Combining Texts

All the ideas for 'Phenomenal and Perceptual Concepts', 'The Philosophy of Mathematics' and 'On Hippocrates and Plato'

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10 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]
15. Nature of Minds / A. Nature of Mind / 1. Mind / d. Location of mind
Galen showed by experiment that the brain controls the body [Galen, by Hankinson]
18. Thought / B. Mechanics of Thought / 5. Mental Files
There is a single file per object, memorised, reactivated, consolidated and expanded [Papineau, by Recanati]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Each part of the soul has its virtue - pleasure for appetite, success for competition, and rectitude for reason [Galen]