Combining Texts

All the ideas for 'Introduction to 'Properties'', 'Content Preservation' and 'The Philosophy of Mathematics'

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12 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
4037 Ockham's Razor is the principle that we need reasons to believe in entities [Mellor/Oliver]
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 / 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 / 6. Categorical Properties
4027 Properties are respects in which particular objects may be alike or differ [Mellor/Oliver]
8. Modes of Existence / B. Properties / 12. Denial of Properties
4029 Nominalists ask why we should postulate properties at all [Mellor/Oliver]
13. Knowledge Criteria / C. External Justification / 1. External Justification
9382 Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge]
18. Thought / E. Abstraction / 5. Abstracta by Negation
4039 Abstractions lack causes, effects and spatio-temporal locations [Mellor/Oliver]