Combining Texts

All the ideas for 'poems', 'Summula philosophiae naturalis' 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]

7. Existence / E. Categories / 5. Category Anti-Realism

16608

Ockham was an anti-realist about the categories [William of Ockham, by Pasnau]

9. Objects / C. Structure of Objects / 4. Quantity of an Object

16599

Ockham says matter must be extended, so we don't need Quantity [William of Ockham, by Pasnau]

16681

Matter gets its quantity from condensation and rarefaction, which is just local motion [William of Ockham]

22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention

6017	Nomos is king [Pindar]