Combining Philosophers

All the ideas for Hecato, R Kaplan / E Kaplan and Albert of Saxony

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11 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 / 2. Types of Existence
16664 Everything that exists is either a substance or an accident [Albert of Saxony]
9. Objects / E. Objects over Time / 6. Successive Things
16703 God could make a successive thing so that previous parts cease to exist [Albert of Saxony]
16699 Successive entities just need parts to succeed one another, without their existence [Albert of Saxony]
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 / C. Virtue Theory / 3. Virtues / a. Virtues
6004 The cardinal virtues are theoretical (based on knowledge), and others are 'non-theoretical' [Hecato, by Dorandi]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
16570 Elements are found last in dismantling bodies, and first in generating them [Albert of Saxony]