Combining Texts

All the ideas for 'The Epistemology of Modality', 'Letters to Thomasius' and 'The Art of the Infinite'

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

---

9 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

15717

Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

15712

1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

15711

The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic

15714

'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]

15715

'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]

9. Objects / D. Essence of Objects / 1. Essences of Objects

13432

The essence of a circle is the equality of its radii [Leibniz]

10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible

19440

How do you know you have conceived a thing deeply enough to assess its possibility? [Vaidya]

14. Science / C. Induction / 3. Limits of Induction

15713

The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]

27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement

12696

Bodies are recreated in motion, and don't exist in intervening instants [Leibniz]