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Fundamental non-qualitative properties

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The distinction between qualitative and non-qualitative properties should be familiar from discussions of the principle of the identity of indiscernibles: two otherwise exactly similar individuals, Castor and Pollux, might share all their qualitative properties yet differ with respect to their non-qualitative properties—for while Castor has the property being identical to Castor, Pollux does not. But while this distinction is familiar, there has not been much critical attention devoted to spelling out its precise nature. I argue that the class of non-qualitative properties is broader than it is often taken to be. When properly construed, it will not only include properties such as being identical to Castor, which somehow make reference to particular individuals, it will also include more general properties such as identity, composition, set membership, as well as various peculiarly ontological properties. Given that some of these more general properties help to explain objective similarity, we have reason to believe that there are fundamental non-qualitative properties.

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  1. A haecceitistic property is a property—like being identical to Plato or being a student of Socrates, and unlike having a beard or being a philosopher—which in some rough, intuitive sense involves or makes essential reference to a particular individual.

  2. The property of presentness, at least given something like the moving spotlight theory of time described in Broad (1923, p. 59, 1938, p. 277), is another potential example of a non-qualitative property.

  3. A categorial property is ‘a property something has by virtue of being or having an item from one of the categories’ (Wedin 2000, p. 194).

  4. The nature of this involvement is often understood in non-linguistic terms. Fine (1977, p. 137) takes it to be a kind of dependence: a property is non-qualitative when its identity depends upon the identity of a particular individual; Rosenkrantz (1979, p. 517) takes it to be a kind of constitution: a property is non-qualitative when it has an individual as a constituent; and Cowling (2015, pp. 289–91) considers an account that takes it to be a kind of grounding: a property is non-qualitative when it is grounded in a particular individual.

  5. I will generally take talk of ‘properties’ to cover both properties and relations.

  6. I have taken this ontology wholesale from Bricker (2001, 2006, 2008, forthcoming).

  7. The parenthetical clause is included in order to accommodate the possibility of island universes. See Bricker (2001).

  8. Let’s say following Bricker (forthcoming) that a collection of entities matches a structure if it instantiates that structure and no more inclusive structure; and that a structure isolates a collection that instantiates it if the structural relations never hold between entities inside and outside of the collection.

  9. I here mostly follow Lewis (1983, pp. 10–19, 1986, pp. 59–69) and Bricker (1996, p. 227, 2001, p. 31).

  10. Modes of being correspond to properties like being actual and being present, while haecceities correspond to properties like being Socrates and being Plato. They appear to underwrite non-qualitative similarities among their instances. (My claim that haecceities are a kind of one over many might seem strange given that haecceities are usually taken to be shared only by individuals that are identical to each other, and these individuals are one, not many. But haecceities have traditionally been taken to be responsible for the identity of the individuals that enjoy them; they take what would have otherwise been many individuals and make them one. Haecceities are, in this respect at least, a kind of one over many. There is, however, a stronger respect in which haecceities might be taken to be a kind of one over many. For if worlds do not overlap and no individual is wholly part of more than one world, then the non-fundamental property being identical to Socrates, had by a single individual at a single world, might be distinguished from the potentially fundamental property being Socrates, had by many different individuals at many different worlds. It is, on this non-traditional view, the latter property that would correspond to a haecceity).

  11. See, for example, Lewis (1983, p. 25, 2001, p. 382 n 6), Eddon (2009, pp. 15–19), and Cowling (2015, pp. 279, 285).

  12. See, for example, Carnap (1947a, p. 84, 1947b, p. 138, 1950, p. 74), Ismael (2001, pp. 186–93), Ismael and van Fraassen (2003, pp. 375–378), and Rickles (2006, pp. 152–153, 159, 2008, pp. 7–9).

  13. See, for example, Carnap (1947b, p. 138), Adams (1979, p. 7), Lewis (1986, p. 221), Gallois (1998, p. 249), and Divers (2002, p. 349 n 12).

  14. I will say that the B-properties ground the A-properties iff the A-properties globally supervene on the B-properties, and the A-properties are all broadly less natural than the B-properties. I thus take the relevant grounding relation to be a relation between properties. It is intended to be irreflexive, asymmetric, and transitive. It is not intended to be hyperintensional.

  15. The negation employed here is not strict negation. I am assuming that the intension of being a non-electron is properly contained in the intension of being strictly a non-electron. The latter, unlike the former, is had by abstract mathematical entities. For more details, see footnote 27 below.

  16. I believe this to be a live possibility. For depending upon the lay of logical space, the property of absolute actuality, which we designate with the impure, directly referential concept being exactly ontologically like me and everything else at my world, might also be designatable with a purely descriptive, infinitely disjunctive concept. But absolute actuality should I think, nevertheless, be taken to be non-qualitative. See Simmons (forthcoming, Sect. 2) for further discussion.

  17. Teller (1984, p. 148) plausibly attributes something like this account to Lewis (1983). It is similar to the supervenience view discussed in Cowling (2015, pp. 295–298).

  18. Fundamental laws should be distinguished from derived laws which cannot be written in purely fundamental terms, but which can be somehow derived from fundamental laws. Similarly, fundamental causal facts should be distinguished from facts that merely underwrite true causal statements.

  19. The related view that fundamental laws must be expressible without impure, non-qualitative predicates is a popular position, but is not without controversy. See Lange (1995, pp. 430–436, 2000, pp. 34–39) for critical discussion.

  20. That the nomic role played by being Hesperides is non-fundamental can be established by considering another world—qualitatively indiscernible from the one described above—where Hesperides has been ‘replaced’ by Eden. It would seem to be a de re law in this other world that all the fruit in Eden are apples. But these two worlds would appear to have the same fundamental causal facts. Thus, while being Eden and being Hesperides play causal and nomic roles at their respective worlds, the roles they play are not fundamental.

  21. The causal account does require the fundamental qualitative properties to play a causal role at some of the worlds in which they are instantiated. A fundamental property that was essentially an idler would be classed as non-qualitative. The causal account is thus incompatible with the view that qualia are both fundamental and essentially epiphenomenal. Thanks to an anonymous referee for pushing me on this point.

  22. To be somewhat more precise, let’s say that two worlds are structurally isomorphic iff there is a one–one correspondence between their parts that preserves the overall pattern of their fundamental qualitative properties and relations; and let’s say that two worlds are qualitatively indiscernible iff there is a one–one correspondence between their parts that preserves not just the overall pattern of their fundamental qualitative properties and relations, but the fundamental properties and relations themselves. We can then define quidditism about worlds as the view that some qualitatively discernible worlds are structurally isomorphic. The quidditist will likely hold that the fundamental qualitative properties are individuated by basic qualitative suchnesses.

    Quidditism should not be confused with haecceitism about properties, which holds that worlds can differ by a permutation or wholesale replacement of properties without differing qualitatively. The haecceitist believes that the properties that play the fundamental causal roles lack basic qualitative suchnesses and have only bare non-qualitative thisnesses. She must therefore deny the causal thesis. I don’t take this to be a problem since I take quidditism to be far more plausible than haecceitism about properties. See Hildebrand (2016) for discussion. Note that Hildebrand calls these views qualitative quidditism and bare quidditism. I’ve adopted the terminology from Bricker (2017, pp. 39, 49 n 18).

  23. We can define structuralism about worlds as the view that no qualitatively discernible worlds are structurally isomorphic (or, alternatively, as the view that two worlds are structurally isomorphic only if they are qualitatively indiscernible). It is, so understood, simply the denial of quidditism. There are, as I see it, two views about properties that motivate structuralism: strong causal essentialism about properties—a view that Hawthorne (2001) calls causal structuralism and Hildebrand (2016) simply calls structuralism—which holds that the fundamental qualitative properties are individuated by their causal roles, and haecceitism about properties which holds that the fundamental properties are individuated by bare non-qualitative thisnesses. Both views tie a world’s qualitative character to its overall structure, and both views hold that the most natural qualitative properties are individuated by their causal roles. But while the strong essentialist believes that these properties are perfectly natural, the haecceitist does not. It is because the haecceitist denies that there are fundamental qualitative properties that she must deny the causal thesis.

  24. The quidditist and the strong causal essentialist agree that the properties that play the fundamental causal roles have qualitative suchnesses. But they disagree about the connection between a property’s playing a causal role and its having a suchness: the strong causal essentialist thinks that a property has a suchness because it plays a fundamental causal role, whereas the quidditist thinks that a property’s qualitative suchness is independent of the causal roles it plays. This might suggest that while both the quidditist and the strong causal essentialist can accept the truth of the causal thesis, only the strong causal essentialist can take it to provide us with an explanation for why the properties that play the fundamental causal roles are qualitative.

    I deny, however, that quidditists cannot take the casual thesis to be adequately informative. So while I am inclined to agree that the thesis that a fundamental property is qualitative because it has a basic qualitative suchness might provide a deeper metaphysical explanation of the nature of a fundamental qualitative property than the causal thesis, I don’t think the concept of a basic suchness is terribly informative. I can gesture at it by giving various analogies, but I can’t really help you acquire it if you lack it. I think the concept of playing a fundamental causal role is more informative. It is one that I could potentially help you to acquire. The causal thesis thus provides a kind of insight into the nature of the fundamental qualitative properties that the basic suchness thesis does not. The quidditist can, I think, accept the causal thesis, deny that it gets to the metaphysical heart of the matter, but still take it to be informative. Thanks to an anonymous referee for pushing me on this point.

  25. Bricker (1996, pp. 233–234, 2006, p. 49) and Hawley (2009, p. 102) take both identity and composition to be non-qualitative. Fine (1977, p. 138) appears to take identity as non-qualitative.

  26. MacFarlane (2000) calls this ‘1-formality’.

  27. In order to maintain that some entities determinately lack all qualitative character, I must deny the commonly held assumption that the qualitative properties are closed under (strict) negation. For while the sui generis natural numbers lie outside the intension of, say, being an electron, they nevertheless instantiate its strict negation, namely, being strictly a non-electron. But although I must deny the letter of this assumption, I can still capture some of its spirit. For the property being concrete and strictly a non-electron is, I believe, appropriately grounded in the property being an electron. This is because, as I suggested in footnote 14 above, grounding should be understood in terms of global supervenience and comparative naturalness. But since global supervenience is defined on concrete possible worlds, being concrete and strictly a non-electron will be grounded in being an electron. This gives negation a kind of closure in the realm of the concrete: the anti-intension of being an electron defined on the concrete possible worlds, which we might call being a non-electron, would seem to be a qualitative property.

  28. The qualitative status of parthood leads to an antinomy. The thesis of this antinomy is that parthood is qualitative; the antithesis is that it is not. The alleged proof of the thesis is that a property is qualitative if it is preserved by duplication, and since parthood is preserved by duplication, it must be qualitative. The proof of the antithesis is that it is possible for there to be things that determinately fail to instantiate any qualitative properties or stand in any qualitative relations, but given that the parthood relation would apply to such things, it must be non-qualitative. This antinomy can be resolved in favor of its antithesis. Consider the ‘proof’ of the thesis. The best motivation for the premise that parthood is preserved by duplication is that it must be included in the definition of duplication itself: to say that two objects are qualitative duplicates is to say that there is a one–one correspondence between their parts that preserves all the fundamental qualitative (as well as all the mereological) properties had by their parts and all the fundamental qualitative (as well as all the mereological) relations between their parts. But, given this definition, the plausibility of the premise that a property is preserved by duplication only if it is qualitative turns on the plausibility of the auxiliary assumption that the mereological properties and relations are themselves all qualitative. This assumption is not, however, particularly plausible: the proof of the antithesis gives us good reason to think it false. Thus, a property or relation can be preserved by duplication—and can thereby contribute to the qualitative character of an object whose parts have that property or stand in that relation—without itself being qualitative. Thanks to an anonymous referee for pushing me on this point.

  29. MacFarlane (2000) calls this ‘2-formality’.

  30. MacFarlane (2000) calls this ‘3-formality’.

  31. Bricker (2008, pp. 117–18, forthcoming) takes the mathematical properties to be non-qualitative. Carnap (1947a, p. 84) and Fine (1977, pp. 138, 177) appear to do so as well.

  32. My argument turns on the plausibility of the claim that purely mathematical entities have no qualitative character whatsoever. I’ll consider two challenges to this claim. The first concerns a pure set’s cardinality. Two pure sets can have the same cardinality. So, for example, the singleton of the empty set, {∅}, and the singleton of the singleton of the empty set, {{∅}}, both have exactly one member. They are similar in this respect. If we thought that similarity must always be qualitative, we should say that these pure sets have qualitative character in virtue of their cardinality. But this strikes me as the wrong thing to say. For a set’s cardinality appears to be a purely quantitative, non-qualitative property. Two sets with the same cardinality thus appear to enjoy a kind of non-qualitative similarity. It is a mistake to think that similarity must always be qualitative. (Note that I am not here claiming that quantitative properties can never be qualitative. Some properties such as having exactly 5 kg mass strike me as both quantitative as well as qualitative, while other properties such as having exactly 5 members strike me as purely quantitative.).

    The second challenge concerns an abstract sui generis geometrical object’s shape. An abstract geometrical object can have the same shape as a concrete possible object. But since the qualitative character of a solid gold cube is different from that of a solid gold dodecahedron, their shape properties would appear to be qualitative. I must, it seems, either give up on the claim that abstract geometrical objects lack qualitative character or else deny that the shape properties had by concrete possible objects are qualitative after all. If forced to choose, I would take the latter option. But maybe I don’t have to. A concretely possible object such as solid gold cube will have a property that might plausibly be thought of as a shape property in virtue of some pattern of the spatiotemporal relations between its parts. And, assuming that these relations are qualitative, this shape property will be qualitative as well. An abstract geometrical object will have a property that might also be thought of as a shape property in virtue of some pattern of the relations between its parts. And, assuming that these relations are non-qualitative, this shape property will be non-qualitative as well. Two objects, whether concrete or purely geometrical, can then be said to have the same shape when there is a mapping between them that preserves the relevant patterns of relations between their parts, call this mapping a shape isomorphism. Given these assumptions, I now have the resources to say everything I want to say. But what should I say about the property that is preserved by shape isomorphism? Is it some third somewhat less natural non-qualitative shape property? Or is it just the non-qualitative shape property had by purely geometrical objects? To put this another way: are the qualitative relations that underwrite qualitative shape properties themselves reinforced by non-qualitative purely geometrical relations or not? If not, there are three distinct shape properties here. If so, there are only two. I prefer to say that there are only two shape properties here: one qualitative and had only by concrete possible objects, the other non-qualitative and had both by concretely possible and purely geometrical objects. (Note that if spatiotemporal relations are non-qualitative, there will only be one, non-qualitative, shape property here.) Thanks to two anonymous referees for pushing me on these matters.

  33. Bricker (2001, pp. 29–31, 2006, pp. 49–50, 2008, pp. 122–125, forthcoming) takes actuality to be non-qualitative.

  34. For Lewis, objective similarity is always qualitative. He thinks that the problem with unnatural properties is that ‘[t]hey pay no heed to the qualitative joints, but carve things up every which way’ (1986, p. 59, emphasis added), and that the ‘[s]haring of [the perfectly natural, or sparse, properties] makes for qualitative similarity’ (1986, p. 60, emphasis added). They help to give us ‘a complete qualitative characterization of things’ (1986, p. 60, emphasis added).

  35. But what about idlers: namely, ‘those fundamental properties, if any, that are instantiated within the actual world, but play no active role in the workings of nature’ (Lewis 2009, p. 205)? Are they qualitative? I guess it depends upon whether they could play an active causal role in the workings of nature. If they could but don’t, that is no threat to their status as qualitative. But if they couldn’t ground causal powers, it seems that they wouldn’t count as qualitative.

  36. See Williams (1962, p. 751) for a similar argument.

  37. See Hume ([1739] 1888, pp. 253–254) for an argument along these lines.

  38. See Merricks (2001, pp. 8–9), Dorr (2002, Sect. 1.4.1), and Rosen and Dorr (2002, p. 155) for arguments along these lines.

  39. I take it that Maddy (1990) would disagree with this claim. For she thinks that we have the ability to detect certain impure sets.

  40. See also Sider (1993, Sect. 3.2.1).

  41. I am assuming here that spatial, temporal, and spatiotemporal relations are all qualitative. I am, however, somewhat skeptical of this assumption. Spatial and temporal relations do not appear to play an active role in the workings of nature. And while the view that matter and spacetime causally interact (and hence that spatiotemporal relations play fundamental causal roles in general relativistic spacetime theories) might enjoy ‘common acceptance’, there are ‘reasons to regard [it] as questionable’ (Hoefer 2009, pp. 701–704).

  42. See Wang (2013, pp. 542–544) and Bricker (2017) for discussion of the exclusion problem. Wang argues that the principles of recombination should either be amended or else abandoned. Bricker attempts to tackle the problem head on by arguing that determinables rather than determinates are fundamental.

  43. See Wang (2013, pp. 539–541) for discussion of the necessitation problem.

  44. The triangle inequality tells us that, for any points x, y, and z, the distance between x and z is less than or equal to the sum of the distance between x and y and the distance between y and z; or, more formally, that d(x, z) ≤ d(x, y) + d(y, z).

  45. We can say, roughly, that properties are determinably-distinct when they are not determinates of the same determinable. See Saucedo (2011, p. 246) for a more precise definition.

  46. See, however, Baxter (2014, pp. 247–249) for an argument to the contrary.

  47. Bricker (2006, pp. 49–50) endorses something like this thesis. He endorses the ‘if’ direction. I’m not sure whether he would also endorse the ‘only if’ direction.

  48. It is a transformed version of the island universe problem for modal realism. See Bricker (2001).

  49. This view is suggested by some remarks in Bricker (1996, p. 237 n 22, 2008, p. 131 n 12) and appears to be endorsed by Cowling (2012, p. 407).

  50. See Bricker (2001, 2006) for a defense of this move.


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Thanks to Sam Cowling, André Gallois, Arturo Javier-Castellanos, Li Kang, Ned Markosian, Kris McDaniel, Preston Werner, two anonymous referees, and an audience at the 2016 Pacific division meeting of the APA for helpful comments on earlier drafts of this paper.

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Simmons, B. Fundamental non-qualitative properties. Synthese 198, 6183–6206 (2021).

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