Combining Texts

All the ideas for 'Reportatio', 'The Philosophy of Mathematics' and 'Three-Dimensionalism v Four-Dimensionalism'

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13 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 / B. Unity of Objects / 3. Unity Problems / a. Scattered objects
If we accept scattered objects such as archipelagos, why not think of cars that way? [Hawthorne]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
Four-dimensionalists say instantaneous objects are more fundamental than long-lived ones [Hawthorne]
10. Modality / A. Necessity / 11. Denial of Necessity
A modal can reverse meaning if the context is seen differently, so maybe context is all? [Hawthorne]
27. Natural Reality / C. Space / 6. Space-Time
Modern metaphysicians tend to think space-time points are more fundamental than space-time regions [Hawthorne]
28. God / A. Divine Nature / 3. Divine Perfections
God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham]
28. God / C. Attitudes to God / 4. God Reflects Humanity
We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham]