Philosophia Mathematica 25 (3):287-291 (2017)

Erich Reck
University of California, Riverside
© The Author [2017]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.comRichard Dedekind was a contemporary of Bernhard Riemann, Georg Cantor, and Gottlob Frege, among others. Together, they revolutionized mathematics and logic in the second half of the nineteenth century. Dedekind had an especially strong influence on David Hilbert, Ernst Zermelo, Emmy Noether, and Nicolas Bourbaki, who completed that revolution in the twentieth century. With respect to mainstream mathematics, he is best known for his contributions to algebra and number theory. With respect to logic and the foundations of mathematics, many of his technical results — his conceptualization of the natural and real numbers, his analysis of proofs by mathematical induction and definitions by recursion (extended to the transfinite by Zermelo, John von...
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DOI 10.1093/philmat/nkx021
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Two Types of Abstraction for Structuralism.Øystein Linnebo & Richard Pettigrew - 2014 - Philosophical Quarterly 64 (255):267-283.

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