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Non-qualitative Properties

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Abstract

The distinction between qualitative properties like mass and shape and non-qualitative properties like being Napoleon and being next to Obama is important, but remains largely unexamined. After discussing its theoretical significance and cataloguing various kinds of non-qualitative properties, I survey several views about the nature of this distinction and argue that all proposed reductive analyses of this distinction are unsatisfactory. I then defend primitivism, according to which the distinction resists reductive analysis.

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Notes

  1. Objects that are indiscernible simpliciter are identical, since they are alike with respect to their non-qualitative properties as well as their qualitative ones.

  2. Our concern in what follows is the distinction between qualitative and non-qualitative properties and relations; however, ‘quality’ has been used to mark other metaphysical distinctions. See, for example, Russell (1918: 522) on the distinction between qualities and relations, understood as the distinction between monadic properties and polyadic relations. See Heil (2004) on the distinction between qualities and powers, understood as a distinction between (roughly) categorical and dispositional properties. See Eddon (2007) on the distinction between qualities and quantities, understood as the distinction between binary properties and properties that admit of degree.

  3. Hawthorne (2003: 8).

  4. For example, Divers (2002: 349) says, “I know of no detailed discussion of the qualitative/non-qualitative distinction for properties”.

  5. More carefully, while qualitative tropes like a particular instance of redness are tied to specific individuals, the property redness is standardly identified with a class of tropes. If, however, classes have their members essentially, then the existence of these classes is correspondingly tied to the existence of specific tropes and, in turn, to specific individuals. On non-transferability and other modal issues for trope theory, see Cameron (2006) and Ehring (2004). Thanks here to an anonymous referee.

  6. See Lewis (1983) on the compatibility of the sparse and abundant conceptions of properties.

  7. Since I assume neutrality about whether there is a metaphysically significant distinction between sparse and merely abundant properties, I leave open whether the sparse-abundant distinction and the qualitative distinction crosscut one another, allowing for qualitative and non-qualitative properties at both the sparse and abundant levels. As noted in Sect. 5, this is a controversial claim. For example, Lewis (1986) holds that all sparse properties are qualitative.

  8. Present interest in this question typically focuses on properties rather than predicates. For discussion, see Lange (1985). See Tooley (1977) for a defense of the possibility of de re laws, which posit nomic connections involving non-qualitative properties.

  9. Hempel and Oppeheim (1948: 155–156).

  10. Recent debates regarding determinism also invoke the qualitative distinction. In particular, the question of whether determinism precludes alternative possibilities or only alternative qualitative possibilities is of considerable importance for the Hole Argument against substantivalism. For discussion, see Brighouse (1997) and Melia (1999).

  11. See Kripke (1980) and Putnam (1975).

  12. On intrinsicality and duplication, see Lewis (1986: 61).

  13. Lewis (2001: 382) invokes the same restriction in his revised analysis of intrinsicality.

  14. I set aside the considerable complications that arise in formulating haecceitism. Perhaps most notably, those who reject possible worlds must recast haecceitism as a thesis about maximal possibilities. See Skow (2008) for discussion.

  15. On the required modifications, compare Lewis (1968) and Lewis (1986). On non-qualitative counterpart theory, see Cowling (2012).

  16. Chalmers (1996: 367) defends anti-physicalism while restricting questions of physicalism to qualitative properties. He says, “I will always be considering worlds ‘qualitatively,’ and abstracting away from question of ‘haecceity.’ That is, I will count two worlds that are qualitatively identical as identical and will not be concerned with questions about whether individuals in those worlds might have different ‘identities.’” On physicalism and haecceities, see Daly and Liggins (2010).

  17. Other versions of deflationism might argue that, while ‘qualitative’ tracks a single distinction, this distinction is, upon close scrutiny, so indeterminate as to be of no metaphysical interest.

  18. Methodological issues about the nature of philosophical analysis loom large here, but, in what follows, I assume that philosophical analysis aims at the provision of jointly necessary and sufficient conditions. For those who take our psychological representations or concepts to have an importantly different structure, this might seem methodologically objectionable. Still, opponents of this view of analysis ought to grant that attempts to provide necessary and sufficient conditions are of some epistemic value (e.g., by drawing out borderline cases) and suitable for a preliminary investigation of the present kind.

  19. Diekemper (2009: 1) endorses primitivism, claiming “[t]he distinction between a qualitative and a non-qualitative property is one that belongs to that family of philosophical distinction which, though not admitting of analysis, can be made easily enough through the use of a loose definition and some intuitive examples”.

  20. On individual essences, see Plantinga (1987: 132). I leave open whether haecceities include the unique non-qualitative properties of pluralities (e.g., being the Rolling Stones).

  21. The category of impure properties includes whatever impure relations there might be. And, while impure relational properties (e.g., being taller than Fred) and qualitative relations (e.g., is five feet from) are familiar, it controversial whether there are any impure relations. Cowling (2012) argues that, for substratum theorists, the relation shares a bare particular with is non-qualitative.

  22. On the metaphysics of negative haecceities or “anti-haecceities”, see Williamson (2013: 270).

  23. A commitment to disjunctive haecceities also suggests a commitment to conjunctive haecceities like being Saul Kripke and David Kaplan. Granted some controversial assumptions, these conjunctive haecceities might naturally be identified with the haecceities of pluralities.

  24. If PII is true, then, given some auxiliary assumptions, a haecceity like Socrateity can be identified with a massively disjunctive property that uniquely characterizes Socrates’ qualitative profile across possible worlds.

  25. On a fundamental tense property of being present, see Zimmerman (2008). On a fundamental property of being actual, see Bricker (2006).

  26. If we count being actually a donkey as a modal property, not all modal properties have a plausible claim to being non-qualitative.

  27. See Bricker (2006) for discussion of structural properties as non-qualitative properties.

  28. For most, structural properties are properties in only the abundant sense. For others, they lack even this status, since broadly logical properties and relations like identity enjoy no metaphysical status whatsoever.

  29. The status of mathematical properties is especially unclear given the diversity of views regarding mathematical entities. For example, if there are sui generis numbers, it is plausible that each has a unique non-qualitative haecceity. If, however, the subject matter of mathematics is purely structural, it is plausible that the status of mathematical properties will turn on the status of structural properties.

  30. Another line of argument for the non-qualitative status of species properties owes to the view that species are individuals and, as a consequence, the species property of tigerhood is something akin to the impure property of being an appropriately distinguished part of the tiger-individual. See Lange (1985) and Kripke (1980: 127-134) for discussion.

  31. Adams’ exact view is somewhat unclear. In addition to a linguistic “definition”, he also offers a second definition, but, since it explicitly appeals to non-qualitative “thisnesses” to define qualitative properties, such a view would constitute a form of primitivism.

  32. Adams (1979: 7).

  33. It is difficult to imagine that any given language is uniquely suited for analyzing the distinction with the potential exception of a Lagadonian language in which entities are their own names. On Lagadonian languages, see Lewis (1986: 145).

  34. Note that this version of the linguistic view entails that absolutely inexpressible properties are non-qualitative. If, however, being non-qualitative is relative to a language, the expressive limitations of different languages requires a far more complicated treatment. Sorting out the status of inexpressible properties is therefore an additional burden for any linguistic view.

  35. Hawley (2009: 102).

  36. Rosenkrantz (1979) defends a version of the modal view, according to which base impure properties are those with concrete constituents while other impure properties are defined in terms of their relations to these base properties. Along with certain of the challenges noted in this section, the appeal to concreteness in Rosenkrantz’s account seems to preclude abstract entities like nations and novels from having haecceities.

  37. This argument turns on what Kripke (1980: 3) waives as “fussy considerations deriving from the fact that x [in our present case, Saul Kripke] need not have necessary existence.” It therefore faces objections from defenders of Serious Actualism, according to which an object, x, has a property F at a world w if and only if x exists at w. Interestingly however, the instantiation of being distinct from Kripke by individuals in Kripke-less worlds is not, on its own, a violation of Serious Actualism given that these individuals do exist at the world in question. For this objection to violate Serious Actualism, it must be the case that Kripke himself instantiates the property being identical to Kripke at a Kripke-less world. To accommodate Serious Actualism, we can allow that individuals can instantiate being distinct from Kripke at a world without Kripke existing or instantiating being identical to Kripke at that world. Alternatively, we can follow Salmon (1990) in rejecting Serious Actualism, and allow that individuals have properties and relations like being thought about, being distinct from or being nonexistent at worlds in which they do not exist. Finally, one might, as I prefer, accept possibilism, which largely avoids these problems.

  38. Perhaps this problem arises even if no specific individual is a necessary existent. For example, if we assume there is a plurality of all possible individuals and that plurality exists at a world so long as some of the plurality exists. The necessary existence of this maximal plurality will also trivialize the above formulation by virtue of a being a necessary condition for the instantiation of any property.

  39. For some, grounding claims subsume supervenience claims. In this subsection, my interest is in those who would posit a sui generis grounding relation. On grounding, see Schaffer (2009) and Rosen (2010).

  40. On the proper relata of the grounding relation, see Rosen (2010).

  41. Whether the grounding relation holds of necessity is a matter of some controversy. For discussion, see Schaffer (2009) and Rosen (2010).

  42. See Lewis (1983) and (1986) for discussion and defense of the indispensability of naturalness.

  43. I ignore issues about whether we should prefer a comparative primitive of more natural than to the primitive perfect naturalness.

  44. A small range of these classes will align with sparse properties, having as members all and only individuals that share a given natural or perfectly natural property. In contrast, all other sets are merely abundant insofar as they are classes of individuals whose members share no common sparse property.

  45. Lewis (1983) considers whether we might analyze the distinction between natural and non-natural properties in terms of sharing tropes or universals. On such a view, the distinction is no longer primitive, but turns on facts about tropes and universals. Here, the definability view can be presented without assuming either of these views.

  46. Lewis (1986: 225).

  47. Lewis (1986: 63).

  48. See Lewis (1986: 220–247).

  49. On the prospects for extending a metaphysical commitment to naturalness beyond properties, see Sider (2012: 85–87).

  50. Lewis’ apparent indecision about precise nature of the qualitative distinction is notable, given his careful attention to the distinction between the natural and the non-natural. Indeed, as noted above and as argued in the next section, both of Lewis’ suggested analyses of the qualitative distinction potentially lead, when coupled with the rejection of qualitatively indiscernible worlds, to the denial that there are any non-qualitative properties. Given Lewis’ agnosticism about qualitatively indiscernible worlds, this suggests that he has comparatively little interest in preserving a metaphysically robust distinction between qualitative and non-qualitative properties. While this comports with his rejection of non-qualitative relations in the analysis of de re modality, it squares poorly with the fact that a suitable account of qualitative distinction is presupposed by his proposed analyses of intrinsicality.

  51. Lewis (2003: 26) draws a distinction between qualitative and non-qualitative propositions (understood as properties of entire worlds), where the latter are miscellaneous classes of worlds that might divide qualitatively indiscernible worlds. He then offers these remarks as a possible reply to concerns about propositions whose truth does not supervene on being. Since he also considers an alternative reply that dispenses with qualitatively indiscernible possible worlds and remains neutral between these replies, it is not clear which is Lewis’s “considered view.”

  52. Bricker (1996: 227). See also McDaniel (2007: 250).

  53. Here, I largely follow Bennett (2004) on the formulation of global supervenience theses.

  54. See Sider (1999) for discussion of these points.

  55. As Sider (1999) notes, any worlds that exhibit the relevant kind of symmetry like those including Black’s spheres suffice for this purpose.

  56. On properties and hyperintensionality, see Eddon (2011).

  57. Given that the modal view can distinguish properties only up to cointensiveness, the same concerns apply to that view as well.

  58. See Tooley (1977) for discussion of de re laws.

  59. Markosian (1998: 218).

  60. For helpful discussion and comments, thanks to Phillip Bricker, Ben Caplan, Wes Cray, Cameron Gibbs, and many helpful referees.

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    Sam Cowling

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Cowling, S. Non-qualitative Properties. Erkenn 80, 275–301 (2015). https://doi.org/10.1007/s10670-014-9626-9

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