Against Parthood∗ - Ted Sider

collections of objects compose a further object. 20 And the familiar paradoxes
of coinciding objects, which are so nicely resolved by a temporal parts metaphysics
combined with composite objects, are resolved just as well by a nihilist
metaphysics. 21 Still, some arguments are genuinely directed against nihilism,
including: 22
1. nihilism goes against common sense
2. knowledge of composites is given in perception
3. the existence of composites is part of our evidence, given Timothy
Williamson’s conception of evidence
4. we are entitled for Cartesian reasons to believe in our own existence
5. the denial of composite objects is conceptually incoherent
6. nihilism is incompatible with “atomless gunk”
7. parts and composite objects are required by spacetime physics
In what follows I will rebut these arguments. The final argument is the most
powerful one, and my response will be tentative. In fact, my response will be to
soften the nihilist position a bit: although there do not exist composites in the
mereological sense—i.e., objects with proper parts—there do exist “composites”
in the set-theoretic sense—i.e., objects with members; i.e., sets. (Also, my
20 Lewis (1986a, 212–13). See also Sider (2001, chapter 4, section 9).
21 Merricks (2001, pp. 38–47). See Sider (2001, chapter 5) for a survey of the issues. McGrath
(2005) argues that since nihilists regard claims about composites as at least being correct in the
sense of section 3 (his word is ‘factual’), they still face the paradoxes at the level of correctness.
But the shift to correctness (or to nonfundamental languages—again, see section 3) dissolves
the paradoxes if some of the claims generating the paradoxes have force only when read as
claims about fundamental truth. Consider, for example, those paradoxes that appeal to the
principle that composition is unique—that no collection of objects composes more than one
thing. The appeal of this principle is “theoretical”: it is based on a putative insight into the
fundamental nature of the part-whole relation. The principle loses its appeal if it is taken as
being merely correct (or as being in a nonfundamental language). For correctness (or truth in
nonfundamental languages) is more closely tied to ordinary speech, and ordinary speech is fine
with there being particles that, say, compose both a statue and a distinct lump of clay.
22 There is also the argument that composites are required to support emergent properties.
The argument would need to assume that “emergent properties” are perfectly fundamental
(otherwise claims about those properties could be “correct” in the sense of section 3 or true
in a nonfundamental language) and incapable of being reconstrued as relations over simples
(perhaps because the putative relations would have no fixed -adicy). I doubt such properties
exist; but if they do, they present a challenge like that discussed in section 11.
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