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Single Idea 18742

[from 'Foundations of Geometry' by David Hilbert, in 6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry ]

Full Idea

In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised.

Gist of Idea

Hilbert's formalisation revealed implicit congruence axioms in Euclid

Source

report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2

Book Reference

'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.17


A Reaction

The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy.