Combining Texts

All the ideas for 'Philosophical Fragments', 'Emile: treatise on education' and 'The Art of the Infinite'

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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 / A. Nature of Existence / 5. Reason for Existence

16007

I assume existence, rather than reasoning towards it [Kierkegaard]

10. Modality / A. Necessity / 2. Nature of Necessity

16013

Nothing necessary can come into existence, since it already 'is' [Kierkegaard]

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

15713

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

23. Ethics / F. Existentialism / 6. Authentic Self

20759

Feelings are prior to intelligence; we should be content to live with our simplest feelings [Rousseau]

24. Political Theory / B. Nature of a State / 4. Citizenship

19854

We all owe labour in return for our keep, and every idle citizen is a thief [Rousseau]