7 ideas
| 8921 | Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman] |
| Full Idea: With developments in modern mathematics, structuralist ideas have become commonplace. We study 'abstract structures', having relations without regard to the objects. As Hilbert famously said, items of furniture would do. | |
| From: Geoffrey Hellman (Structuralism [2007], §1) | |
| A reaction: Hilbert is known as a Formalist, which suggests that modern Structuralism is a refined and more naturalist version of the rather austere formalist view. Presumably the sofa can't stand for six, so a structural definition of numbers is needed. |
| 8922 | Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman] |
| Full Idea: There is the tantalizing possibility that perhaps mathematical objects 'have no nature' at all, beyond their 'structural role'. | |
| From: Geoffrey Hellman (Structuralism [2007], §1) | |
| A reaction: This would fit with a number being a function rather than an object. We are interested in what cars do, not the bolts that hold them together? But the ontology of mathematics is quite separate from how you do mathematics. |
| 18439 | Because things can share attributes, we cannot individuate attributes clearly [Quine] |
| Full Idea: No two classes have exactly the same members, but two different attributes may be attributes of exactly the same things. Classes are identical when their members are identical. ...On the other hand, attributes have no clear principle of individuation. | |
| From: Willard Quine (On the Individuation of Attributes [1975], p.100) |
| 18442 | You only know an attribute if you know what things have it [Quine] |
| Full Idea: May we not say that you know an attribute only insofar as you know what things have it? | |
| From: Willard Quine (On the Individuation of Attributes [1975], p.106) | |
| A reaction: Simple, and the best defence of class nominalism (a very implausible theory) which I have encountered. Do I have to know all the things? Do I not know 'red' if I don't know tomatoes have it? |
| 18441 | No entity without identity (which requires a principle of individuation) [Quine] |
| Full Idea: We have an acceptable notion of class, or physical object, or attribute, or any other sort of object, only insofar as we have an acceptable principle of individuation for that sort of object. There is no entity without identity. | |
| From: Willard Quine (On the Individuation of Attributes [1975], p.102) | |
| A reaction: Note that this is his criterion for an 'acceptable' notion. Presumably that is for science. It permits less acceptable notions which don't come up to the standard. And presumably true things can be said about the less acceptable entities. |
| 18440 | Identity of physical objects is just being coextensive [Quine] |
| Full Idea: Physical objects are identical if and only if coextensive. | |
| From: Willard Quine (On the Individuation of Attributes [1975], p.101) | |
| A reaction: The supposed counterexample to this is the statue and the clay it is made of, which are said to have different modal properties (destroying the statue doesn't destroy the clay). |
| 21097 | Modern monarchies are (like republics) rule by law, rather than by men [Hume] |
| Full Idea: In modern times monarchical government seems to have made the greatest advances towards perfection. It may now be affirmed of civilized monarchies, what was formerly said in praise of republics alone, that they are a government of laws, not of men. | |
| From: David Hume (Of Civil Liberty [1750], p.54) | |
| A reaction: Dreams of simple 'government by law' disappeared with the rise of modern media, which can be controlled by wealth. |