Combining Texts

All the ideas for 'Introduction to 'Virtues of Authenticity'', 'The Art of the Infinite' and 'Thinking and Experience'

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

19 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 / C. Powers and Dispositions / 2. Powers as Basic
14329 Some dispositional properties (such as mental ones) may have no categorical base [Price,HH]
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]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
9032 Before we can abstract from an instance of violet, we must first recognise it [Price,HH]
9035 If judgement of a characteristic is possible, that part of abstraction must be complete [Price,HH]
9034 There may be degrees of abstraction which allow recognition by signs, without full concepts [Price,HH]
9036 There is pre-verbal sign-based abstraction, as when ice actually looks cold [Price,HH]
9037 Intelligent behaviour, even in animals, has something abstract about it [Price,HH]
18. Thought / A. Modes of Thought / 1. Thought
9033 Recognition must precede the acquisition of basic concepts, so it is the fundamental intellectual process [Price,HH]
18. Thought / E. Abstraction / 1. Abstract Thought
9030 Abstractions can be interpreted dispositionally, as the ability to recognise or imagine an item [Price,HH]
9029 If ideas have to be images, then abstract ideas become a paradoxical problem [Price,HH]
18. Thought / E. Abstraction / 2. Abstracta by Selection
9031 The basic concepts of conceptual cognition are acquired by direct abstraction from instances [Price,HH]