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Full Idea
One geometry cannot be more true than another; it can only be more convenient.
Gist of Idea
One geometry cannot be more true than another
Source
Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics
Book Ref
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.154
A Reaction
This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate.
| 18203 | Avoid non-predicative classifications and definitions [Poincaré] |
| 15923 | Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine] |
| 10180 | Mathematicians do not study objects, but relations between objects [Poincaré] |
| 10245 | One geometry cannot be more true than another [Poincaré] |
| 9916 | Convention, yes! Arbitrary, no! [Poincaré, by Putnam] |
| 15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |