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1.51 Here is a natural train of thought. Things objectively belong together when they are similar in important ways. Things are similar in some way if and only if there is some way that those things all are. We call ways that things are properties. So, what it is for things to belong together is for them to share certain important properties.

1.52 But although this train of thought is natural, someone might reasonably worry that we won’t travel very far on it. After all, this train of thought leads us to the question “What makes a property an important property?” If our only answer to that question is that important properties are those that things have when they objectively belong together, we are riding the train on a circular track, and we are no better off than we were when we started. (Circular explanations seem to get you nowhere, intellectually speaking.)

1.53 The question “What makes a property an important property?” matters if we assume both that there are some important properties and that there are some unimportant properties as well. But maybe the latter assumption is one that we shouldn’t make; maybe we should believe that the only properties that exist are the important properties. If the only properties that exist are the important properties, then we can say that things objectively belong together if and only if they have a property in common. This train of thought is less obviously on a circular track. We still need to face the question of what properties there are though.

1.54 In order to address the question of what properties there are, it might be useful to have a quick discussion about how we attribute properties to things in ordinary language.

1.55 Consider the sentence “Kris is short.” The subject of this sentence is the name “Kris.” The remainder of the sentence is the predicate “is short.” Very roughly, in general, a predicate is that part of a sentence which contains a verb and is used to state something about what is named by the subject of that sentence. Other examples: in the sentence, “Ranger is a dog,” “Ranger” is the subject and “is a dog” is the predicate; in the sentence “Ben eats French fries,” “Ben” is the subject and “eats French fries” is the predicate; in the sentence “José was an awesome teacher,” “José” is the subject and “was an awesome teacher” is the predicate. I hope this rough definition of the word “predicate” and the examples just mentioned have succeeded in giving you the idea of what a predicate is.

1.56 Predicates are used to say something about what is named by the subject of the sentence. Does this mean that, for every predicate, there is a corresponding property? Should we say that, since we can state something true of Ranger when we say “Ranger is a dog,” there is a property of being a dog? Ranger is a dog. Is there therefore a property of being a dog that Ranger has? This thought might seem plausible at first—what is the something that is true of Ranger if it is not a property had by Ranger? But if there is a property corresponding to every predicate, then there must be unimportant properties as well as important properties. For the following sentence is true: “Ranger is a dog or a fish or an automobile,” and so corresponding to the predicate “is a dog or a fish or an automobile” is a property, namely, the property of being a dog or a fish or an automobile. If there is a property of being a dog or a fish or an automobile, it is a property had by Ranger, the fish in my daughter’s fish tank, and the leaf‐filled convertible rusting on the street down the block. But these things do not objectively belong together simply because they have this property. The property of being a dog or a fish or an automobile is not an important property.

1.57 So, we have a choice to make. One option is to believe that for every predicate, there is a corresponding property and some, but not all, of these properties are important, and then give a theory of what it is for a property to be an important property. Another option is to deny that every predicate corresponds to a property: on this option, although it is, for example, true of both Ranger and Mars that they are either dogs or planets, nonetheless there is no property of being a dog or a planet. On this second option we don’t obviously need a theory of when some property is an important property, since we can just say that all properties are important properties. (That said, if being an important property is something that comes in grades or degrees—if all properties are important but some important properties are more important than other important properties—then we still need a theory of grades or degrees of importance.) We do need a theory to tell us which predicates have properties corresponding to them. I suspect that on either option, the theories that we will give will look very similar to each other when they are fully developed, but I encourage you to see whether this suspicion ends up being correct. (We will further discuss the idea of an important property in Sections 2.4 and 2.9.)

1.58 Here’s another idea worth considering: maybe we can’t define or explain what it is for some things to objectively belong together in terms of anything simpler. Instead of trying to define this concept, we could try to use it to define other concepts—such as, for example, the concept of an important property. It’s not clear to me how to do this, but that doesn’t mean this isn’t a project worth pursuing, especially since we already know that some expressions in our language can’t be explicitly defined.

1.59 Either way, the metaphysics of classification and the metaphysics of properties are deeply connected. And so, if we want to know more about the former, it will help to know more about the latter. Chapter 2 will focus on the metaphysics of properties, although we will on occasion revisit some of the issues discussed in this chapter.