Combining Texts

All the ideas for 'The Problem of Empty Names', 'The Virtues and Human Nature' 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 / F. Referring in Logic / 1. Naming / e. Empty names
Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer]
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]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
Motives produce intentions, which lead to actions [Driver]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
Virtue should be defined by consequences, not by states of mind [Driver]
Virtues are character traits or dispositions which produce good consequences for others [Driver]
Control of pregnancy and knowledge of paternity have downgraded chastity [Driver]
Good intentions are not necessary for virtue [Driver]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
If generosity systematically turned recipients into parasites, it wouldn't be a virtue [Driver]