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All the ideas for 'Precis of 'Limits of Abstraction'', 'works' and 'The Problem of Empty Names'

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8 ideas

2. Reason / D. Definition / 2. Aims of Definition
10528 Definitions concern how we should speak, not how things are [Fine,K]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
3340 Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
3355 Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
18946 Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
22716 Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
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]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]