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All the ideas for 'Precis of 'Limits of Abstraction'', 'works' and 'Russell's Mathematical Logic'

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20 ideas

2. Reason / D. Definition / 2. Aims of Definition
10528 Definitions concern how we should speak, not how things are [Fine,K]
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 / 3. Nature of Numbers / g. Real numbers
13445 Descartes showed a one-one order-preserving match between points on a line and the real numbers [Descartes, by Hart,WD]
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 / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10529 If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
10530 Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
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 / B. Unity of Objects / 2. Substance / e. Substance critique
16774 Descartes thinks distinguishing substances from aggregates is pointless [Descartes, by Pasnau]
12. Knowledge Sources / B. Perception / 3. Representation
7400 Descartes said images can refer to objects without resembling them (as words do) [Descartes, by Tuck]
16. Persons / F. Free Will / 4. For Free Will
4310 We have inner awareness of our freedom [Descartes]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
6553 Descartes discussed the interaction problem, and compared it with gravity [Descartes, by Lycan]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
26. Natural Theory / A. Speculations on Nature / 1. Nature
19676 Nature is devoid of thought [Descartes, by Meillassoux]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / c. Matter as extension
6518 Matter can't just be Descartes's geometry, because a filler of the spaces is needed [Robinson,H on Descartes]