Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Philosophical Fragments' and 'Explanation in Mathematics'

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7 ideas

2. Reason / D. Definition / 2. Aims of Definition

10528

Definitions concern how we should speak, not how things are [Fine,K]

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]

7. Existence / A. Nature of Existence / 5. Reason for Existence

16007

I assume existence, rather than reasoning towards it [Kierkegaard]

9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities

13166

Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu]

10. Modality / A. Necessity / 2. Nature of Necessity

16013

Nothing necessary can come into existence, since it already 'is' [Kierkegaard]

18. Thought / E. Abstraction / 7. Abstracta by Equivalence

10527

An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]