7 ideas
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong. | |
| From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1 |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory. | |
| From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2 | |
| A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 23395 | Mohists desire wealth, population and social order as the best consequences [Mozi, by Norden] |
| Full Idea: The consequentialist Mohists give a fairly objective characterisation of benefits as wealth, populousness, and social order, and harm as poverty, depopulation, and social chaos. | |
| From: report of Mozi (The Mozi [c.440 BCE]) by Bryan van Norden - Intro to Classical Chinese Philosophy 4.I | |
| A reaction: That is a formula favoured by many authoritarian leaders in modern times. |
| 23394 | If people regarded other states as they did their own, they would never attack them [Mozi] |
| Full Idea: If people regarded other people's states in the same way that they regard their own, who then would incite their own state to attack that of another? | |
| From: Mozi (The Mozi [c.440 BCE], 16), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 4.I | |
| A reaction: A nice case of the application of golden rule thinking to states, instead of to individuals. I can't see Putin (in 2022) being impressed by 'how would you like it if another country invaded Russia?'. The Golden Rule is an analogy argument. |
| 23396 | Mozi condemns partiality, which is the cause of all the great harms in the world [Mozi] |
| Full Idea: It is those who are partial in their dealings with others who are the real cause of all the great harms in the world. That is why our teacher Mozi says 'I condemn partiality'. | |
| From: Mozi (The Mozi [c.440 BCE], 16), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 4.II | |
| A reaction: This is morality as the rule of law, rather than as the result of human affections. He is on the same wavelength as Kant. Mozi was criticising Confucius, who favoured family over strangers. |
| 23397 | Those who are against impartiality still prefer impartial protectors [Mozi] |
| Full Idea: Even though one may not advocate impartiality, one would certainly want to entrust one's family to the person who is impartial. | |
| From: Mozi (The Mozi [c.440 BCE], 16), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 4.II | |
| A reaction: In the modern world his example would be the police, so he effectively he wants the impartiality of the law. But who wants legal impartiality within the affairs of a family? |