(A new paradigm for) the problem of the many


This paper offers an original solution to the problem of the many, built on a foundation of powers-based causation. At its most basic, the solution should be understood as a type of maximality response, and on those grounds its originality might be questioned. However, it is argued that novelty of the solution owes as much to the meta-metaphysical context (the paradigm) in which the solution is framed as it does the model of causal powers. A discussion of paradigms in metaphysics is included.

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  1. 1.

    Kuhn (1962).

  2. 2.

    Kuhn (1962); Bird (2000).

  3. 3.

    My point isn’t to claim that the study of metaphysics perfectly mirrors that of science, just that some of what is understood by the term ‘paradigm’ in science applies to metaphysics. However, I am not here suggesting (as Kuhn did of scientific paradigms) that terms can’t be translated across metaphysical paradigms, nor that the processes by why one metaphysical paradigm replaces another involves a revolution (though I remain open to the possibility of each).

  4. 4.

    Those so inclined could ignore my talk of paradigms and treat my solution as a fleshed-out form of maximality. But you’d be missing out on some interesting meta-metaphysics.

  5. 5.

    Paradigms only seem to have well-defined boundaries when viewed through historical lenses.

  6. 6.

    Lewis (2008), Langton (1998) and Hildebrand (2016).

  7. 7.

    Jessica Wilson (2010, 2015).

  8. 8.

    Armstrong (1989).

  9. 9.

    Lewis (1986).

  10. 10.

    Lewis (1973) and Collins et al. (2004).

  11. 11.

    Ellis (2001), Bird (2007), Molnar (2003) and Williams (2019).

  12. 12.

    Mumford (2004), Bird (2007) and Williams (2010).

  13. 13.

    Borghini and Williams (2008) and Vetter (2015).

  14. 14.

    Martin (2008) and Williams (2019).

  15. 15.

    This is the version considered in Lewis (1999).

  16. 16.

    Unger’s original (1980) presentation of the problem arguably includes both versions; at the very least, his talk of outer water molecules of clouds sounds like the vagueness version. He later (2006: p. 397) makes crystal clear that what he thinks matters most is the overlapping aggregates version of the problem. I channel him in the passage that follows.

  17. 17.

    This presentation of the argument owes a lot to Woods (2019).

  18. 18.

    See van Inwagen (1990).

  19. 19.

    Woods (2019: p. 3).

  20. 20.

    Geach (1980: p. 215); bracketed phrase inserted by me. As we’ll see in the sequel, I believe that this claim is particularly susceptible to interpretation relative to the paradigm in which it’s considered.

  21. 21.

    Woods (2019: p. 3).

  22. 22.

    Sider (2001).

  23. 23.

    Or perhaps they all can, but they are rarely alone. It won’t matter for what I argue.

  24. 24.

    Actually, this is over-simplified. More correctly, you cannot ensure a type-identical manifestation from two instances of different constellation types, but nothing prevents their manifestations from being the same. For simplicity I’ll just speak as if instances of different constellation-types always produce instances of different manifestation types. I offer a detailed account in Williams (2019).

  25. 25.

    At least as far as the naked eye is concerned. Telescopes might help us locate duller stars within the gaps. As the point is meant to be illustrative, we can just stick to the main/brightest stars.

  26. 26.

    We can thus ignore Unger’s (2006) claim that these powers can be excluded because they are redundant. According to the current model, redundancy is an epistemic notion, tied to explanatory significance, and not a metaphysical one.

  27. 27.

    Or at least temporarily identical with Felix. I don’t mean to suggest that Felix is incapable of losing or gaining parts, but we are talking about right now.

  28. 28.

    I offer what I take to be a necessary condition, but I don’t claim that it’s also sufficient. My aim isn’t, when all is said and done, to spell out “what it takes” to be a cat. That perhaps involves historical properties that I’ve not here discussed. My concern is with the problem of the many, and thus I’m focusing on the thought that being a cat is going to require (at least) the capacity for some cat-like behaviours, which lesser CCs won’t be capable of performing.

  29. 29.

    The internet informs me that in the 1800s cat burning was a ‘thing’ in France, and considered entertainment. The justification came from the belief that cats were associated with witchcraft or the Devil. Nevertheless, yikes.

  30. 30.

    For those already formulating objections, no, there’s no such things as a gappy-cats, and even if there were, they would be a distinct kind regardless (as I explain at the end of this section). If it helps, we could speak of the region occupied by the heart as picking out a ‘quasi-constellation’: a smaller (but still internally maximal) constellation that “operates” in virtue of being part of the larger constellation.

  31. 31.

    Were I to hazard an answer, it would start with our tracking chemical and biological processes—of similarity and change—in a given region. Constellations (of any size) will determine the future state(s) of the region, and we can track these diachronic similarities and changes in all or part of the region. We then annex certain processes to given types of objects. I suspect these will result in objects with mostly fuzzy boundaries (which I take to be a good thing).

  32. 32.

    Sutton (2014).

  33. 33.

    As something of an art-imitating-philosophy case, in 2007, Menolo Valdés presented a giant sculpture composed of 22,000 replica sculptures. See Varzi (2014).

  34. 34.

    Sutton (2014) discusses a case of a mosaic tile with a very large tile at its centre.

  35. 35.

    Thanks to Francesco Franda for noting that the larger sculpture already answers to a distinct kind term.

  36. 36.

    Lewis (2009) and Langton (1998).

  37. 37.

    Van Inwagen (1990).

  38. 38.

    I suspect they are also involved in shaping the space of reasonable responses. After all, they will demand of any reasonable response that it show how differences in the inert subvenient base could be large enough as to result in supervenient capacities and behaviours we would no longer count as cattish. These changes would surely have to be more significant than those we imagine when considering the CCs.

  39. 39.

    A point discussed at length in Williams (2019).


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I’d like to thank Francesco Franda, Elisa Paganini, the audience at the New Foundations of Dispositionalism Conference, and two anonymous referees, for their helpful comments on earlier drafts.

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Correspondence to Neil E. Williams.

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Williams, N.E. (A new paradigm for) the problem of the many. Synthese (2021). https://doi.org/10.1007/s11229-021-03034-6

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  • Paradigms
  • Meta-metaphysics
  • Problem of the many
  • Powers
  • Humeanism
  • Composition