Combining Texts

All the ideas for 'On Motion', 'Letters to Queen Charlotte' and 'The Theory of Transfinite Numbers'

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8 ideas

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 / 4. Axioms for Number / a. Axioms for numbers

23026

We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz]

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

13189

A necessary feature (such as air for humans) is not therefore part of the essence [Leibniz]

10. Modality / D. Knowledge of Modality / 1. A Priori Necessary

19432

Intelligible truth is independent of any external things or experiences [Leibniz]

12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities

19430

We know objects by perceptions, but their qualities don't reveal what it is we are perceiving [Leibniz]

12. Knowledge Sources / D. Empiricism / 1. Empiricism

19431

There is nothing in the understanding but experiences, plus the understanding itself, and the understander [Leibniz]

27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity

12709

Motion is not absolute, but consists in relation [Leibniz]