5 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. |
| 335 | Do the gods also hold different opinions about what is right and honourable? [Plato] |
| Full Idea: Do the gods too hold different opinions about what is right, and similarly about what is honourable and dishonourable, good and bad? | |
| From: Plato (Euthyphro [c.398 BCE], 07e) |
| 336 | Is what is pious loved by the gods because it is pious, or is it pious because they love it? (the 'Euthyphro Question') [Plato] |
| Full Idea: Is what is pious loved by the gods because it is pious, or is it pious because they love it? | |
| From: Plato (Euthyphro [c.398 BCE], 10a) | |
| A reaction: The famous Euthyphro Question, the key question about the supposed religious basis of morality. The answer of Socrates is Idea 337. |
| 337 | It seems that the gods love things because they are pious, rather than making them pious by loving them [Plato] |
| Full Idea: So things are loved by the gods because they are pious, and not pious because they are loved? It seems so. | |
| From: Plato (Euthyphro [c.398 BCE], 10e) | |
| A reaction: Socrates' answer to the Euthyphro Question (see Idea 336). The form of piety precedes the gods. |