Combining Texts

All the ideas for 'fragments/reports', 'The Art of the Infinite' and 'The Nature of Necessity'

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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]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
18383 Plantinga says there is just this world, with possibilities expressed in propositions [Plantinga, by Armstrong]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
11891 Possibilities for an individual can only refer to that individual, in some possible world [Plantinga, by Mackie,P]
14. Science / C. Induction / 3. Limits of Induction
15713 The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
20704 A possible world contains a being of maximal greatness - which is existence in all worlds [Plantinga, by Davies,B]