Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Conceptions of Consequence' and 'The Theory of Transfinite Numbers'

expand these ideas     |    start again     |     specify just one area for these texts

7 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 / F. Set Theory ST / 1. Set Theory
9616 A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
15896 Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
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]
11. Knowledge Aims / A. Knowledge / 2. Understanding
18810 Aristotle's proofs give understanding, so it can't be otherwise, so consequence is necessary [Smiley, by Rumfitt]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]