Combining Texts

All the ideas for 'Protagoras', 'fragments/reports' and 'Remarks on axiomatised set theory'

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18 ideas

2. Reason / B. Laws of Thought / 4. Contraries
Only one thing can be contrary to something [Plato]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Axiomatising set theory makes it all relative [Skolem]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Mathematician want performable operations, not propositions about objects [Skolem]
8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication
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
The only real evil is loss of knowledge [Plato]
The most important things in life are wisdom and knowledge [Plato]
15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
Everything resembles everything else up to a point [Plato]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
Courage is knowing what should or shouldn't be feared [Plato]
22. Metaethics / B. Value / 2. Values / j. Evil
No one willingly and knowingly embraces evil [Plato]
22. Metaethics / C. The Good / 1. Goodness / h. Good as benefit
Some things are good even though they are not beneficial to men [Plato]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
Some pleasures are not good, and some pains are not evil [Plato]
People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato]
23. Ethics / A. Egoism / 1. Ethical Egoism
The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Socrates did not believe that virtue could be taught [Plato]
Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato]
If we punish wrong-doers, it shows that we believe virtue can be taught [Plato]