Combining Texts
Ideas for
'Parmenides', 'Necessary Beings' and 'Philosophy of Mathematics'
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8 ideas
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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19296
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If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale]
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5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
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19289
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Maybe conventionalism applies to meaning, but not to the truth of propositions expressed [Hale]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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9605
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If a proposition is false, then its negation is true [Brown,JR]
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5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
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19298
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Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems [Hale]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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9649
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Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR]
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5. Theory of Logic / L. Paradox / 3. Antinomies
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13986
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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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14150
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Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato]
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5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
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9638
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Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR]
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