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Ideas for 'Introduction to 'Properties'', 'On the Nature of Mathematical Reasoning' and 'Structuralism Reconsidered'

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3 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers

8923	Numbers are identified by their main properties and relations, involving the successor function [MacBride]

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 / e. Structuralism critique

8926	For mathematical objects to be positions, positions themselves must exist first [MacBride]