Combining Philosophers

All the ideas for Peter B. Lewis, R Kaplan / E Kaplan and Crawford L. Elder

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13 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]
8. Modes of Existence / B. Properties / 1. Nature of Properties
13795 Properties only have identity in the context of their contraries [Elder]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
13798 Maybe we should give up the statue [Elder]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
13797 The loss of an essential property means the end of an existence [Elder]
9. Objects / D. Essence of Objects / 9. Essence and Properties
13794 Essential properties by nature occur in clusters or packages [Elder]
13796 Essential properties are bound together, and would be lost together [Elder]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
21912 Fichte, Schelling and Hegel rejected transcendental idealism [Lewis,PB]
21911 Fichte, Hegel and Schelling developed versions of Absolute Idealism [Lewis,PB]
14. Science / C. Induction / 3. Limits of Induction
15713 The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]