Combining Texts

All the ideas for 'Through the Looking Glass', 'Rule Utilitarianism and Euthanasia' and 'Russell's Mathematical Logic'

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14 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]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
21982 I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
20883 Modern utilitarians value knowledge, friendship, autonomy, and achievement, as well as pleasure [Hooker,B]
23. Ethics / E. Utilitarianism / 5. Rule Utilitarianism
20884 Rule-utilitarians prevent things like torture, even on rare occasions when it seems best [Hooker,B]
25. Social Practice / F. Life Issues / 2. Euthanasia
20885 Euthanasia is active or passive, and voluntary, non-voluntary or involuntary [Hooker,B]
20882 Euthanasia may not involve killing, so it is 'killing or not saving, out of concern for that person' [Hooker,B]