Combining Texts

All the ideas for 'poems', 'Possible Worlds and Necessary A Posteriori' and 'The Philosophy of Mathematics'

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12 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
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
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
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
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
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
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
9. Objects / D. Essence of Objects / 9. Essence and Properties
How do we tell a table's being contingently plastic from its being essentially plastic? [Jackson]
An x is essentially F if it is F in every possible world in which it appears [Jackson]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Quine may have conflated de re and de dicto essentialism, but there is a real epistemological problem [Jackson]
10. Modality / D. Knowledge of Modality / 3. A Posteriori Necessary
How can you show the necessity of an a posteriori necessity, if it might turn out to be false? [Jackson]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Nomos is king [Pindar]