Ideas from 'The Philosophy of Mathematics' by Michael Dummett [1998], by Theme Structure
[found in 'Philosophy 2: further through the subject' (ed/tr Grayling,A.C.) [OUP 1998,0198751788]].
Click on the Idea Number for the full details 
back to texts

expand these 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

9194

The main alternative to ZF is one which includes looser classes as well as sets

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

5. Theory of Logic / G. Quantification / 5. SecondOrder Quantification
9186

Firstorder logic concerns objects; secondorder adds properties, kinds, relations and functions

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9187

Logical truths and inference are characterized either syntactically or semantically

6. Mathematics / A. Nature of Mathematics / 3. Numbers / c. Priority of numbers
9191

Ordinals seem more basic than cardinals, since we count objects in sequence

6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / e. Structuralism critique
9192

The number 4 has different positions in the naturals and the wholes, with the same structure
