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Full Idea
If abstract entities are not located, then a set of things does seem to have a location, though perhaps a divided one; and universals, if they are wholly present in each particular, are where their instances are, so negation can't define abstraction.
Gist of Idea
If abstractions are non-spatial, then both sets and universals seem to have locations
Source
David Lewis (On the Plurality of Worlds [1986], 1.7)
Book Ref
Lewis,David: 'On the Plurality of Worlds' [Blackwell 2001], p.83
A Reaction
He admits that non-spatial accounts of sets and universals are possible, but the jury is out on both of them, and more cautious theories, even if they are realist, will give them both locations. A good argument.
| 8903 | Abstracta can be causal: sets can be causes or effects; there can be universal effects; events may be sets [Lewis] |
| 8902 | If abstractions are non-spatial, then both sets and universals seem to have locations [Lewis] |
| 8905 | If universals or tropes are parts of things, then abstraction picks out those parts [Lewis] |
| 8906 | If we can abstract the extrinsic relations and features of objects, abstraction isn't universals or tropes [Lewis] |
| 8916 | Conflating abstractions with either sets or universals is a big claim, needing a big defence [Rosen] |