Combining Texts

All the ideas for 'Morals and Modals', 'works' and 'The Art of the Infinite'

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9 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]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
14629 If we are told the source of necessity, this seems to be a regress if the source is not already necessary [Blackburn]
14529 If something underlies a necessity, is that underlying thing necessary or contingent? [Blackburn, by Hale/Hoffmann,A]
14. Science / C. Induction / 3. Limits of Induction
15713 The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16714 The state should kill blasphemous heretics [Erasmus]