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Reals by Abstraction. An Inquiry about Epistemic Economy in Mathematics: Volume II
The Real Numbers
Introduction
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.
Examples and Approaches
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.
Details and Comparisons
These definitions are presented in detail (by often going further than any available presentation) and compared with respect to their epistemic economy.
Results and Insights
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.
Conclusion
This ensures the book is of interest to scholars and students in the philosophy of mathematics and logic.
