Internalism, externalism, and beyond: 19th-century British algebra

Abstract

This paper discovers the roots of symbolical algebra in a three-quarters-of-a-century British discussion of sound reasoning, general terms, and signs—a discussion in which mathematical and philosophical elements were freely and perhaps inseparably intermingled. It establishes, in particular, a link between early-19th-century symbolical algebra and nominalism. Opening with a review of recent attacks on the rigid internal/external dichotomy, which underlies much of the modern history of science, the paper also serves as an example of the fertility of suspending the dichotomy in pursuit of earlier mathematical subcultures.