Combining Texts

All the ideas for 'The Middle Works (15 vols, ed Boydston)', 'On Metaphysics (frags)' and 'Russell's Mathematical Logic'

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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 / 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]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
22868 The value and truth of knowledge are measured by success in activity [Dewey]
16. Persons / B. Nature of the Self / 1. Self and Consciousness
22865 Habits constitute the self [Dewey]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
22871 The good people are those who improve; the bad are those who deteriorate [Dewey]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
22876 Democracy is the development of human nature when it shares in the running of communal activities [Dewey]
22875 Democracy is not just a form of government; it is a mode of shared living [Dewey]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
22874 Individuality is only developed within groups [Dewey]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
5990 Theophrastus doubted whether nature could be explained teleologically [Theophrastus, by Gottschalk]