Combining Texts

All the ideas for 'fragments/reports', 'works' and 'Russell's Mathematical Logic'

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19 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
5988 Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
1496 The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle]
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 / 1. Nature of Existence
14874 Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / a. Preconditions for ethics
20739 Levinas took 'first philosophy' to begin with seeing the vulnerable faces of others [Levinas, by Aho]
24. Political Theory / D. Ideologies / 9. Communism
20445 Levinas says Marxism is the replacement of individualist ethics, by solidarity and sociality [Levinas, by Critchley]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
13222 The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander]
1495 Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius]
404 Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander]
405 The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander]
27. Natural Reality / E. Cosmology / 2. Eternal Universe
1746 The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius]