display all the ideas for this combination of philosophers
6 ideas
| 9789 | You can't abstract natural properties to make Forms - objects and attributes are defined together [Aristotle] |
| Full Idea: Those who say there are Forms abstract natural properties, even though they are less separable than mathematical properties. This is clear if you try to define both the objects themselves and their attributes. | |
| From: Aristotle (Physics [c.337 BCE], 193b36) | |
| A reaction: (Compare Idea 9788) This is Frege's black and white cats, where you cannot abstract the black without thinking of the cat, but Aristotle thinks mathematical abstraction is more feasible. |
| 9070 | We learn primitives and universals by induction from perceptions [Aristotle] |
| Full Idea: We must get to know the primitives by induction; for this is the way in which perception instils universals. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 100b04) | |
| A reaction: This statement is so strongly empirical it could have come from John Stuart Mill. The modern post-Fregean view of universals is essentially platonist - that they have a life and logic of their own, and their method of acquisition is irrelevant. |
| 9788 | Mathematicians study what is conceptually separable, and doesn't lead to error [Aristotle] |
| Full Idea: Mathematicians abstract properties which are conceptually separable from the world of change. It makes no difference if you treat them as separate, in the sense that it does not result in error. | |
| From: Aristotle (Physics [c.337 BCE], 193b33) | |
| A reaction: This strikes me as a crucial point to make against Frege (if Aristotle is right). Frege hates abstractionism precisely because it is psychological, and hence admits subjective error, instead of objective truth. Does 'pure' abstraction avoid error? |
| 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. |