Combining Texts

All the ideas for 'A Puzzle about Belief', 'The Art of the Infinite' and 'Reply to Sixth Objections'

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

---

10 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]

7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience

3644	Two things being joined together doesn't prove they are the same [Descartes]

13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism

3621	Only judgement decides which of our senses are reliable [Descartes]

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

15713

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

18. Thought / B. Mechanics of Thought / 5. Mental Files

16383

Puzzled Pierre has two mental files about the same object [Recanati on Kripke]

28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality

3637	Ideas in God's mind only have value if he makes it so [Descartes]