Combining Texts
Ideas for
'Parmenides', 'Necessary Beings' and 'works'
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8 ideas
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
9188
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Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett]
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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
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 / H. Proof Systems / 4. Natural Deduction
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 / I. Semantics of Logic / 2. Formal Truth
10620
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Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17883
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Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner]
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5. Theory of Logic / L. Paradox / 3. Antinomies
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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