Axiomatizing Changing Conceptions of the Geometric Continuum II: Archimedes- Descartes-Hilbert-Tarski?

摘要

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 π. In contrast we find Hilbert's full second-order system immodest for geometrical purposes but appropriate as a foundation for mathematical analysis.