display all the ideas for this combination of texts
3 ideas
| 16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
| Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
| From: Plato (Parmenides [c.364 BCE], 144a) | |
| A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |
| 21559 | We need rules for deciding which norms are predicative (unless none of them are) [Russell] |
| Full Idea: We need rules for deciding what norms are predicative and what are not, unless we adopt the view (which has much to recommend it) that no norms are predicative. ...[146] A predative propositional function is one which determines a class. | |
| From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141) | |
| A reaction: He is referring to his 'no class' theory, which he favoured at that time. |
| 21558 | 'Predicative' norms are those which define a class [Russell] |
| Full Idea: Norms (containing one variable) which do not define classes I propose to call 'non-predicative'; those which do define classes I shall call 'predicative'. | |
| From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141) |