3 ideas
| 10632 | The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright] |
| Full Idea: The real numbers may be introduced by abstraction as ratios of quantities. ..They are not defined by Dedekind cuts; rather, the cuts constitute a domain with the properties that are a necessary precondition. | |
| From: report of Bob Hale (Reals by Abstraction [1998]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' 3.3 | |
| A reaction: This is Hale's neo-logicist attempt to derive the real numbers from Hume's Principle. |
| 19398 | Minds are best explained by their ends, and bodies by efficient causes [Leibniz] |
| Full Idea: Whatever concerns reasonable substances (the minds of men) is more naturally explained by the consideration of ends, whereas other substances (bodies) are better explained by efficient causes. | |
| From: Gottfried Leibniz (Geometrical Method and Metaphysics [1712], p.89) | |
| A reaction: That is, I take it, that the type of causal explanation considered most appropriate is the one that leads to the greatest understanding. So there is no absolute or correct answer as to which type of causation is the more important. |
| 7294 | No crime and no punishment without a law [Roman law] |
| Full Idea: An ancient principle of Roman law states, nullum crimen et nulla poene sine lege, - there is no crime and no punishment without a law. | |
| From: [Roman law] (Roman Law [c.100]), quoted by A.C. Grayling - Among the Dead Cities Ch.6 | |
| A reaction: That there is no 'punishment' without law seems the basis of civilization. Suppose a strong person imposed firm punishment in order to forestall more brutal revenge by others? What motivates the creation of criminal laws? |