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Ideas for 'fragments/reports', 'Principia Mathematica' and 'The Question of Ontology'

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5 ideas

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

18079

Newton developed a kinematic approach to geometry [Newton, by Kitcher]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits

18082

Quantities and ratios which continually converge will eventually become equal [Newton]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers

12215

The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

12211

It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

12209

The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K]