4 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. |
| 16210 | Humean supervenience says the world is just a vast mosaic of qualities in space-time [Lewis] |
| Full Idea: Humean supervenience says the world is a vast mosaic of local matters of particular fact. We have a geometry of external relations of spatio-temporal distance between points, and local qualities at points. …In short: we have an arrangement of qualities. | |
| From: David Lewis (Introduction to Philosophical Papers II [1986], p.ix-x) | |
| A reaction: [compressed] This is the key fundamental tenet of David Lewis's philosophy. He names it after Hume because it contains no necessary connections. It is 'supervenient' because all worldly truths reduce to and depend on the mosaic. His thesis is contingent. |
| 7628 | Broad rejects the inferential component of the representative theory [Broad, by Maund] |
| Full Idea: Broad, one of the most important modern defenders of the representative theory of perception, explicitly rejects the inferential component of the theory. | |
| From: report of C.D. Broad (Mind and Its Place in Nature [1925]) by Barry Maund - Perception Ch.1 | |
| A reaction: Since the supposed inferences happen much too quickly to be conscious, it is hard to see how we could distinguish an inference from an interpretation mechanism. Personally I interpret things long before the question of truth arises. |
| 9426 | The world is just a vast mosaic of little matters of local particular fact [Lewis] |
| Full Idea: The world is a vast mosaic of local matters of particular fact, just one little thing and then another. | |
| From: David Lewis (Introduction to Philosophical Papers II [1986]) | |
| A reaction: Basing laws on this picture is what Lewis calls 'Humean Supervenience'. |