Combining Texts

All the ideas for 'Reflections on my Critics', 'Russell's Mathematical Logic' and 'De Natura Corporis'

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13 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10041 Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
12129 'Truth' may only apply within a theory [Kuhn]
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]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
12710 As well as extension, bodies contain powers [Leibniz]
14. Science / B. Scientific Theories / 1. Scientific Theory
6809 Kuhn came to accept that all scientists agree on a particular set of values [Kuhn, by Bird]
14. Science / B. Scientific Theories / 5. Commensurability
12128 In theory change, words shift their natural reference, so the theories are incommensurable [Kuhn]