Combining Texts

All the ideas for 'fragments/reports', 'Aristotle on Essence and Explanation' and 'Russell's Mathematical Logic'

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16 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]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
11993 Jones may cease to exist without some simple property, but that doesn't make it essential [Kung]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
11997 A property may belong essentially to one thing and contingently to another [Kung]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
11992 Aristotelian essences underlie a thing's existence, explain it, and must belong to it [Kung]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
11995 Some peripheral properties are explained by essential ones, but don't themselves explain properties [Kung]
11996 Some non-essential properties may explain more than essential-but-peripheral ones do [Kung]
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]