Abstract
In Part I [Bal14a], we defined the notion of a modest complete descriptive axiomatization and showed that HP5 and EG are such axiomatizations of Euclid’s polygonal geometry and Euclidean circle geometry1. In this paper we argue: 1) Tarski’s axiom set E is a modest complete descriptive axiomatization of Cartesian geometry (Section 2; 2) the theories EGπ,C,A and E π,C,A are modest complete descriptive axiomatizations of Euclidean circle geometry and Cartesian geometry, respectively when extended by formulas computing the area and circumference of a circle (Section 3); and 3) that Hilbert’s system in the Grundlagen is an immodest axiomatization of any of these geometries. As part of the last claim (Section 4), we analyze the role of the Archimdedean postulate in the Grundlagen, trace the intricate relationship between alternative formulations of ‘Dedekind completeness’, and exhibit many other categorical axiomatizations of related geometries.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
