Combining Philosophers

Ideas for Rescher,N/Oppenheim,P, Henri Poincar and Max Horkheimer

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5 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

10245

One geometry cannot be more true than another [Poincaré]

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 [Poincaré, by Lavine]

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

10180

Mathematicians do not study objects, but relations between objects [Poincaré]

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

9916	Convention, yes! Arbitrary, no! [Poincaré, by Putnam]

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

18203

Avoid non-predicative classifications and definitions [Poincaré]