Combining Texts

All the ideas for 'Identity and Spatio-Temporal Continuity', 'The Philosophy of Mathematics' and 'Philosophy and Politics'

expand these ideas     |    start again     |     specify just one area for these texts


12 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]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
Democratic institutions become impossible in a fanatical democracy [Russell]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
Liberal opinions are tentative rather than dogmatic, and are always responsive to new evidence [Russell]
Empiricism is ethically superior, because dogmatism favours persecution and hatred [Russell]
Empiricist Liberalism is the only view for someone who favours scientific evidence and happiness [Russell]