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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

18221	'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H]
	Full Idea: There are two approaches to axiomatising geometry. The 'metric' approach uses a function which maps a pair of points into the real numbers. The 'synthetic' approach is that of Euclid and Hilbert, which does without real numbers and functions.
	From: Hartry Field (Science without Numbers [1980], 5)