Combining Texts

All the ideas for 'Warrant and Proper Function', 'The Philosophy of Mathematics' and 'Goodness and Choice'

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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]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
6356 Maybe a reliable justification must come from a process working with its 'proper function' [Plantinga, by Pollock/Cruz]
22. Metaethics / B. Value / 2. Values / b. Successful function
22381 Being a good father seems to depend on intentions, rather than actual abilities [Foot]
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
22380 Some words, such as 'knife', have a meaning which involves its function [Foot]