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Full Idea
At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers.
Gist of Idea
Hilbert's geometry and Dedekind's real numbers were role models for axiomatization
Source
Penelope Maddy (Defending the Axioms [2011], 1.3)
Book Ref
Maddy,Penelope: 'Defending the Axioms' [OUP 2013], p.31
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |