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Inverse functionalism and the individuation of powers

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Abstract

In the pure powers ontology (PPO), basic physical properties have wholly dispositional essences. PPO has clear advantages over categoricalist ontologies, which suffer from familiar epistemological and metaphysical problems. However, opponents argue that because it contains no qualitative properties, PPO lacks the resources to individuate powers, and generates a regress. The challenge for those who take such arguments seriously is to introduce qualitative properties without reintroducing the problems that PPO was meant to solve. In this paper, I distinguish the core claim of PPO: (i) basic physical properties have dispositional essences, from a hitherto unnoticed assumption: (ii) the dispositional essences of basic physical properties exclusively involve type-causal relations to other basic physical properties. I reject (ii), making room for structuralist ontology in which all basic physical properties are pure powers, individuated by their places in a causal structure that includes not only other powers, but also physically realized qualitative properties such as shapes, patterns and structures. Such qualities individuate pure powers in the way that non-mental input and output properties individuate realized mental properties in functionalist theories of mind, except that here it is the basic physical powers that are individuated by relations to realized non-powers. I distinguish one Platonic and two Aristotelian version of this theory, and argue that the Aristotelian versions require that grounding is not always a relative fundamentality relation, because the powers ground the qualities that individuate them. I argue that symmetric grounding is the best way to make sense of the relational individuation common to all structuralist ontologies, and is therefore no additional commitment of the one proposed here.

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Notes

  1. The reason I use ‘basic’ rather than ‘fundamental’ will become clear in Sect. 3. I also use ‘basic’ to describe (putatively) non-composite physical particulars such as electrons and quarks. I likewise apply ‘complex’ to both properties and particulars.

  2. Shoemaker (1980), Ellis (2002), Heil (2003), Molnar (2003), Mumford (2004), Bird (2007a), and Martin (2007).

  3. For a canonical statement and defence of MRL, see Lewis (1994); for DTA see Armstrong (1983).

  4. Lewis (1994), pp. 478–9.

  5. For both these objections, see Armstrong’s (1983) critique of the regularity theory.

  6. Bird (2005a, 2007a, ch. 4).

  7. Lewis (2009).

  8. Shoemaker (1980).

  9. I assume for simplicity that both the stimulus and manifestation types of a power are individuative.

  10. See Bird (2007b) for a particularly clear treatment along these lines.

  11. Molnar (2003) and Bird (2016).

  12. For more on the distinction between powers and dispositions, see Yates (2013).

  13. As in, for example, Mumford and Anjum (2011).

  14. This is also true on the reciprocal partner powers model defended in Martin (1997) and Heil (2012), but I don’t endorse the view that only powers can stimulate powers.

  15. See Bird (2007b) for full discussion.

  16. Armstrong (1997), p. 80.

  17. See Jacobs (2011) and Smith (2016) for more on the thin conception of categorical properties. I return to this issue later in this section.

  18. Here is Black on Humean fundamental properties: “Just about all there is to a Humean fundamental quality is its identity with itself and its distinctness from other qualities. A Humean fundamental quality is intrinsically inert and self-contained”, (2000), p. 91.

  19. Bird (2007b), pp. 521–2.

  20. Mumford and Anjum (2011), pp. 5–7; note that they endorse a ‘passing powers around’ conception of qualitative change, and deny Armstrong’s intuition that this amounts to no change at all.

  21. It’s also not obvious that powers are intrinsic; see Tugby (2013) and Yates (2016a).

  22. Lowe (2006), p. 138. Similar concerns are raised by Howard Robinson; see his (1982), pp. 114–5.

  23. Bird (2007b).

  24. As Bird notes, positing a single symmetric manifestation relation entails that the number of powers is either one, or at least five, which is odd to say the least. Positing an asymmetric manifestation relation can iron out this particular wrinkle, but there are bound to remain purely mathematical constraints on the structures that could serve to determinately identify their nodes. See Bird (2007b), pp. 528–33 for full discussion.

  25. Lowe (2010, 2012). The material presented here occurs in a similar form in both papers.

  26. Lowe (2012), p. 214. I return to the notion of identity-dependence in Sects. 2 and 3, where the distinction between this and weaker forms of ontological dependence will be crucial to the theory I develop.

  27. For the arguments that follow, see Lowe (2012), pp. 228–31.

  28. Numbers with no predecessors trivially have the same predecessor, and sets with no members trivially have the same members, so the proposed individuating principles guarantee the uniqueness of 0 and the empty set.

  29. Lowe (2012), p. 229.

  30. Bird (2007b), p. 526.

  31. Heil (2003) and Martin (2007).

  32. Jacobs (2011).

  33. Smith (2016).

  34. Op. Cit., p. 252; it isn’t clear that Smith would deny the identity claim as Jacobs understands it.

  35. In my (2013) account of dispositional essentialism, according to which a property has a (perhaps partially) causal essence iff some causal law is true in virtue of the nature the property, powerful qualities as conceived by Jacobs and Smith do have (at least partially) causal essences. Whether this is the right thing to say—and relatedly, whether my account has the resources to distinguish non-recombinatorial quidditism from standard powers ontologies—is another matter. If causal laws can be true in virtue of the natures of properties that don’t have causal essences, then note too that this also causes problems for the Finean theory of essence upon which I depend.

  36. Molnar is clear that his ontology doesn’t suffer from regress problems, due to the addition of basic categorical properties, although he also doubts that these problems are serious for PPO. See Molnar (2003), pp. 173–81.

  37. Op. Cit. (2003), pp. 164–6.

  38. See Smith (2016), pp. 249–56 for full discussion.

  39. Lowe (2010), pp. 18–21.

  40. I use ‘causally self-contained’ as a term for properties that have their causal roles in virtue of being the properties they are, like the thick quiddities of the powerful qualities ontology.

  41. The ‘not vice-versa’ clause secures the asymmetry of realization.

  42. Gillett (2003), Melnyk (2003). Gillett’s account allows that the realized and realizer property are instantiated by distinct individuals; Melnyk’s account allows for non-causal \({\upphi }\).

  43. I treat sphericality as mathematically defined, but this is not to say that sphericality is an abstract or mathematical property. I prefer to think of it as a broadly physical property with a mathematically specifiable essence.

  44. Similar points are made in Lowe (2010).

  45. Bird (2016), pp. 354–7; Bird offers several other examples, all of broadly structural or geometric properties that cannot plausibly be construed as causally individuated—nor, it follows right away, as functionally realized.

  46. Yates (2016b).

  47. See Wilson (2015) for a detailed defence of causal conceptions of various forms of emergence.

  48. I omit the mathematics for brevity, but an explanation can be given, in terms of sphericality alone, of why spheres are capable of moving with constant and non-zero linear and angular velocity, while in constant contact with surface, without sliding. The mechanics of rolling of course involves rigid body physics as well, but the possibility of such motion can be explained in purely geometric terms.

  49. Bird (2016), pp. 358–60.

  50. The details needn’t concern us here; see Bird (2005b, 2009) for defence, and Livanios (2008) for opposition.

  51. See Tugby (2013) for a defence of Platonism about powers in standard powers ontologies. Tugby’s central argument is that only on Platonic powers ontologies are powers intrinsic to their bearers, and it depends on the fact that Aristotelian powers must satisfy an instantiation condition, so that any given power instance presupposes other concrete particulars as bearers of the powers upon which it is identity-dependent. For further discussion of the intrinsicality of powers in Aristotelian ontologies, see Yates (2016a).

  52. I thank an anonymous referee for drawing my attention both to this problem, and to the one that follows it.

  53. I’ll refer to this as construction to distinguish it from token realization, but the reader shouldn’t lose sight of the fact that the crucial explanatory relation is qualitative realization, albeit within the scope of a possibility operator.

  54. Fine (2012), Sect. 1. Here ‘in virtue of’ is a sui generis relation appropriate to claims of metaphysical explanation. The relation is hyperintensional: Socrates grounds {Socrates}, but not vice versa, despite the fact that necessarily, Socrates exists iff {Socrates} exists. Grounding is therefore not amenable to reductive modal analysis. Grounding is also sometimes treated as holding between facts, but the nature of the relata need not concern us here.

  55. Thompson (2016). Those who endorse symmetric grounding must also, obviously, reject transitivity or irreflexivity or both. I prefer to reject transitivity, but to argue for that here would take us too far afield.

  56. Gonzalo Rodriguez-Pereyra offers a similar example, but suggests instead that the fact that \(p_{1}\) is true is grounded in the fact that \(p_{2}\) is true, and vice-versa. See Rodriguez-Pereyra (2015).

  57. This is arguably the position endorsed in French and Ladyman (2003); many of the claims made in Ladyman and Ross (2007) also suggest an eliminativist approach, but see below.

  58. Ladyman and Ross (2007), pp. 134–7.

  59. Op. cit. p. 154.

  60. See Briceño and Mumford (2016) for a critique of OSR based on the intuitive priority of relata.

  61. Pooley (2006), p. 93; Ainsworth (2010), pp. 51–2; Ainsworth (2011), pp. 77–8.

  62. Esfeld and Lam (2008), p. 33; (2011) pp. 148–9.

  63. See for instance Ladyman and Bigaj (2009) and Ainsworth (2011).

  64. Esfeld and Lam (2011), p. 146; see also Esfeld and Lam (2008), pp. 31–4.

  65. Esfeld and Lam (2008), p. 34.

  66. Interestingly, in their (2011), Esfeld and Lam claim that weak discernibility is sufficient to ground the numerical distinctness of the primitive objects, meaning they no longer need primitive individuation, but claim in addition that this “does nothing to show how objects could be derived from relations”, (p. 149).

  67. These remarks also apply to orthodox functionalism, mutatis mutandis—we can’t assign priority to mental properties over the psychological causal structure, because they are individuated by their places in it; and we can’t assign priority to the structure over the properties, because it’s partially composed of them.

  68. See Huggett and Wüthrich (2013) for discussion of various results, from several independent quantum gravity research programmes, which have been taken by some to suggest that spacetime is not basic physical.

  69. Lam and Esfeld (2013) argue that spacetime must be basic physical in quantum gravity given that entanglement is a defining feature of quantum mechanics, and entanglement is typically defined in terms of spatially separated systems whose dynamics can’t be independently specified. On my proposal, a property needn’t be basic physical to play a defining or individuative role that suffices for its fundamentality.

  70. Earlier versions of this paper were presented at the SBFA IV Conference 2016 in Campinas, Brazil; and at a seminar at the University of Lisbon. Many thanks to all who commented. I am particularly grateful to two anonymous referees for Synthese, for many insightful and constructive criticisms. Based on research funded by an FCT Investigator grant from the Fundação para a Ciência e a Tecnologia (IF/01736/2014).

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    David Yates

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Yates, D. Inverse functionalism and the individuation of powers. Synthese 195, 4525–4550 (2018). https://doi.org/10.1007/s11229-017-1417-9

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