Combining Philosophers

All the ideas for Anaxarchus, Eduard Hanslick and R Kaplan / E Kaplan

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8 ideas

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

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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

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

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

13. Knowledge Criteria / D. Scepticism / 1. Scepticism

3061	Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]

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

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

21. Aesthetics / C. Artistic Issues / 4. Emotion in Art

20344

Music is not an expressive art, because it expresses no familiar emotions [Hanslick, by Wollheim]