Combining Philosophers

All the ideas for Archimedes, R Cook / P Ebert and James Baillie

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3 ideas

5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic

3299	In logic identity involves reflexivity (x=x), symmetry (if x=y, then y=x) and transitivity (if x=y and y=z, then x=z) [Baillie]

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

13007

Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]

18. Thought / E. Abstraction / 7. Abstracta by Equivalence

9141	Abstraction theories build mathematics out of second-order equivalence principles [Cook/Ebert]