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8901
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Abstraction is usually explained either by example, or conflation, or abstraction, or negatively [Lewis]
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Full Idea:
Abstraction is usually explained in one of four ways: the Way of Example (cf. donkeys and numbers), the Way of Conflation (same as sets), the Negative Way (non-spatial and non-causal) or the Way of Abstraction (incomplete descriptions).
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From:
David Lewis (On the Plurality of Worlds [1986], 1.7)
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A reaction:
[Compressed; a footnote dismisses Dummett's fifth way] Example has blurred boundaries, and explains nothing. Gerrymandered sets don't produce concepts. Negative accounts explain nothing. So it's the Way of Abstraction!
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8938
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The Way of Example compares donkeys and numbers, but what is the difference, and what are numbers? [Lewis]
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Full Idea:
The Way of Example says concrete entities are things like donkeys and puddles, but abstract entities are things like numbers. That gives us little guidance. There are no uncontroversial accounts of numbers, and donkeys and number differ in too many ways.
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From:
David Lewis (On the Plurality of Worlds [1986], 1.7)
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A reaction:
That demolishes that fairly swiftly. It may be unfair to demand an agreed account of numbers, but the respect(s) in which donkeys and numbers differ needs to be spelled out before anything useful has been said.
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8903
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Abstracta can be causal: sets can be causes or effects; there can be universal effects; events may be sets [Lewis]
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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?
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From:
David Lewis (On the Plurality of Worlds [1986], 1.7)
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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.
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8902
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If abstractions are non-spatial, then both sets and universals seem to have locations [Lewis]
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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.
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From:
David Lewis (On the Plurality of Worlds [1986], 1.7)
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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.
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8906
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If we can abstract the extrinsic relations and features of objects, abstraction isn't universals or tropes [Lewis]
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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.
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From:
David Lewis (On the Plurality of Worlds [1986], 1.7)
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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.
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