# Axiomatizing changing conceptions of the geometric continuuum

@inproceedings{Baldwin2014AxiomatizingCC, title={Axiomatizing changing conceptions of the geometric continuuum}, author={John T. Baldwin}, year={2014} }

We begin with a general account of the goals of axiomatization, introducing a variant (modest) on Detlefsen’s notion of ‘complete descriptive axiomatization’. We examine the distinctions between the Greek and modern view of number, magnitude and proportion and consider how this impacts the interpretation of Hilbert’s axiomatization of geometry. We argue, as indeed did Hilbert, that Euclid’s propositions concerning polygons, area, and similar triangles are derivable (in their modern…

## One Citation

Bridging the gap between analytic and synthetic geometry: Hilbert’s axiomatic approach

- MathematicsSynthese
- 2015

It is argued that Hilbert not only sought to show that geometry could be considered a pure mathematical theory, once it was presented as a formal axiomatic system; he also aimed at showing that in the construction of such an axIomatic system one could proceed purely geometrically, avoiding concept formations borrowed from other mathematical disciplines.

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