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18. Thought / E. Abstraction / 6. Abstracta by Conflation

[treating abstractions as actually sets or universals]

5 ideas

8903	Abstracta can be causal: sets can be causes or effects; there can be universal effects; events may be sets [Lewis]
	Full Idea: Is it true that sets or universals cannot enter into causal interaction? Why can't we say that a set of things causes something, or something causes a set of effects? Or positive charge has characteristic effects? Or an event is a sort of set?
	From: David Lewis (On the Plurality of Worlds [1986], 1.7)
	A reaction: This idea, and 8902, form a devastating critique of attempts to define abstraction in a purely negative way, as non-spatial and non-causal. Only a drastic revision of widely held views about sets, universals and events could save that account.

8902	If abstractions are non-spatial, then both sets and universals seem to have locations [Lewis]
	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.
	From: David Lewis (On the Plurality of Worlds [1986], 1.7)
	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.

8906	If we can abstract the extrinsic relations and features of objects, abstraction isn't universals or tropes [Lewis]
	Full Idea: Why can't we abstract a highly extrinsic aspect of something, say its surname, or its spatiotemporal location, or its role in a causal network, or its role in some body of theory? But these are unsuitable candidates for being genuine universals or tropes.
	From: David Lewis (On the Plurality of Worlds [1986], 1.7)
	A reaction: (This is a criticism of the proposal in Idea 8905) Obviously we can abstract such things. In particular the role in a causal network is a function, which is a central example of an abstract idea. Russell keeps reminding us that relations are universals.

8905	If universals or tropes are parts of things, then abstraction picks out those parts [Lewis]
	Full Idea: A theory of non-spatiotemporal parts of things, whether recurring universals or non-recurring tropes, makes good sense of some abstractions. Unit negative charge is a universal common to particles, and an abstraction by being part of them.
	From: David Lewis (On the Plurality of Worlds [1986], 1.7)
	A reaction: He cautiously refers to 'some' abstractions. It is one of Donald Williams's proud boasts concerning his trope theory that it will handle this problem well. I'm not sure that we should be saying that abstractions are actually concrete bits of things.

8916	Conflating abstractions with either sets or universals is a big claim, needing a big defence [Rosen]
	Full Idea: The Way of Conflation account of abstractions (identifying them sets or with universals) is now relatively rare. The claim sets or universals are the only abstract objects would amount to a substantive metaphysical thesis, in need of defence.
	From: Gideon Rosen (Abstract Objects [2001], 'Way of Con')
	A reaction: If you produce a concept like 'mammal' by psychological abstraction, you do seem to end up with a set of things with shared properties, so this approach is not silly. I can't think of any examples of abstractions which are not sets or universals.