5 Tools and Terminology

This chapter offers a few basic tools of metaphysics, including the following:

This is a long list. Rather than giving a complete or systematic presentation, I will try to offer a reasonably precise way to make and assess claims about the nature of the social world. There are many models we might use for accomplishing this, but as much as possible I will stick to the standard interpretation of the standard tools. (The discussion of “grounding” is a minor exception, for reasons I will discuss.)

Let’s start with a couple of facts: The Earth is round, and Bill Clinton was president of the United States in 1994. These are facts about the world. We use language to talk about them, but they are facts about a planet, a shape, a person, and a social property, not facts about language.

A three-part model for organizing these points distinguishes (1) the world, (2) abstract representations of the world, and (3) language, or ways of speaking about the world. According to this model, the sentence ‘Bill Clinton was president of the United States in 1994’ expresses a proposition. The same proposition can be expressed with other sentences as well. For example, ‘The President of the United States in 1994 was Bill Clinton’, or ‘Bill Clinton était président des États-Unis en 1994.’ Because it is a fact that Bill Clinton was president of the United States in 1994, the proposition representing that fact is true.

Facts are things in the actual world. Propositions are abstract representations of the world. Some propositions are true and some are false. The true propositions are the ones that correspond to the facts, and the false propositions are the ones that do not. Each fact corresponds to a true proposition.¹

Sentences are expressions in particular languages, but propositions do not depend on language. Before there were people, there was no language, and no sentences to express propositions. But there were still true and false propositions.² The proposition expressed by the sentence ‘The Earth is round’ would have been true even if people had never existed, because it is an abstract representation of the fact that the Earth is round. Which would be true even without us. Some propositions are about language, like the proposition expressed by the sentence, ‘“A” is the first letter of the alphabet.’ But many propositions are not.

Propositions are not linguistic, nor are most of them about language. Still, we do use language to express propositions. Furthermore, we also use language to denote facts and propositions, i.e., to specify which fact or proposition we are talking about. When I am being precise, I will use italics for propositions, and bold italics for facts. For instance:

(5.1) The proposition The Earth is round is true.

(5.2) The fact The Earth is round obtains.

Notice that (5.2) does not say that the fact The Earth is round is “true.” Facts are not true or false, any more than a chair or a lake is true or false. An object exists and similarly a fact obtains, or is the case. A proposition corresponding to a fact is true if and only if that fact obtains.

Some propositions are true, and some are false. For example, the proposition Bill Clinton was president of the United States is true, and the proposition Chelsea Clinton was president of the United States is false. Equally, we can distinguish (actual) facts from possible facts. Possible facts are things that might obtain in the world, some of which actually obtain and others of which do not. For example, the possible fact Bill Clinton was president of the United States actually obtains, whereas the possible fact Chelsea Clinton was president of the United States does not. But both are alike in terms of being possible facts.

Some people are queasy about talk of possibilities, and about treating possible facts similarly to how we treat facts. But this model is convenient. Possible facts correspond to propositions, and each possible fact that obtains in the actual world corresponds to a true proposition. This is particularly helpful for thinking systematically about the sciences. When we build models in the sciences, we are not only interested in the way things actually are, but how they would be if things changed. How would unemployment change if we raised interest rates? How would educational attainment change if we increased standardized testing? These are questions about ways the world might be. Similarly, we might model the circumstances in which Chelsea Clinton is president of the United States obtains. In such a model, we could consider what other facts have to obtain in order for it to obtain.

Another convenience is to talk about “possible worlds” as a whole, and to compare them to one another. A good deal of debate in metaphysics is dedicated to the question of how to understand possible worlds. Are they fictions? Concrete objects? Linguistic constructions? Complex properties? Shadowy “ways things might be”? For our purposes, it does not much matter which of these we adopt. We can avail ourselves of talk like “In some possible worlds, Chelsea Clinton is president of the United States,” and “In all possible worlds, two plus two equals four,” without committing ourselves to a particular theory of possible worlds, or possible facts.³

It is now standard to cash out the ideas of necessity, contingency, and impossibility, in terms of possible worlds. Whether a proposition is true or false often depends on the way the world is, although some propositions are true or false regardless of the way the world is. For instance, the proposition Bill Clinton was president of the United States is true. If things were different in the world, that proposition would be false. Such a proposition is contingent. The proposition 2 + 2 = 4, on the other hand, is true however the world might be. This proposition is necessary—that is, true in every possible world. And the proposition 2 + 2 = 5 is false however the world might be. It is, in other words, impossible—false in every possible world.

Just as the person Bill Clinton is not the same thing as the name ‘Bill Clinton’, we also need to distinguish properties from the predicates we use to denote them. The expression ‘being president of the United States’ is a predicate. It is a linguistic item. That predicate denotes a property, that is, the property being president of the United States.

The predicate ‘is taller than’ expresses a relation between two objects, not a property of a single object. The predicate ‘is taller than’ is called a binary (or two-place) predicate, and the relation is taller than is called a binary (or two-place) relation. Thus the sentence ‘Bill is taller than Hillary’ consists of two names and a binary predicate, and the proposition Bill is taller than Hillary consists of two objects—Bill and Hillary—and a binary relation that holds between them—the is taller than relation. Sometimes I will flank the relation with letters, to make it clear that is a binary relation: for instance, the relation A is taller than B.

There are also three-place predicates and relations, four-place predicates and relations, and so on up. For instance, if Carol is sitting between Bob and Alice, then the three-place sitting between relation holds of the three objects Carol, Bob, and Alice.

Objects actually have (or instantiate) some properties, and possibly have others. Chelsea Clinton, for instance, has the property being the daughter of Bill and Hillary, and possibly has the property being president of the United States. In any possible world, any given object either does or does not have any given property. Additionally, it should be stressed that how a property is instantiated does not change over time. Of course, the properties that a given object instantiates can change over time. For instance, the color of a particular piece of clothing may fade over time, for example from bright red to pale red to pink. But what it takes for something to have the property being bright red remains invariant over time.

To put this point differently, we might associate with a property a set of “instantiation conditions.” For a given property P, the instantiation conditions are simply other properties, such that necessarily an object has P if and only if that object has properties R and S and T, for example.⁴ Instantiation conditions like these do not change over time or possibilities. Even a property that involves a particular time, such as being president of the United States in 1994, has fixed instantiation conditions.

I will use this same model of properties for social properties, just like any other property. For instance, Bill Clinton changed from having the property being governor of Arkansas to being president of the United States. But the conditions for his having either of these properties did not. “But suppose,” one might object, “the Arkansas legislature changed the law about how governors are elected. In that case, wouldn’t it be true that the instantiation conditions for the property being governor of Arkansas have changed?” Not according to the model of properties we are using. To make sense of this, we can understand the instantiation conditions to be something like satisfying whatever conditions the Arkansas legislature sets out for being governor. Or we can simply take there to be two different properties having different instantiation conditions, the property being-governor-of-Arkansas-before and the property being-governor-of-Arkansas-after.

This model is, of course, an idealization. We do identify the before and after versions of such properties, as being a change in a single property. But there are two good reasons for pushing that burr under the carpet. First, in order to make sense of it, we would need a more sophisticated apparatus than I can discuss in this book. We would need a model of how a given property can be “anchored” and “re-anchored,” over and over again, while remaining the same property. (Anchoring is a topic I introduce in the next chapter.) That, however, would require us to revise more metaphysics than is practical or needed for now. So, for our purposes, properties have unchanging instantiation conditions, both over all times and across all possibilities.

Second, there are advantages to this model of properties—that is, as having unchanging instantiation conditions over time. When we want to assess whether a given object has a given property, we want to do it in a single way, regardless of the time or circumstances we are assessing. Otherwise there is no way to compare whether things have changed. Consider, for instance, a proposition about some change over time, something like Clothing has become more brightly colored over the course of the last century. We do not want the truth or falsity of that proposition to depend on changing conditions for what it takes to be brightly colored. Instead, we take the property being brightly colored to have fixed instantiation conditions, throughout that period.⁵

So long as we are being clear about properties and relations, we should also be clear about what sorts of things they apply to—that is, their relata. For instance, I have already mentioned the supervenience relation. The literature sometimes gets quite confused because it is vague about the relata of this relation, that is, what supervenes on what. As I pointed out, supervenience is best (and most commonly) understood as a relation between sets of properties. But this is often muddied, with people talking about it as relating sets of facts, events or even sets of predicates. Although these may seem innocuous, they are not, as I will discuss later on.

In the passage I quoted earlier, Kincaid says: “Once all the relevant facts (expressed in the preferred individualist vocabulary) about individuals are set, then so too are all the facts about social entities, events, etc.” But when is a given fact a fact about individuals? Kincaid seems to suggest that it has something to do with being expressed in “the preferred individualist vocabulary.” But this cannot be right. Facts are unaffected by the way we describe them, in the same way that the moon is unaffected by the ways we describe it—e.g., calling it ‘la luna’. Fortunately, the model I have described points us in a more fruitful direction. Consider an example from the last chapter:

(5.3) Bob, Jane, Tim, Joe, Linda, . . . and Max ran down Howe Street.

(5.4) The mob ran down Howe Street.

Are (5.3) and (5.4) the same fact? It is understandable why one might think they are. Both obtain, and at least in some limited sense, there is nothing more to the mob than those people. But there are at least two reasons that (5.3) and (5.4) denote different facts. One is that there is a possible world in which (5.3) is the case and (5.4) is not, and another possible world in which the reverse is the case. (Consider a world in which Bob and the others are running down different parts of Howe Street, maybe in different directions. Though they are all running down Howe Street, they are not a mob. And consider a world in which the mob is running, but Bob leaves the mob.) If they denoted the same fact, one could not obtain without the other.

Here, however, I also want to highlight another reason these are two different facts. In the model I have described, facts correspond to propositions, and the corresponding propositions are different. One is a proposition having Bob, Jane, and the others as constituents,⁶ and the other is a proposition having the mob as a constituent. There are two different propositions, and hence there are two different facts: one about individuals and one about a mob.⁷ Notice that this has nothing to do with language, or the vocabulary in which anything is expressed. The way we distinguish facts from one another corresponds to the way we distinguish propositions from one another, not the way we distinguish sentences from one another.

As a rough guide, we can take a social fact to be a fact that corresponds to a proposition that has any social entity as a constituent. It might have social objects as constituents, or it might have social properties as constituents, or both. Of the four facts listed in table 5a, the first three are all plausibly social facts, and the fourth is not:

Some people talk only about social objects, and some only about social properties. But if we are talking about social facts, we cannot limit ourselves to just one or the other.⁸

It is common nowadays for philosophers to speak of “social kinds” or “human kinds.” This is a term introduced by analogy to “natural kinds,” which have long been discussed in metaphysics and philosophy of language. The intuitive idea of a natural kind is a category of objects grouped naturally, rather than arbitrarily or by fiat. Typical examples given of natural kinds include kinds in physics, such as electron and charge, kinds in chemistry, such as gold and water, and kinds in biology, such as the various species. A gold ring, a gold bar, and a gold nugget, for instance, all group together into a category because of their chemical composition, which does not depend on human choices or interests.

It is controversial which kinds are natural, and even whether there are any natural kinds at all. But, these debates notwithstanding, natural kinds seem to have some distinctive characteristics. John Stuart Mill, for instance, observed that they form the basis for inductive inferences in the sciences. By investigating certain gold things, testing and analyzing their characteristics, we can draw inductive inferences about other gold things. Another characteristic natural kinds seem to have is that they are essential to their members. If something is a piece of gold, then it is essentially a piece of gold: it could not be changed into lead without being destroyed. This is a more controversial thesis, and the relation between natural kinds and essentialism remains hotly debated.

The notion of a social kind is somewhat looser. It is convenient to distinguish social kinds from social properties more generally, largely because social kinds seem to figure in the social sciences similarly to how natural kinds figure in the natural sciences. Social scientists commonly use terms like ‘class division’, ‘religiously sanctioned inequality’, ‘economic factor’, ‘material circumstances’, ‘public good’, ‘commodity’, and so on. These terms are grammatically similar to natural kind terms, and the things they refer to seem to work in inductions, just as natural kinds do. On the other hand, it is certainly wrong to think of these categories as being independent of human activity, and it is not clear that they have the other distinctive characteristics that natural kinds do.

In speaking about social kinds, then, it is useful to think of them as the categories we might use in the social sciences, but remain open-minded about the sorts of categories these might be. Maybe the social kinds are the same as the social properties. Maybe they are a subset of the social properties. Or maybe they are a different thing altogether. To make progress, we do not need to start with a comprehensive understanding. We can just regard “social kind” as a generic way of referring to categories like these.

Social kinds—like social properties—have fixed instantiation conditions. Or, more appropriately, we might say that kinds have fixed membership conditions. The conditions under which something is a member of a social kind are the same across all times and possibilities. The reason for this is the same as the one I gave above. Social kinds serve a variety of functions: we employ them for recognizing things, classifying things in various situations, finding and correcting departures from norms, drawing inductive inferences, and accomplishing other practical matters.

As such, they are applicable across a universe of different situations: we can look at any object whatever, in any situation, and assess whether that object is a member of the kind teacher, tire, hem, or hipster. That does not mean that social kinds are not put in place by local contexts in the actual world. The kind hipster, for instance, is put in place by a range of idiosyncratic facts about our current society. But its potential instantiation is not limited to that current situation. The membership conditions for hipster, in other words, are what they are for a panoply of reasons. But the conditions are the conditions, and we can look around at all possible objects in all possibilities to see if those conditions apply, not just at the objects in our local context.

Consider again the following two facts:

(5.3) Bob, Jane, Tim, Joe, Linda, . . . and Max ran down Howe Street.

(5.4) The mob ran down Howe Street.

As I pointed out earlier, (5.3) and (5.4) are different facts. Nevertheless, they are intimately related. On Tuesday evening, both obtained at 10:00 and were the case until 10:25. Then, at 10:26 neither obtained. Then at 11:08 they obtained again, and at 11:37 did not obtain.⁹ In fact, every time those people ran together down Howe Street, the mob did. An amazing coincidence!

Of course, the coincidence is not so amazing. These are not two arbitrary facts, but are related to one another in a particular way. Fact (5.4) obtains at 10:00 p.m. because (5.3) does. The two facts are metaphysically related to one another. They are not the same fact, nor is (5.3) quite sufficient for (5.4) to obtain. If Bob and the others disperse, then even if (5.3) is the case, (5.4) might not be. So to be more precise, (5.4) obtains at 10:00 in part because (5.3) does.

We use the word ‘because’ in many different ways. Often, it connects causes and effects. We say that the barn burned down because Mrs. O’Leary’s cow knocked over the lamp. The lamp is causally related to the fire, not metaphysically related to it. Knocking over the lamp “makes” the fire in a causal sense, not a metaphysical one. The flames, on the other hand, are metaphysically related to the fire. The flames do not cause the fire; in a sense, they are the fire.¹⁰

Facts (5.3) and (5.4) are not causally related to one another. The fact that Bob and the others ran down Howe Street was not the causal reason that the mob did, but the metaphysical reason.

To assign a word to this “metaphysical reason” relation, we say that fact A grounds fact B. The fact The barn door, walls, and roof are burning grounds the fact The whole barn is burning; the fact I am married grounds the fact I am not a bachelor; and the fact a million herring turned in such-and-such directions grounds the fact the school split in two. All of these pairs of facts are metaphysically related in the sense that the first fact “metaphysically makes” the second fact the case. Grounding will be a central part of the discussion from here on, so I will say a bit more about a few of its characteristics.

Grounding is usually understood to involve a kind of priority, or fundamentality. The more fundamental fact grounds the less fundamental fact. For instance, the fact A million herring turned in such-and-such directions grounds the fact The school of herring split in two, but not the other way around.

This is perhaps the most controversial part of the notion of grounding, since many people worry about the idea that some parts of the world are “more fundamental” than others. In developing a model for thinking about social facts, however, it is hard to imagine how we could do without a notion of fundamentality. The fact Bob and Jane ran down Howe Street is part of what we look for in seeking the metaphysical explanation for the fact The mob ran down Howe Street. But not the other way around: the fact The mob ran down Howe Street does not metaphysically explain the fact that Bob and Jane did.

In some of the examples of grounding I have mentioned so far, the grounding facts are metaphysically sufficient for the things they ground. In the following case, for instance, the first fact is metaphysically sufficient for the second:

(5.5) I am married.

(5.6) I am not a bachelor.

Two facts, however, can stand in a relation where one is part of the metaphysical explanation for the other, but is not quite metaphysically sufficient. For instance, the following pair of facts:

(5.7) Bob and Jane ran down Howe Street.

(5.8) The mob ran down Howe Street.

Fact (5.7) is part of the metaphysical explanation for (5.8), because Bob and Jane were participants in the actual event. On its own, however, (5.7) is not enough. Two people do not make a mob. In this case, we say that the former fact partially grounds the latter fact. (Sometimes I will talk about fact G “fully grounding” fact F. But there is no difference between G fully grounds F and G grounds F. I add the word ‘fully’ just to make the contrast with partial grounding clear.)

Looking at some of the other cases, it actually takes some thought as to whether they are examples of full or partial grounding. For instance, look again at (5.3) and (5.4). Suppose that (5.3) is the case, but that all the people are actually running in different parts of Howe Street—some at the end, others a mile behind them, and others at the beginning. Then, even though (5.3) obtained, (5.4) might not. Another fact should be added to (5.3), in order to fully ground (5.4). For instance, the fact that all those people were clustered together. Or else the fact that other running people filled in the gaps between Bob, Jane, Tim, and the others. On its own, (5.3) only partially grounds (5.4). Together with one of those other facts, it fully grounds (5.4).

Here I will mention a point of departure between the way I will use the grounding relation, and the way it is usually understood in the literature. Most people take full grounding to involve necessity. That is, if fact F fully grounds fact G, then it is necessary that if F obtains, then G obtains. In my view, this is not the best way to understand full grounding.¹¹ Instead, I will distinguish full grounding from an even stronger relation, the relation A determines B. Determination, as I will discuss later, is basically just full grounding plus necessitation. There are practical reasons for making this distinction, but it is easier to explain this in the context of examples I will present later on.

So for now, I will just flag the point. If F fully grounds G, then F is metaphysically sufficient for G. That does not mean that in every possible world where you have F, you also have G. Still, (full) grounding is a pretty strong relation, and it is most important to keep grounding distinct from partial grounding.¹²

How do we tell if one fact partially grounds another? How do we tell if one fact fully grounds another? There is no infallible method that works in all cases. But there are ways of working it out. One way is just to think things through. Is fact (5.3) metaphysically sufficient for (5.4)? Or is there something to (5.4) over and above (5.3)? Sometimes we can come up with conceptual justifications for various grounding claims. Another method is to apply certain tests, or diagnostic tools. One especially valuable test, for instance, is to examine the ways that various facts vary in lockstep with one another.

Above I pointed out that (5.3) and (5.4) co-vary with each other over time. By that I mean that when one obtains the other also does. And when one does not obtain, the other does not. This co-variation is decent evidence that there is some relation between the two facts. On the other hand, there can be lots of reasons for co-variance even without grounding. They might be causally connected: where there’s smoke, there’s fire, but the presence of smoke and the presence of fire are causally related, not metaphysically. Or two facts might co-vary by accident.

Nonetheless, different sorts of co-variation can be useful tools for diagnosing different sorts of grounding relations. When we consider the co-variation of facts, we can consider how facts change over time, but also how facts change over different possibilities. This is what supervenience is about. Supervenience is built using the idea of co-varying properties: a set A of properties supervenes on a set B of properties just in case any change in the A-properties must be accompanied by a change in the B-properties.¹³ As such, it is a diagnostic tool for assessing whether facts of the form x has such-and-such an A-property are grounded by facts of the form x, y, z, . . . have such-and-such B-properties. (More accurately, it is a test for metaphysical dependence. But dependence can also be evidence for determination, so supervenience is a useful tool for diagnosing both. I discuss these topics in more detail in chapter 8.)

To make headway, it is crucial to work with a simple and powerful toolkit, to be precise, and to apply the tools consistently. With regard to the nature of the metaphysical tools themselves, I tend to approach them with a lightly accepting temperament. For instance, do propositions really exist? Some people insist they do, while others scoff. For our purposes, neither hill is worth dying on. To develop a model for making sense of the social world, I use propositions and these other tools freely, without worrying here about the commitment to a rich ontology.

It may seem ironic or even hypocritical to be casual about the “reality” of propositions, while refusing to be casual about the “reality” of governments, money, and other social entities. But this little hypocrisy is worth the payoff, at least to get us going. These tools of metaphysics are powerful for their precision, and for how much detailed work has gone into assembling them into a cohesive model. They enable us to think about the social world in much clearer ways than without them. And we have to use some toolkit or another, so we might as well start with a powerful one. We use the best tools at our disposal to investigate things they might help with. And then with those new insights, maybe over time we can scrutinize the tools themselves with more success.

Now let’s return to the two models discussed in the last chapter, applying these new tools to assemble the models into a unified picture. That will allow us to discuss the anchoring relation and the notion of a frame principle.