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2 ideas
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
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. | |
From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |