² Parfit, Derek, ‘We Are Not Human Beings’, Philosophy 87 (2012), 5–28 CrossRefGoogle Scholar. Olson, Eric, ‘Parfit on Human Beings’, in Mind, Self and Person edited by O'Hear, Anthony (Cambridge University Press, forthcoming)Google Scholar

³ Representatives of this tradition include many of the biggest names in contemporary metaphysics: Lewis, David, The Plurality of Worlds (Blackwell, 1986)Google Scholar, van Inwagen, Peter, Material Beings (Cornell University Press, 1990)Google Scholar, Fine, Kit, ‘Things and Their Parts’, Midwest Studies in Philosophy XXIII (1999)Google Scholar, Sider, Ted, Four-Dimensionalism (Oxford University Press, 2001)CrossRefGoogle Scholar, Koslicki, Kathrin, The Structure of Objects (Oxford University Press, 2008).CrossRefGoogle Scholar

⁴ The terminology ‘arranged K-wise’ is van Inwagen's (Material Beings, 109), picking out a potentially complex relational condition distinctive of the parts of Ks, a condition which may be met by pluralities of different cardinalities (as pluralities of different cardinalities may each be arranged in a circle). But it should be noted that compositionalism is not as such committed to the position that the nature of an ordinary thing is fundamentally to be explained in terms of a relation among parts. An alternative is to think of an ordinary thing as generated by a certain function or operation upon given things, in the way one could think of a set as generated by the application of the operation of ‘set-building’ to some given elements. There need be no metaphysically illuminating relation among the elements of a set so generated (see Fine, Kit, ‘Towards a Theory of Part’, Journal of Philosophy 107 (2010), 559–589 CrossRefGoogle Scholar). In what follows ‘things arranged K-wise’ will be used loosely, to cover both things being related in a certain way distinctive of the parts of Ks, and things being input to a generative operation in a way distinctive of Ks.

⁵ Sellars, Wilfrid, ‘Philosophy and the Scientific Image of Man’, in Sellars, Wilfrid, Empiricism and the Philosophy of Mind (London: Routledge & Kegan Paul Ltd, 1963), 1–40 Google Scholar

⁶ Sellars, ‘Philosophy and the Scientific Image of Man’, 20

⁷ Ibid., 6

⁸ Sellars, ‘Philosophy and the Scientific Image of Man’, 19

⁹ See Fine, ‘Things and Their Parts’, for the view that ordinary material things are ‘rigid embodiments’ or ‘variable embodiments’, composites in some respects more set-like in their character than classical mereological sums.

¹⁰ For expressions of the view that it would be arbitrary to deny that ordinary objects form a vanishingly small subset of a massively plenitudinous class, see Yablo, Stephen, ‘Identity, Essence and Indiscernibility’, Journal of Philosophy 84 (1987), 293–314 CrossRefGoogle Scholar, Fine, ‘Things and Their Parts’, Hawthorne, John, Metaphysical Essays (Oxford University Press, 2006)CrossRefGoogle Scholar

¹¹ For examples of restrictive theories of composition see Van Inwagen, Material Beings, and Hoffman, Gary and Rosenkrantz, Joshua, Substance: its Nature and Existence (Routledge, 1996)CrossRefGoogle Scholar

¹² This is an instance of the so-called Problem of the Many. See Unger, Peter ‘The Problem of the Many’, Midwest Studies in Philosophy V (1980), 411–467 CrossRefGoogle Scholar

¹³ For this eliminativist view see Dorr, Cian and Rosen, Gideon, ‘Composition as Fiction’, in The Blackwell Guide to Metaphysics edited by Gale, Richard (Blackwell, 2002)Google Scholar, and Sider, Ted ‘Against Parthood’ in Oxford Studies in Metaphysics Volume 8, edited by Bennett, Karen and Zimmerman, Dean (Oxford University Press, 2013), 237–93Google Scholar

¹⁴ Zimmerman and Unger have each in effect suggest that immaterialism is required in order to save the manifest image of the human self from the overpopulation worries that beset materialist views. See Zimmerman, Dean, ‘Material People’, in The Oxford Handbook of Metaphysics, edited by Loux, Michael and Zimmerman, Dean (Oxford University Press, 2003)Google Scholar, and Unger, Peter, ‘The Mental Problem of the Many’, in Oxford Studies in Metaphysics volume 1, edited by Zimmerman, Dean (Oxford University Press, 2004), 195–222 Google Scholar

¹⁵ Sider, ‘Against Parthood’, mounts a tenacious defence of the position that the ideological economy of eliminativism about composites defeats ordinary appearances to the contrary.

¹⁶ See Fine, Kit ‘Essence and Modality’, Philosophical Perspectives 8 (1994), 1–16 Google Scholar

¹⁷ See Bennett, Karen, ‘Spatio-Temporal Coincidence and The Grounding Problem’, Philosophical Studies 118 (2004), 339–371 CrossRefGoogle Scholar

¹⁸ On multiple realizability and the autonomy of the special sciences see Fodor, Jerry, ‘Special Sciences (Or: The Disunity of Science as a Working Hypothesis)’, Synthese 28 (1974), 97–115 CrossRefGoogle Scholar

¹⁹ I do not mean to suggest that there are no broadly compositionalist approaches to the grounding problem on the market. On the ‘four-dimensionalist’ view that ordinary objects have temporal parts as well as spatial parts, a difference in parts can be found between (temporarily) coinciding objects (See Lewis, The Plurality of Worlds, and Sider, Four-Dimensionalism). The ‘hylomorphic’ view that ordinary objects have formal parts as well as material parts also permits a difference in parts between coinciding objects (See Koslicki, The Structure of Objects, and Fine, Kit, ‘Coincidence and Form’, Proceedings of the Aristotelian Society Supplementary Volume LXXXII (2008), 101–118 CrossRefGoogle Scholar). But I believe that in the light of the availability of a non-compositionalist picture of ordinary objects, the appeal to differences in (intuitively unfamiliar) parts starts to look like a theory-driven, Procrustean attempt to force the facts into a compositionalist mould.

²⁰ Dennett, Daniel, ‘Real Patterns’, Journal of Philosophy 88 (1991), 27–51 CrossRefGoogle Scholar

²¹ See Jones, Nicholas K., ‘Multiple Constitution’, Oxford Studies in Metaphysics volume 9, edited by Bennett, Karen and Zimmerman, Dean (Oxford University Press, forthcoming)Google Scholar for a detailed presentation of an ‘Aristotelian’ solution to the Problem Of The Many in roughly this spirit. The view that ordinary objects are individuated by nomological activity along a spatio-temporal path is developed extensively in Wiggins, David, Sameness and Substance Renewed (Cambridge University Press, 2001)CrossRefGoogle Scholar

²² Fodor, Jerry, ‘Special Sciences: Still Autonomous After All These Years’, Philosophical Perspectives 11 (1997), 149–163 Google Scholar

²³ Van Inwagen, Material Beings, Snowdon, Paul, ‘Persons, Animals, and Ourselves’ in The Person and the Human Mind (Clarendon, 1990)Google Scholar, Olson, Eric, The Human Animal (Oxford University Press, 1997)Google Scholar

²⁴ For a classic statement of a neo-Lockean view, see Shoemaker, Sydney, ‘Personal Identity: A Materialist's Account’, in Shoemaker, Sydney and Swinburne, Richard, Personal Identity (Blackwell, 1984)Google Scholar

²⁵ It is an interesting question, to be left for another occasion, what the naturalist should say about a ‘fission’-type case, in which a human is not whittled down to a cerebrum but is instead divided into cerebrum and otherwise intact cerebrum-complement.