Priority monism and part/whole dependence


Priority monism is the view that the cosmos is the only independent concrete object. The paper argues that, pace its proponents, Priority monism is in conflict with the dependence of any whole on any of its parts: if the cosmos does not depend on its parts, neither does any smaller composite.

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  1. 1.

    Simons (1987, p. 268) cites the former, Künne (1998, pp. 237f.) the latter as an example of (some form of) dependence of wholes on their parts.

  2. 2.

    For the purposes of this paper, I take priority to be the converse of dependence, so that \(x\) is prior to \(y\) (and, thus, priority runs from \(x\) to \(y\)) just in case \(y\) depends on \(x\).

  3. 3.

    For heuristic reasons, I present the argument with the help of Kripkean possible worlds machinery, presupposing that one and the same individual may inhabit different worlds. As a reviewer for this journal pointed out, it is unclear whether an alternative counterpart-theoretic framework would serve the argument as well. In particular, it is unclear whether there is a suitable counterpart relation with the help of which any non-trivial but true modal dependence thesis can be formulated. To this extent it is doubtful whether there are unproblematic counterpart-theoretic variants of the assumptions I will be using (in particular of Internality, to be stated presently). However, the assumptions are already plausible in their theoretically unloaded formulations in terms of what is and what is not necessary or possible (cf. fn. 11 below). Thus, if it should turn out that counterpart theory does not yield plausible renderings of the assumptions, I take this to be a shortcoming of the former rather than the latter.

  4. 4.

    This is only a first stab at the principle required by the argument. It will be discussed and suitably restricted later in the paper.

  5. 5.

    Given the fourth assumption that dependence is necessarily a well-founded partial ordering on the concreta, the stronger result that all proper parts depend on their wholes if priority monism is true can be established. Although Schaffer himself seems to be badly placed to deny this additional assumption about dependence structure (see Schaffer (2010, p. 37) for the corresponding assertion about the actual world), the well-foundedness condition is rather controversial, and plays no role in the argument in the main text.

  6. 6.

    See, e.g., Fine (1995), Correia (2005), Schnieder (2006), Lowe (2010) on ontological dependence, and Rosen (2010), Fine (2012), Correia and Schnieder (2012) on grounding.

  7. 7.

    Schaffer (2010, p. 347) raises the possibility that Schaffer-dependence may be analysable as ontological dependence as spelled out by Fine (1995) or Lowe (2010). queryPlease check the publisher name of reference Lowe (2010). Recently, Jenkins (2013) argued that it should be explicated in terms of fact-grounding.

  8. 8.

    See, e.g., P3 in Correia (2005, p.  61) of which the Necessity of Grounding is a straightforward consequence. Cp. also Fine (2012, pp. 76f.).

  9. 9.

    In a recent paper (Schaffer 2013, p. 81), Schaffer seems to come close to denying internality:

    [Independence] seems inessential. The monist can grant that her cosmic substance may be embedded in a larger whole, and then it would no longer be [independent]. Likewise, the pluralist who treats, say, a given electron as [independent] can grant that it may be divisible into smaller constituents, and then it would no longer (by her lights) be [independent]. And all sides can agree that a given mind is a dependent entity at a physicalist world, but that it may be [independent] at a dualist world.

    Close, but not quite: the larger cosmos only exists at the non-actual world, so the actual cosmos’ independence from it is consistent with Internality; likewise, the alleged possible parts of an actual atom do not actually exist, and, thus, Internality of Dependence does not guarantee the atom’s dependence on them at the actual world. And if whatever a given mind depends on at the physicalist world, some brain say, does not exist at the dualist world, Schaffer’s third case is not a counterexample against Internality of Dependence either. The case only conflicts with Internality of Dependence, if we further assume that both one and the same mind and one and the same brain exist at physicalist and dualist worlds. But, far from being acceptable on all sides, this assumption seems highly controversial.

  10. 10.

    In any case, this is standardly assumed in discussions of supervenience in which reduplication principles of worlds like Isolation have played a prominent role. See, e.g., Paull and Sider (1992).

  11. 11.

    In the main text our assumptions are framed directly in terms of possible worlds. This could have been avoided in favour of the following replacements:

    1. A1

      If priority monism is true then it is necessary that priority monism is true;

    2. A2

      For any \(x\), \(y\), if \(x\) depends on \(y\), then necessarily, if \(x\) and \(y\) exist, \(x\) depends on \(y\).

    3. A3

      For any concrete composite \(c\) and any of its concrete parts \(p\), it is possible that (\(p\) is a part of \(c\) and the only existing concreta are \(c\) and its parts).

    The resulting argument may be shown to be valid in the weakest normal modal logic K. (To be sure, the subtraction argument for A3 relies on the transitivity of the accessibility relation.)

  12. 12.

    Thanks to an anonymous referee for pressing me on this point.

  13. 13.

    The quotation in fn. 9 above shows that Schaffer would not attempt to take this way out.

  14. 14.

    The locus classicus is Gibbard (1975).

  15. 15.

    Cp. Cameron (2008, pp. 413ff.).


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This paper has started out during a stretch of collaborative work with Robert Schwartzkopff. I’d like to thank him for discussing the material at various stages of completion. Thanks are also due to audiences at the Hamburg metaphysics research seminar, and workshops in Essen and Mainz, as well as to three anonymous referees for very helpful comments. Work on this paper was partly funded by the DFG-ANR research project Nominalizations.

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Correspondence to Alex Steinberg.

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Steinberg, A. Priority monism and part/whole dependence. Philos Stud 172, 2025–2031 (2015).

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  • Priority monism
  • Dependence
  • Parts/wholes
  • Schaffer, Jonathan