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)

Dans la première moitié du xixe siècle en Angleterre, autour de Charles babbage (1791–1871), John F. W. Herschel (1792–1871), George Peacock (1791–1858), Duncan F. Gregory (1813–1844), Augustus de Morgan (1806–1871), George Boole (1815–1864), et d'autres auteurs moins connus, un réseau d'algébristes renouvelle singulièrement la conception de l'algèbre, à tel point que leur travail est le plus souvent interprété comme émergence des travaux sur l'algèbre abstraite. Comme ces algébristes sont également des réformateurs impliqués dans la réorganisation de la science, il s'agira (...) de proposer de ces travaux une lecture plus contextuelle, afin d'éclairer leur inscription parmi les effects de la Révolution industrielle (1760–1830), et d'analyser leur rôle de médiation culturelle entre les racines d'un savoir universitaire fondé sur la fidélité aux Anciens, et de nouvelles formes d'élaboration des connaissances. Une médiation marquée par un premier rapprochement entre algèbre et logique. (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)