Universals and Particulars

A postbox and a tomato are both red. Nothing about the sentence "they are both red" looks puzzling, and yet it reports something that seems to hold of two quite different things at once. The postbox is made of cast iron and stands on a pavement. The tomato is made of pulp and sits in a bowl. They share no parts, no location and no history, and still there is a respect in which they are exactly alike.

The beginner tier fixed the vocabulary needed to ask what that respect is. This article asks it, and sets out the three answers that have organised the debate since Plato: that there is one thing, redness, wholly present in both; that there is no such thing, and the likeness of the two objects is all there is to say; and that each object has its own redness, a particular one, and that the two are alike without being one.

One property, two things

Call a thing that can be wholly present in many places at once a universal, and a thing that cannot, a particular. The postbox is a particular: it is here and not in the bowl. Whether redness is a universal is exactly what is in dispute, so the term is best read as naming the role the realist wants redness to fill, not as settling that anything fills it.

The problem that generates the dispute is old enough to have a traditional name.

This is the problem of the one over many: one respect, many things that exhibit it. Notice how little the argument says. It does not conclude that the accounting thing is a universal, or that it is a thing of any very exotic kind. The conclusion states a demand for an account, and the three positions differ in what they offer.

The third premise is where the pressure is applied, and a good deal of the nominalist tradition is a refusal to accept it. If agreement in a respect is just a brute fact about how things are, nothing needs to account for it. The realist replies that this makes every case of exact likeness a separate coincidence, and that science could not be done on that basis. That exchange recurs throughout the article.

Realism about universals

Plato's version places the universal outside the world of particulars. The Form of the Beautiful, or of Equality, exists whether or not anything is beautiful or equal, and particular things resemble it imperfectly. This is realism of the strong sort, since universals exist independently of their instances and could in principle go uninstantiated.

Aristotle rejected the separation. On his view there is no redness apart from red things, and a universal exists only in the particulars that have it. The modern descendant of this line is David Armstrong, whose A Theory of Universals (1978) defends what he called the principle of instantiation: there are no uninstantiated universals. A universal is real because it is somewhere, in each thing that has it, and the postbox and the tomato literally share a constituent.

Armstrong adds a second restriction that matters for the rest of the debate. He holds that universals are sparse, and are to be discovered by physics and not read off from the predicates of English. Being an electron's charge is a universal. Being a thing that is either a postbox or a prime number is not. This keeps realism from exploding into an inflated ontology with a universal behind every predicate, a worry the beginner tier met under the heading of sparse and abundant properties.

Realism has two chief attractions. It gives an explanation of resemblance that does not itself consist of more resemblance: two things are exactly alike in colour because the same thing is in both. And it gives a natural account of laws. Armstrong, Fred Dretske and Michael Tooley each argued, in 1977 and 1978, that a law of nature is a relation between universals, so that a law like "charge repels like charge" says something about charge and not merely about every charged particle that happens to exist.

The costs are equally clear. A universal that is wholly present in the postbox and wholly present in the tomato is unlike anything else we encounter, and the realist has to say how something can be in two places at once without being divided. The usual reply is that this is precisely what it is for a thing to be a universal, which is correct and unsatisfying in equal measure. Then there is the relation between the particular and the universal, which is instantiation, and which gives rise to Bradley's regress, covered earlier.

Nominalism

The word is slightly misleading, since it suggests that the only thing in common is a name. Medieval nominalists did say something close to that, and the label stuck, but a contemporary nominalist need not say the likeness is merely verbal. The core commitment is negative, and it admits several positive developments.

The bluntest is predicate nominalism, a position Quine sketches in "On What There Is" (1948). The red houses, the red roses and the red sunsets are all red, and that is simply how they are. "Red" is a predicate that applies to each, and to ask for an entity corresponding to it is to repeat the question the nominalist declined. The position has the virtue of being cheap and the vice of looking like a refusal to answer. Quine's description is that it takes the redness of the things as ultimate and irreducible.

A more ambitious version tries to give the likeness a content. The postbox and the tomato are both red because they belong to the same class, the class of red things. That sounds like a trivial reformulation, but classes of particulars are, on most views, nothing over and above their members, so no new kind of entity has been added. This is class nominalism, and its natural refinement is the one that dominates the rest of the section.

Resemblance classes and their troubles

The class nominalist faces an immediate difficulty, which draws on an example of Quine's in "Two Dogmas of Empiricism" (1951). Every creature with a heart is a creature with kidneys, and the other way round, so the two classes have exactly the same members. If properties just are classes, being a creature with a heart and being a creature with kidneys are the same property. They are plainly not. Nor does it help to say they differ in other possible worlds, since a class of actual things is already settled by its members.

Resemblance nominalism is designed to meet this. A red thing is red not because it belongs to an arbitrary class but because it resembles the paradigms, and resemblance is a relation that holds or does not hold between particulars without any further entity being involved. Two things being exactly alike in colour is a fact about those two things.

Two problems follow, and both are serious.

The first was identified by Nelson Goodman in The Structure of Appearance (1951). A class of things that all resemble each other need not be a class of things sharing one property. Take three objects, each of which has two of three features, in such a way that each pair shares one feature but no single feature is common to all three. The three resemble one another pairwise and nevertheless have nothing in common. This is the problem of imperfect community, and it shows that pairwise resemblance does not guarantee a shared respect. Goodman's companionship difficulty is related: if every red thing that exists also happened to be round, resemblance among them would not separate redness from roundness, so resemblance alone does not say which respect it is a resemblance in.

The second problem is Russell's. In The Problems of Philosophy (1912) Bertrand Russell argued that the resemblance nominalist cannot escape universals, because resemblance is itself something that holds in many cases.

The standard defence takes the second horn and denies that the series is vicious. Gonzalo Rodriguez-Pereyra argued in Resemblance Nominalism (2002) that a regress is only a fault when it blocks an explanation, and that each stage here is explained by the particulars involved, with no stage depending on the next for its truth. The realist replies that a theory whose basic notion is a relation among many particulars, with no explanation of why those particulars should stand in it, has relocated the mystery. The disagreement is whether primitive resemblance is more or less acceptable than a primitive universal, and the argument alone does not settle it.

Tropes

G. F. Stout argued in 1921 that the characters of things are as particular as the things, and Donald C. Williams gave the idea its modern form in "On the Elements of Being" (1953), borrowing the word "trope" from Santayana. Keith Campbell's Abstract Particulars (1990) is the most developed systematic statement.

The motivation is a point about particularity. The postbox's redness is dented where the postbox is dented, was painted on a Tuesday, and is destroyed if the postbox is melted down. It can be exactly like the tomato's redness without being it. If we take this seriously, the particular trope is the right thing to say a property is at the level of the world, and the universal is an abstraction from many tropes.

Tropes do well on two points. Causation and perception seem to relate particular events and states, and a trope is a good candidate for what is actually causing or perceived: it is the heat of this flame, here, that burns the finger. And a trope theory avoids the strangeness of multiple location: each trope is in one place.

Its difficulty is that exact resemblance between tropes does the work that sharing a universal did. The resemblance class of colour tropes is the class of all tropes that exactly resemble one another, and being red is belonging to that class. So the trope theorist faces Russell's regress as well, and often responds as the resemblance nominalist does. The position differs from resemblance nominalism in what it takes the resemblance to hold between. Resemblance among ordinary objects has to be traced to a respect, and respects are what trouble Goodman's cases. Resemblance among tropes has no respect to trace, because each trope has only one nature: a red trope is red through and through, and two red tropes are exactly alike without needing a further feature in which they agree. That is how the theory escapes imperfect community.

What the choice costs

None of the three positions is free, and the debate is better understood as a comparison of what each takes as primitive than as a contest in which one side has refuted the others.

The realist takes the universal and its instantiation as primitive, and pays in strangeness: an entity wholly present in many places, and a tie between it and its instances that resists explanation. The resemblance nominalist takes resemblance between particulars as primitive, and pays in explanatory depth: the pattern of likeness in the world has no source beyond the particulars that display it, and Russell's regress and Goodman's cases are the price of declining to say more. The trope theorist takes particular natures and their exact resemblance as primitive, and pays in a fresh category of entity, with a large number of tropes for every ordinary object.

Which is preferred tends to follow what a philosopher is most unwilling to lose. Someone who wants an ontology of laws will lean to realism. Someone who wants to keep everything located and concrete will lean to nominalism or tropes. Someone who thinks that causes are particular occurrences will find tropes the natural fit.

One consequence deserves to be flagged, because it carries on into the next article. All three accounts have been framed as accounts of what makes the postbox red. Each assumes that there is a postbox which is red, a bearer in which the redness, or the red trope, resides. But if the properties of a thing are universals, or tropes, or members of resemblance classes, one can ask whether the postbox is anything over and above them. That question was set aside in the beginner tier and now cannot be deferred.

The next article asks whether a particular is anything more than the properties it has.