display all the ideas for this combination of texts
3 ideas
| 9792 | Mathematicians study quantity and continuity, and remove the perceptible features of things [Aristotle] |
| Full Idea: The mathematician conducts a study into things in abstraction (after the removal of all perceptible features, such as weight and hardness, leaving only quantity and continuity). | |
| From: Aristotle (Metaphysics [c.324 BCE], 1061a26) | |
| A reaction: Frege complained that there is nothing left if you remove the perceptible features, but clearly Aristotle is not an empiricist in this passage, and it is doubtful if even Mill can be totally empirical in his account. We have relations of ideas. |
| 9077 | Mathematicians suppose inseparable aspects to be separable, and study them in isolation [Aristotle] |
| Full Idea: Study things as mathematicians do. Suppose what is not separable to be separable. A man qua man is an indivisible unity, so the arithmetician supposes a man to be an indivisible unity, and investigates the accidental features of man qua indivisible. | |
| From: Aristotle (Metaphysics [c.324 BCE], 1078a19) | |
| A reaction: This is the abstractionist view of mathematics. Qua indivisible, a man will have the same properties as a toothbrush. Aristotle clearly intends the method for scientists as well. It strikes me as common sense, but there is a lot of modern caution. |
| 9075 | If health happened to be white, the science of health would not study whiteness [Aristotle] |
| Full Idea: If we have a science of the healthy, and the healthy happens to be white, the science of the healthy does not deal with the white. | |
| From: Aristotle (Metaphysics [c.324 BCE], 1077b30) | |
| A reaction: Given this point, we certainly cannot think of Aristotle as believing in simple abstractionism. The problem of the coextension of renates and cordates looms here (Idea 7317). 'Relevant' similarities require extensive cross-referencing. |