Combining Texts

All the ideas for 'Protagoras', 'Comments on a Certain Broadsheet' and 'Sets and Numbers'

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24 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 / 7. Natural Sets
17824 The master science is physical objects divided into sets [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17825 Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy]
17826 Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy]
17828 Numbers are properties of sets, just as lengths are properties of physical objects [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
17827 Sets exist where their elements are, but numbers are more like universals [Maddy]
17830 Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
17823 If mathematical objects exist, how can we know them, and which objects are they? [Maddy]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
17829 Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy]
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]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
2602 What experience could prove 'If a=c and b=c then a=b'? [Descartes]
15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
191 Everything resembles everything else up to a point [Plato]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
2600 The mind's innate ideas are part of its capacity for thought [Descartes]
2601 Qualia must be innate, because physical motions do not contain them [Descartes]
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
197 Some pleasures are not good, and some pains are not evil [Plato]
200 People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
188 Socrates did not believe that virtue could be taught [Plato]
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]