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Full Idea
Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness.
Gist of Idea
Set-theory tracks the contours of mathematical depth and fruitfulness
Source
Penelope Maddy (Defending the Axioms [2011], 3.4)
Book Ref
Maddy,Penelope: 'Defending the Axioms' [OUP 2013], p.82
A Reaction
This seems to make it more like a map of mathematics than the actual essence of mathematics.
| 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] |