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All the ideas for 'Philosophical Insignificance of A Priori Knowledge', 'Russell's Mathematical Logic' and 'fragments/reports'

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15 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
13407 All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau]
2. Reason / D. Definition / 8. Impredicative Definition
10041 Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21716 In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10035 Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10042 Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10038 A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10046 The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10039 Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10043 Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
10045 Impredicative definitions are admitted into ordinary mathematics [Gödel]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
13409 Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
13406 A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
13408 Intuition and thought-experiments embody substantial information about the world [Papineau]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
13410 Verificationism about concepts means you can't deny a theory, because you can't have the concept [Papineau]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
467 A virtue is a combination of intelligence, strength and luck [Ion]