Ideas of Henri Poincaré, by Theme
[French, 1854  1912, Professor of Mathematics at the Sorbonne.]
green numbers give full details 
back to list of philosophers 
expand these ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
10245

One geometry cannot be more true than another

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
15923

Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Lavine]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10180

Mathematicians do not study objects, but relations between objects

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
9916

Convention, yes! Arbitrary, no! [Putnam]

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
18203

Avoid nonpredicative classifications and definitions

26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
15877

The aim of science is just to create a comprehensive, elegant language to describe brute facts [Harré]
