Combining Texts

All the ideas for 'Of Human Freedom', 'Liberal Individualism and Liberal Neutrality' and 'The Philosophy of Mathematics'

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11 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 / A. Nature of Existence / 3. Being / c. Becoming
Being is only perceptible to itself as becoming [Schelling]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
We must show that the whole of nature, because it is effective, is grounded in freedom [Schelling]
16. Persons / F. Free Will / 2. Sources of Free Will
Only idealism has given us the genuine concept of freedom [Schelling]
24. Political Theory / D. Ideologies / 6. Liberalism / e. Liberal community
Liberals are not too individualistic, because people recognise and value social relations [Kymlicka]