Combining Texts

All the ideas for 'Extrinsic Properties', 'Modal Logic as Metaphysics' and 'The Philosophy of Mathematics'

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11 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
9193 ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
9194 The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
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 / 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 / I. Semantics of Logic / 3. Logical Truth
9187 Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
9191 Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9192 The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
14979 Being alone doesn't guarantee intrinsic properties; 'being alone' is itself extrinsic [Lewis, by Sider]
15454 Extrinsic properties come in degrees, with 'brother' less extrinsic than 'sibling' [Lewis]
9. Objects / A. Existence of Objects / 5. Individuation / b. Individuation by properties
15455 Total intrinsic properties give us what a thing is [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
18925 If talking donkeys are possible, something exists which could be a talking donkey [Williamson, by Cameron]