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. |
| 7667 | There are two sides to men - the pleasantly social, and the violent and creative [Diderot, by Berlin] |
| Full Idea: Diderot is among the first to preach that there are two men: the artificial man, who belongs in society and seeks to please, and the violent, bold, criminal instinct of a man who wishes to break out (and, if controlled, is responsible for works of genius. | |
| From: report of Denis Diderot (works [1769], Ch.3) by Isaiah Berlin - The Roots of Romanticism | |
| A reaction: This has an obvious ancestor in Plato's picture (esp. in 'Phaedrus') of the two conflicting sides to the psuché, which seem to be reason and emotion. In Diderot, though, the suppressed man has virtues, which Plato would deny. |
| 20558 | Your representative owes you his judgement, and betrays you if he gives your opinion instead [Burke] |
| Full Idea: Your representative owes you, not his industry only, but his judgement; and he betrays instead of serving you if he sacrifices it to your opinion | |
| From: Edmund Burke (Address to the Voters of Bristol [1774]), quoted by Adam Swift - Political Philosophy (3rd ed) | |
| A reaction: Nice rhetoric, but I'm not sure about the logic of it. Do I betray you if I give my stupid judgement rather than your wise one? Am I so arrogant as to think my judgement is always preferable? His audience was entirely of property owners. |