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Ideas for 'Mathematical Methods in Philosophy', 'How the Laws of Physics Lie' and 'Intro to Gdel's Theorems'

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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

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Second-order arithmetic can prove new sentences of first-order [Smith,P]

5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic

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Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]