Combining Philosophers

All the ideas for Gorgias, Rescher,N/Oppenheim,P and R Kaplan / E Kaplan

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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 / 3. Being / d. Non-being

18933

Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius]

9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts

12887

A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim]

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

15713

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

19. Language / F. Communication / 1. Rhetoric

9866	Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato]

5864	Destroy seriousness with laughter, and laughter with seriousness [Gorgias]