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Peacock's "History of Arithmetic", an Attempt to reconcile empiricism to universality

Abstract : When the Whig Anglican algebraist Rev. George Peacock (1791-1858) conceived of his new abstract view of Symbolical Algebra in the 1830s, he had already written an impressive little known « History of Arithmetic » for the Encyclopaedia Metropolitana, eventually published in 1845, back in the 1820s. This paper studies why this « History of Arithmetic » was conceived and how it reinforced Peacock's general view of algebra as a symbolizing process. As a fellow, tutor and lecturer at Trinity College since 1814, Peacock was already involved in the renewal of mathematics curriculum and mathematical research in Cambridge, as well as in the cultivation and the diffusion of science. As a reformer, Peacock along with his colleagues in Cambridge, faced the Industrial Revolution, its varied pressures on the country's academic institutions, and its concern with transformation processes. As soon as the 1820s, Peacock sought out a universal genesis from arithmetic to algebra, founded on the mathematical language of operations, and he launched his « History of Arithmetic » as a large inquiry into the vocabulary that all known tribes and nations used for elementary computations. In this way, he supported a moderate empiricist approach to science, deeply rooted in Locke's philosophy of human understanding. With a comparative and philological approach to numeral languages in hand, Peacock presented first arithmetic and then algebra as the progressive developments of asbtract calculating languages,.symbolising algorithmical processes. This view accounted for the special place he gave to Indian and Arabic arithmetics in his exposition of contemporaneous knowledge on numbers.
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Contributor : Marie-José Durand-Richard Connect in order to contact the contributor
Submitted on : Friday, November 5, 2010 - 2:12:57 AM
Last modification on : Tuesday, April 14, 2020 - 2:38:37 PM
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Marie-José Durand-Richard. Peacock's "History of Arithmetic", an Attempt to reconcile empiricism to universality. 2010. ⟨halshs-00530818⟩



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