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Predicativity and Structuralism in Dedekind’s Construction of the Reals

Erkenntnis 71 (2):157-173 (2009)

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Introduction to Special Issue: Dedekind and the Philosophy of Mathematics.Erich Reck - 2017 - Philosophia Mathematica 25 (3):287-291.details © The Author [2017]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] 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 (...) Download Export citation Bookmark
What we talk about when we talk about numbers.Richard Pettigrew - 2018 - Annals of Pure and Applied Logic 169 (12):1437-1456.details In this paper, I describe and motivate a new species of mathematical structuralism, which I call Instrumental Nominalism about Set-Theoretic Structuralism. As the name suggests, this approach takes standard Set-Theoretic Structuralism of the sort championed by Bourbaki and removes its ontological commitments by taking an instrumental nominalist approach to that ontology of the sort described by Joseph Melia and Gideon Rosen. I argue that this avoids all of the problems that plague other versions of structuralism. Download Export citation Bookmark 4 citations
Peano’s structuralism and the birth of formal languages.Joan Bertran-San-Millán - 2022 - Synthese 200 (4):1-34.details Recent historical studies have investigated the first proponents of methodological structuralism in late nineteenth-century mathematics. In this paper, I shall attempt to answer the question of whether Peano can be counted amongst the early structuralists. I shall focus on Peano’s understanding of the primitive notions and axioms of geometry and arithmetic. First, I shall argue that the undefinability of the primitive notions of geometry and arithmetic led Peano to the study of the relational features of the systems of objects that (...) Download Export citation Bookmark

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