Axiomatizing Changing Conceptions of the Geometric Continuum II: Archimedes-Descartes-Hilbert-Tarski. Issue 1 (23rd November 2017)

• Record Type: Journal Article
• Authors: Baldwin, John T
• Is Part Of: Philosophia Mathematica. Volume 27:Issue 1(2019)
• Page Start: 33
• Page End: 60
• Publication Date: 2017-11-23
• Subjects: Mathematics -- Philosophy -- Periodicals; Wiskunde; Filosofische aspecten; Mathematics -- Philosophy; Periodicals; 510.105
• DOI: 10.1093/philmat/nkx031
• Languages: English
• ISSNs: 0031-8019

Abstract

ABSTRACT: In Part I of this paper we argued that the first-order systems HP5 and EG are modest complete descriptive axiomatization of most of Euclidean geometry. In this paper we discuss two further modest complete descriptive axiomatizations: Tarksi's for Cartesian geometry and new systems for adding $\pi$ . In contrast we find Hilbert's full second-order system immodest for geometrical purposes but appropriate as a foundation for mathematical analysis.