3 ideas
| 17783 | A number is not a multitude, but a unified ratio between quantities [Newton] |
| Full Idea: By a Number we understand not so much a Multitude of Unities, as the abstracted Ratio of any Quantity to another Quantity of the same Kind, which we take for unity. | |
| From: Isaac Newton (Universal Arithmetick [1669]), quoted by John Mayberry - What Required for Foundation for Maths? p.407-2 | |
| A reaction: This needs a metaphysics of 'kinds' (since lines can't have ratios with solids). Presumably Newton wants the real numbers to be more basic than the natural numbers. This is the transition from Greek to modern. |
| 23218 | The brain has no responsibility for sensations, which occur in the heart [Aristotle] |
| Full Idea: And of course, the brain is not responsible for any of the sensations at all. The correct view is that the seat and source of sensation is the region of the heart. | |
| From: Aristotle (The Parts of Animals [c.345 BCE]), quoted by Matthew Cobb - The Idea of the Brain 1 | |
| A reaction: [Need a reference] Hippocrates's assertion a century earlier made no impression on the great man. I wish he had been a little more circumspect with his own view. |
| 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? |