Combining Texts

All the ideas for 'The Philosophy of Mathematics', 'Repetition' and 'An Argument for the Identity Theory'

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11 ideas

3. Truth / A. Truth Problems / 8. Subjective Truth
Subjective truth can only be sustained by repetition [Kierkegaard, by Carlisle]
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]
17. Mind and Body / C. Functionalism / 4. Causal Functionalism
Experiences are defined by their causal role, and causal roles belong to physical states [Lewis]
'Pain' contingently names the state that occupies the causal role of pain [Lewis]
23. Ethics / F. Existentialism / 8. Eternal Recurrence
Life is a repetition when what has been now becomes [Kierkegaard]