Combining Texts

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

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20 ideas

1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
16123 Whenever you perceive a community of things, you should also hunt out differences in the group [Plato]
2. Reason / D. Definition / 2. Aims of Definition
16125 To reveal a nature, divide down, and strip away what it has in common with other things [Plato]
16124 No one wants to define 'weaving' just for the sake of weaving [Plato]
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]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / b. Recollection doctrine
5961 The soul gets its goodness from god, and its evil from previous existence. [Plato]
19. Language / F. Communication / 1. Rhetoric
283 The question of whether or not to persuade comes before the science of persuasion [Plato]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
282 Non-physical beauty can only be shown clearly by speech [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
281 The arts produce good and beautiful things by preserving the mean [Plato]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
22559 Democracy is the worst of good constitutions, but the best of bad constitutions [Plato, by Aristotle]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]
28. God / A. Divine Nature / 2. Divine Nature
279 Only divine things can always stay the same, and bodies are not like that [Plato]