Drawing Lines Through Rivers and Cities: The Meaning and Evolution of the Notion of a “Postulate” in Geometry
The talk discusses Euclid’s notion of a geometrical principle, and contrasts definitions, axioms and postulates as different principles of geometry. It deals with the development of such notions in the middle ages and the early modern age, and the consequent changes in mathematical epistemology. The birth and early meaning of of “logicism” is also discussed. The talk ends with a few remarks on the transformation of the pre-modern notion of a mathematical principle into Hilbert’s conception of an axiom.