Combining Texts

All the ideas for 'Protagoras', 'Introductions to 'Aesthetics and the Phil of Art'' and 'The Art of the Infinite'

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22 ideas

2. Reason / B. Laws of Thought / 4. Contraries
192 Only one thing can be contrary to something [Plato]
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 / c. Self-predication
190 If asked whether justice itself is just or unjust, you would have to say that it is just [Plato]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
20184 The only real evil is loss of knowledge [Plato]
20185 The most important things in life are wisdom and knowledge [Plato]
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 / 7. Seeing Resemblance
191 Everything resembles everything else up to a point [Plato]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
203 Courage is knowing what should or shouldn't be feared [Plato]
21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics
20327 Modern attention has moved from the intrinsic properties of art to its relational properties [Lamarque/Olson]
21. Aesthetics / B. Nature of Art / 1. Defining Art
20326 Early 20th cent attempts at defining art focused on significant form, intuition, expression, unity [Lamarque/Olson]
21. Aesthetics / B. Nature of Art / 7. Ontology of Art
20330 The dualistic view says works of art are either abstract objects (types), or physical objects [Lamarque/Olson]
22. Metaethics / B. Value / 2. Values / j. Evil
202 No one willingly and knowingly embraces evil [Plato]
22. Metaethics / C. The Good / 1. Goodness / h. Good as benefit
193 Some things are good even though they are not beneficial to men [Plato]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
200 People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato]
197 Some pleasures are not good, and some pains are not evil [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
204 Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato]
189 If we punish wrong-doers, it shows that we believe virtue can be taught [Plato]
188 Socrates did not believe that virtue could be taught [Plato]