Abstract
In this paper, I examine Peter Schulte’s “Grounding Nominalism” (Schulte, 2018), understood as the claim that first-order properties and relations are grounded in the concrete particulars which instantiate them. While Schulte offered reasons to think that this view is consistent, along with answers to a number of objections, a more straightforward argument for GN is still needed. I take on this task here, by discussing and defending what I call the “argument from abstraction”. The latter, I suggest, offers more grounds to Grounding Nominalism.
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Notes
It should be stressed that instantiation, here, is used in a neutral fashion. To say that a instantiates F merely means that a is F.
It is true that all of these alleged features of grounding might be –and have been– challenged. I admit that it would be interesting to see how GN fares in light of non-standard accounts of grounding. Yet, it is not my concern here, as I intend to defend GN just as it was understood and defined by Schulte.
Likewise, the existence of particulars –tomatoes, people, tables, stars, electrons– will here be taken for granted without argument.
While tempting, one should better not say that GN takes thick particulars as fundamental. A “thick particular”, indeed, is generally defined as being the conjunction of a bare particular plus its properties. Seeing thick particulars as the most basic ontological units would therefore suggest that properties and particulars are equally fundamental, something which GN should obviously reject.
In Schulte’s words: “the proponent of GN characterizes objects on the fundamental level by using many different predicates, like ‘red’, ‘spherical’, or ‘transparent’ and treats these characterizations (e.g. ‘a is red’, ‘b is spherical’, and ‘c is transparent’) as primitive” (2018, 15). For similar claims, see Quine (1948, 30); Devitt (1970, 436); Imaguire (2018, 53); Melia (2005, 72).
Of course, this only goes if grounding is indeed factive. Also note that an advocate of GN could in principle claim that she accepts properties/relations which are actually non-instantiated but only contingently so. This would allow her to accept the existence of properties/relations which have no instances in the actual world but which are instantiated in other possible worlds. But even with this more flexible principle, necessarily uninstantiated properties/relations (i.e., properties/relations having no instances in any possible world) would still be rejected.
Some might ask what happens when properties (relations) are instantiated by other properties (relations). GN, as defined above, states that particulars ground the first-order properties or relations they instantiate. But what about higher-order ones? As a matter of fact, GN denies that higher-order properties or relations cause any particular trouble: if higher-order properties and relations are grounded in lower-order ones, and if all of those are in turn grounded in particulars, nothing will be at odds with the view: since grounding is transitive, we get the desired result that all higher-order properties and relations are (mediately) grounded in particulars. See Schulte (2018, 17-19) for the details of this strategy.
I suppose that one might complain that (S) and (S′) are not equivalent, for the former does not say anything about which specific property a and b have in common, contrarily to the latter. But this is no objection to GN. The point of the present analysis is not epistemic (i.e., as if one intended to construct a salva informatione paraphrase) but ontological: it states what is the ground for a and b having a property in common. It would not do, either, to object to (S′) on the grounds that a and b may have more that one property in common, besides redness: as Schulte argues (2018, 4–5), a property/relation can unproblematically have a plurality of distinct full grounds.
I think that an argument of this type was first envisioned (although not worked out in detail) by Schaffer, who proposed that “grounding relations are relations of abstraction” (2009, 377).
Some might object that this type of claim pertains to an obsolete philosophy of mind. However, it seems clear that we can selectively focus our attention on certain aspects of the things which surround us – as Armstrong put it, “whatever the nature of the mental process is, it seems that we can do it” (1997, 123).
The notion of “separation” is potentially misleading. We should beware of understanding it as meaning that it would be possible to imagine some aspects of things as standing independently of others. Indeed, and as Berkeley famously objected to Locke, it seems impossible to form an idea of, say, a red thing that would not be extended; or of a triangle that would be neither isosceles nor equilateral nor scalene. The advocate of abstraction as I characterized it rather proposes that abstraction is a form of emphasis, or a selection. The point is not that we imagine a determination (colour, shape, etc.) as if it could subsist by itself. It is, rather, that we focus our attention on it, ignoring the others with which it is de facto conjoined.
Lewis discusses a proposal of the sort: “abstract entities are abstractions from concrete entities. They result from somehow subtracting specificity, so that an incomplete description of the original concrete entity would be a complete description of the abstraction” (1986, 85).
Understanding abstracta as being “less” than concreta, as I do, has the potentially problematic consequence of blurring the distinction between the qualitative aspects and the material parts of an object. I shall come back to this issue later on.
I am fully aware that tropes are often defined as “abstract particulars”, an expression which intends to capture the fact that they differ both from ordinary concrete objects and from universals. But note that this mere label does not licence any sort of objection to (P1): while tropes are taken to be particular in nature (insofar as they are non-repeatable and non-shareable), they should nonetheless be understood as qualitative characters, and therefore, as properties. The “particulars” which (P1) refers to are concrete, ordinary individuals, not properties.
Note that my view of abstraction commits me to say that bare substrata or bare particulars –canonically understood as particulars considered independently of all their properties– are abstract, insofar as they are incomplete and partial entities. Armstrong held a similar view (1980, 447; see also Heil, 2003, 172). It is true, though, that proponents of bare particulars tend to describe those as being concrete. But I suspect that they do so to stress that bare particulars are spatiotemporally located; not to claim that they are complete entities. At any rate, this does not matter for GN, since the view has no use for (and should reject) substrata or bare particulars, as I shall make clear later on.
Some might dispute the claim that all particulars are concrete on independent grounds. Williamson, for instance, considers that past entities are non-concrete particulars (2013, 13), which are taken to differ both from abstract entities and from concrete particulars. I do not think that this should worry the advocate of GN who accepts the argument from abstraction, though. Before all, it is of course incumbent to proponents of non-concrete particulars to show that these are indispensable. Even if it were established, the proponent of GN could still maintain that non-concrete particulars have the features of ordinary particulars (i.e., properties, a spatio-temporal location, etc.), the only difference being that they aren’t present. But if that is so, no special problem seems to be raised by non-concrete particulars, save a terminological one. As such, GN might perhaps accept, e.g., that the relation being the son of is grounded in the existence of my living father (a concrete particular) and my deceased grandfather (a non-concrete particular, for Williamson). Thanks to Vincent Grandjean for prompting me to reflect on these matters.
“Property-instances are ontologically dependent entities, depending for their existence and identity upon the individual substances which they characterise, or to which they “belong”. A particular redness or squareness can, ultimately, be identified as the particular property-instance that it is only by reference to the individual substance which it characterises. This is not an epistemic point but a metaphysical one: it concerns individuation in the metaphysical rather than in the cognitive sense –that is, individuation as a determination relation between entities rather than individuation as a kind of cognitive achievement” (Lowe, 2006, 27).
An avatar of GR might be Carmichael’s “Deep Platonism” (Carmichael, 2016).
I borrow this label to Kriegel (2004).
Let it be said, however, that to the difference of traditional bundle theories, GR and TF accept that ordinary concrete particulars exist over and above their properties (although with a derivative ontological status). This enables these views to accept at face value our ordinary talk about particulars, instead of having to interpret it as (or paraphrase it by) a discourse about bundles of properties.
Various replies to this objection against BTU have been proposed over the years. They might also be used to defend GR. A first option might be to say that, just like an immanent universal is capable of being wholly present in different places at the same time, and thus to be at some distance from itself, one single bundle of universals may be at some distance from itself. If this is so, the case envisioned by Black is one where a single sphere is wholly present in two places at once, rather than a scenario involving two numerically distinct but qualitatively identical spheres (see O’Leary Hawthorne & Cover, 1995, 192–3). This rejoinder, however, is controversial (see e.g. Valicella, 1997; Zimmerman, 1997). The advocate of GR might also solve the issue by accepting the existence of haecceities (Carmichael, 2016), a proposal that raises issues of its own and that I cannot examine in detail here. To mention a last strategy, one could perhaps avoid this problem by indexing GR’s compresence relation to particulars. The advocate of GR, that is, could claim that for any particular a, a exists becauseg some universals F, G, …, are a-compresent (where a-compresence is understood as a primitive relation which may only relate those universals bundling a). This answers the objection under consideration: since numerically distinct bundles of universals will involve different relations of a-compresence, Black’s scenario can be accounted for. I think that the advocate of GN, however, could complain that this proposal illicitly reintroduces particulars as fundamental. Particulars, indeed, are required to define a-compresence, as the relation must select only those universals which are relevant for the particular under consideration. My thanks to Pierre Saint-Germier for drawing my attention on this possible strategy.
Trope theorists are indeed far from being unanimously committed to the claim that tropes are ontologically independent entities. Some defend that tropes inhere in and ontologically depend on irreducible substrates (see e.g., Martin, 1980). Others admit that tropes are (inter)dependent entities, incapable of existing aside from one another (see Simons, 1994). The proponent of GN can presumably invoke to her own benefit the reasons advanced by such theorists, in order to resist the claim that tropes are ontologically independent entities.
Armstrong, for instance, claimed that “a trope of a particular mass or particular charge seems nearly as insubstantial, as incapable of independent existence, as the corresponding universal” (1989, 115). Some friends of tropes, however, bite the bullet and argue that this is plainly possible, if not actual (see Campbell, 1981, 353).
To be clear, what 4-D versions of GR and TF claim isn’t that the particular tomato grounded by b1 at t1 is identical to the particular tomato grounded by b2 at t2 (for where the ground differs, the grounded entities differ also). It is, rather, that the persisting particular which is the tomato is a bundle of momentary bundles (among which b1 and b2), and thus, a bundle of derivative particulars.
Some may wonder, though, if GN isn’t burdened by similar worries. I do not think so, even if knowing how the view accounts for change –a topic left unaddressed by Schulte– isn’t that simple. At first glance, GN could say that a particular changes just by gaining or losing (derivative) properties. Yet, since this view contends that properties are grounded, any property-change must be underlain by a change of what grounds them, i.e., by a change in the fundamental particulars themselves. But how are we to explain this latter change? Not by appealing to properties, it seems, as these are supposed to intervene at a later stage. I think that GN must therefore admit as a primitive fact that fundamental particulars are different ways at different times. This prompts another question: what makes it that GN’s fundamental particulars remain numerically the same through qualitative change? I take it that the proponent of GN shall refuse to posit bare substrates to answer this question. She might however account for change in another way, perhaps by defending threedimensionalism cum adverbialism or cum presentism, or again, by embracing quadridimensionalism. Examining these leads, at any rate, is beyond the scope of this paper
This objection, in fact, more generally leads to the conclusion that all the entities which are proper parts of something else are strictly speaking abstract. The only genuine concrete particular, under this assumption, would be the World or the Cosmos, taken as an all-inclusive whole or maximal mereological sum. D.C. Williams perceived this problematic result of the theory of abstraction under consideration: “since there must be, for everything but the World All, at least something, and indeed many things, of which it is a proper part, everything but the World All is ‘abstract’ in this broad sense” (1953, 15). While a view of this sort can be certainly defended (see Schaffer, 2010), it seems at odds with the argument from abstraction and more generally with GN, whose original intent is to take a multiplicity of concrete particulars as metaphysically fundamental. Note, however, that Schaffer seems to connect his own “Priority Monism” with something akin to the argument from abstraction (Schaffer, 2010, 47).
Some might think that these definitions lead GN to accept the problematic view that, while the aspects of a particular (taken individually) are abstract, their total sum is concrete. Indeed, the latter exhausts the content of the relevant spatiotemporal region. But this would be to forget that GN does not identify particulars with the maximal collection of their derivative aspects –this, technically, is guaranteed by the irreflexivity of grounding. Therefore, the sum of the aspects of a particular still counts as something less than the particular itself.
My thanks to an anonymous referee for bringing up this objection.
I am grateful to Pierre Saint-Germier for helpful discussion here.
My thanks to Donnchadh O'Conaill for making me consider this line of argument.
Additionally, one may think that this specific instantiation’s identity is determined in part by the identity of a. To individuate and single out F(a) as this particular instantiation, that is, we need to make an appeal to the particular a, alongside with the property F. But this suggests at best that a and F are both ontologically prior to F(a); not that properties are prior to particulars, as GD wants.
Armstrong indeed regarded bare particulars and uninstantiated universals as “vicious abstractions” from states of affairs (1980, 447).
Now, some might point out that this isn’t per se a problem, for any theory is committed to accept some truths or facts as primitive or brute (see e.g. Lewis, 1983, 353). GN is no exception, as we saw, for it takes predication or instantiation as primitive. I think, though, that GN fares better than SOAF on this score, as it seems perfectly able to account for resemblance between particulars. Suppose that a and b are similar in a certain respect F. GN may explain this by saying that a is similar to b becauseg a is F and b is F. If this is right, similarity is explained away by predication, which is itself taken to be unanalysable and primitive (see also Devitt, 1980, for an illustration of this strategy).
My thanks to the attendees of the Universals Workshop 2019 at the Complutense University of Madrid and to my friends and colleagues of the Groupe d'Etudes Métaphysiques in Collège de France . I also want to express my gratitude to Peter Schulte, Claudine Tiercelin, Pierre Saint-Germier, Donnchadh O'Conaill, Vincent Grandjean, Louis Pijaudier-Cabot, Filipe Drapeau Contim, Jean-Baptiste Guillon, Javier Cumpa, , and two anonymous referees, for their helpful comments on earlier versions of this paper.
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Declos, A. More Grounds for Grounding Nominalism. Philosophia 49, 49–70 (2021). https://doi.org/10.1007/s11406-020-00215-4
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DOI: https://doi.org/10.1007/s11406-020-00215-4