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.
| ISBN: | 9783032004307 |
| Publication date: | 11th June 2026 |
| Author: | Marco Panza |
| Publisher: | Springer an imprint of Springer Nature Switzerland |
| Format: | Hardback |
| Pagination: | 249 pages |
| Series: | Synthese Library |
| Genres: |
Philosophy of mathematics Philosophy: logic History of science |
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.
Reals by Abstraction. An Inquiry About Epistemic Economy in Mathematics: Volume II features in the following genres: Philosophy of mathematics, Philosophy: logic, History of science
Reals by Abstraction. An Inquiry About Epistemic Economy in Mathematics: Volume II is available in Hardback
Reals by Abstraction. An Inquiry About Epistemic Economy in Mathematics: Volume II was written by Marco Panza and published by Springer an imprint of Springer Nature Switzerland
Reals by Abstraction. An Inquiry About Epistemic Economy in Mathematics: Volume II has 249 pages
Yes it is part of Synthese Library series
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