Combining Texts

All the ideas for 'Science and Method', 'The Sublime and the Good' 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 / 2. Geometry
One geometry cannot be more true than another [Poincaré]
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]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
21. Aesthetics / B. Nature of Art / 1. Defining Art
We should first decide what are the great works of art, with aesthetic theory following from that [Murdoch]
21. Aesthetics / C. Artistic Issues / 6. Value of Art
Great art proves the absurdity of art for art's sake [Murdoch]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Art and morals are essentially the same, and are both identical with love [Murdoch]
Because art is love, it improves us morally [Murdoch]
22. Metaethics / B. Value / 2. Values / g. Love
Love is realising something other than oneself is real [Murdoch]