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Full Idea
By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge.
Gist of Idea
By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge
Source
David Hilbert (Axiomatic Thought [1918], [56])
Book Ref
'From Kant to Hilbert: sourcebook Vol. 2', ed/tr. Ewald,William [OUP 1996], p.1115
A Reaction
This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc.
| 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] |