3 ideas
| 10180 | Mathematicians do not study objects, but relations between objects [Poincaré] |
| Full Idea: Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter. | |
| From: Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6 | |
| A reaction: This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 17009 | I won't object if someone shows that gravity consistently arises from the action of matter [Newton] |
| Full Idea: If someone explains gravity along with all its laws by the action of some subtle matter, and shows that the motion of the planets and comets will not be disturbed by this matter, I shall be far from objecting. | |
| From: Isaac Newton (Letters to Leibniz 1 [1693], 1693.10.16) | |
| A reaction: Important if you think that Newton is the hero of the descriptive regularity theory of laws. Newton probably thought laws came from God, but he wouldn't object to Leibniz's view, that God planted the laws within the matter. |