Combining Texts

All the ideas for 'fragments/reports', 'Events as property exemplifications' and 'The Philosophy of Mathematics'

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14 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]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
How fine-grained Kim's events are depends on how finely properties are individuated [Kim, by Schaffer,J]
Events are composed of an object with an attribute at a time [Kim, by Simons]
Events cannot be merely ordered triples, but must specify the link between the elements [Kim, by Simons]
If events are ordered triples of items, such things seem to be sets, and hence abstract [Simons on Kim]
Since properties like self-identity and being 2+2=4 are timeless, Kim must restrict his properties [Simons on Kim]
Kim's theory results in too many events [Simons on Kim]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA]