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Ideas for 'Two Problems of Epistemology', 'Logic for Philosophy' and 'A Structural Account of Mathematics'

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3 ideas

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

9553	Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order

13701

A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism

10192

We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]