Combining Texts

All the ideas for 'Protagoras', 'Contextualism Contested (and reply)' and 'Must We Believe in Set Theory?'

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

26 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 / 1. Set Theory
10482 The logic of ZF is classical first-order predicate logic with identity [Boolos]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10492 A few axioms of set theory 'force themselves on us', but most of them don't [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
10485 Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10484 The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10491 Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
10483 Mathematics and science do not require very high orders of infinity [Boolos]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10490 Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
8. Modes of Existence / D. Universals / 1. Universals
10488 It is lunacy to think we only see ink-marks, and not word-types [Boolos]
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]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10487 I am a fan of abstract objects, and confident of their existence [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10489 We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
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]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
19555 People begin to doubt whether they 'know' when the answer becomes more significant [Conee]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
19557 Maybe low knowledge standards are loose talk; people will deny that it is 'really and truly' knowledge [Conee]
19556 Maybe knowledge has fixed standards (high, but attainable), although people apply contextual standards [Conee]
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]
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]