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All the ideas for 'Philosophical Fragments', 'Russell's Mathematical Logic' and 'Putnam's Paradox'

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16 ideas

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 / J. Model Theory in Logic / 2. Isomorphisms
14212 A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those [Lewis]
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 / A. Nature of Existence / 5. Reason for Existence
16007 I assume existence, rather than reasoning towards it [Kierkegaard]
7. Existence / D. Theories of Reality / 4. Anti-realism
14213 Anti-realists see the world as imaginary, or lacking joints, or beyond reference, or beyond truth [Lewis]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
14210 A gerrymandered mereological sum can be a mess, but still have natural joints [Lewis]
10. Modality / A. Necessity / 2. Nature of Necessity
16013 Nothing necessary can come into existence, since it already 'is' [Kierkegaard]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
14215 Causal theories of reference make errors in reference easy [Lewis]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
14209 Descriptive theories remain part of the theory of reference (with seven mild modifications) [Lewis]