Combining Texts

All the ideas for 'fragments/reports', 'Enquiry concerning Principles of Morals' and 'Russell's Mathematical Logic'

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23 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]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
22. Metaethics / B. Value / 2. Values / f. Altruism
3926 The human heart has a natural concern for public good [Hume]
23. Ethics / A. Egoism / 1. Ethical Egoism
3929 No moral theory is of any use if it doesn't serve the interests of the individual concerned [Hume]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
3925 Personal Merit is the possession of useful or agreeable mental qualities [Hume]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
3922 Justice only exists to support society [Hume]
23560 If we all naturally had everything we could ever desire, the virtue of justice would be irrelevant [Hume]
23. Ethics / D. Deontological Ethics / 2. Duty
3918 Moral philosophy aims to show us our duty [Hume]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
3919 Conclusions of reason do not affect our emotions or decisions to act [Hume]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
3928 Virtue just requires careful calculation and a preference for the greater happiness [Hume]
23. Ethics / E. Utilitarianism / 3. Motivation for Altruism
3923 No one would cause pain to a complete stranger who happened to be passing [Hume]
3924 Nature makes private affections come first, because public concerns are spread too thinly [Hume]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
3921 The safety of the people is the supreme law [Hume]
24. Political Theory / C. Ruling a State / 3. Government / a. Government
3927 Society prefers helpful lies to harmful truth [Hume]
25. Social Practice / B. Equalities / 4. Economic equality
3920 If you equalise possessions, people's talents will make them unequal again [Hume]