Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'On Platonism in Mathematics' and 'Reductive Theories of Modality'

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8 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined

9218	Maybe what distinguishes philosophy from science is its pursuit of necessary truths [Sider]

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 / 8. Critique of Set Theory

10304

Very few things in set theory remain valid in intuitionist mathematics [Bernays]

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

10303

Restricted Platonism is just an ideal projection of a domain of thought [Bernays]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

10306

Mathematical abstraction just goes in a different direction from logic [Bernays]

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

10527

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