Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Model Theory for Modal Logic I' and 'Letter to Shumacher'

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6 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 / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
9560 S5 provides the correct logic for necessity in the broadly logical sense [Fine,K]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
10855 Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss]
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]