Combining Texts

All the ideas for 'fragments/reports', 'Three-Dimensionalism v Four-Dimensionalism' and 'The Art of the Infinite'

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12 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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
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
The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
9. Objects / B. Unity of Objects / 3. Unity Problems / a. Scattered objects
If we accept scattered objects such as archipelagos, why not think of cars that way? [Hawthorne]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
Four-dimensionalists say instantaneous objects are more fundamental than long-lived ones [Hawthorne]
10. Modality / A. Necessity / 11. Denial of Necessity
A modal can reverse meaning if the context is seen differently, so maybe context is all? [Hawthorne]
14. Science / C. Induction / 3. Limits of Induction
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
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / C. Space / 6. Space-Time
Modern metaphysicians tend to think space-time points are more fundamental than space-time regions [Hawthorne]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]