Article ID: CBB438218611

Strategical Use(s) of Arithmetic in Richard Dedekind and Heinrich Weber's Theorie Der Algebraischen Funktionen Einer Veränderlichen (2017)

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In this paper, I study Richard Dedekind and Heinrich Weber's 1882 Theorie der algebraischen Funktionen einer Veränderlichen, with a focus on the inherently arithmetical aspects of their work. I show that their paper provides an arithmetical rewriting of Riemannian function theory, i.e. a rewriting built on elementary arithmetical notions such as divisibility. I start with contextual elements concerning what is “arithmetical”, to put Dedekind and Weber's works into perspective from that viewpoint. Then, through a detailed analysis of the 1882 paper and using elements of their correspondence, I suggest that Dedekind and Weber deploy a strategy of rewriting parts of mathematics using arithmetic, and that this strategy is essentially related to Dedekind's specific conception of numbers and arithmetic as intrinsically linked to the human mind.

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Authors & Contributors
Haffner, Emmylou
Gillies, Douglas A.
Rodríguez-Consuegra, Francisco A.
Weiner, Joan
Avigad, Jeremy
McLarty, Colin
Journals
Archive for History of Exact Sciences
Mathesis: Filosofía e Historia de las Matemáticas
Synthese
History and Philosophy of Logic
Journal of Dialectics of Nature
Foundations of Science
Publishers
Van Gorcum
Open Court
Birkhäuser
Crítica
Princeton University Press
Indiana University
Concepts
Mathematics
Arithmetic
Algebra
Logic
Philosophy of mathematics
Set theory
People
Dedekind, Richard
Frege, Gottlob
Cantor, Georg Ferdinand Ludwig
Noether, Emmy
Weber, Heinrich
Peano, Giuseppe
Time Periods
19th century
20th century, early
Places
Germany
France
Great Britain
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