Abstract
Haecceitism and Hume’s Dictum are each controversial theses about necessity and possibility. According to haecceitism, there are qualitatively indiscernible possible worlds that differ only with respect to which individuals occupy which qualitative roles. According to Hume’s Dictum, there are no necessary connections between distinct entities or, as Humeans sometimes put it, reality admits of “free recombination” so any entities can co-exist or fail to co-exist. This paper introduces a puzzle that results from the combination of haecceitism and Hume’s Dictum. This puzzle revolves around the free recombination of non-qualitative properties like being Socrates. After considering several responses to this puzzle, I defend an ideology-driven solution, which dispenses with non-qualitative properties like being Socrates in favour of primitive theoretical ideology while, at the same time, preserving a commitment to both haecceitism and Hume’s Dictum.
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Notes
Paradigmatic qualitative properties and relations include redness, being hexagonal, and is five feet from. Paradigmatic non-qualitative properties include haecceities like being Socrates and other properties and relations that are intuitively dependent upon specific individuals like being five feet from Socrates. Despite much agreement on these paradigm cases, there is considerable disagreement over the precise distinction between qualitative and non-qualitative properties. On the qualitative/non-qualitative distinction, see Adams (1979), Cowling (2015a), and Simmons (forthcoming).
The most influential contemporary statement of Hume’s Dictum is Lewis (1986a: pp. 86–91). For subsequent appeals to Hume’s Dictum in Lewis, see Lewis (1986b, 1992, 2009). On Lewis’ Humeanism, see Beebee and MacBride (2015), Cowling (2015b), and Wilson (2015). Representative appeals to Hume’s Dictum or recombination after Lewis include Bricker (1991, 2017), Schaffer (2005), and Saucedo (2011). Critical examinations of the consequences and potential formulations of Hume's Dictum include Forrest (2001), Nolan (1996), Hofmann (2006), Efird and Stoneham (2008), Stoljar (2008), and, more recently, a series of papers by Wilson (2010, 2014, 2015). Wilson (2015) notes a variety of worries about recombination principles under-generating possibilities. The puzzle set out below might naturally be taken to supplement Wilson’s case by showing how the interaction of Hume’s Dictum and haecceitism leads to the systematic over-generation of possibilities.
Complications regarding the distinction between possible worlds and maximal possibilities abound once we take into account Lewis’ modal realist version of haecceitism. I omit these complications for the moment and speak with some deliberate looseness, but see Sect. 2 for discussion. See Lewis (1986a: pp. 220–247, 2009) on Lewis’ haecceitism. For critical responses to Lewis’ haecceitism, see Fara (2009), Baltimore (2014), Cowling (2012, 2015b), Skow (2011), Kment (2012), and Russell (2013).
For example, some anti-essentialist haecceitists will accept worlds that differ from actuality in that you “swap” qualitative roles with a poached egg. Other essentialist haecceitists will reject such possibilities on account of, say, the essentiality of kindhood, even while they accept other haecceitistic differences—e.g., ones where you swap qualitative roles with another human. For discussion, see Mackie (2006). Entity-specific debates about the legitimacy of haecceitist differences notably include disagreement over whether worlds might differ solely concerning the non-qualitative properties of spacetime points and spatiotemporal regions. For discussion, see Brighouse (1994), Pooley (2006), Melia (1999), and Dasgupta (2011). As noted above, precisely which haecceitistic differences one accepts between worlds is orthogonal to the puzzle at hand.
Throughout, I take talk of “properties” to include both monadic properties and n-place relations.
I assume in what follows that fundamentality is incompatible with redundancy, so that the stock of fundamental properties constitutes a minimal supervenience base. Depending on one’s views regarding fundamentality, this might prove to be a dispensable constraint. See Lewis (2009: p. 205) and Schaffer (2004) for discussion of minimality and fundamental properties.
At least some non-qualitative properties will depend upon other qualitative or non-qualitative properties—e.g., being between Socrates and Xenophon depends upon the instantiation of being Socrates, being Xenophon and various qualitative spatial properties. See Simmons (forthcoming) for discussion.
While the name points back to Hume, I make no assumption that this specific thesis is rightly drawn from Hume’s philosophy. On the disconnect between Hume’s empiricist case against necessary connections and contemporary arguments for Hume’s Dictum, see Wilson (2010).
Bricker (1991) argues that a satisfactory treatment of plenitude requires three principles concerning recombinations, world-structures, and world-contents, respectively.
It is difficult to understand the complexities that arise in connecting ontological categories and modal freedom. Since my primary aim here is marking a puzzle regarding recombination for properties and haecceitism, some key questions are set aside here including how alternative combinatorialism frameworks bear upon this issue. See, e.g., Wang (forthcoming).
Those unmoved by the problem set out below might at least point to the discussion that follows as a cautionary tale of what happens when we “soup up” recombination principles and apply them to properties rather than intrinsically-typed entities.
A parallel puzzle regarding the co-instantiation of being Socrates and being Xenophon arises, since Humeans must explain why no individual can instantiate both haecceities. Note, however, that this puzzle is of a piece with the general puzzle of property incompatibilities that arises for Humeans—i.e., explaining why all fundamental properties are possibly co-instantiated or, if not, how their incompatibility is consistent with Humeanism. The ideological solution I consider below addresses both puzzles regarding haecceities (if successful), but it remains silent on the general issue of property incompatibility as it concerns qualitative properties.
As I’ll discuss below, this isn’t the only puzzle in the neighbourhood: Humeans who are not anti-essentialists owe some account of how Hume’s Dictum and haecceitism might be true without requiring bizarre de re possibilities according to which you could be a waterfall or woodchuck. Notably, Lewis (1986a) relies on counterpart theory to accommodate our inconstant modal intuitions via counterpart theory. See Sect. 5.
The present appeal to Ramsification is intended only as an aid to grasping the problem at hand. Note, for example, that it describes the recombination of non-qualitative matters in terms of the individual constants when e might do so via haecceitistic predicates instead. In this way, the artifact of representation should not be mistaken for the metaphysical structure at issue.
See Lewis (1968 and 1983 reprinting postscript, 1986a).
See Lewis (1986a: p. 223).
Lewis (1986a: p. 224) is agnostic about whether there are qualitatively indiscernible worlds. If, however, one posited such entities and held that numerical distinctness must be grounded in fundamental differences, there would be reason to take them as differing in their fundamental properties. I set this complication aside here.
Lewis (1986a: p. 231).
Within a modal realist treatment of properties as sets of possibilia, Lewis takes our talk of haecceities to be ambiguous between singletons of objects and sets of transworld individuals suitably counterpart-related. See Lewis (1986a: p. 225).
This point cuts deeper into Lewis’ metaphysics of properties since it requires that, if propositions are to be identified with sets of ways things could have been, then, since there are more maximal possibilities than possible worlds, propositions must ultimately be identified with sets of maximal possibilities. Given Lewis’ interest in the reduction of properties to sets, a similar point generalizes to the case of properties. See Cowling (2012).
The particular notion of intrinsic duplicate does considerable work in the Humean picture here. See Wilson (2015: p. 141) for some complications.
On the Lewisian interpretation of our talk of recombination, see Lewis (1986a: p. 89).
Depending upon how one conceives of the de dicto/de re distinction, this is controversial as there will be de re modal claims regarding properties, which Lewis treats without the help of counterpart theory. See, however, Heller (1989).
See Lewis (1986b, 1992, 2009). On Lewis’ Humean argument against structural universals and magical ersatzism, see Hawley (2010) and Nolan (forthcoming). To be clear, while Lewis argues against admitting such a relation, his argument for doing so presumes that we can rightly apply the Humean stricture to non-qualitative relations rather than, say, merely regions of spacetime.
Lewis (1986a: p. 174).
There are a variety of ways to pursue “restrictions” on recombination some of which import rich or distinctive ideological or modal commitments. Vetting these options is critical for the broader assessment of Humeanism. One prospective view holds recombination to concern exclusively “wordly” matters, in the sense of Fine (2005). Such a view would apply recombination to matters regarding, say, Socrates’ height and location, but not to “transcendental” matters like Socrates’ self-identity. Whether haecceitistic truths are worldly or transcendent is uncertain and, more generally, work is needed to see whether this distinction can be reconciled with the core tenets of Humeanism. I hope to say more about the interaction of this distinction and Humeanism elsewhere. My thanks here to an anonymous referee.
That’s not to say that it couldn’t be replicated with the right package of ersatzist views about possible worlds and a revised version of counterpart theory relies upon something other than qualitative resemblance to make sense of de re representation. See Heller (1989) and Cowling (2012) for discussion.
Bricker (2008) notes the qualitative does not depend upon particular individuals and so general identity properties and relations would be disqualified from the non-qualitative. As I note in Cowling (2015a: p. 285), the status of being self-identical and relevantly similar properties is an open and difficult question for accounts of this distinction.
The metaphysical waters run deeper than space here permits. See, e.g., Bueno (2014) and Krause and Arenhart (2019). Along with the options of taking identity facts (or properties) to be derivative or fundamental, we might also hold them to be “zero-grounded” rather than “ungrounded.” For discussion, see Shumener (2017).
If the identity relation were a part of the property being Socrates, the fact that necessary connections among the non-mereologically disjoint are permissible might be used to block the Multiple Socrates Problem. For non-Humeans, this seems to be the best available explanation, but, for would-be Humeans, such a solution is acceptable only if our metaphysics of properties is exhaustively mereological. But, following Lewis (1986b), there seems to be purely mereological means of building properties including non-qualitative ones like not being identical with Socrates and being identical with non-Socrates. For Humeans content to broaden the means for constructing properties beyond the mereological, this looks to be an especially promising route, but, given our pursuit of strict Humeanism, I set it aside here. Thanks here to an anonymous referee.
My thanks to a referee for pressing this line of response.
For the hardcore Humean who is not content to restrict recombination to the fundamental, the natural option is a radically sparse conception of properties that denies the reality of any abundant properties that would be implicated in necessary connections.
Throughout, I assume that there is a stock of fundamental properties and so set aside the possibility of infinite non-qualitative descent. I therefore set aside the threat of non-qualitative “onion worlds.” For discussion, see Williams (2007).
I set aside complications regarding the possibility of fundamental properties of fundamental properties. For discussion, see Eddon (2013).
See Lewis’ case against structural universals in Lewis (1986b).
On (qualitative) heterogeneity and extended simples, see Spencer (2010).
On worlds of two-way eternal recurrence, see Lewis (1986a: p. 227).
Thanks to Ranpal Dosanjh for the part-haecceity proposal considered here.
As I argue in Cowling (2013), it remains uncertain how to compare the cost of ideological commitments across ideological categories and when compared to ontological costs. In the present context, at least one central concern is whether introducing non-qualitative ideology constitutes a commitment over and above a commitment to purely qualitative primitive predicates. Sorting out this delicate matter is critical for the ultimate evaluation this view, but not for the project of explicating and motivating it, which is my aim here.
To see that ideological commitments are importantly different from ontological ones, consider the debate between the nominalist modalist and the nominalist modal eliminativist. The parties are—let’s suppose—in ontological agreement, but disagree over whether the world has any modal aspect as only one holds that certain truths about the world are expressible only via modal notions. Kment (2014: p. 150) describes a version of ideological realism along the following lines: “It shouldn’t be assumed that all ingredients of reality must be individuals, properties, or relations—or entities of any kind, for that matter. For example, it’s possible that in order to describe reality completely, we need to use some primitive piece of ideology that relates to some aspect of reality that doesn’t belong to one of these three ontological categories, and which may not be an entity at all.”
On the ideological gambit of dispensing with these and other relations, see Melia (2008).
On the “tie” of instantiation, see Armstrong (1978: pp. 109–111) and Nolan (forthcoming).
The prospects of exempting ideological notions for Humean demands upon modality have been considered before. See, in particular, Nolan (forthcoming), who considers precisely such an option in addressing Lewis’ argument against magical ersatzism.
This, of course, falls short of an argument against competing views about the metaphysics of identity, haecceities, and individuation absent an examination of their compatibility with Hume’s Dictum. For some metaphysical options regarding haecceities, see Diekemper (2015).
Curiously, such a view affords a direct way to make good on the implementation of Russell’s theory of description in Quine (1948) without requiring the assumption that a predicate like “Socratizes” is analyzable in terms of some unique qualitative profile.
Note that this is not put forward as anything like an account of the qualitative/non-qualitative distinction. There is nothing in this view that requires all primitive predicates to be non-qualitative.
There is room here for an interesting debate over the modal constancy of ideological structure—e.g., whether the “stock” of ideology is invariant across worlds. This debate has a parallel in debates regarding the necessary existence of non-qualitative properties. See, for example, Adams (1981), Bennett (2006), and Plantinga (1974).
I assume here that Humeans ought to be realists about qualitative properties. In the event that Humeans incline towards a broader “ostrich nominalism,” the interface between Hume’s Dictum and the metaphysics of properties plays out quite differently. Since these Humeans will not abide necessary connections among certain qualitative features of the world, their view will require a worked account of which ideology is subject to recombination. One proposal on this score might draw this line precisely at the qualitative/non-qualitative distinction, though it is by no means obvious that this is the uniquely best option.
Would-be anti-essentialist might, for example, put forward a principle of plenitude that takes qualitative maximal possibilities as in puts and outputs a space of maximal possibilities in accord with a “consistent predication principle”—roughly, for any consistent way of attaching primitive predicates to qualitative roles, there is a maximal possibility according to which the relevant individuals occupy the relevant qualitative roles. Such a principle would bake in restrictions like the impossibility of Socrates and Xenophanes being identical and multiple qualitative roles being occupied by Socrates. Since the relevant constraints pertain to ideology, no Humean stricture is violated.
I make no claim that a view on which being present is a fundamental non-qualitative is the natural or most defensible variety of the moving spotlight view, though it is at least one way to make good on the notion of a privileged present. On the moving spotlight view, see Cameron (2015). On modal realism supplemented with absolute actuality, see Bricker (2006).
For comments and helpful discussion, my thanks to Phil Bricker, Ben Caplan, Wesley Cray, Ranpal Dosanjh, Boris Kment, Maria Scarpati, Byron Simmons, Kelly Trogdon, and audiences at Hong Kong University, Lingnan, Neufchâtel, and Wisconsin-Madison.
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Cowling, S. Recombining non-qualitative reality. Synthese 198, 2273–2295 (2021). https://doi.org/10.1007/s11229-019-02204-x
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DOI: https://doi.org/10.1007/s11229-019-02204-x