Combining Texts

All the ideas for 'Russell's Mathematical Logic', 'The Origin of Forms and Qualities' and 'Aesthetic as Science of Expression'

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20 ideas

2. Reason / D. Definition / 4. Real Definition
15957 Essential definitions show the differences that discriminate things, and make them what they are [Boyle]
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]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
15965 Boyle attacked a contemporary belief that powers were occult things [Boyle, by Alexander,P]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
16735 In the 17th century, 'disposition' usually just means the spatial arrangement of parts [Boyle, by Pasnau]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
16034 Form is not a separate substance, but just the manner, modification or 'stamp' of matter [Boyle]
15953 To cite a substantial form tells us what produced the effect, but not how it did it [Boyle]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
15962 Boyle's term 'texture' is not something you feel, but is unobservable structures of particles [Boyle, by Alexander,P]
15964 Boyle's secondary qualities are not illusory, or 'in the mind' [Boyle, by Alexander,P]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
15960 Explanation is deducing a phenomenon from some nature better known to us [Boyle]
21. Aesthetics / C. Artistic Issues / 1. Artistic Intentions
7270 Historical interpretation aims to recapture the author's view of the work [Croce]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
15952 The corpuscles just have shape, size and motion, which explains things without 'sympathies' or 'forces' [Boyle, by Alexander,P]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / b. Corpuscles
15972 The corpuscular theory allows motion, but does not include forces between the particles [Boyle, by Alexander,P]