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All the ideas for 'Precis of 'Limits of Abstraction'', 'The Architecture of Mathematics' and 'Counting and the Natural Numbers'

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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]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
17423 The essence of natural numbers must reflect all the functions they perform [Sicha]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17425 To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha]
17424 Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha]
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 / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10190 From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]