Reals by Abstraction. An Inquiry about Epistemic Economy in Mathematics: Volume II: The Real Numbers (Synthese Library, 523, Band 523) - Couverture rigide

Panza, Marco

Couverture rigide

ISBN 10 : 3032004306 ISBN 13 : 9783032004307

Editeur : Springer, 2026

Synopsis

This second of a two-volume book prolongs the inquiry of volume 1 by considering other examples apt to better illustrate the ideal of epistemic economy in mathematical recasting. The new examples are drawn from second-order definitions of real numbers and allow the comparison of three different approaches to the definition of these numbers: by domain extension, as ratios of magnitudes, and as bicimal developments. These definitions are presented in detail (by often going further than any available presentation) and compared with respect to their epistemic economy. In doing so, original results and insights are offered, such as a faithful and still consistent rephrasing of Frege’s definitions of reals, and an original and epistemically highly economical definition of real numbers as bicimal developments. This ensures the book is of interest to scholars and students in the philosophy of mathematics and logic.

A propos du livre

À propos de l'auteur

Marco Panza is The Kennedy Professor of Philosophy at Chapman University and a Research Director of First Class at the CNRS. Historian and philosopher of Logica and mathematics, he has studied in Milano and Paris and taught at the University of Geneva, the University of Nantes, the UNAM (Mexico City), the Pompeu Fabra Univ. in Barcelona, the universities of Paris 7 and Paris 1, and Chapman University. Author of about 150 papers and books in different Languages (including English, French, Italian, Spanish, and Portuguese) that appeared in the most recognized journals in his domain, and for some prestigious publishers, like Flammarion, Vrin, and Springer. His scientific expertise includes the history of Greek and Early modern mathematics (especially, Euclid, Viète, Descartes, Newton, Euler, and Lagrange), Frege’s foundational program and his contemporary legacy, the philosophy of mathematical practice (he is a founding member of the Association of Philosophy of Mathematical Practice).

À propos de la quatrième de couverture

This second of a two-volume book prolongs the inquiry of volume 1 by considering other examples apt to better illustrate the ideal of epistemic economy in mathematical recasting. The new examples are drawn from second-order definitions of real numbers and allow the comparison of three different approaches to the definition of these numbers: by domain extension, as ratios of magnitudes, and as bicimal developments. These definitions are presented in detail (by often going further than any available presentation) and compared with respect to their epistemic economy. In doing so, original results and insights are offered, such as a faithful and still consistent rephrasing of Frege’s definitions of reals, and an original and epistemically highly economical definition of real numbers as bicimal developments. This ensures the book is of interest to scholars and students in the philosophy of mathematics and logic.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2026
• Langue: anglais
• ISBN 10: 3032004306
• ISBN 13: 9783032004307
• Reliure: Gebundene Ausgabe
• Nombre de pages: 255
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne