Combining Texts

All the ideas for 'Introduction to 'Virtues of Authenticity'', 'The Art of the Infinite' and 'Phenomenal and Perceptual Concepts'

expand these ideas     |    start again     |     specify just one area for these texts

10 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]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
17945 Forms are not a theory of universals, but an attempt to explain how predication is possible [Nehamas]
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
17946 Only Tallness really is tall, and other inferior tall things merely participate in the tallness [Nehamas]
11. Knowledge Aims / A. Knowledge / 2. Understanding
17944 'Episteme' is better translated as 'understanding' than as 'knowledge' [Nehamas]
14. Science / C. Induction / 3. Limits of Induction
15713 The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
18. Thought / B. Mechanics of Thought / 5. Mental Files
16369 There is a single file per object, memorised, reactivated, consolidated and expanded [Papineau, by Recanati]