6 ideas
| 10196 | The Axiom of Choice needs a criterion of choice [Black] |
| Full Idea: Some mathematicians seem to think that talk of an Axiom of Choice allows them to choose a single member of a collection when there is no criterion of choice. | |
| From: Max Black (The Identity of Indiscernibles [1952], p.68) |
| 10194 | Two things can only be distinguished by a distinct property or a distinct relation [Black] |
| Full Idea: The only way we can discover that two things exist is by finding out that one has a quality not possessed by the other, or else that one has a relational characteristic that the other hasn't. | |
| From: Max Black (The Identity of Indiscernibles [1952], p.67) | |
| A reaction: At least this doesn't conflate relations with properties. Note that this idea is clearly epistemological, and in no way rules out the separateness of two objects which none of us can ever discern. Maybe the Earth has two Suns, which imperceptibly swap. |
| 16629 | By comparing qualities and features, reason can gradually infer the nature of substance [Grosseteste] |
| Full Idea: Awakened reason distinguishes color from size and shape from body and then shape and size from the substance of body, and so by drawing distinctions and abstracting, it arrives at a grasp of the substance of body, which supports size, shape and color. | |
| From: Robert Grosseteste (Commentary on 'Posterior Analytics' [1226], I.14), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 07.4 | |
| A reaction: This optimistic view influenced Aquinas, and is called 'incrementalism' by Pasnau. It is the spirit of scientific essentialism, and a nice instance of inference to the best explanation (though 'substance' in itself explains virtually nothing). |
| 10193 | The 'property' of self-identity is uselessly tautological [Black] |
| Full Idea: Saying that 'a has the property of being identical with a' is a roundabout way of saying nothing - a useless tautology - and means not more than 'a is a' | |
| From: Max Black (The Identity of Indiscernibles [1952], p.66) | |
| A reaction: This matter resembles the problem of the number zero, and the empty set, which seem to be crucial entities for logicians, but of no interest to a common sense view of the world. So much the worse for logic, I am inclined to say. |
| 10195 | If the universe just held two indiscernibles spheres, that refutes the Identity of Indiscernibles [Black] |
| Full Idea: Isn't it logically possible that the universe should have contained nothing but two exactly similar spheres? ...So two things would have all their properties in common, and this would refute the Principle of the Identity of Indiscernibles. | |
| From: Max Black (The Identity of Indiscernibles [1952], p.67) | |
| A reaction: [Black is the originator of this famous example] It also appears to be naturally possible. An observer at an instant of viewing will discern a relational difference relative to themselves. Most people take Black's objection to be decisive. |
| 3029 | Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius] |
| Full Idea: Stilpo asked a man whether Athena is the daughter of Zeus, and when he said yes, said,"But this statue of Athena by Phidias is the child of Phidias, so it is not a god." | |
| From: report of Stilpo (fragments/reports [c.330 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.10.5 |