States of affairs of this kind can be thought of as the constituents of thick particulars. We could, if we wished, identify the snowball (the thick particular) with the combination of all the states of affairs that connect some underlying thing (a thin or bare particular) with some property.
A fact is a nexus or tie between one or more particulars and a property or universal. If a snowball is white, then there exists a single, simple thing (the tie or nexus) that connects the snowball (the particular) with whiteness (the property). This very nexus could not exist unless the snowball were in fact white. Hence, the mere existence of the nexus is sufficient to ground the truth of the sentence ‘The snowball is white.’ (A Totality Fact Maximalist version would posit nexuses that simultaneously connect some property with all of its instances.)
These different accounts of facts will naturally combine with the different accounts of particulars that we will take up in the next section. As a quick preview: Trope Theorists will naturally prefer to think of facts as tropes (option 1). Relational Ontologists will prefer to think of facts as nexuses (option 3), and Constituent Ontologists will think of them as states of affairs or thick particulars (option 2).
REALISM AND NEXUSES If we were to combine UP-Realism (7.1T.1T) with Classical Truthmaker Theory (2.1T), then we would have to suppose that whenever a particular P instantiates a universal U, there must be a truthmaker for the corresponding truth. If the U is the essence of P (something P could not exist without), then P itself could be the truthmaker, since the existence of P in that case would be sufficient for the truth that P instantiates U. However, if it is only an accidental truth that P instantiates U, that is, if it is possible that P exist but not instantiate U, then we would have to posit some further truthmaker for the instantiation relation's actually holding in this case. Such a truthmaker could be what has been called an ‘instantial tie’ or a ‘nexus’, an entity that connects the particular to the universal. Alternatively, the truthmaker could be a state of affairs, a whole that is composed of the P and U as parts.
There is one obvious drawback to positing the existence of nexuses or states of affairs. Adding a new sort of thing counts as a demerit of a theory, according to Ockham's Razor (PMeth 1.4). But there are three advantages to positing nexuses or states of affairs:
Positing nexuses or states of affairs makes UP-Realism consistent with Classical Truthmaker Theory in the case of accidental predications.
Positing nexuses or states of affairs provides us with entities that can serve as aspects of particular things, which in turn can serve as the relata of causation (as we will discuss in Chapter 27), as well as objects of perception and thought. (This advantage is less clear for Totality Fact Maximalists, since they may lack the local, atomic facts needed for causal connection.)
Nexuses or states of affair can also serve as the reference of possessive gerunds. For example, if Socrates is bald, then the gerund phrase ‘Socrates’ baldness' can be taken as a name of the nexus connecting the particular Socrates with the universal BALDNESS. However, Atomic Truthmaker Theory (2.1T.4) would provide such nexuses only for atomic gerunds, not for ontologically complex ones, like negations (‘Socrates’ not participating in the Assembly'), disjunctions (‘Socrates’ walking or running') or gerunds involving non-fundamental entities or properties.
In fact, nexuses or states of affairs play the very same three roles for Realists that modular tropes play for the Trope Nominalists (8.1T.4.1A). Nexuses have also been called ‘moments’, ‘modes’, or ‘individual accidents’.
ARE NEXUSES PARTICULARS OR UNIVERSALS? There are several reasons for thinking that nexuses must be particulars. First, it seems right to suppose that each nexus is intrinsically indiscernible from any other nexus. Hence, nexuses violate the Identity of Indiscernibles, the characteristic feature of particulars according to definition Def D5.1. Second, nexuses are not instantiated by anything. If a nexus were instantiated by the particular that it is tied to, then there would have to be a second nexus acting as the truthmaker of this instantiation, leading to an infinite regress of truthmakers. Finally, each nexus inherits its particularity from the particulars that it ties to universals, since otherwise it could not play the three roles mentioned above.
Since a nexus is a particular that does not itself instantiate any universals, it is what is called a ‘bare’ particular. Its being a bare particular does not mean that we cannot attribute any properties to it. We can certainly say that each nexus is a particular, that it is identical to itself and distinct from other things, that it is a truthmaker for some truth about instantiation, and that it figures in certain causal, perceptual, and epistemic facts. None of these properties require that the nexus instantiate any universals. Nexuses have no intrinsic character or intrinsic similarity to other nexuses that requires the existence of a universal as an explanation.
ARE STATES OF AFFAIRS PARTICULARS? Similarly, there are good reasons to think that states of affairs would have to be particulars. They are not instantiated by anything, and they inherit their particularity from their particular parts. If they didn't, they couldn't serve as the truthmaker for the claim that this particular instantiates that universal. In fact, some philosophers, such as David Armstrong, have suggested that all ordinary thick particulars are simply states of affairs.
IDENTITY CONDITIONS FOR NEXUSES AND STATES OF AFFAIRS If a nexus N is a tie between particular P and universal U, is it essentially so? Could the same nexus N become a tie between a different particular P2 and U or between P and a different universal U2? It would seem not, since if the nexus were transferable in this way, we would need to find a truthmaker for its connection with this or that particular or universal, leading again to an infinite regress of nexuses. If nexus N is a nexus between P and U, then it must be a matter of N's very essence that it be so.
For similar reasons, the constituents of a state of affairs must be essential to it. Otherwise, it could exist even though its actual constituents did not stand in the instantiation relation.
NEXUSES VS. STATES OF AFFAIRS If we do suppose that there are truthmakers for the connection between particulars and the universals they instantiate, should we suppose that the truthmakers are nexuses or states of affairs? The difference between the two lies in the fact that states of affairs are supposed to have particulars and universals as parts, while nexuses are simple entities that are supposed to be the connection between particulars and universals. Should we suppose that the particulars and universals are parts of the truthmaker, or is the truthmaker something disjoint from both of them that somehow ties one to the other?
There is a problem with the state-of-affairs model. If we suppose that for every pair of things, there is a whole that contains just the two of them as parts, then we will end up with far too many states of affairs. If some horse H exists, and the universal G exists that is instantiated by all and only galaxies, then there will be a whole composed of H+G, and this whole will be the state of affairs of H's being a galaxy! We clearly don't want that. We have two options. (1) Suppose that in such cases, there is no whole composed of H+G (i.e., that wholes composed of particulars and universals exist only when the particular instantiates the universal). (2) Suppose that the whole H+G exists, but it isn't an actual state of affairs. In the second case, we would need something to be the truthmaker for the truth that some particular-universal composite is an actual state of affairs, which would force us to introduce nexuses. So, believers in states of affairs must take the first option.1
9.3 Substances
In this section, we will develop a taxonomy of theories of substance. To make our way toward this taxonomy, we must first get on the table an intuitive understanding of what we're talking about when we talk about substances, an understanding toward which we've merely gestured to this point. And the best way to do this is by example. Substances include naturally occurring inanimate objects like rocks and clouds, living things from viruses to trees to lizards to cats to human beings to angel
s to God, and artifacts like tables, stereos, and skyscrapers. So by ‘substances’ we here have in mind, more or less, the ordinary objects of everyday experience. What we're up to here is trying to understand the metaphysical makeup, if you will, of these ordinary objects.
Substances, unlike other particulars such as simple states of affairs and (if there are any) tropes, are thickly charactered. That is, substances have multiple features, multiple dimensions of character. A table is not just made of wood—it also has a definite size, mass, and shape.
One note before we get started. For the remainder of this section, we will be setting the trope-free or Extreme varieties of Nominalism (like Extreme Resemblance Nominalism) aside. The reason for this is simple: the fundamental question that will drive us concerns how substances relate to the things that ground their character. Since Extreme Nominalists don't think that anything grounds the character of substances, there's really no issue here to deal with.
So we assume that there are properties that ground character and begin with a question. Are properties constituents of substances? This question results in a bifurcation of theories of substance into Relational and Constituent Ontologies:
9.1A Relational Ontology. Instantiation is a fundamental relation between substances and properties, and instantiation is not a case of the part-whole relation.
9.1T Constituent Ontology. When a substance instantiates a property, the instantiation relation between the two consists in the fact that the property is a part of the substance.
The first thing to notice about the two approaches is that Constituent Ontology has a significant advantage in terms of qualitative simplicity over Relational Ontology (see PMeth 1.4). Relational Ontologists must posit a special relation of instantiation holding between substances and properties in addition to the part-whole or parthood relation. Constituent Ontologists, in contrast, can make do with just one relation, parthood. For Constituent Ontologists, instantiation can be defined in terms of parthood. For a substance to have a property is for it to have the property as a part. Relational Ontologists must argue that instantiation is irreducible and primitive.
We examine these two approaches to substance in turn.
9.3.1 Relational Ontology
Relational Ontology requires that substances and properties stand in the fundamental relation of instantiation. As a result, Relational Ontology cannot analyze properties in terms of substances and thus demands that Extreme Nominalism is false. Similarly, Relational Ontology precludes analyzing substances in terms of properties and thus entails that there are fundamental properties and fundamental particulars. Therefore, if Relational Ontology is true, then so is either UP-Realism or something like UP-Realism with tropes instead of universals.
If one is a Relational Ontologist who embraces UP-Realism and rejects Trope Theory, endorsing Classical UP-Realism (8.2A.2), then one is a Classical Relational Realist:
9.1A.1T Classical Relational Realism: Relational Ontology and Classical UP-Realism are both true.
On the other hand, if one embraces Trope Theory, then one is a Trope Relational Ontologist:
9.1A.1A Trope Relational Ontology: Relational Ontology and Trope Theory are both true.
As we have seen, tropes can be thought of as modifying tropes or modular tropes. Trope Relational Ontologists must choose between these two conceptions. Thinking of tropes as modular tropes (recall that modular tropes have the character they ground) is uncomfortable for the Relational Ontologist because Relational Ontology requires that instantiation be a fundamental relation between substances and properties. Regardless whether tropes instantiate the character they ground, Relational Ontologists must insist that substances instantiate properties. This means that if tropes are modular, whenever a substance has some type of character, two things turn out to have the character: the substance and the modular trope that grounds the character in the substance. There is duplication of character if both Relational Ontology and Modular Trope Theory (8.2T.1A) are true.
Therefore, Trope Relational Ontologists ought to think of tropes as modifying tropes. Here we arrive at the central problem for Modifying Trope Theory (8.2T.1T), namely that given the presence of fundamental particulars, modifying tropes wind up seeming an awful lot like universals. Indeed, Modifying Trope Relational Ontology turns out to be a quantitatively bloated Classical Relational Realism. Why is this the case?
Modifying tropes, recall, do not have the character they ground, and this means that modifying tropes only have what we might call ‘formal’ character. Modifier tropes only have features like being a trope, being a property, and being self-identical. If tropes only have formal character, though, it is difficult to see why they can be instantiated by just one thing.
To press this point, consider this question. What underwrites the claim that tropes are numerically distinct? A standard answer is tropes are distinct in virtue of occupying different spatiotemporal locations. That tropes are spatiotemporally isolated then goes to explain why it is that a trope can only be instantiated by one thing. For if a trope were instantiated twice or more, it would have to be in more than one place at once. This is impossible on the view that spatiotemporal location individuates tropes. The trouble with the spatiotemporal individuation of tropes is that it runs afoul of a plausible thickening principle (see Section 8.2.2 for the initial discussion of these principles):
Location Thickening. If something is located, then it has a definite size and shape.
Location Thickening creates a problem for modifying tropes, since they are meant to have only formal character. Location Thickening, given spatiotemporal individuation, entails that modifying tropes have some size or other, and size properties are not formal properties. Likewise for shape. (Importantly, Location Thickening does not require that the size of a thing be more than point-sized. For example, a trope might have a size of zero cubic meters.) This tension puts pressure on Trope Theorists to adopt a different view of the individuation of tropes, and it is hard to see how there is space for anything but insisting that tropes are primitively distinct. This, however, looks to be no more than merely stipulating that tropes are not like universals in being shareable. What is being gained by this stipulation?
If modifying tropes are potentially shareable, then they are no different from universals. Even if there were multiple rednesses, as Trope Theory claims, this would just be like the Realist claiming that there are multiple REDNESS universals. Modifier Trope Theory, therefore, just posits many things of exactly the same sort that the Realist posits. This quantitative cost comes with no added explanatory power, and so by Ockham's Razor (PMeth 1), should not be embraced. Trope Relational Ontology, if tropes are modifiers, is only quantitatively bloated Classical Relational Realism.
Trope Relational Ontologists have one line of defense that is worth considering, however. The task they face is that of differentiating modifying tropes from universals. Here is one way in which they might differ: some modifying tropes might be modified by other modifying tropes. For example, suppose that the property of being a living human being is a modifying trope (something like Aristotle's conception of a soul, pneuma in Greek). This soul-trope might itself be modified by other properties, such as properties ascribing various sensory and intellectual states to the soul. Similarly, there might be spatial quantity tropes, that correspond to volume and shape, and these spatial tropes might themselves be modified by various quality tropes, like color, mass density, charge, or temperature. Schlolastic philosophers, following Aristotle's lead, took spatial (extensive) quantity to be the first of a substance's accidents (changeable, non-essential properties), with other accidents inhering in quantity. This sort of account is not available to the Realists, since they cannot suppose that universals (like HUMANITY) are modified when their instances take on new qualities.
Nonetheless, Classical Relational Realism is a quite plausible understanding of Relational Ontology. On this view, universals ground the character of substances, and instantiation is
a fundamental relation between substances and universals. In fact, this is the only type of Relational Ontology that has been defended in the literature. However, it faces a serious and well-known challenge, the Extrinsicality Objection.
9.3.1.1 The Extrinsicality Objection.
Classical Relational Realists propose that a substance's having some character consists in its standing in a certain fundamental relation to a universal. However, a substance's having character is an intrinsic feature of that thing (something to do with that thing, and that thing alone), whereas standing in a relation to some further entity (like a universal) is a paradigm of an extrinsic feature (something to do not just with that thing and its parts, but with that thing and something else). Classical Relational Realism, therefore, mistakes something intrinsic to a substance for something extrinsic to it.
What does it mean for a property to be intrinsic to a substance? Here is an answer that we introduced in Chapter 2:
Def D2.3 Intrinsicality. x is intrinsically F if and only if nothing that is not x or a part of x is part of the ground of x's being F.
According to Relational Ontology, x's being F is always a matter of x's standing in the instantiation relation to the universal F, which is not part of x. Thus, it is hard to see how any substance can have a property intrinsically on this account.
The Atlas of Reality Page 29
