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)

Early Victorian analogical arguments were used to order the natural and the social world by maintaining a coherent collective experience across cultural oppositions such as the ideal and material, the sacred and profane, theory and fact. Maxwell's use of analogical argument in ‘On Faraday's lines of force’ was a contribution to that broad nineteenth-century discussion which overlapped theology and natural philosophy. I argue here that Maxwell understood his theoretical work as both a technical and a socially meaningful practice and that (...) embedding his use of analogy in the social and intellectual context of Victorian Britain provides a means of telling a sociocultural history of Maxwell's development of a new cognitive tool: a way of thinking on paper analogous to thinking with objects in the laboratory. (shrink)