it eventually yielded. I would like to trace that development in the following pages and reflect as best I can on where it has lead and left me. (shrink)