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)

ABSTRACT In a series of papers read to the Cambridge Philosophical Society through the 1820s, the Cambridge mathematician George Peacock laid the foundation for a natural history of arithmetic that would tell a story of human progress from counting to modern arithmetic. The trajectory of that history, Peacock argued, established algebraic analysis as a form of universal reasoning that used empirically warranted operations of mind to think with symbols on paper. The science of counting would suggest arithmetic, arithmetic would suggest (...) arithmetical algebra, and, finally, arithmetical algebra would suggest symbolic algebra. This philosophy of suggestion provided the foundation for Peacock's “principle of equivalent forms,” which justified the practice of nineteenth-century English symbolic algebra. Peacock's philosophy of suggestion owed a considerable debt to the early Cambridge Philosophical Society culture of natural history. The aim of this essay is to show how that culture of natural history was constitutively significant to the practice of nineteenth-century English algebra. (shrink)