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Aquinas’s Ontology of the Material WorldChange, Hylomorphism, and Material Objects$

Jeffrey E. Brower

Print publication date: 2014

Print ISBN-13: 9780198714293

Published to Oxford Scholarship Online: October 2014

DOI: 10.1093/acprof:oso/9780198714293.001.0001

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Substantial vs. Accidental Change

Substantial vs. Accidental Change

Chapter:
(p.74) 4 Substantial vs. Accidental Change
Source:
Aquinas’s Ontology of the Material World
Author(s):

Jeffrey E. Brower

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198714293.003.0004

Abstract and Keywords

This chapter examines Aquinas’s specific account of the two main subtypes or categories in terms of which all generation and corruption are to be understood—namely, substantial vs. accidental change. In addition to filling out the functional hylomorphism associated with Aquinas’s general account of change, this chapter highlights two important commitments of Aquinas’s views that his commentators have yet to appreciate—namely, (1) that hylomorphic compounds are best understood as concrete states of affairs or facts, and (2) that distinct hylomorphic compounds can bear to one another a form of numerical sameness that falls short of identity.

Keywords:   substantial change, accidental change, prime matter, substantial form, material substance, accidental form, accidental unity, numerical sameness without identity, functional hylomorphism

In Chapter 3, I presented Aquinas’s general account of change as generation and corruption and explored its hylomorphic implications. In this chapter, I fill out Aquinas’s views about change and hylomorphism by examining his specific account of the two main subtypes or categories in terms of which all generation and corruption are to be understood—namely, substantial and accidental change.

As we have seen, Aquinas’s general account of change captures two intuitions associated with our pre-theoretical understanding of the world: first, that change involves a subject that endures the change (i.e., some matter or substratum); and second, that change involves something with respect to which this enduring subject is changed (i.e., some forms or properties). As will become clear shortly, his specific account of change captures some further intuitions about the types of change that occur in the world—namely, that some of these changes involve pre-existing substances, whereas others involve the generation and corruption of substances themselves.

Despite the intuitive basis of Aquinas’s specific account of change, it raises some serious difficulties or puzzles. Although Aquinas does not explicitly deal with these puzzles in the specific form that I shall present them, it is not hard to reconstruct his solutions to them. Moreover, these reconstructions are worth considering because they serve to highlight two of the most important aspects of his hylomorphism: first, that hylomorphic compounds are best understood as substratum-property complexes (i.e., as concrete rather than abstract states of affairs);1 and second, that distinct hylomorphic compounds can be one and the same material object, and hence bear to one another a form of numerical sameness that falls short of identity.2

(p.75) 4.1 Two Types of Change

In discussing Aquinas’s general account of change in Chapter 3, we focused on a single example—that in which a statue is generated from a spherical lump of bronze—though we also had occasion briefly to discuss one other example—that in which a human being comes to be white. Although Aquinas thinks that both examples can be used to illustrate the nature of change in general, he also thinks we must be careful not to focus exclusively on them. Otherwise, we might be led (as I think contemporary philosophers often are) to associate a feature distinctive of one specific type of change with the nature of change in general.3

Let us consider, therefore, a third example that Aquinas habitually appeals to in the context of change—namely, one involving the generation of a human being from sperm and menstrual blood (or, as we now know better, sperm and ovum). Like other examples of change, Aquinas conceives of this one in terms of matter successively taking on distinct and incompatible forms, and thereby entering into distinct hylomorphic compounds.4 Even so, he recognizes that this example is importantly different from the previous two. For this example involves the generation of a substance—that is, a concrete individual falling under some natural kind (in this case, human being). By contrast, neither of the previous examples involved the generation of any substances. On the contrary, they both presupposed the existence of a single substance throughout (namely, a lump of bronze or a human being) which merely changes with respect to one of its contingent properties or accidents (namely, shape or color). For obvious reasons, Aquinas refers to the type of change involved in the generation of a human being as ‘substantial change’ (generatio simpliciter vel motus ad formam substantialem), whereas he refers to that involved in the other two examples as ‘accidental change’ (generatio secundum quid vel motus ad formam accidentalem).5

In order to account for the intuitive difference between substantial and accidental change, Aquinas appeals to the different ways in which matter functions in each. Speaking once again of matter in terms of potentiality, he says:

Something can be in potentiality with respect to two kinds of being [namely, substantial and accidental being]. One sort of thing is in potentiality with respect to being human (for example, (p.76) sperm and menstrual blood), whereas another sort of thing is in potentiality with respect to being white (for example, a human being). Now both that which is in potentiality with respect to substantial being and that which is in potentiality with respect to accidental being can be called ‘matter’ (as sperm [and menstrual blood] is called ‘the matter of a human being’ and a human being is called ‘the matter of a white thing’). But they differ in this: the matter that is in potentiality with respect to substantial being is called the ‘matter from which’ [something comes to be], whereas the matter that is in potentiality with respect to accidental being is called the ‘matter in which’ [something comes to be]. (DPN 1.9–19)

Here Aquinas signals the difference between substantial and accidental change by calling attention to a difference in the specific way that matter functions in each. In substantial change, it functions as “matter from which” something comes to be (materia ex qua), whereas in accidental change, it functions as “matter in which” something comes to be (materia in qua). What these differences come to can best be seen from Aquinas’s own examples.

Consider first Aquinas’s example of substantial change—the generation of a human being. Like any other example of change, this one involves some matter—that is, something that endures the change by taking on a form or property it previously lacked (in this case, we can call the relevant form or property ‘humanity’).6 Even so, Aquinas thinks, it makes no sense to speak of the matter in this case as becoming human. As he explains elsewhere:

When a human comes to be, we can truly say not only that it previously was not human, but also that it previously was not (full stop). (In Phys. 1.12.10)

Every case of generation involves matter “from which” something comes to be. And the generation of a human being is no exception in this regard. Even so, Aquinas tells us here, when a human being comes to be, we cannot speak of its matter—or indeed of anything else that previously existed—as coming to be human. And the reason for this is straightforward. Whatever is human, he thinks, is human essentially. Evidently, therefore, if something is human at any time of its existence, it must be human at all times of its existence.7 For the same reason, the matter that exists prior to the generation of a human being cannot be that “in which” the human being comes to be. Since nothing can go from being non-human to human or vice versa, such matter must be merely that “from which” the human comes to be. And, of (p.77) course, the point applies not just to the generation of human beings, but to substantial change more generally.

We can express the point that Aquinas is making here a bit more clearly if we draw a distinction between property possession and property characterization. Every change involves some matter that possesses different forms or properties at different times. Even so, Aquinas wants to say, the matter for substantial change is not characterized by the forms or properties it possesses at these different times—where the notion of characterization can be expressed at least partially as follows:8

Of course, all of this raises an obvious question: What exactly is the matter for a substantial change? That is to say, what sort of matter can possess a form (such as humanity) without being characterized by it? The answer, as we’ll see shortly, is prime matter.9

Aquinas’s commitment to distinguishing property possession from property characterization raises a serious difficulty for his account of substantial change. We will return to this difficulty in §4.3. But first let us continue with Aquinas’s own development of the contrast between the different sorts of matter involved in substantial and accidental change. For there are a number of important hylomorphic implications that follow from it.

As we have seen, in the case of a substantial change by which a human being is generated, it makes no sense to speak of the matter as coming to be characterized by the form or property it takes on. To repeat, humanity is not a type of form or property that can characterize its subject accidentally or contingently. Notice, however, that there is no such obstacle to speaking in this way in the case of an accidental change by which a human being comes to be white. Unlike humanity, whiteness is a type of form that can characterize its subject contingently. Indeed, in the case of such (p.78) an accidental change, we would appear to have no choice but to claim that the matter or subject of such a change comes to be characterized by the forms it successively takes on. For, evidently, to speak of the generation of a white human being, say in the particular case of Socrates, just is to speak of Socrates himself coming to be white. And likewise for other such changes. It is, I think, precisely for this reason that Aquinas contrasts the matter of a substantial change with that of an accidental change by saying that the former is merely that “from which” something comes to be, whereas the latter is that “in which” something comes to be.

As the foregoing helps to make clear, Aquinas thinks there are two different ways of specifying the functional role associated with matter in the context of change. Insofar as every change involves an enduring subject, it will involve something playing what we can think of as the generic matter role. But insofar as a given change is substantial or accidental, its matter will also play one of two more specific functional roles, depending on whether or not it can be characterized by the new forms it takes on. If it cannot be so characterized, it will function as what we might call a ‘mere subject of endurance’, whereas if it can be so characterized, it will function as what we might call a ‘subject of characterization’. For the sake of clarity, let us set out these notions and their relationship to one another more precisely as follows:

As it turns out, these definitions not only clarify the different types of subject involved in substantial and accidental change, but also provide us with all we need to make precise Aquinas’s understanding of the different types of change themselves, as well as their relationship to his account of change in general. Thus, drawing on these definitions, we can express Aquinas’s understanding of accidental change, in which matter functions not only as a subject of endurance, but also as a subject of characterization, by simply adding a fourth condition to our earlier statement of his account of change in general: (p.79)

The first three conditions guarantee that the matter involved in accidental change functions as a subject of endurance, whereas the fourth condition guarantees that it also functions as a subject of characterization.10

As for substantial change, it is just like accidental change, except that it fails the final “subject of characterization” condition. Hence, we can express Aquinas’s understanding of it by saying that it satisfies his general account but is not accidental (and so involves matter functioning as a mere subject of endurance):

As the statement of these two definitions is intended to show, Aquinas takes the distinction between substantial and accidental change to provide an exclusive and exhaustive division of the possible types of generation and corruption. That is to say, he thinks every case of generation and corruption belongs to one of these two types, but none belongs to more than one. Taken together, therefore, substantial and (p.80) accidental change provide us with the two main subtypes or categories in terms of which change in general is to be understood.11

4.2 Functional Hylomorphism Revisited

Now as Aquinas recognizes, his specific account of substantial and accidental change has important implications for his hylomorphism. Indeed, as he sees it, this account requires us to distinguish two different types of matter, form, and compound. Thus, immediately after distinguishing the two specific roles that matter can play in change (namely, “that from which” vs. “that in which” something comes to be), he goes on to say:

Properly speaking, that which is in potentiality with respect to substantial being is called ‘prime matter’, whereas that which is in potentiality with respect to accidental being is called ‘a subject’. (DPN 1.20–24)

Prime matter, Aquinas tells us here, is what plays the role of matter in substantial change—that is to say, it is the matter that endures the generation (or corruption) of substances and, hence, functions as “that from which” they come to be (or pass away). As its name suggests, moreover, prime matter is taken by Aquinas to be matter in the primary or proper sense of the term. For the same reason, he often refers to prime matter simply as ‘matter’.12

Unlike matter in the primary or proper sense, Aquinas thinks that what plays the role of matter in accidental change—that is, the matter that functions as “that in which” something comes to be—is something that qualifies as matter only in a secondary or derivative sense. Indeed, we have just seen that he refers to the matter of an accidental change simply as the ‘subject’ of such a change. We shall see later that Aquinas has good reason for wanting to avoid the use of ‘matter’ in this context.13 For now, however, let us simply note what he says about the use of ‘subject’ here:

It is significant that what is in potentiality with respect to accidental being is called ‘a subject’, for we say that an accident [i.e., an accidental form] is in a subject, whereas we do not say of a substantial form that it is in a subject [but in matter]…although we sometimes use one term in place of the other—that is, ‘matter’ for ‘subject’ and vice versa. (DPN 1.24–35)

As this passage makes clear, when Aquinas uses the term ‘subject’ to refer to the matter of an accidental change, he has in mind the specific way in which matter (p.81) functions in accidental change—namely, as a subject of characterization. No doubt Aquinas expects this sense of ‘subject’ to be the one uppermost in the minds of his readers, given their familiarity with Aristotle’s Categories. For in this work, Aristotle famously describes accidents as “in a subject” (1a25), where it is clear that accidents characterize the subjects in which they inhere.

As Aquinas immediately goes on to point out, however, he also recognizes a broader sense of ‘subject’ according to which “we sometimes use…‘matter’ for ‘subject’ and vice versa”. When he uses the term ‘subject’ in this broad sense, he has in mind the generic way in which matter functions in change—namely, as a subject of endurance. To avoid complications arising from Aquinas’s different notions of subject, I shall hereafter use the terms ‘prime matter’ and ‘secondary matter’ to refer to the beings or entities that play the specific functional roles associated with matter.

In addition to distinguishing two different types of matter (or subjects) for change, Aquinas also draws a parallel distinction between two different types of form corresponding to them. Thus, in the passage just quoted, he introduces the term ‘substantial form’ (forma substantialis) to refer to the type of form possessed by prime matter (or mere subjects of endurance), and hence involved in substantial change. And he introduces the term ‘accidental form’ (forma accidentalis) or ‘accident’ (accidens) to refer to the type of form possessed by secondary matter (or subjects of characterization), and hence involved in accidental change.

Finally, as Aquinas tells us elsewhere, the distinction between these two types of matter and form brings with it a further distinction—that between two different types of hylomorphic compound. On the one hand, there is the type of compound that exists in virtue of some prime matter possessing a substantial form—what he calls a ‘material substance’ (substantia materialis) or ‘composite substance’ (substantia composita). On the other hand, there is the type of compound that exists in virtue of some secondary matter possessing some accident—what he calls an ‘accidental unity’ (unum per accidens) or ‘accidental being’ (ens per accidens) or sometimes simply ‘accident’ (accidens).14

In short, Aquinas’s specific account of change leads him to further specify the sort of functional hylomorphism introduced by his general account. For the sake of completeness, we can set out these further specifications more precisely as follows: (p.82)

In Chapter 3 (§3.2) we saw that Aquinas’s general account of change has some important realist implications—namely, that change in general is to be explained by appeal to matter, form, and compound (where these are understood as three distinct types of being). As we can now see, something similar is true of Aquinas’s specific account of change. Indeed, according to the latter account, specific types of change are to be explained by appeal to specific types of matter, form, and compound (again, understood as distinct types of being). Thus, substantial change is to be explained by appeal to prime matter, substantial forms, and material substances, whereas accidental change is to be explained by appeal to secondary matter, accidental forms, and accidental unities.

It seems to me that Aquinas’s commentators have not always appreciated the force of these realist implications, especially when it comes to his views about prime matter and accidental unities. It is important to emphasize, therefore, that just as Aquinas’s realism about matter (or enduring substrata) is an immediate consequence of his general account of change, so too his realism about prime matter (or enduring substrata for substantial change) is an immediate consequence of his specific account of change. Again, just as his realism about hylomorphic compounds (including his commitment to postulating distinct compounds to serve as the termini for every change) is an immediate consequence of his general account of change, so too his realism about accidental unities (including his commitment to postulating distinct accidental unities to serve as the termini for every accidental change) is an immediate consequence of his specific account of change.15

(p.83) As the definitions just given are intended to show, the different types of matter, form, and compound associated with Aquinas’s specific account of change are to be understood in primarily functional (rather than categorial) terms. In this respect, these definitions are like those required by his general account of change (§3.3). That is to say, they pick out their referents via certain metaphysical roles or functions played in change. Although these definitions leave open the possibility of more than one type of being playing the roles associated with different types of matter, form, and compound, Aquinas thinks that the roles themselves place some significant ontological constraints on the types of being that can play them. This is perhaps clearest in the case of his two specific types of matter—namely, primary and secondary matter.

Consider first the case of secondary matter. According to the aforementioned definition, anything capable of undergoing accidental change, and hence taking on an accidental form or property, can qualify as matter in this sense. Following Aristotle, however, Aquinas repeatedly insists that only substances are capable of possessing accidents, and hence of undergoing changes of the type in question.16 The precise reason for Aquinas’s insistence in this regard is not altogether clear, though it is no doubt connected with the correlativity of the notions of substance and accident. In any case, it clearly follows from such insistence that substances are the only type of being that can play the role associated with secondary matter—and this is, of course, a significant ontological constraint.17

What about prime matter? To clarify the ontological constraints on what can play the relevant role here requires a bit more development. To begin, note that Aquinas sometimes speaks as if the role of prime matter, like that of secondary matter, could be played by substances. Indeed, in the early parts of the De principiis, he speaks as if sperm and menstrual blood (both substances, on his view) not only can function as prime matter in the generation of human beings, but actually do so function.18 But this way of speaking is misleading. For, as we have seen, prime matter is supposed to be that which endures the generation and corruption of substances.19 But neither sperm nor menstrual blood endures the generation of a human; on the contrary, they (p.84) are both corrupted in the course of such a change. Clearly, then, sperm and menstrual blood are not functioning as prime matter in the generation of a substance.

But if that is true, why does Aquinas speak in such a misleading way? The answer, it turns out, has to do with limitations of ordinary language. To see this, note first what Aquinas says about the way in which we ordinarily refer to the matter of a given change:

Sometimes we refer to matter together with a privation, but other times we refer to matter without privation. For example, when we use ‘bronze’ for the matter of a statue, this does not imply privation: for when I call something ‘bronze’, no lack of shape or arrangement is understood. By contrast, ‘flour’ does imply the privation of the form of bread: for when I call something ‘flour’, this brings to mind the sort of shapelessness or lack of arrangement required by the form of bread. Now, what endures (permanet) the process of generation is the matter or subject, not the privation or even what is composed of matter and privation. The matter that endures, therefore, does not imply privation, whereas matter that implies privation is [merely] transient. (DPN 2.57–69)

As Aquinas tells us here, some of the terms we use to refer to matter are bound up with the notion of privation (or lack of a specific form). This is true of ‘flour’, used to refer to the matter involved in the generation of some bread, and it would also appear to be true of ‘sperm and menstrual blood’, used to refer to the matter involved in the generation of some human being. In each case, Aquinas seems to think that the terms in question succeed in referring to matter that is capable of enduring the change, but only insofar as that matter lacks the form that serves as the terminus for the change. Thus, the meaning of ‘flour’ excludes the possession of the form of bread, and the meaning of ‘sperm and menstrual blood’ excludes the possession of the form of humanity.

What is interesting about these two cases, and indeed about the case of substantial change generally, is that we lack terms for picking out the relevant matter without recourse to privative expressions. Unlike the case of ‘bronze’, we have no way in ordinary language to refer either to the matter that endures the generation of bread or to the matter that endures the generation of a human being. Thus, if we want to single out such matter for discussion, we must begin by using expressions in ordinary language privatively and then attempt to clarify our meaning from there. At some point, of course, it will be useful to introduce a new term into our language (or stipulate a new use of an old term) that refers to such matter non-privatively. This, in effect, is what Aquinas does with the term ‘prime matter’. Indeed, as he goes on to point out, in the text immediately following the passage just quoted, once we have such a term in hand we can begin to appreciate what a special nature this matter must have:

It must be known that some matter—for example, bronze—is composed of [matter and] form. For even though bronze is matter in respect of a statue, it is itself composed of matter and form. Now because bronze has matter [and form], it is not called ‘prime matter’. On the contrary, only that matter which is understood without any form or privation, or rather underlies all (p.85) forms and privations, is called ‘prime matter’. For only it has no other matter [and form] before it. And such matter is also called hyle. (DPN 2.70–78)

As Aquinas suggests here, if we want to refer to the sort of matter involved in substantial change non-privatively, we can do so by introducing the technical term ‘prime matter’ (or by stipulating a technical use of the Greek term hyle). It is clear, moreover, that he thinks that what we thereby succeed in picking out is a being of an ontologically distinctive type. And this, of course, brings us back to the issue of the ontological constraints on what can play the role of prime matter.

Insofar as prime matter is understood functionally, as that which survives the generation and corruption of ordinary substances, it cannot itself be an ordinary substance. But neither can it be any sort of form or privation. On the contrary, Aquinas tells us, it must be that which ultimately “underlies all forms and privations”. What is more, he takes this line of reasoning to be what lies behind Aristotle’s famous description of prime matter in Metaphysics 7 as “neither a what, nor a quality, nor any of the other categories by which being is divided or determined”:

The Philosopher here accepts the account of matter that he had established in the Physics, saying: “I claim that matter considered in itself”—that is, in accordance with its essence—“is neither a what”—that is, neither a substance—“nor a quality, nor any of the other categories by which being is divided or determined.” (In Meta. 7.2.1285)20

I will have more to say about Aquinas’s conception of prime matter in the next chapter (esp. §§5.4–5). But insofar as he approves here of Aristotle’s famous description, it should already be clear that he is assuming that only a being of a very special type can play the role associated with prime matter.21

As all of this goes to show, Aquinas’s specific account of change places some significant constraints on the types of being that can satisfy both of his specific notions of matter (namely, primary and secondary matter). Aquinas doesn’t explicitly identify any similar constraints on his specific notions of form (namely, substantial and accidental form) or on his specific notions of compound (namely, material substance and accidental unity). Even so, we would expect there to be some. After all, we’d expect the distinction between the different types of form and compound to reflect some important ontological differences, given the way they are defined. For substantial forms and material substances are both defined by their relation to prime matter, whereas accidental forms and unities are both defined by (p.86) their relation to substances. What is more, in the case of Aquinas’s specific notions of compound, there is a further reason to expect ontological differences in what satisfies them—namely, that material substances and accidental unities appear in many cases to belong to very different ontological categories.22

4.3 A Puzzle about Substantial Change

By now the basic contours of Aquinas’s distinction between substantial and accidental change should be clear. There are, however, some serious difficulties that can be raised for his understanding of both types of change. Since these difficulties bear on Aquinas’s theory of change as a whole, as well as on its hylomorphic implications, it is worth examining them in some detail. I begin in this section with a puzzle about substantial change, and then turn in the next section to a related puzzle about accidental change.

As we have seen, Aquinas’s account of substantial change requires the existence of prime matter, where this is to be understood as a mere subject of endurance—that is to say, a being that can successively take on distinct forms or properties without being characterized by them. But the very idea of a mere subject of endurance seems problematic. To see why, consider again the functional nature of forms or properties, as Aquinas is conceiving of them. Whatever else is true of forms or properties, they would appear to be essentially such as to characterize their possessors. Indeed, this would appear to be a straightforward consequence of Aquinas’s general account of change. For according to it, forms or properties—say, sphericity and statuehood—just are those beings (whatever they are in themselves) that account for the difference involved in change—say, the fact that our lump is a sphere at one time and a statue at another. But, then, if forms are essentially such as to characterize their possessors, the possibility of a mere subject of endurance (and hence of prime matter as Aquinas is conceiving of it) would seem to be ruled out. In short, Aquinas’s views appear to commit him to the following three claims, the conjunction of which yields an inconsistent triad:

(p.87) As it turns out, Aquinas has a straightforward way of resolving this puzzle—namely, by rejecting the third claim. In order to see how he can coherently do this, it must be recognized that the plausibility of the claim itself owes to a specific conception of forms or properties—or better, to a specific conception of form or property possession. According to this conception, forms or properties are wholly distinct or “separate” from the subjects that possess them. For convenience, let us refer to this as the Platonic conception of forms and let us refer to the relation of form or property possession associated with it as exemplification or participation.23 On this conception, if Socrates is human or white, this is because he exemplifies (or participates in) humanity or whiteness.24 As this example helps to illustrate, there is no room on the Platonic conception for a distinction between property possession and property characterization. On the contrary, for a subject to be characterized by a property just is for it to possess the property in question. For future reference, we can summarize the most important features of the Platonic conception as follows:

Obviously, if we consider our puzzle about substantial change in the context of this particular conception, there is no way to make sense of the idea of mere subjects of characterization. But this is not the only possible conception of form or property possession available. On the contrary, there is another conception, which for the sake of contrast we can call the Aristotelian conception. According to this further conception, form or property possession is to be understood, in the first place, in terms of constituency rather than exemplification—that is to say, in terms of a relation that holds between a complex whole and one of its constituent parts. On this conception, if Socrates is human or white, it is because he possesses humanity or whiteness as a proper part or constituent.25 As this example helps to illustrate, on the Aristotelian (p.88) conception, forms or properties are conceived of as “immanent to” (rather than “separate from”) their subjects of characterization.

So far so good. But there is a further wrinkle. According to the Aristotelian conception, whenever a complex whole possesses a form or property as a constituent, and hence is characterized by it, that same whole will also possess a constituent of another type. Thus, in order to explain how Socrates is human, Aristotelians appeal not only to Socrates and his constituent humanity, but also to a further constituent—some matter or substratum—to which Socrates’s humanity can also be said to belong (though in a different sense). Indeed, proponents of the Aristotelian conception typically think that it is precisely because there is some matter or substratum possessing the form of humanity (in its distinctive way) that there exists a substance (Socrates) which both has humanity as a constituent and is characterized by it.26

This appeal to a further type of property possession—one that holds between matter (or substrata) on the one hand, and forms (or properties) on the other—is perhaps what makes the Aristotelian conception most distinctive. Aristotelians often speak of this relation in terms of predication or instantiation.27 But since this might suggest that matter is itself characterized by the forms or properties it possesses, I shall follow Aquinas in speaking of this relation in terms of inherence instead.

With this terminology in hand, we can summarize the most important features of the Aristotelian conception as follows:

As this summary helps to bring out, Aristotelians differ from Platonists both in the number of beings and in the number of relations that they appeal to in their conception of property possession. Thus, Platonists appeal to just two beings (a subject and a property) and one relation (exemplification, which links things wholly distinct from one another). By contrast, Aristotelians appeal to three beings (a complex, a property, and a (p.89) substratum) and two relations (constituency and inherence, the former of which links complexes with their proper parts or constituents, and the latter of which links distinct parts of a common whole).

For the sake of clarity, let us illustrate these differences with respect to a particular example of property possession. Consider, therefore, the diagram at Fig. 4.1, which represents the different ways in which Platonists and Aristotelians conceive of Socrates’s being human (using circles to stand for Socrates, rectangles to stand for properties and substrata, and spatial relations to indicate the presence or lack of constituency).

As this diagram indicates, Platonists and Aristotelians differ not only in the number of beings and relations they appeal to, but also in their understanding of characterization. Thus, whereas Platonists associate characterization with property possession as such, Aristotelians associate it with only one type of property possession—namely, constituency.

Now it might be objected that, in separating inherence from characterization, Aristotelians have made it impossible for us to have any clear grasp of inherence as a type of property possession. It seems to me, however, that this objection is mistaken. For at least as Aquinas is conceiving of inherence, it is simply that relation which links subjects of endurance—or the substrata involved in change—to the forms or properties with respect to which they change.28 Granted, it is initially tempting to assume that if something changes with respect to some forms or properties, it must

Substantial vs. Accidental Change

Figure 4.1 Ordinary Property Possession: Socrates’s Being Human

(p.90) also be characterized by the forms or properties with respect to which it changes. But as our earlier discussion of substantial change indicates, this is not in fact the case. Indeed, if we’re going to preserve the possibility that substances themselves can be generated and corrupted—something taken for granted by our pre-theoretical view of the world—then it would seem that we must distinguish subjects of endurance from subjects of characterization.

If we return to our puzzle about substantial change with the Aristotelian conception of forms in mind, we can see that there is no longer any obstacle to rejecting the third member of the inconsistent triad. For although forms or properties, on this conception, are essentially such as to characterize certain of their possessors—namely, the compounds (or complexes) of which they are a part—this is perfectly consistent with their also having possessors that qualify as mere subjects of endurance. In fact, as we can now see, mere subjects of endurance are best understood in terms of mere subjects of inherence—that is to say, subjects having properties that inhere in but do not characterize them. And, of course, this is precisely the sort of subject that the Aristotelian conception makes possible.

The question, of course, is whether Aquinas accepts the Aristotelian conception of forms. There can, I think, be little doubt that he does. For one thing, this conception appears to be required by his repeated insistence, both in the context of change and elsewhere, that hylomorphic compounds are genuinely complex—that is to say, entities that literally possess their matter and form as proper parts or constituents. To cite just two of the clearest examples of such insistence from the De principiis naturae:

Matter and form are said to be intrinsic to a thing because they are parts which constitute the thing. (DPN 3.48–50)

They [i.e., matter and form] are said to be related to a compound as parts to a whole, or as what is simple to what is complex. (DPN 4.42–43)29

As we have seen, moreover, the Aristotelian conception of forms appears to be tailor-made for rendering Aquinas’s views about substantial change intelligible. Indeed, I think this conception’s ability to make sense of substantial change (together with the fact that the existence of such change is intuitively plausible to begin with) not only provides us with compelling evidence that Aquinas was operating with such a conception, but also explains his insistence on the composite nature of hylomorphic compounds.30

(p.91) Finally, it seems to me that there are good independent reasons, deeply entrenched in the medieval discussion of universals, for thinking that Aquinas accepts the Aristotelian conception. In De ente et essentia, for example, he offers the following two reasons for preferring an Aristotelian conception of forms to one according to which they are “something existing outside singulars, as the Platonists believed”:

For in the latter case, a genus [such as animal] or a species [such as human] could not be [essentially] predicated of an individual; for Socrates cannot be said to be something that is separate from him. Again, what is separate would be of no use in the cognition of such a singular. (DEE 3.16–20)

These two objections to the Platonic conception—that only immanent forms or properties can essentially characterize substances and hence explain our knowledge of them—are not likely to convince anyone not already antecedently disposed to accept the Aristotelian conception of property possession. Even so, they leave us with little doubt about which conception of forms or properties Aquinas himself endorses.

4.4 A Puzzle about Accidental Change

I have been arguing that, if we want to make sense of Aquinas’s account of substantial change, we must interpret it in light of the Aristotelian conception of forms. For reasons I will now explain, this same interpretation appears to raise trouble for Aquinas’s account of accidental change.

Recall what is supposed to be the distinctive feature of accidental change—namely, that it involves a subject (more specifically, a substance) that not only possesses distinct forms or properties over time, but is successively characterized by these same properties.31 The Aristotelian conception of forms threatens to make this feature of accidental change unintelligible. To see why, return once again to the change involved in our statue example, in which the enduring subject or matter is the lump of bronze. If we approach this example from the perspective of the Aristotelian conception, we will think of the lump of bronze as having the distinct properties of sphericity and statuehood successively inhering in it. Given the distinction between inherence and characterization, however, it would appear that the lump of bronze cannot be successively characterized by these properties. For according to the Aristotelian conception, the only things characterized by properties are the complex wholes of which the properties themselves are constituent parts—in this case, the sphere and statue, respectively. Not only does this conflict with what we described as the distinguishing feature of accidental change, it also threatens the coherence of the very idea that a subject can be contingently characterized by certain of its forms or properties. For insofar as Aristotelians conceive of spheres, statues, and other such (p.92) entities as complex wholes that exist in virtue of their constituent properties inhering in some matter, it would appear to follow that all property characterization is non-contingent or essential.

Once again, therefore, Aquinas’s views appear to commit him to an inconsistent triad:

As with our previous puzzle, Aquinas’s resolution of this one is straightforward—he rejects the third member of the triad. And once again, the coherence of his rejecting the relevant claim depends on his appeal to a broadly Aristotelian doctrine—though this time the doctrine concerns the relationship between distinct hylomorphic compounds rather than subjects and properties. To see what this further Aristotelian doctrine amounts to, and how it enables Aquinas to avoid this further puzzle, it will be best to approach the doctrine itself indirectly, by turning first to certain developments in the secondary literature on Aristotle regarding his views about accidental unities.32

In recent years, an increasing number of commentators on Aristotle have come to think that his accidental compounds or unities stand in a very special relation to the substances that function as their matter (what are often referred to as the parent substances of such compounds).33 The reason for this is that Aristotle himself suggests, at various places in his writings, including his Physics and Metaphysics, that entities such as white-Socrates and Socrates, or musical-Coriscus and Coriscus are one in number but not in being.34 Or again, that such entities are distinct, but nevertheless to be counted as one.35 In some of these texts, Aristotle even seems to extend this doctrine to accidental compounds that are distinct, but share a common parent substance (so that, for example, white-Socrates and musical-Socrates are not (p.93) only numerically the same as Socrates, but also numerically the same as each other). Because Aristotle takes the sameness in these particular cases to hold only accidentally—on the grounds that parent substances can typically exist without the accidental compounds of which they are a part—commentators habitually describe this doctrine as one of ‘accidental sameness’.36 It seems to me, however, that we would do better to describe this doctrine as one of ‘numerical sameness without identity’, since the sameness in question is clearly a variety of numerical sameness and it is the claim that this variety of sameness is compatible with the non-identity of its relata that makes the doctrine itself so distinctive.37

But however we describe the doctrine, it is hard not to balk at it, at least on first hearing. After all, what could it possibly mean to say of two (or more) distinct things that they are numerically one and the same object, and hence to be counted as one? A little reflection, however, reveals that there is a straightforward answer to this question: it just means that the things in question completely overlap with respect to their matter (at some time).38 This way of understanding the doctrine has a number of advantages. First, it makes the doctrine perfectly intelligible (since there is no obvious absurdity in distinct things completely overlapping with respect to their matter—say, a material object and some event it enters into). Second, it provides a simple explanation for why Aristotle would apply the doctrine to accidental unities sharing the same parent substance (since in virtue of sharing the same parent substance, such entities will share all of their matter in common). Finally, and perhaps most importantly, it makes the doctrine plausible in particular cases—namely, in those cases that give rise to the so-called problem of material constitution. This last point requires a bit of explanation.39

Suppose we set our bronze statue on an otherwise empty table and ask: How many material objects are there in the place filled by our statue—one or more than one? Because the statue and lump of bronze completely overlap with respect to their matter, it is tempting to think the answer is ‘one—and only one—object’. If we wanted to sell the statue, for example, we wouldn’t charge for the statue and the lump. And this is because, in line with common sense, we count statues and lumps, and ordinary objects more generally, by their matter. Note, however, that insofar as we are inclined to think that statues are distinct from lumps, we also appear to have (p.94) reason for thinking that there is, in fact, more than one object in the place occupied by our statue. After all, we could always melt down our statue and recast it as a sphere, in which case the same lump of bronze would remain (albeit in a different shape) but the statue would not. This fact strongly suggests that the lump is not identical with the statue after all, because they have different persistence conditions. But, then, this latter judgment—itself fairly intuitiveappears to be in conflict with common sense.

As it turns out, the Aristotelian doctrine of numerical sameness without identity allows us to reconcile these conflicting intuitions—and in a particularly elegant way.40 For the doctrine tells us to count material objects by their matter, but hylomorphic compounds by identity. Or, more precisely, it tells us the following:

In light of this understanding of the doctrine, we can explain why we are tempted to think of our statue and lump as both one and many. For according to it, they turn out to be one and the same material object, but many, distinct hylomorphic compounds.41

We are now in a position to appreciate the relevance of this broadly Aristotelian doctrine to our puzzle about accidental change. For once we combine this doctrine with the Aristotelian conception of forms, it becomes possible to distinguish more than one way in which a subject can be characterized by forms or properties. Given the Aristotelian conception, we can always say that subjects are characterized, primarily or in the first instance, by the forms (or properties) that they possess as proper parts or constituents—or better, as immediate proper parts or constituents.42 Thus, our sphere is characterized primarily or simpliciter by the form or property of sphericity, whereas our statue is characterized primarily or simpliciter by the form or property of statuehood. In addition to such primary property characterization, however, the doctrine of numerical sameness without identity enables us to say that subjects are also characterized in a secondary or derivative sense by the constituent properties of things with which they are numerically the same but not identical. The intuitive idea here is that numerical sameness is such an intimate relation that, by virtue of coming to bear it to something else, a compound can take on or inherit (p.95) certain characteristics of that other thing.43 Thus, even if it is true that only statues or spheres can be characterized by statuehood or sphericity primarily or simpliciter, since only they possess the relevant properties as immediate proper parts or constituents, nonetheless when a lump of bronze comes to share the same matter as a statue or sphere (which it can do merely by having statuehood or sphericity come to inhere in it), it will thereby come to be characterized by the relevant property derivatively.44 To state these notions of property characterization more precisely:

As it turns out, these two different types of property characterization are all we need to resolve our puzzle.45 Accidental change, as we’ve seen, requires the possibility of a subject’s being contingently (or accidentally) characterized by some form or property. But this possibility makes perfect sense in light of the notion of derivative characterization. For as the definition just given makes clear, derivative characterization is something that holds when a substance is part of a larger accidental compound. But since substances can, in general, exist independently of the accidental compounds of which they are a part, the sort of characterization that holds in virtue of such a relation will also be contingent or accidental.46

In short, the distinction between primary and derivative characterization helps us to see why the third member of our puzzle about accidental change is false. Although the Aristotelian conception of forms does entail that things cannot be successively (and so contingently) characterized primarily by the forms or properties inhering in them, it doesn’t rule out the possibility of their being successively (and so (p.96) contingently) characterized derivatively by these same forms or properties. Indeed, if the Aristotelian doctrine of numerical sameness without identity is true, it is precisely in terms of such derivative characterization that we should understand all accidental change.

As in the case of our previous puzzle, here too we have an Aristotelian doctrine tailor-made for resolving a difficulty in Aquinas’s views. And once again, this seems to create a strong presumption in favor of attributing the doctrine to Aquinas himself—a presumption that can likewise be further strengthened on the basis of textual evidence.

As far as I know, there are no texts in which Aquinas straightforwardly and unequivocally asserts the doctrine of numerical sameness without identity in precisely the form that I have presented it. Even so, there are texts in which he comes close to doing so. To take the clearest first, consider the following passage from his commentary on the Metaphysics:

Those things are one in number whose matter is one…Indeed, it is on account of matter that a singular thing (singulare) is both one in number and divided from other things. (In Meta. 5.8.876)

The first sentence of this passage is naturally read as an assertion of the central idea behind the doctrine of numerical sameness without identity—namely, that matter-sharing (at a time) is sufficient for numerical sameness (at that time).47 For, as we have seen, Aquinas’s views about change commit him to the existence of compounds sharing all the same matter (e.g., material substances such as Socrates and accidental unities such as white-Socrates). But according to the first sentence, such things must be regarded as “one in number” precisely because their “matter is one”. The second sentence of the passage goes even further, insisting as it does that matter is just that in virtue of which things count as singular. Assuming, as seems natural, that Aquinas is using ‘singulare’ in this context to refer only to material objects (i.e., only to things possessing matter), the passage as a whole comes close to stating the doctrine in precisely the form presented earlier: two (or more) hylomorphic compounds that share the same matter (at some time) are the same material object (at that time).48

There are other passages that provide more indirect support for the doctrine. For example, Aquinas discusses accidental compounds or unities at a number of places in his writings, and many of the things he says about them are precisely the sorts of (p.97) things that have led commentators to attribute the doctrine of numerical sameness without identity (or accidental sameness) to Aristotle.49 To take just one example directly associated with Aquinas’s views about accidental change, consider the following passage from his Physics commentary:

When someone becomes musical, the man survives, but the [form or property] contrary [to being musical] does not…Nor does the compound of subject and contrary survive, for the non-musical man does not survive after the man has become musical. (In Phys. 1.12.5)

Here Aquinas is discussing a change involving someone (say, Socrates) acquiring the accidental form or property of being musical. In this connection, he makes three points, which appear to extend to accidental changes in general. First, the subject of change does not merely take on a form or property, but comes to be characterized by it—Socrates himself becomes musical. Second, this change involves the generation and corruption of distinct accidental compounds—say, musical-Socrates and non-musical-Socrates. Third and finally, the subject of change must be regarded as distinct from the accidental compounds that serve as the termini of the change, since it can exist without them. Thus, when Socrates becomes musical, Aquinas tells us, “the man survives” but not the “form or property” or even the “compound” composed of the man and such a form or property. Evidently, therefore, Aquinas is assuming that, when Socrates becomes musical, we have two distinct things (namely, Socrates and musical-Socrates) that become numerically one and the same.50

Finally, the doctrine of numerical sameness without identity appears to be required not only by Aquinas’s views about accidental change, but also by his views about accidental predication. To see why, suppose that each of the following two ordinary predications is true:

As Aquinas sees it, the first of these predications is essential (or substantial), whereas the second is accidental. What is more, Aquinas thinks there are two different types of question that we can ask about these predications.51 The first has to do with their basis in extramental reality: In virtue of what are they true? The second has to do with their content: What is being asserted by predications of each type? In order to answer the first question, Aquinas thinks that we need only appeal to the existence of the (p.98) right sort of hylomorphic compound—namely, a material substance in the first case, and an accidental unity in the second. For in each case, he says, their truth is explained by compounds composed of the right sort of matter and form:

When I say ‘Socrates is human’, the truth of this statement is explained by the composition of the form of humanity with the individual matter by which Socrates is this human. Likewise, when I say ‘Socrates is white’, the explanation of its truth is the composition of whiteness with a subject. And similarly in other such cases. (In Meta. 9.11.1898)52

So much for the extramental basis for such predications. What about their content?

Here, too, Aquinas often relies on talk of compounds (or composition) to explain his views. Just as hylomorphic compounds arise from the composition of matter and form in extramental reality, so too, he suggests, affirmative predications, which he takes to be mental propositions, arise from the composition of subjects and predicates in the mind. Even so, Aquinas insists, the type of “composition” involved here is very different from that involved in extramental compounds of matter and form:

Composition in the mind (compositio intellectus) differs from composition in extramental reality (compositio in re). For the things that are brought together in extramental reality to compose something [namely, matter and form] are distinct, whereas composition in the mind signifies the sameness (identitatis) of the things that it brings together [namely, subject and predicate]. Thus, the mind does not bring things together in such a way as to assert that a man is whiteness. On the contrary, what it asserts is that a man is white—that is, that a man is something having whiteness. But the man and the thing having whiteness are the same in subject. And something similar holds for the composition of [substantial] form and [prime] matter. (ST 1.85.5 ad 3)

As this passage suggests, what Aquinas takes to be distinctive about composition in the mind is that it results in complexes (namely, predications or propositions) that assert some form of sameness (identitas) holding between their parts (namely, subjects and predicates).53 And this has an obvious bearing on our question about how Aquinas understands the content of ordinary predications of the form ‘a is F’. (p.99) Indeed, it suggests that he just takes them to be asserting the sameness of a with an F. But if that’s right, then, strictly speaking, predications (1) and (2) above should be interpreted as follows:

In the case of (1*), the interpretation seems unproblematic. To say that Socrates is the same as a human is presumably just to say that he is identical to something having humanity as a constituent—which is precisely what we would expect, given Aquinas’s view that Socrates just is a material substance. In the case of (2*), however, things are more problematic. On Aquinas’s view, Socrates is not identical to a thing having whiteness as a constituent, but is rather himself a constituent part of such a thing. But, then, in what sense can Socrates be said to be the same as something having whiteness as a constituent? The doctrine of numerical sameness without identity provides a straightforward (and, indeed, what appears to be the only possible) answer: insofar as Socrates and the white thing in question share all the same matter, they are numerically the same but not identical.54 Interpreting (2*) in this way helps us to see that Aquinas’s views about accidental predication are, in fact, part of a unified theory of predication according to which (i) ordinary (intrinsic) predications are to be interpreted in terms of numerical sameness (with or without identity), (ii) essential or substantial predications are to be interpreted in terms of identity, and (iii) accidental (intrinsic) predications are to be interpreted in terms of numerical sameness without identity.55

In addition to making sense of Aquinas’s views about accidental predication, it is worth noting that this interpretation has a further benefit, insofar as it enables us to make sense of something that often strikes contemporary philosophers as puzzling—namely, the idea, common in medieval philosophy and explicitly endorsed by Aquinas, that there are propria or necessary accidents (i.e., accidents not contingently possessed by their bearers).56 In the contemporary literature, it is standard to identify accidental (or non-essential) properties with contingent properties. From the (p.100) contemporary perspective, therefore, the puzzle about propria or necessary accidents is how there could be any.57

But notice that Aquinas does not accept this identification. On his view, the distinction between a substance’s essential (or substantial) and accidental properties is not that between its necessary (or non-contingent) and contingent properties. On the contrary, it is the distinction between its constituent and inherent properties—or better, between its constituent properties and the constituent properties of the larger wholes or complexes of which it is the matter (or parent substance). There is, however, no absurdity in supposing that a substance is necessarily (as opposed to merely contingently) part of certain larger complexes. Thus, when Aquinas speaks of risibility (or the capacity for laughter) as a necessary accident or proprium of human beings, we can take this to mean that certain types of material substance (those composed of prime matter and humanity) cannot exist without there also being certain larger wholes of which they are a proper part (those composed of human beings and the form of risibility).

For all these reasons, therefore, I conclude that Aquinas accepts the doctrine of numerical sameness without identity, and that just as we can make sense of his views about substantial change in terms of the Aristotelian conception of forms, so too we can make sense of his views about accidental change in terms of this broadly Aristotelian doctrine. Indeed, if the arguments of this chapter are successful, there would, in the end, appear to be no inconsistency in Aquinas’s views about substantial or accidental change, provided we understand these views in the broadly Aristotelian way that Aquinas intends them.

Notes:

(1) See §§11.4–5 and §§12.4–5 for some complications raised by the special case of human beings for this conception of hylomorphic compounds.

(2) Given the close connection between numerical sameness and counting, it will often be convenient to speak of the relation of numerical sameness as one whose relata are to be counted as one (regardless of whether they are also identical). So as to forestall misunderstanding, however, I should emphasize that the appeal to counting here is in no sense pragmatic. On the contrary, I assume throughout that things are to be counted as one only if they are one.

(3) See §7.5 for a defense of the claim that contemporary discussions tend to focus on only one type of intrinsic change—namely, what Aquinas calls ‘accidental change’.

(4) Strictly speaking, this example involves what I referred to in §3.2 as a ‘many–one change’, so we should speak of the combined matter of the sperm and menstrual blood (or ovum) taking on a new form. But since nothing turns on this point, I shall ignore it for the time being. See §11.2 for further discussion.

(5) See again the passages from DPN 1 cited at the beginning of Ch. 3. See also the following passage, in which Aquinas makes it clear that his distinction between substantial and accidental change corresponds to that which he draws between generation in the narrow and broad senses:

Because generation is a motion to form, there are two types of generation corresponding to the two types of form. Generation in an unqualified sense corresponds to substantial form, and generation in a qualified sense corresponds to accidental form. (DPN 1.47–50)

(6) I use the term ‘humanity’ to refer to the substantial form of a human being for two reasons: first, because it serves to highlight the parallel between our human and statue examples; and second, because Aquinas says that this is the form that locates human beings within their specific natural kind (e.g., DEE 2). It should be noted, however, that Aquinas himself often reserves the term ‘humanity’ (humanitas) for the natural kind or essence itself (e.g., DEE 3), which as we’ll eventually see (§5.3) includes not only substantial form but also common (prime) matter. See §1.3 for the distinction between individual and common matter.

(7) Aquinas’s views about the Incarnation of Christ, according to which God himself becomes human, introduces a complication for this understanding of what it means for a form or property to be essential. See Ch. 13 (esp. §§13.3–4 and §13.6). For our purposes here, however, we can ignore such complications.

(8) See §§6.3–5 for a more complete expression of the relationship between predication, property possession, and characterization. As will become clear in this context, not all characterization involves properties.

(9) Aquinas sometimes speaks as if prime matter were capable of being characterized by the forms it takes on. Thus, in the passage just quoted from DPN 1, he speaks of prime matter as “in potentiality with respect to being human”. As Aquinas explains elsewhere, however, this way of speaking must be regarded as elliptical for “prime matter is in potentiality with respect to taking on the form of humanity, and hence with respect to being part of something human”:

For just as it is true that ‘a human is white’ but not true that ‘a human is whiteness’ or ‘humanity is whiteness’, so, too, it is true that ‘this enmattered thing (materiatum) is human’ but not true that ‘matter is human’ or ‘matter is humanity’. (In Meta. 7.2.1289)

There is also the question as to why prime matter cannot be characterized by the forms it takes on. This is a difficult question, one to which I shall return in §5.5. The short answer, I argue there, has to do with the non-individuality of prime matter. See also the discussion in §§6.4–5.

(10) The addition of such a fourth condition might seem puzzling, since it is natural to think that M’s having F-ness is sufficient by itself to guarantee that M functions as a subject of characterization. I shall return to this puzzle in §4.3. For now, however, I shall simply assume that Aquinas has a coherent way of drawing the distinction between M’s having F-ness and M’s being F.

(11) But again, see Chs 11 and 13 (esp. §§11.1–2 and §13.6) for complications.

(12) See, e.g., ST 1.45.2 ad 2 (quoted in §3.1), where Aquinas says that “in cases of substantial change…the subject is matter”. As we’ll see shortly, Aquinas thinks that part of what accounts for the primacy of prime matter is the fact that (unlike other matter) it is not itself composed of any further matter and form.

(13) See §8.2, where I discuss Aquinas’s claim that even an immaterial substance can qualify as a subject, and hence as “matter” in the secondary or derivative sense. See also §11.3 for further complications associated with Aquinas’s use of the term ‘subject’.

(14) For a list of references to the various ways that Aquinas refers to compounds of substances and accidents, see Brown 2005, 64, n. 27.

(15) It is, perhaps, worth emphasizing that Aquinas’s views about change do not automatically commit him to an infinite number of hylomorphic compounds, much less to an infinite number of accidental unities. On the contrary, they commit him to distinguishing only as many such compounds or unities as there are distinct forms or properties possessed by their matter or substratum. For evidence that the number of such forms or properties is limited, see the discussion in §§6.3–4 and §9.3. See also the discussion in §2.4.

(16) See, e.g., In Sent. 1.23.1.1; ST 1.77.7 ad 2; and QDP 9.1.

(17) Eventually, we shall see that Aquinas is prepared to relax this constraint in the context of the Eucharist (§11.3). Indeed, in this particular context it becomes clear that Aquinas’s repeated insistence that only substances (but not accidents) are capable of possessing accidents must be understood with the implicit qualification ‘apart from divine intervention’.

(18) See again DPN 1.9–19, quoted at the outset of §4.1.

(19) See also the following remarks from Aquinas’s commentary on the Metaphysics:

Since there is substantial change—namely, [unqualified] generation and corruption—there must be a common subject underlying the contrary motions involved in [such] generation and corruption. What is more, this subject underlies the terms [of the change], form and privation, in such a way that sometimes it is in actuality by virtue of the form, whereas other times it is the subject of the privation of that form. (In Meta. 8.1.1688)

(20) Note that in this passage Aquinas speaks of prime matter as having an “essence” (essentiam). Ordinarily, Aquinas reserves talk of natures or essences for things possessing a substantial form. But here he relaxes his ordinary way of speaking, presumably to emphasize the sui generis character of prime matter. For a very different understanding of the nature or essence of prime matter, one whose connection to Aquinas’s account of change is not altogether clear, see Pasnau 2002, 131–42.

(21) Indeed, as we shall see in Chapter 5, Aquinas thinks there is only one type of being that can play the role of prime matter. For the same reason, his functional characterization of prime matter is not “multiply realizable” but rather gives us an indirect way of latching on to a being of a very special type. See again my remarks about Aquinas’s functionalism in §1.1, n. 11.

(22) As we shall see, material substances include such ordinary objects as Socrates and Bucephalus, whereas accidental unities include such extraordinary (or “kooky”) objects as white-Socrates and brown-Bucephalus.

(23) In speaking of form or property possession as a ‘relation’ here and in what follows, I don’t mean to insist that it must be conceived of as an ordinary relation (that is, as a polyadic property as opposed, say, to a nexus or non-relational tie). For the standard worries about conceiving of exemplification as an ordinary relation, see Loux 2006.

(24) Proponents of the Platonic conception are usually happy to allow that something can exemplify some of its properties essentially and others of them contingently or accidentally, and hence that exemplification itself is a relation that can hold either essentially or contingently.

(25) I’m ignoring here some complications that arise for the possession of contingent or accidental properties. Strictly speaking, if Socrates is white, for Aquinas, this is because he is appropriately related to something else that possesses whiteness as a proper part or constituent. See §4.4.

(26) For an example of someone who attributes this sort of view to Aristotle, see Loux 2005. For an example of someone who takes himself to be a contemporary Aristotelian in this regard, see Armstrong 1989 and 1997.

(27) Loux 2005 speaks of predication, and Armstrong 1989 and 1997 speak of instantiation.

(28) This conception creates difficulties for understanding Aquinas’s account of accidental change, but I shall hold off discussing these until the next section.

(29) For similar such remarks outside DPN, see also SCG 2.54, QDA 1.1 ad 13, and In Meta. 7.2.1295.

(30) As noted in Chapter 3 (§3.5, n. 25), there is a debate in the secondary literature on Aristotle concerning the proper interpretation of his hylomorphic compounds, and in particular whether they should be regarded as literally composed of matter and form. If Aquinas is right in thinking that his position reflects Aristotle’s own, we have an answer to this question: such entities must be regarded as literally composite, if for no other reason than because Aristotle’s analysis of substantial change requires it. For a summary and critical evaluation of this debate, including a different (but perhaps not ultimately incompatible) reason for accepting this interpretation of Aristotle, see Loux 2005.

(31) As argued previously (§4.2), this is the point of Aquinas’s describing the subject of accidental change as the matter “in which” something comes to be.

(32) I should perhaps emphasize that it is no part of my project in what follows to take a stand on the proper interpretation of Aristotle. On the contrary, I merely help myself to an increasingly popular interpretation of his views in order to facilitate the introduction of an otherwise puzzling and unfamiliar doctrine.

(33) See F. Lewis 1982 and Matthews 1982 and 1992, as well as the further sources cited in Cohen 2008.

(34) Topics A7, 103a23–31; Physics A3, 190a17–21, 190b18–22; Metaphysics D6, 1015b16–22, 1016b32–1017a6; Metaphysics D9, 1024b30–1.

(35) Topics A7, 103a23–31; Metaphysics D6, 1015b16–22, 1016b32–1017a6.

(36) See again the references cited in n. 33, this chapter.

(37) Indeed, once we admit this variety of sameness, there would seem to be no reason in principle not to allow it to hold essentially. See Brower and Rea 2005 for one context (namely, the Christian doctrine of the Trinity) that appears to require a form of numerical sameness without identity to hold essentially.

(38) Three clarifications. First, when I speak of ‘matter’ here, I am using the term in its primary or proper sense—that is, to refer to what Aquinas calls ‘prime matter’. Second, I have added the qualification ‘at some time’ in order to emphasize that this doctrine applies only to synchronic (as opposed to diachronic) sameness. Things may share all the same matter over time (or diachronically) and yet fail to be numerically the same (as is the case in all one–one changes). Third and finally, from the fact that things share all of the same matter it doesn’t follow that they are numerically the same F, for every F. On the contrary, for reasons to be explained shortly, it follows only that they are the same material object.

(39) The discussion that follows builds on ideas first presented in Rea 1998a, and further developed and defended in Brower and Rea 2005 and Brower 2011. See also §7.3, this volume.

(40) Whether or not this understanding of the doctrine captures Aristotle’s own views, I shall assume in what follows that it is of at least broadly Aristotelian provenance.

(41) For further development and defense of this doctrine, see Chs 6–7 and 10 (esp. §6.4, §7.3, and §§10.2–4).

(42) Let us say that x is an immediate proper part of y if and only if (i) x is a proper part of y, and (ii) there is no z such that x is a proper part of z and z is a proper part of y.

(43) Strictly speaking, one does not have to accept the doctrine of numerical sameness without identity to accept this point. A subject’s coming to share all the same matter as another thing would by itself seem to be sufficient for it to be characterized by the constituent properties of that other thing (regardless of whether complete overlap of matter is taken to be sufficient for a type of sameness without identity). See Ch. 6 (esp. §§6.3–5) for further discussion of how exactly such property characterization is supposed to work.

(44) See Cohen 2008, which provides textual grounds for attributing this sort of view to Aristotle. See also Baker 2000 for a different account of derivative property characterization.

(45) The distinction between these two types of property characterization corresponds roughly to the standard medieval distinction between per se and denominative predication.

(46) I’m ignoring here a complication having to do with propria or necessary accidents—though I shall return to it shortly.

(47) The reference to time, though not explicit, is clearly required by Aquinas’s views, since as already indicated (n. 38, this chapter), in paradigm cases of one–one change numerically distinct objects possess the same matter at different times.

(48) Admittedly, this passage is not part of a discussion of change. But that by itself would seem to be of little consequence. The fact that Aquinas’s clearest statement of the doctrine comes from outside the context of change gives us no reason to doubt that he endorses the doctrine within that same context. On the contrary, it gives us further reason to suppose he accepts it, especially if (as I’ve been suggesting) the theory of change is one of the contexts that motivates the doctrine in the first place.

(49) For an extensive list of passages where Aquinas discusses such compounds, see Brown 2005, 65, n. 27.

(50) See Cohen 2008, who develops the same line of argument in connection with the corresponding passage of Aristotle’s Physics.

(51) See the texts and discussion in Ashworth 2004, esp. 524–7.

(52) Like other medieval philosophers, Aquinas often speaks of forms or properties as “that in virtue of which” (quo) things are characterized in various ways. In previous work (see Brower 2008 and 2009), I followed Fox 1987 in taking this to show that medievals regard forms or properties themselves as the extramental basis or “truthmakers” for ordinary predications of the form ‘a is F’. But I now regard this as a mistake, at least in the case of Aquinas. Although speaking of a form or property F-ness as “that in virtue of which a is F” can be taken to imply that F-ness is a complete explanation of a’s being F, it needn’t be. On the contrary, it can be taken more modestly to imply merely that F-ness is a salient or important part of the explanation of a’s being F. And as the passage just quoted makes clear, when Aquinas adopts the relevant mode of speech in the context of forms alone, he should be understood in the more modest way (since the complete explanation involves appeal to the composition of form with matter).

(53) See ST 1.13.12: “In every true affirmative proposition, the subject and predicate must somehow signify the same thing in reality (idem secundum rem).” It is important to note that ‘identitas’ is a term of art in medieval philosophy, covering a number of different relations, and hence it should not be assumed that it can be straightforwardly transliterated as ‘identity’. For some discussion of Aquinas’s use of this term, see Schmidt 1966, 195–6.

(54) This, I take it, is the point of Aquinas’s talk of Socrates and white-Socrates as “the same in subject”. Indeed, insofar as Socrates just is the subject (or secondary matter) of white-Socrates, they will share all the same (prime) matter, and hence be numerically the same (but not identical).

(55) I shall have more to say about Aquinas’s views about predication in §§6.3–5. See also Ashworth 2004 (esp. 527) for some complications concerning the signification of ordinary nouns vs. adjectives.

(56) See, e.g., ST 1.9.2, 1–2.2.6; QDV 21.1 ad 10.

(57) See, e.g., Gorman 2005 for discussion and references.