Combining Texts

All the ideas for 'The Logic of Boundaryless Concepts', 'Properties and Predicates' and 'The Philosophy of Mathematics'

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

14 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 [Dummett]
9194 The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
9390 Logic guides thinking, but it isn't a substitute for it [Rumfitt]
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 [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
9186 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
9187 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
9191 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
9192 The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
8. Modes of Existence / B. Properties / 2. Need for Properties
8568 A property is merely a constituent of laws of nature; temperature is just part of thermodynamics [Mellor]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
8564 There is obviously a possible predicate for every property [Mellor]
8. Modes of Existence / D. Universals / 2. Need for Universals
8566 We need universals for causation and laws of nature; the latter give them their identity [Mellor]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
8565 If properties were just the meanings of predicates, they couldn't give predicates their meaning [Mellor]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9389 Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt]
26. Natural Theory / C. Causation / 8. Particular Causation / e. Probabilistic causation
8567 Singular causation requires causes to raise the physical probability of their effects [Mellor]