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Ideas for 'Parmenides', 'works' and 'Introduction to the Philosophy of Mathematics'

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5 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

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Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

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Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

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Axioms are 'categorical' if all of their models are isomorphic [Colyvan]

5. Theory of Logic / L. Paradox / 3. Antinomies

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Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle]

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Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato]