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Full Idea
The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases.
Gist of Idea
The facts of geometry, arithmetic or statics order themselves into theories
Source
David Hilbert (Axiomatic Thought [1918], [03])
Book Ref
'From Kant to Hilbert: sourcebook Vol. 2', ed/tr. Ewald,William [OUP 1996], p.1108
A Reaction
This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us.
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |