Reals by Abstraction. An Inquiry about Epistemic Economy in Mathematics: Volume II
The Real Numbers
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Beschreibung
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.
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.
Considers other examples drawn from second-order definitions of real numbers by comparing three different approaches Rephrases Frege's definition of reals in a consistent and faithful manner Suggest an original and epistemically highly economical definition of real numbers as bicimal developments
Autor*in
Marco Panza
Themen in »Reals by Abstraction. An Inquiry about Epistemic Economy in Mathematics: Volume II«
Philosophy of Mathematics and Logic Epistemic Economy in Mathematics Real numbers natural numbers abstraction principles for natural and real numbers epistemic economy reals by abstraction