Abstract
Fundamental concrete particulars are needed to explain facts about non-fundamental concrete particulars. However, the former can only play this explanatory role if they are properly discernible from the latter. Extant theories of how to discern fundamental concreta primarily concern mereological structure. Those according to which fundamental concreta can bear, but not be, proper parts are motivated by the possibilities that all concreta bear proper parts (mereological “gunk”) and that some properties of wholes are not fixed by the properties of their proper parts (“emergence”). In response, theorists who hold that the fundamental concrete particulars can be proper parts may appeal to the possibility that every concrete particular is a proper part—that there is no mereologically maximal whole world (mereological “junk”), as well as to the intuition that fundamental concreta are qualitatively homogeneous “blocks” from which non-fundamental concreta are built. After motivating the plausibility of gunk and junk, the present essay proposes a constraint on fundamental concrete particulars based on topology instead of mereology: the fundamental concrete particulars must be appropriately connected. This constraint has the unique advantage of consistency with each of gunk, emergence, junk, and the building block intuition.
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Notes
Of course, immanent universals would not be concrete particulars. I will not attempt to give a formal characterization of the distinction between particulars and non-particulars here. Unofficially, I am partial to basing such a distinction on the capacity of concrete non-particulars to be wholly located at distinct spatial locations at some one time. I believe objections to this approach (e.g. from extended simple particulars) can be discharged, but doing so is not a project I will pursue here.
The examples to follow in the text are not intended to exhaust the ways in which fundamental concreta are important to wider philosophical issues.
See, for example, Armstrong’s discussion of what he calls ‘relative atoms’ (1989, 69).
A good introduction to this conceptual terrain is section 11 of Chalmers (2002).
I intend here and throughout to be neutral with respect to the underwriting ontology of spatiotemporal and topological notions like distance, arrangement, continuity, and path. It may be that using these notions commits us to extra entities (likely also fundamental) over and above fundamental concrete particulars. Or it may be that such putative entities are best understood as derivable from or reducible to concreta and their intrinsic properties. Since present concern is with concreta alone, the desired neutrality ought to be uncontroversial.
The idea that infinite mereological complexity poses a problem for fundamentality is not new. In addition to Aristotle’s Physics and Leibniz (1989), see Armstrong (1978), Lewis (1991), Schaffer (2003, 2010), Cameron (2008) and Bohn (2009). Section 4 below does, however, contain new reasons for taking the possibilities of gunk and junk seriously.
My use of ‘ontological responsibility’ may in fact be the same as some other philosopher’s use of one of the mentioned expressions. But since the mentioned expressions are not always used the same way in the literature, I prefer to introduce my own name for the relation in question.
Let ‘w′’ name the world that is exactly like w at t except that y is absent there at t. Let ‘{Z}’ name the set of worlds that are exactly like w at t except that, at them: (i) y is absent at t and (ii) there is some concrete particular z that does not exist at w at t and that stands in for y at t. Stipulation: w′ is closer to w than is any member of {Z}. This stipulation bears on the contingency of ontological responsibility, to be discussed shortly in the text. The contingency of ontological responsibility allows, with respect to the present example, that some member Z1 of {Z} might contain a z that is responsible for x existing or having F at t at Z1, even though y is responsible for x existing (or having F) at t at w. Without the present stipulation, the contingency thesis would undermine the informal characterization of ontological responsibility to which this note is appended.
As worded, this characterization implies that ontological responsibility is irreflexive, for it is clear that no concrete particular can exist (or have its intrinsic properties) if it is absent in the relevant sense. So any putatively fundamental concrete particular would fall under the ontological responsibility of itself (if that were allowed) and thus not be fundamental after all. However, there is at least conceptual room for two relations, reflexive ontological responsibility and irreflexive ontological responsibility, and I am happy to be neutral officially between them. The former would require the characterization of fundamental concrete particulars in the text to include ‘numerically distinct’ before the third occurrence of ‘concrete particulars’. I see no deep difference between these two relations that requires us to choose one for present purposes.
One might worry that this way of characterizing the ontologically fundamental concrete particulars rules out the view that the whole world is the sole fundamental particular. After all, the whole world would be different intrinsically if some one of its parts were made absent. But it is unclear that this result satisfies the asymmetry requirement of ontological responsibility because it is unclear whether the part in question would differ intrinsically if the whole world were made absent. And this in turn is unclear because it is unclear whether the absence of the whole world entails the absence (and thus a difference in intrinsic facts about) the part in question. I suspect that there may be an interesting challenge from these kinds of considerations for the theorist who thinks that the whole world is fundamental, but it is not a challenge that I will pursue here. Rather, I will assume hereafter that holding the whole world to be the sole fundamental concrete particular is consistent with the present framework of ontological responsibility.
See two footnotes up for reflexivity. The definitions that follow in the text are intentionally ambiguous between ontological responsibility for something’s existence and ontological responsibility for something’s having some intrinsic property. The relevant disambiguations tend to present themselves on a case-by-case basis.
One might worry that the absence criterion for ontological responsibility is consistent with models that violate asymmetry. For example, suppose the closest world to w in which either x or y is absent is one in which both x and y are absent. One response to this worry is to invoke Hume and deny any such model for concrete particulars. While I am partial to this response, there is a second, less controversial response available, namely, that the worry falsely presupposes that the formal property of asymmetry ought to follow from the absence criterion. The absence criterion is the basis for an informal characterization of ontological responsibility, not a formal definition.
Purity ensures that fundamental explanations involve only fundamental notions. Absoluteness ensures that fundamentality is not gradient. cf. Schaffer (2014).
Some versions of ontic structural realism entail that there are no concrete property instances at the fundamental level, only non-concrete relational structures. But that entailment is consistent with there being interesting questions about how to construct a fundamentality ordering for the property instances, even if each such instance depends on more fundamental facts about non-concrete relational structure.
Ascribing mereological structure to property instances does not break neutrality with respect to universal realism. Universal realists deny that universals have proper parts, but they need not deny that instances of universals have proper parts. Certain trope or states of affairs theorists may also bristle at talk of proper parts of property instances, but any seeming trouble here is terminological. Schemes for translating talk of parthood for tropes/states of affairs into talk of parthood among the relevantly related material objects are readily available (and required for bristling tropes/states of affairs theorists who want to defend tropes/states of affairs as the fundamental spatiotemporally located entities). However, detailing any such scheme here would prohibitively complicate exposition.
Ostrich nominalists may take exception to this claim, holding that MP just is P. But in general, property instances need not be material objects.
Both approaches have more or less direct ancestors that precede the work of the philosophers listed above, for example, Russell (1927) and Quine (1981) for MIN and Campbell (1990) for MAX, not to mention a wide range of precursors from the more distant history of the subject. The present interpretation of Sider’s approach is based on the ontology given at Sider (2011, 292), which explicitly describes the fundamental level of entities as including spacetime points. However, Sider’s view also allows for fundamental sets of points and thus does not require all fundamental property instances to be pointy. Moreover, Sider (2011, 133) claims that fundamentality per se does not require that anything be pointy, citing ways to account for point-excluding continuous qualitative variety so long as that variety matches the mereological structure. But it is far from clear that any such accounts are available for qualitative descent that “jumps” mereological levels or appears for the first time only at some low level. Such patterns are possible given mere infinite qualitative descent (see objection 4 below), which is crucially weaker than the infinite ideological descent dismissed in Sider (2011, 133). Qualitative descent does not entail that there is an infinite “descent” of fundamentality.
Notice that SC is merely a necessary constraint. It is compatible with, for example, rejecting modal notions like supervenience as definitive of fundamentality and opting instead for a primitive notion of naturalness.
That the present pro-gunk argument is novel is suggested in part by its omission from the interesting and wide-ranging critique of pro-gunk arguments in Sider (2013). Sider mentions arguments that accuse pointy entities of being conceptually incoherent, but not the argument by elimination from the metaphysics of properties. Sider does note that one might reject the thesis that I have been calling ‘Vanilla Mereology’.
I discuss this kind of example and some of its consequences further in Giberman (2014).
A proponent of MAX might wish to respond to this case by rejecting temporal parts. However, there are two reasons to doubt the utility of this response within the larger dialectic. First, having infinite extent is all that is needed to be a plausible candidate for being junky, so long as Unrestricted Composition is not upheld. And it is plausible, given a suitably liberal (even if restricted) composition principle, that there are actual property instances of infinite spatial length, area, or volume at some one time at the actual world. Second, Schaffer himself argues that temporal parts theory and priority monism (which entails that the actual world satisfies MAX) are co-members of the best available package of theses in the ontology of concreta (Schaffer 2009).
One might object further that this response neglects a way of relating mereology and topology that allows for entirely scattered regions: Arntzenius’s (2008) measure theoretic approach to atomless space. I would respond that the matter is not one of neglect but of appropriate omission. CON is a thesis about concrete property instances, not abstract regions. Arntzenius’s proof that his measure theoretically gunky space entails entirely scattered regions turns on an artifact of the mathematical formalism he deploys, a complete Boolean algebra, which requires an abstract null element (2008, 245. The proof relates to axioms given by Roeper (1997)). But there is no null concrete property instance. Indeed, there is no null concrete particular whatsoever. If we constrain our gunky space so that its regions are exclusively concrete, Arntzenius’s proof (ingenious as it is) is not applicable.
Alternatively, for any putative example of strong emergence X, one could offer an account of how to understand (or re-characterize the deep nature of) the properties at issue in X (as opposed to their locations) such that no non-supervening properties in fact have scattered instances in X. Perhaps no one at present (certainly not I) can do this in a fully satisfying way for quantum entanglement, but the strategy remains live from the perspective of fundamental ontology. One advantage of the strategy suggested in the main text over this alternative is that the former does not require the metaphysician to tell the physicist about the deep nature of physical properties.
That the connecting path should be the shortest one-dimensional path is a consequence of basic Ockhamism. Any longer or more voluminous path would be superfluous. That gunky concrete particulars may be located (though not exactly located) at less than three-dimensional spatial regions is argued for in Giberman (2012b).
In order to avoid requiring that the one-dimensional connecting path contains a part of the property instance, the definition of full connectedness above would need to be modified to quantify over locations of property instances instead of parts of property instances. The only controversy brought on by this modification that I can see concerns whether quantification over locations entails commitment to spacetime substantivalism. I doubt the entailment holds, but I will not try to decide the issue here.
A notable exception to standard trope theory is the MAX-friendly account developed in chapter 6 of Campbell (1990), which rejects thesis (ii) of standard trope theory by denying that fundamental tropes must be both simple and maximally determinate. Insofar as I understand the details of Campbell’s view, it is consistent with CON + SC.
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Acknowledgments
This essay has benefitted greatly from commentary on ancestor versions. I would like to thank Sam Cowling, Mark Crimmins, Anna-Sofia Maurin, Tom Ryckman, Alex Skiles, and several anonymous referees for their generous help in this regard. I am particularly grateful to John Perry and Jonathan Schaffer for very helpful discussions early in my thinking about this topic.
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Giberman, D. A topological theory of fundamental concrete particulars. Philos Stud 172, 2679–2704 (2015). https://doi.org/10.1007/s11098-014-0432-7
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DOI: https://doi.org/10.1007/s11098-014-0432-7