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Ideas for 'works', 'The Philosophy of Mathematics' and 'Necessary Beings'

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7 ideas

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

19296

If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale]

5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention

19289

Maybe conventionalism applies to meaning, but not to the truth of propositions expressed [Hale]

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

9195	Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]

5. Theory of Logic / E. Structures of Logic / 1. Logical Form

4730	For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]

5. Theory of Logic / G. Quantification / 5. Second-Order Quantification

9186	First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]

5. Theory of Logic / H. Proof Systems / 4. Natural Deduction

19298

Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems [Hale]

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth

9187	Logical truths and inference are characterized either syntactically or semantically [Dummett]