Combining Texts

All the ideas for 'fragments/reports', 'Russell's Mathematical Logic' and 'Of the standard of taste'

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16 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction
12268 Contradiction is impossible [Antisthenes (I), by Aristotle]
2. Reason / D. Definition / 8. Impredicative Definition
10041 Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
2. Reason / D. Definition / 13. Against Definition
602 Some fools think you cannot define anything, but only say what it is like [Antisthenes (I), by Aristotle]
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 / A. Aesthetic Experience / 2. Aesthetic Attitude
18552 Forget about beauty; just concentrate on the virtues of delicacy and discernment admired in critics [Hume, by Scruton]
21. Aesthetics / A. Aesthetic Experience / 3. Taste
6608 Strong sense, delicate sentiment, practice, comparisons, and lack of prejudice, are all needed for good taste [Hume]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
1664 I would rather go mad than experience pleasure [Antisthenes (I)]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
21385 Antisthenes said virtue is teachable and permanent, is life's goal, and is like universal wealth [Antisthenes (I), by Long]
28. God / C. Attitudes to God / 2. Pantheism
2631 Antisthenes says there is only one god, which is nature [Antisthenes (I), by Cicero]