Groups are everywhere. We rely on them when we marry, matriculate, and mortgage, when we pray, purchase, and patronize, and when we lend, loot, and lecture. They systematically guide our interactions. They have members, they do things, and they come and go. They matter. As a result, the question arises: What are they?

As with “What is $\mathrm{X}$?” questions generally, this one’s ambiguous. On the one hand, to ask what a group is is to ask what it is to be a group. That’s a question about what defines the kind group. It’s asking: What is it for a particular collection of individuals to be a group rather than a mere collection of individuals? Call it the definitional question.¹

On the other hand, to ask what a group is is to ask what kinds of things groups are. That isn’t a question about what defines the things we call groups qua groups. It’s asking: What, say, instantiates group? Groups are the kinds of things that fit into churches, corridors, and courtrooms. And it might be—indeed, it’s quite plausible—that group doesn’t fit into churches, corridors, or courtrooms. As a result, we’ll want to know what does. Call this the ontological question.^2,3

Interestingly, philosophers have nearly universally privileged the ontological question. Predictably, there’s significant disagreement among them. Nonetheless, the vast majority of philosophers accept that groups are “one,” that they’re fundamentally singular things (e.g., Effingham 2010; Ritchie 2013, 2015, 2020; Hawley 2017; and Fine 2020).⁴ I call their view monism. Nonetheless, a minority of philosophers accept that groups are “many,” that they’re fundamentally plural “things” (i.e., pluralities) (Uzquiano 2018; Faller 2021; Horden and López de Sa 2021; and Wilhelm 2022). They accept that a group is in some sense its members, that they are “it.”⁵ I call their view pluralism.

In general, monists accept the following argument against pluralism:

Moreover, they accept:

I call these “the arguments from Difference and Sameness.” In this paper, I argue that they’re unsound. Both (2) and (5) are false.

Admittedly, my argument takes some—ultimately necessary—twists and turns. Here’s how it’ll go. In section 1, I articulate a functionalist account of groups as an answer to the definitional question. In section 2, I argue that functionalism is neutral with respect to both monism and pluralism. In section 3, I argue that by obscuring the definitional question, the arguments from Difference and Sameness assume a particularly naïve version of pluralism, and show that an attractive version of functionalist pluralism is invulnerable to them. Lastly, in section 4, I raise a challenge for functionalist monism: whereas functionalism seems to favor “external” individuation conditions, monism seems to favor “internal” individuation conditions, and it’s up to the functionalist monist to square them. I don’t claim that my challenge is dispositive, however. Rather, I claim that it exposes an important source of disagreement that’s worth pursuing.

Although the implications for monism and pluralism are clear, one of my aims is to generate interest in functionalism, whether monistic or pluralistic. Although functionalism about social goings-on—specifically, about artifacts—has pedigree, its application to groups hasn’t been explored.⁶ There are details to sort out, of course. And though I’ll make suggestions as I go, ultimately, I hope to have provided a framework for sorting them out that’s worthy of our attention.

1 The Definitional Question: Functionalism

As an answer to the definitional question, I propose a functionalist account of groups. Functionalism about social goings-on is an established view; in particular, functionalism about artifacts (Searle 1995, 2010; Baker 2007; Thomasson 2019; Evnine 2016; Guala 2016; Koslicki 2018). However, it hasn’t been pursued as an account of what groups are. But as Haslanger (1995) suggests, we might think of groups as special kinds of artifacts, as products of some of the things we do, whether intentionally or unintentionally. We might think of them as things we in some sense “use” to do them. And this suggests we might expand functionalism to account for them. In this section, I give it a try.

First, a note. Generally, philosophers think of artifactual functions teleologically, as things that serve purposes artificers impose on their products. However, I take my cue from functionalism about mental states, according to which functions aren’t teleological but, e.g., causal. Ultimately, that’s a choice point. One might translate the account I propose in terms of teleological functions (see Thomasson 2019 for rumblings). As a result, it’s easily assimilated into the wider literature.

1.1 Functionalism

In general, functionalism about $x$ is the view that $x$ is a functional kind. A kind, $\mathrm{K}$, is a functional kind when something is an $\mathrm{K}$ because of its extrinsic rather than its intrinsic properties; specifically, what it does—the way it functions—within a particular system in which it’s embedded. Ordinarily, functionalism is associated with a particular account of mental states.⁷ Functionalists about mental states accept that kinds of mental states (e.g., pain) are defined by functions (e.g., to avoid physical harm) that are realized⁸ by whatever plays the relevant roles (e.g., the “pain role”) within a particular cognitive system. Generally, they accept that pain’s realizations are pains.

Functionalism’s claim to fame is the ease with which it accommodates multiple realizability. Multiply realizability is a feature of mental states whereby a single mental state might be grounded in multiple non-mental (e.g., physical) states. In creatures with cognitive systems like ours, pain is realized by c-fibers that cause the relevant kinds of responses; flinches, winces, and wails, for instance. In extraterrestrials with cognitive systems unlike ours, however, pain might be realized by gunky she-fibers that cause relevantly similar responses; shlinches, shinces, and shails, for instance. But both are pains because pains are what function that way.

Although there are many details about which functionalists disagree, I’ll assume that pain is a higher-order property of the form an-input-linking-an-output, where the relevant kind of linking is causal.⁹ A particular pain might be a-pinch-causing-a-flinch within a particular cognitive system or a shinch-causing-a-slinch in theirs. But that’s merely for convenience. For the important thing is this: to be a pain is to do what pains do. As a result—and with relevant disagreements aside—I propose

where $xx$ is either a singular or a non-singular plurality. Here, I argue that Functionalism provides an attractive answer to the definitional question because it does what an account of groups should do; it satisfies several desiderata.

First, a clarification. One might worry that in appealing to group kinds, Functionalism is circular. Group kinds are group kinds, and one might reasonably insist that group can’t be defined by them.¹⁰ (See Bealer 1997 for the corresponding objection about mental states.) Here, then, is a conception of group kinds I’ll assume throughout:

where, again, $rr$ is either a singular or non-singular plurality. Clearly, Functionalism plus Group Kind Functionalism isn’t circular. Group Kind Functionalism says nothing about group. Rather, it says that a particular collection of individuals—Jonathan, Jennifer, and Julia, say—is, e.g., a department of philosophy because they realize roles that push them around in particular ways—in ways characteristic of departments of philosophy. In other words, their being a group isn’t what makes them a department. Rather, their being a department is what makes them a group. Of course, Group Kind Functionalism assumes we understand what roles are. But because everyone owes us an account of them, that’s okay. As a result, I’ll carry on as planned.¹¹

1.2 Desiderata

Functionalism satisfies several desiderata. In particular, it accounts for

That it does is reason to take it seriously.

As for (a): again, Functionalism is the view that groups are what they are because they do what they do.¹³ A paradigmatic group like the Department of Philosophy is the group it is because the individuals that are its members in some way “do philosophy” within a particular college, within a particular university, and as part of a particular department of education.¹⁴ Whatever their doing what they do amounts to, the Department of Philosophy is the particular group it is because the individuals that are its members do what they do. It’s a department of philosophy, an instance of department of philosophy, and, so, it’s a group.

And this feature of Functionalism underwrites a plausible explanation of the distinction between groups and mere collections of individuals. It’s uncontroversial that groups, in some sense, consist of collections of individuals. The Department of Philosophy, in some sense, consists of the individuals that are its members, of Jonathan, Jennifer, and Julia. Similarly, the Supreme Court, in some sense, consists of the individuals that are its members, of Roberts and his colleagues, and the Boston Red Sox of the individuals that are its members, of Martinez and his teammates.

But the Department of Philosophy, the Supreme Court, and the Red Sox are relevantly unlike collections of individuals like those wearing white t-shirts, those driving rental cars, and those that prefer chocolate to vanilla ice cream. Intuitively, whereas groups like the Department of Philosophy, the Supreme Court, and the Red Sox are such that the individuals that are their members do what they do because they’re members, there’s nothing the collection of individuals wearing white t-shirts do because they’re “members.” Of course, there’s something they do: they wear white shirts. Unlike the groups in question, however, they’re its members because they’re wearing white shirts. In other words, whereas the individuals that are a group’s members play particular kinds of roles—and so can act in their capacity as members—mere collections of individuals don’t and can’t. And, again, that’s what Functionalism implies: because groups are individuated by what they do, the Department of Philosophy is a group because the individuals that are its members play the roles that define it, and not conversely.

As for (b): Functionalism explains how and why groups and the individuals that are their members might malfunction as the kinds of things they are. Groups are like thermostats. Thermostats are what measure temperature. There’s something they do and with respect to which they might fail. If they do, they’re bad thermostats. Similarly, departments of philosophy are what do philosophy in the relevant ways. Like thermostats, there’s something they do with respect to which they might fail. If they do, they’re bad departments of philosophy.¹⁵

As for (c): Functionalism explains how and why particular groups are embedded in wider social systems. Again, particular pains are what protect the pained, are causing’s to avoid hot stoves, stubbed toes, and unfriendly blows. This entails that they function within wider cognitive systems that enable the relevant kinds of behaviors; in other words, that there are pained things—organisms or otherwise—to protect. They’re parts of cognitive systems, are what function to avoid the physical harms that might befall the things they cause to behave in the relevant ways. In a word: no things, no cognitive systems, no pains.

Analogously, particular departments of philosophy are what do philosophy in the relevant ways, what in some sense account for the fact that the individuals that are their members give particular kinds of seminars, invite particular kinds of speakers, and host particular kinds of events. Again, this entails that particular departments of philosophy function within wider social systems that enable these kinds of behaviors. Again, the Department of Philosophy is the group it is because its members do philosophy as part of a particular college that’s part of a particular university that’s part of a particular department of education, and these ultimately underwrite, say, its seminar offerings. These groups require that the Department follow a particular curriculum and, so, ultimately constrain how the Department of Philosophy does philosophy.

Relatedly, Functionalism explains how and why the social systems in which particular groups are embedded are structured. What social structures are is an important and underexplored issue in contemporary philosophy. But a few things are clear.

Minimally, structures are arrangements. They’re complexes of relations. They consist of “positions” at the intersections of these relations, and things “occupy” them. Naturally, then, group structures are social arrangements; complexes of social relations that consist of intersecting positions things occupy. Baseball teams are structured, for instance. Every baseball team has a pitcher and a catcher. In other words, a baseball team’s structure partly consists of particular asymmetric, irreflexive, and non-transitive relations—pitches to and returns to, say—whose relata intersect in a particular way: pitchers pitch to catchers and catchers return to pitchers. And that the relevant elements—this and that individual—occupy the relevant positions—that they’re arranged in the relevant way—partly grounds the fact that they’re part of a baseball team rather than a mere heap of individuals.

More than this, though, that a particular group functions in the particular ways it does is explained by the general arrangements of its elements. For instance, the Red Sox and the individuals that are their members play roles that are determined by the wider social system in which they’re embedded.¹⁶ Like the Department of Philosophy and the Supreme Court, in other words, the Red Sox are part of other groups; for instance, the American League East (ALE) and Major League Baseball (MLB).¹⁷ And this wider social system partly determines in which relations the individuals that are members of the Red Sox stand both to one another and to other groups. For instance, we can’t explain the fact that the Red Sox won the World Series in 2018 by appealing to how well they played. Rather, we must appeal to the relational fact that they played better than the Los Angeles Dodgers—themselves part of the National League West (NLW) and, so, the MLB—and to the rules that legitimated their win. In other words, we must appeal to the social system in which both the Red Sox and the Los Angeles Dodgers are embedded—the MLB—to explain important facts about them. As a result, it’s not merely that particular groups are embedded in wider social systems, the social systems in which they’re embedded structure them. And, again, Functionalism bears this out. (See Haslanger 2000 for a similar thought.)

As a result, Functionalism satisfies desiderata (a)–(c) and thereby provides a powerful framework for thinking both about what it is to be a group per se and what it is to be a group of a particular kind. But because it’s a sketch of an account, there are details about which we might meaningfully disagree. I’ll consider a particularly important detail about which we might disagree in section 3. But there’s more.

1.3 Open Questions

Here’s a brief survey. We might disagree about what a social system is and about what it is for a complex of relations to constitute a structure. Both Ritchie (2013, 2015, 2020) and Haslanger (2016) understand both in terms of Shapiro (1997)’s influential conception of mathematical structure according to which

a system [is] a collection of [entities] with certain relations. […] A structure is the abstract form of a system, highlighting the interrelationships among the [entities], and ignoring any features of them that do not affect how they relate to other [entities] in the system. (Shapiro 1997, 73–74)

However, we needn’t accept Shapiro’s conception of structure to accommodate this feature of Functionalism. What’s important is that we accept that the social systems in which groups are embedded are holistic. And, again, Functionalism bears this out.

Moreover, we might disagree about whether particular individuals are unified in coming to be elements in a functionalist structure or whether it’s sufficient that the relevant network of social relations is interdependent. (Indeed, I discuss its importance in section 4.) Relatedly, we might disagree about what the relevant functions are and what it is to realize them. For instance, there might be “basic” kinds of groups that correspond to basic kinds of functions—for instance, to competition—and non-basic kinds of groups that correspond to ways individuals might compete—for instance, to playing baseball.

Lastly, we might disagree about which types of collections of individuals are groups—in particular, whether genders and races are.¹⁸ Functionalist accounts of genders and races are well-represented. For instance, MacKinnon (1993)’s remarkably influential account of gender—according to which for one to be a woman is for one to be sexually subordinated to men and to be a man to sexually subordinate women—is recognizably functionalist. (See Jenkins 2017 for a compelling case for this functionalist interpretation of MacKinnon; see also Young 1990; Witt 2011; and Haslanger 2012 for additional evidence.) Similarly, Charles Mills (1997)’s account of race—according to which to be, e.g., black is to be positioned within a social system (i.e., a “vertical race system”) such that one is treated as a “sub-person”—is recognizably functionalist, too. (See Griffith 2020 for discussion.) But the important point is this: Functionalism paves the way for a unification of otherwise disparate literatures about the metaphysics of groups generally.

Although Functionalism is ultimately neutral with respect to these disagreements, it both clarifies what’s at issue and provides a framework for thinking about how they might be resolved. (My many footnotes attest to it!) To the extent that they’re meaningful disagreements, then we’ve reason to take it seriously.¹⁹

2 The Ontological Question: Monism & Pluralism

Though Functionalism allows for significant disagreements among functionalists, there’s an important detail that’s central to what I’ve called the arguments from Difference and Sameness, namely, whether groups are one or many. In this section, I argue that Functionalism is compatible both with what I’ve called monistic and pluralistic answers to the ontological question. Ultimately, in section 3, I show that the arguments from Difference and Sameness are unsound because of it.

Again, monism is the view that groups are singular things. Some monists accept that groups are sets (Sider 2001; Effingham 2010), some that they’re “realizations of structure” (Ritchie 2013, 2015, 2020), some that they’re fusions (Hawley 2017), and some that they’re “embodiments” of structure (Fine 2020). Sets, realizations of structure, fusions, and embodiments of structure are “something over and above” the collections of individuals out of which they’re made up, and, in each case, that something is one.²⁰

And though pluralism is widely rejected, some have come to its defense. In particular, some accept that groups are pluralities of individuals that embody “plural conditions” (Uzquiano 2018), and others that they’re “instantaneous pluralities” (Wilhelm 2020). In each case, however, groups are many in the sense that they’re fundamentally plural “things” (i.e., pluralities), “the very kind of [‘object’] of which many is to be asserted,” as Russell (1903) suggests.

But the important point is this: one can be a functionalist, whether one is a monist or a pluralist. In this section, I focus on Kit Fine and Gabriel Uzquiano’s monistic and pluralistic accounts of groups, respectively. Because each appeals to Fine (1999)’s “theory of embodiment,” focusing on theirs tidies things up. Though other monists and pluralists will answer the ontological question in meaningfully different ways, what I say in restricting myself to embodiments is ultimately compatible with them.

First, the framework. According to Fine (2020), groups are embodiments. Embodiments are quite like Aristotelean compounds.²¹ Generally, Aristotelean compounds consist not only of “matter”—say, of a plurality of flowers—but of “form”—say, of a “being bunched” arrangement—where form is understood to structure matter, to turn a plurality of flowers into a bouquet. Similarly, embodiments consist not only of their parts but of “principles of embodiment” (henceforth: principle/s) that specify the relevant arrangements that structure their parts. The bunch is a plurality of flowers that embody the arrangement the relevant principle specifies; the bunch is the flowers-qua-bunch: a bouquet.²²

Fine distinguishes two kinds of embodiments, what he calls “rigid” and “variable” embodiments. On the one hand, rigid embodiments have their parts necessarily. For instance, the bouquet is a rigid embodiment because exactly the relevant flowers embody exactly the relevant bunching arrangement at all times and in all worlds. The bouquet is the bouquet it is because it has exactly those flowers arranged in exactly that way; replace one and you’ll have another bouquet.

On the other hand, variable embodiments have their parts contingently. For instance, my bike is a variable embodiment because it has different “manifestations” that embody a particular arrangement at particular times and in particular worlds. Clearly, my bike has different bits of rubber, plastic, and metal as parts, and these are arranged ‘bicycley’ at different times and in different worlds. In other words, my bike isn’t identical to its manifestations, to the objects consisting of bits of rubber, plastic, and metal arranged ‘bicycley’ at particular times and in particular words. Rather, it’s constituted by them then and there. As a result, it persists when I replace a tire. (We might disagree about examples, of course, but the distinction is clear enough.)

Ultimately, groups can be either rigid or variable embodiments, though Fine (2020) focuses on those that are variable embodiments. The Department is the group it is because it has manifestations at particular times and in particular worlds consisting of the individuals that are its members and the arrangements they embody at those times and in those worlds. What this arrangement is is specified by the relevant principle; something like ‘being arranged “departmentally”.’ And in embodying that arrangement, the Department isn’t identical to its manifestations but constituted by them at particular times and in particular worlds.²³

But Fine’s theory is remarkably flexible. He places no restrictions on the content of principles of embodiment generally. It’s up to say what they are. Uzquiano (2018) exploits this flexibility and argues that groups are structured by principles that encode plural rather than singular conditions, as Fine assumes. In particular, he argues that their principles are relevantly like “being scattered,” where to be scattered implies that what’s scattered isn’t one but many.

Moreover, he argues that because his account of groups can accommodate what might be groups that others can’t—in particular, supposed groups like queues and multitudes that are significantly less structured than, e.g., departments of philosophy—we should prefer it to Fine’s. As he puts it, “neither queues nor multitudes appear to demand much of their individual members.” They must “[embody] a certain spatial arrangement but they do not seem to require a shared intentionality or agency from their members” (Uzquiano 2018, 423). In other words, though individuals that are “members” of queues embody minimal arrangements such that they’re queues, this doesn’t entail that they’re one.²⁴

However, neither Fine nor Uzquiano say what kinds of principles define groups rather than other variable embodiments. In other words, neither gives us an account of what it is to be a group—what defines group—such that we can distinguish embodiments that are groups from those that aren’t. Ultimately, that’s a desirable feature of the theory of embodiment. It was developed as an alternative to traditional accounts of mereological composition. It tells us what kinds of things groups are, not what it is to be a group per se. As a result, it doesn’t presuppose an answer to the definitional question. And that’s good.

But now we can see how both Fine and Uzquiano might answer it. For we can trace the differences between bikes and departments of philosophy to the principles they embody. Whereas my bike’s parts might embody one functional arrangement—a principle that specifies what the relevant bits of rubber and metal do (e.g., enable riding)—a department of philosophy will embody another functional arrangement—concerning what it does (i.e., philosophy). As a result, Fineans can appeal to Functionalism to explain what it is to be a group per se. In particular, it can explain which embodiments are groups and which aren’t by appealing to the distinctive kinds of principles the individuals that are their members embody. Because Fine and Uzquiano can agree that groups are functional, then Functionalism is compatible with both monism and pluralism.

3 The Arguments from Difference & Sameness

Now we’re ready for the biggest bit: the arguments from Difference and Sameness. (Here²⁵ they are for easy access.) Again, they’re supposed to be problems for a pluralistic account of the kinds of things groups are and not for a functionalist account of group. They’re supposed to imperil the pluralist’s answer to the ontological question. In this section, I argue that an attractive version of functionalist pluralism is invulnerable to them. In particular, I argue that the arguments from Difference and Sameness obscure a distinction between relations I call “being grouped” and “being a member.” Once we distinguish them, Functionalism comes to the rescue, and pluralism is back in business.

3.1 The Arguments

Again, that paradigmatic groups can have different members both at different times and in different worlds is widely accepted as a constraint on accounts of what they are. I call it:

It’s plausible that departments of philosophy can, e.g., hire professors. In particular, it’s plausible that the department once had members it no longer does and that it might have had members it never did. Nonetheless, it’s precisely the department it either was or might have been. If so, Difference is true.

Moreover, that different groups can have the same members both at the same times and in the same worlds is widely accepted as a constraint on accounts of what they are. I call it:

The department and its bowlers, the HaeXeities, might have exactly the same members. Nonetheless, it’s plausible that the department isn’t identical to the HaeXeities. For instance, whereas members of the department are expected to behave decorously in departmental dealings—and, so, might be sanctioned for misbehaving—the HaeXeities aren’t; anything goes on the lanes. If so, Sameness is true.

But because it’s widely accepted that pluralities have their “members” essentially, it’s widely accepted that pluralities can’t have different members at either different times or in different worlds. If the plurality of individuals that are members of the department here and now—Jonathan, Jennifer, and Julia—consists of them essentially, it consists of them necessarily and, so, at every time and in every world.

As a result, both Difference and Sameness presuppose a principle of extensionality for pluralities:

Assuming Extensionality, pluralism entails that for groups to be different is for them to have different members, and for them to be the same is for them to have the same members. Because Jonathan, Jennifer, and Julia couldn’t be Jonathan, Jennifer, and Julia, and Jim, pluralism entails that each is a different plurality and, so, that the department can’t have different members at different times and in different worlds. Hence the argument from Difference. Similarly, if groups are pluralities, the department and the HaeXeities aren’t different groups because they have exactly the same members: Jonathan, Jennifer, and Julia. Hence the argument from Sameness.

The arguments from Difference and Sameness have become the arguments against pluralism in the literature, and, so, they’re rarely resisted.²⁶ Nonetheless, the arguments are misleading. In keeping with Extensionality, it’s important to emphasize that (2) and (5) are true if and only if pluralism is the view that

Again, Extensionality entails that the department is its members, that they are the department, because the relevant individuals are “members” of the plurality with which it’s identical. Similarly, the HaeXeities is its members, they are the HaeXeities, because the relevant individuals are “members” of the plurality with which it’s identical.

However, there’s no one thing it is to be either one or many, and, so, there are different versions of pluralism to which the arguments are inattentive.²⁷ As a result, neither (i) nor (ii) is entailed by pluralism per se. Rather, they constitute a—particularly naïve—version of pluralism that both monists and pluralists are right to resist. Because both (i) and (ii) are required to substantiate the arguments from Difference and Sameness, then they misrepresent pluralism.

The basic idea is this. The arguments from Difference and Sameness assume that Extensionality entails that pluralism per se is false. However, there’s an intuitive version of functionalist pluralism that’s compatible with Extensionality. If that’s right, (2) and (5) are false, and the arguments from Difference and Sameness are unsound. That’s what I argue in this section.

3.2 Being Grouped vs. Being a Member

I begin with a distinction:

And

Minimally, Being Grouped is a multigrade relation. Although it’s a relation between $\mathrm{G}$ and its members, its members’ slot doesn’t have a definite degree: at some times and in some worlds, some number of members stand in this relation, and at other times and in other worlds, another number of members do. However, Being a Member is a unigrade relation; its members’ slot does have a definite degree. In particular, it’s a binary relation in which a group stands to a particular individual.²⁸

That’s sufficient to distinguish Being Grouped and Being a Member. They’re different relations because they have different properties. But it’s especially important to distinguish them because they imply the distinction between (i) and (ii). For the claim that $\mathrm{G}$ is identical to $ab$ is a claim about the relation between a group and its members. Something makes a particular collection of individuals a group rather than a mere collection of individuals. Jonathan, Jennifer, and Julia are the department, in other words, because they’re related to it in a particular way; they do this and not that. Again, if (i) is true, this relation is identity (i.e., to $ab$).

Moreover, the claim that to be a member of $ab$ is to be a “member” of $ab$ is a claim about the relation between the individuals that are a group’s members and the group of which they’re members. Again, something makes a particular individual a member of a particular group. Julia is a member of the department because she’s related to it in a particular way. And, again, if (ii) is true, this relation is identity (i.e., to either $a$ or $b$).

3.3 Functionalist Pluralism: Roles

Importantly, to distinguish Being Grouped from Being a Member is to recognize both that they needn’t be identity and that neither (i) entails (ii) nor that (ii) entails (i). Here’s a version of pluralism that does the work:

Simply: the collection of individuals we call the Department of Philosophy is a group because the kind of which it’s an instance—department of philosophy—is defined by a set of functional roles the individuals that are its members realize.³⁰

Importantly, in defining groups in terms of functional roles, Roles is a structuralist account of groups. As I suggested in section 1, arrangements are essentially relational. There are no roofs without frames, and there are no frames without foundations. Analogously, there are no pitchers without catchers, no catchers without pitchers. The position pitcher is defined by the pitches to relation and thereby catcher, and the position catcher is defined by the returns to relation and thereby pitcher. And that’s what Roles implies. Every group is defined by a plurality of functional roles, each of which is played by particular individuals that are embedded within wider social systems. Roles is holistic, too.

A quick clarification. It’s plausible that a version of the ontological question arises for Roles. Philosophers interested in groups have said remarkably little about the metaphysics of roles and, so, about what it is to play one.³¹ Here, then, is another detail about which functionalists might disagree. I’ll refer to role-types and role-tokens to simplify matters, but I intend to remain ecumenical with respect to their metaphysics. We can reasonably expect any account of roles to satisfy the corresponding versions of Difference and Sameness.

3.4 Responding to the Arguments from Difference and Sameness

Roles reveals that (i) doesn’t entail (ii). The first of these claims—that $\mathrm{G}$ is identical to $ab$—is neutral both with respect to what $a$ and $b$ are and with respect to what it is to be a member of $\mathrm{G}$. In particular, it tells us that $a$ and $b$ aren’t individuals but the roles they play.³² And, in that case, (ii) doesn’t entail (i) either.

For if $\mathrm{G}$ is identical to a plurality of functional role-types, $rr$, that define the kind in question—and not to a plurality of individuals, $ab$, with which they’re easily confused—to be a member of $\mathrm{G}$ is to be a “member” of $rr$, to be identical to either role-type. To identify a plurality’s “members” is to identify that of which it’s a plurality; to identify a group’s members isn’t to identify the role-types of which it’s a plurality. To claim that role-types are members of groups would significantly strain our—admittedly pre-theoretical—conception of membership. Rather, it’s to identify the individuals that play the roles of which it’s a plurality, that “are” the role-tokens of those role-types in the way that Jonathan “is” the department’s chair. As a result, there are grounds for claiming that whereas “membership” is extensional, membership proper is non-extensional, and, so, that membership isn’t “membership” (contra (ii)).

As a result, the claim that to be a member of $\mathrm{G}$ is to be a “member” of $ab$ is neutral both with respect to what $a$ and $b$ are and with respect to what it is for the individuals that are a group’s members to be grouped. We can suppose that $a$ and $b$ are particular individuals rather than the roles they play and that to be a member of $\mathrm{G}$ is to be a “member” of $ab$. Still, it’s compatible with this view that the relation between $\mathrm{G}$ and $ab$ isn’t identity. Again, on Functionalism, it’s realization. In other words, it’s compatible with (ii) that $\mathrm{G}$ exists because $rr$ does, that $\mathrm{G}$ is a plurality of these role-types that’s realized by a plurality of individuals that play them at particular times and in particular worlds (contra (i)). And this allows that $\mathrm{G}$ itself might be realized by different pluralities at different times and in different worlds. As a result, the functionalist pluralist needn’t reject Extensionality to reply to the arguments from Difference and Sameness.³³

To summarize: Roles entails that (2) and (5) are false because it distinguishes being grouped (via (A)) from being a member of (via (C)), where Being a Member is non-extensional (via (B)). Pluralism is back in business.³⁴

4 Functionalist Monism vs. Functionalist Pluralism: A Challenge

That’s interesting enough. Whether the argument that follows is successful, we’ll have made some progress: the arguments from Difference and Sameness presuppose an account of pluralism that we shouldn’t accept, and, so, they’re unsound. But that does nothing to recommend pluralism. That pluralism is invulnerable to the arguments from Difference and Sameness is one thing. That we should accept it is another.

In this section, I give it a try. I argue that the fact that groups are partly individuated by the structured social systems in which they’re embedded (per Functionalism) is an obstacle for functionalist monism. Because monism recommends the view that groups are exclusively individuated by the relations their members realize “internally,” its conception of the kinds of things groups are is a liability. To the extent that we favor Functionalism, then we’ve reason to disfavor functionalist monism and to favor functionalist pluralism.

A note. I’m not claiming that the challenge I raise for functionalist monism is dispositive. Functionalist monism is a powerful view of the metaphysics of groups, and it has powerful resources. Rather, I’m claiming that it’s a meaningful challenge for functionalist monism, both independently and because of its implications for functionalist pluralism. As a result, I offer it to both functionalist monists and functionalist pluralists. It represents a significant point of disagreement among them that’s worth exploring.

4.1 Internal and External Structure

Let’s return to the view that groups are embedded in structured social systems. In a series of influential papers, Ritchie (2013, 2015, 2020) defends an account of groups according to which groups are—deep breath—elements-realizing-social-structure. Groups are singular things, and their elements (e.g., their members) are arranged in particular ways.³⁵ As a result, her account substantiates the arranging/arrangement distinction I introduced in section 1: a group’s elements are arranged in realizing an arrangement, and arrangements are the social structures they realize. The Red Sox’s members realize a particular social structure consisting in part of pitcher and catcher.

Ritchie’s is an exceptionally insightful account of groups, innovative and rich with nuance. But one of its innovations is especially important in understanding both groups and the structured social systems in which they’re embedded. She distinguishes what she calls “internal” and “external” ways the individuals that are a group’s members realize social structure. In particular, she claims that a group is internally structured when precisely its members are arranged in particular ways and externally structured when it and/or its members and other groups and/or their members are arranged in particular ways. For instance, Bertrand Russell University is internally structured relative to both the College of Liberal Arts and the Department of Philosophy, the College of Liberal Arts is externally structured relative to the Bertrand Russell University and internally structured relative to the Department of Philosophy, and the Department of Philosophy is internally structured relative to its members and externally structured relative to both the College of Liberal Arts and Bertrand Russell University.

That’s quite plausible. But there are several things to emphasize about Ritchie’s account. First, she claims that groups are internally and externally structured relative to both their members and other groups and/or their members. The Department of Philosophy is externally structured relative to both the College of Liberal Arts and Bertrand Russell University, yes. But it’s externally related relative to the HeXaeities, with which it’s co-extensive, too. There are uncountably many social structures particular groups realize and, so, uncountably many ways they’re structured relative to one another.

Second, and again, Ritchie develops the internal/external distinction by appealing to Shapiro (1997)’s account of mathematical structure. Shapiro distinguishes “systems” and “structures” and claims that a system is a “collection of [particular elements] with certain relations” (Shapiro 1997, 73), and a structure is “the abstract form of a system, highlighting the interrelationships among the [particular elements]” (Shapiro 1997, 74). Analogously, Ritchie accepts that whereas groups are systems whose elements are arranged in this or that way, a group’s structure is the arrangement their elements realize. Groups are internally and externally structured in whatever ways the arrangements they realize specify.

Shapiro represents structures hypergraphically in terms of “nodes”—or positions things occupy—and edges—or relations that link them. Ritchie does, too, claiming that

the structure of a group can be represented with nodes […] and edges connecting nodes to other nodes. The edges of a structure capture the relations that hold between nodes. Since all members of a group are related to some degree, each node in structure S is connected to every other node in S. (Ritchie 2013, 268)

As a result, she precisifies her internal/external distinction hypergraphically: a group is internally structured when “all the relevant nodes are occupied by its members and every member occupies some node or other” (Ritchie 2020, 409), and externally structured if and only if its elements “occupy only some node/s” of the relevant internal structures and when “other nodes […] are occupied by entities or systems that are not” among them (Ritchie 2020, 410).

Third, the internal/external distinction doesn’t tell us how particular groups are individuated. But we can and should ask how they are. In particular, we can and should ask why—that is, in virtue of what³⁶—the College of Liberal Arts is externally structured relative to Bertrand Russell University rather than to the ALE and internally structured relative to the Department of Philosophy rather than to the Red Sox in the ways it is. Again, the internal/external distinction doesn’t say which of these social structures is privileged relative to the College of Liberal Arts. But, of course, exactly one is: the department of philosophy structure. As a result, we’ll want more.

4.2 A Challenge

Luckily, Functionalism gives us more. Suppose the individuals that are the Red Sox’s members are precisely the individuals that are the Department of Philosophy’s members. But, of course, they’re different groups, and Functionalism accounts for the fact that they’re different groups by appealing to the functions they serve. It says that whereas the Red Sox function in one way—the baseball team way—the Department of Philosophy functions in another way—the department of philosophy way—whatever these amount to.

As a result, Functionalism implies that we can’t account for the fact that the Red Sox and the Department of Philosophy are different groups by appealing to the ways the relevant individuals are arranged. We’ve supposed that the individuals that are members of both groups are arranged in both ways. Nonetheless, the individuals that are the Red Sox’s members aren’t arranged in being, e.g., teachers, nor are the individuals that are members of the Department of Philosophy’s arranged in being pitchers. In other words, although the individuals that are the Red Sox’s members are teachers, they don’t do philosophy as members of a baseball team. Likewise, although the individuals that are the Department of Philosophy’s members are pitchers, they don’t play baseball as members of a department of philosophy. However, we can account for the fact that the Red Sox and the Department of Philosophy are different groups by appealing to the different functions they serve.

Here it’s especially important to emphasize that, according to Functionalism, the Department of Philosophy is the kind of group it is because the collection of individuals that are its members serve a particular function within a particular social system. The individuals that are members of the Red Sox don’t play baseball simpliciter. Rather, they play baseball in the ALE. If we can’t appeal to the ALE in individuating the Red Sox, we can’t distinguish it from either departments of philosophy with the same members or—more importantly—from other baseball teams (e.g., The Dodgers). Similarly, the individuals that are members of the Department of Philosophy don’t do philosophy simpliciter. Again, if we can’t appeal to the College of Liberal Arts, we can’t distinguish it from either baseball teams with the same members or—again, more importantly—from other departments of philosophy (e.g., at David Lewis University). As a result, Functionalism implies that a group’s external structure plays a distinctive role in individuating them. In particular, it implies that the Red Sox and the Department of Philosophy are different groups because each is embedded in different social systems that thereby structure them.

Now for the important point. The functionalist’s emphasis on external structure seems to be in tension with the view that the individuals that are a group’s members are singular entities. For if groups are “unified wholes,” they have identifiable boundaries that mark them off from one another. In particular, they’re marked off by their intrinsic rather than their extrinsic properties. Indeed, that’s what intrinsic properties are: properties things have that don’t “mention” other things. But because Functionalism entails that group kinds are extrinsic to the collections of individuals that realize them, it seems in conflict with the view that they’re singular entities that exclude the groups that are external to them.

Although Ritchie isn’t my primary target, let’s consider an explicitly functionalist version of her account and see whether it has the resources to respond. Surely, her conception of internal/external structure captures the fact that the Department of Philosophy is externally structured relative to the College of Liberal Arts in being bound by its charter. Per Shapirian structuralism, the relevant complex of relations is there, and we abstract it. But as singular entities with identifiable boundaries, it’s not clear that she’s entitled to the view that particular groups are partly individuated by their external structures. Again, as she suggests, whereas a group is internally structured when “all the relevant nodes are occupied by its members and every member occupies some node or other” (Ritchie 2020, 409), it’s externally structured if and only if its elements “occupy only some node/s” of the relevant internal structures and when “other nodes […] are occupied by entities or systems that are not” among them (Ritchie 2020, 410, emphasis added). And it’s precisely this that makes a group’s external structure “stand outside” the singular entities—the groups—that are thereby externally related to it. In other words, the view that groups are singular entities seems to imply that they’re individuated exclusively by their internal structures. But that’s the problem.

There’s a good question about how singular entities are individuated, of course.³⁷ There are certainly accounts of singular entities that don’t have this result. (Fine’s is one of them, and I’ll consider it shortly.) But because Ritchie’s account of groups has it that we abstract structures from whatever social systems are there already, it’s difficult to see how she might individuate precisely the “right” social systems (i.e., the Department of Philosophy) rather than others (e.g., the Department of Philosophy + the Red Sox) without privileging their internal structures. In other words, it’s difficult to see how she isn’t committed to the view that a particular group is individuated exclusively by its internal structure when what’s there to be extracted is a tangle of relations, both internal and external, only some of which unify the group in question.

Luckily, Ritchie has options, and each is worthy of significant consideration. Again, I don’t claim that this challenge to functionalist monism is dispositive, only that it’s worth considering. I’ll consider one.

She might accept that the Department of Philosophy and the College of Liberal Arts are asymmetrically, internally related. It’s certainly true that they stand in a kind of asymmetric relation. There’s a function they serve that entails it, and that’s realized when the Department of Philosophy is bound by its charter. But that seems to require that the College of Liberal Arts and Department of Philosophy aren’t different groups. In particular, it seems to require that the realization of structure to which the Department of Philosophy corresponds is the realization of structure to which the College of Liberal Arts since the function they serve unifies them.

And this problem compounds the further up the hierarchy we go. For to retain the view that the relevant functions are served by whatever singular entities they unify, we seem compelled to search out ever larger social systems to accommodate the view that the groups to which they correspond have identifiable boundaries. Again, the Department of Philosophy will become a member of the College of Liberal Arts such that the members of each are in fact internally related. Moreover, the College of Liberal Arts will become a member of Bertrand Russell University such that all of their members are internally related, too. But, again, that robs us of the view that these are different groups. Whether this commits Ritchie to the existence of a single group—society itself, say—is beside the point.³⁸ The point is that in order to accommodate the view that groups are individuated by whatever functions unify their members, she’ll commit herself to an implausible view of their interrelations.³⁹

Functionalist Fineanism recommends a different response, one that might be available to Ritchie, too. (However, her failure to account for the role group kinds play in individuating groups remains a problem.) But although Fine doesn’t have the problem I’ve raised for Ritchie’s account, he has a relevantly similar problem.

Importantly, Fine can reasonably deny that groups are individuated solely by the relations their members realize internally; in particular, because there are no restrictions on the content of the principles of embodiment they manifest. Again, he might accept that though we individuate the department by its relation to the university, the university isn’t part of that thing, the department. In particular, he might insist that because the relevant principles of embodiment are functional, particular extrinsic—or, in Ritchie’s sense, external—relations are needed to pick out the particular collections of individuals they unify. He’s entitled to use Ritchie’s distinction in that way.

For instance, he might say that to the extent that the Red Sox are a baseball team, the individuals that are its members are unified by the relations that define baseball team. Nonetheless, they’re individuated by their relations to, e.g., the ALE—and, so, to the MLB—and to the City of Boston, too, because the relations between them are what make the Red Sox the unique instance of the kind it is; the very group it is. In other words, whereas the internal relations that make them a baseball team unify them, the external relations that make them the baseball team in question—the Red Sox—don’t.

Nonetheless, this response makes Finean principles of embodiment intolerably arbitrary.⁴⁰ In particular, it suggests that if a group is individuated both by the structures it realizes internally and externally, there isn’t a principled distinction between a particular group and the groups to which it’s externally related. This is a version of the challenge raised for Ritchie. For if, in order to individuate the relevant collections of individuals, principles of embodiment appeal to relations that aren’t definitional of the kinds of groups in question, it will be difficult to say which groups are which and why. That the department is unified by a principle that appeals to relations that don’t unify the individuals that are its members—in this case, to the university—is at best stipulative. In other words, if variable embodiment is unifying, it’s not clear why that which is externally related to that which is internal to a particular group doesn’t have as much a right to be counted as part of the same group. As a result, it’s not clear that he's justified in claiming that genuine unification occurs.

Relatedly, this response makes it impossible to tell whether to prefer Fine’s monism to Uzquiano’s pluralism. Again, Uzquiano claims that the relevant principles of embodiment don’t stamp out singular but plural “entities.” But since each assumes that principles of embodiment are either singular or plural, it’s difficult to know how to decide between them. For both Fine and Uzquiano accept that for variable embodiments to be identical is for “them” to embody the same principle of embodiment. But if principles of embodiment are individuated by their modal profiles—as Fine (1999, 70) and Uzquiano (2018, 442)’s remarks suggest—it’s not clear why we should think that a given group embodies a plural rather than a singular condition.⁴¹ (This is as much a problem for Uzquiano as it is for Fine, of course, but I’ll set that aside.)

4.3 Functionalist Pluralism: Redux

However, this isn’t a problem for the functionalist pluralist; in particular, for Roles. For given the distinction between internal and external structure, we can accept that groups are structured by the internal relations among the roles that ground their existence. We can accept that some of the roles departments of philosophy realize depend on others. For instance, we can accept that the role of being an associate professor is tied to the role of being an assistant professor in the way the role of being a pain is tied to that of being a wince. And though the proponent of Roles accepts that the roles in question are interrelated, they get to deny that groups are unified by the relations among them. In particular, they have principled reasons to deny that groups are individuated solely by these relations and to accept that they’re at least partly individuated by the social systems in which they’re embedded. Their pluralism is precisely what vindicates their Functionalism.

But, again, there are details to sort out. And, again, how a functionalist pluralist ought to conceive of structured social systems is important. Here’s what I’m inclined to say. As I suggested in section 1, Functionalism ranges over social systems. Given what I’ve said here, then, we might think of social systems as consisting of clusters of role-tokens, each of which corresponds to a group.⁴² How tightly pluralities of roles cluster will correspond to the specificity of the functions they realize. For instance, the Red Sox play roles that are clearly defined by the function they serve—again, to play baseball in a particular way within a particular set of institutions. However, genders—for instance, women—play roles that aren’t as clearly defined and that interact with different roles—for instance, with race and class roles—in complicated ways.

But, again, because clusters of roles aren’t singular entities, we can individuate them both by the structures they realize internally—that is, by the relations among the roles in question and because of which they can be said to cluster—and/or the structures they realize externally—that is, by their relation to other clusters. For instance, we can individuate the Department of Philosophy by identifying the roles the relevant individuals realize. And we can identify these by identifying the function they realize within the relevant set of institutions—and, ultimately, the maximal social system—in question. The Department of Philosophy is the department it is because it does philosophy in a particular way within a broader social system within which the other groups to which it’s related are embedded, too.

5 Conclusion

In this paper, I’ve argued that the arguments from Difference and Sameness are unsound. They obscure both the distinction between the definitional and ontological questions and between Being Grouped and Being a Member. I’ve articulated a version of functionalist pluralism—what I called Roles—that bears this out.

Moreover, I’ve argued that once we make these distinctions, we see that the crucial question is whether the grouping relation is monistic or pluralistic, in particular, whether or not grouping is unifying. I’ve argued that if groups are one, the grouping relation is unifying and that this raises an important difficulty for the functionalist monist, namely, the problem of how to individuate groups. I’ve argued that if groups are many, this problem doesn’t arise.

Although the implications for pluralism are clear, one of my aims is to generate interest in Functionalism about groups, whether monistic or pluralistic. As I’ve suggested, there are important details about which we might reasonably disagree. Nonetheless, I hope to have shown we have reason to attend to them and, so, to treat Functionalism as a viable metaphysical framework for theorizing about groups.

Acknowledgements

THANKS

References