Reals by Abstraction. An Inquiry about Epistemic Economy in Mathematics: Volume II
The Real Numbers
Series: Synthese Library; 523;
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Product details:
- Publisher Springer Nature Switzerland
- Date of Publication 22 January 2026
- Number of Volumes 1 pieces, Book
- ISBN 9783032004307
- Binding Hardback
- No. of pages222 pages
- Size 279x210 mm
- Language English
- Illustrations X, 222 p. 4 illus. 700
Categories
Long description:
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.
MoreTable of Contents:
Part III: Theories of Real Numbers.- 9 Defining Real Numbers through Relatives and Rationals.- 10 Defining Real Numbers as Ratios of Magnitudes.- 11 Defining Real Numbers as Bicimal Pairs.- Part IV: Conclusions.- Appendices.- Bibliographical References.
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