Combining Texts

All the ideas for 'The Philosophy of Mathematics', 'On a supposed right to lie' and 'The Structure of Science'

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10 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 / C. Structure of Existence / 2. Reduction
3425 Reduction has been defined as deriving one theory from another by logic and maths [Nagel,E, by Kim]
23. Ethics / B. Contract Ethics / 3. Promise Keeping
22442 If lies were ever acceptable, with would undermine all duties based on contract [Kant]
23. Ethics / D. Deontological Ethics / 2. Duty
22441 The law will protect you if you tell a truth which results in murder [Kant]