Combining Philosophers

Ideas for Xenophanes, Hartry Field and Gottfried Leibniz

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3 ideas

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

12937

We shouldn't just accept Euclid's axioms, but try to demonstrate them [Leibniz]

18221

'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers

23026

We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz]