Combining Texts

All the ideas for 'fragments/reports', 'The Raft and the Pyramid' and 'The Philosophy of Mathematics'

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14 ideas

2. Reason / A. Nature of Reason / 6. Coherence
8797 The negation of all my beliefs about my current headache would be fully coherent [Sosa]
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]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
8794 There are very few really obvious truths, and not much can be proved from them [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / e. Pro-foundations
8796 A single belief can trail two regresses, one terminating and one not [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
8799 If mental states are not propositional, they are logically dumb, and cannot be foundations [Sosa]
8795 Mental states cannot be foundational if they are not immune to error [Sosa]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
8798 Vision causes and justifies beliefs; but to some extent the cause is the justification [Sosa]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
1556 By nature people are close to one another, but culture drives them apart [Hippias]