Ideas from 'Precis of 'Limits of Abstraction'' by Kit Fine [2005], by Theme Structure

[found in 'Philosophical Studies' (ed/tr -) [- ,]].

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2. Reason / D. Definition / 2. Aims of Definition
Definitions concern how we should speak, not how things are
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / d. Hume's Principle
If Hume's Principle can define numbers, we needn't worry about its truth
Hume's Principle is either adequate for number but fails to define properly, or vice versa
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
An abstraction principle should not 'inflate', producing more abstractions than objects