Combining Philosophers

All the ideas for Seymour Lipschutz, Johann Herbart and Henri Poincar

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8 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
8920 Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz]
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]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
8120 Objects can be beautiful which express nothing at all, such as the rainbow [Herbart, by Tolstoy]
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 [Poincaré, by Harré]