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All the ideas for 'Russell's Mathematical Logic', 'Explanation in Mathematics' and 'The Elements of Law'

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19 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
7396 Hobbes created English-language philosophy [Hobbes, by Tuck]
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]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
13166 Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
16638 The qualities of the world are mere appearances; reality is the motions which cause them [Hobbes]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
16688 Evidence is conception, which is imagination, which proceeds from the senses [Hobbes]
7405 Experience can't prove universal truths [Hobbes]
20. Action / C. Motives for Action / 1. Acting on Desires
7408 It is an error that reason should control the passions, which give right guidance on their own [Hobbes, by Tuck]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
7407 Good and evil are what please us; goodness and badness the powers causing them [Hobbes]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
7410 Self-preservation is basic, and people judge differently about that, implying ethical relativism [Hobbes, by Tuck]
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
7409 Hobbes shifted from talk of 'the good' to talk of 'rights' [Hobbes, by Tuck]
28. God / C. Attitudes to God / 4. God Reflects Humanity
7411 The attributes of God just show our inability to conceive his nature [Hobbes]