Universals

Universals are a class of mind independent entities, usually
contrasted with individuals (or so-called "particulars"), postulated
to ground and explain relations of qualitative identity and
resemblance among individuals. Individuals are said to be similar in
virtue of sharing universals. An apple and a ruby are both red, for
example, and their common redness results from sharing a universal. If
they are both red at the same time, the universal, red, must be in two
places at once. This makes universals quite different from
individuals, and controversial.

Whether universals are in fact required to explain relations of
qualitative identity and resemblance among individuals has engaged
metaphysicians for two thousand years. Disputants fall into one of
three broad camps. Realists endorse universals. Conceptualists and
Nominalists, on the other hand, refuse to accept universals and deny
that they are needed. Conceptualists explain similarity among
individuals by appealing to general concepts or ideas, things that
exist only in minds. Nominalists, in contrast, are content to leave
relations of qualitative resemblance brute and ungrounded. Numerous
versions of Nominalism have been proposed, some with a great deal of
sophistication. Contemporary philosophy has seen the rise of a new
form of Nominalism, one that makes use of a special class of
individuals, known as tropes. Familiar individuals have many
properties, but tropes are single property instances. Whether Trope
Nominalism improves on earlier Nominalist theories is the subject of
much recent debate. In general, questions surrounding universals touch
upon some of the oldest, deepest, and most abstract of philosophical
issues.

1. Introduction

An inventory of reality's most fundamental entities would almost
certainly include individuals. Individuals are singular objects. They
can exist over time, but in only one place at a time. Individuals also
have properties (also called qualities), at least most of which can
vary over time. A ripening apple goes from being green to being red,
for instance. Almost everyone agrees that individual apples exist, and
that they are colored, but are redness and greenness entities
themselves? If so, what are they like? And if redness and greenness
are not real entities, how could our apple be colored at all? Without
its distinctive qualities, an apple wouldn't even be an apple.

Let us use the term "universal" for properties (or qualities.) In a
philosophical tone of voice we can now ask, "Are there really such
universals? If so, what is their nature? How are they related to
individuals?" These questions start us down a road philosophers have
been exploring since Philosophy itself was young.

We can approach the question about the existence of universals from a
linguistic perspective. Consider how often we speak of things having
properties: "That apple is red;" "The oven is hot;" or "My shirt is
dirty." Such sentences have a subject-predicate structure. The subject
term refers to the individual described in the sentence. The
predicate, on the other hand, describes; it tells us something about
the way that individual is, how it is qualified. Do predicates also
refer? Some philosophers think they do. Alongside the individuals
picked out by subject terms of sentences, it is thought, there are
entities of a different kind, picked out by predicates. Once again we
can call these "universals".

Prima facie, there seems to be every reason to believe in universals.
They look to be just as much a part of our experience as individuals
are. Philosophical questions and problems arise, however, when we try
to specify their natures. If universals are real, but are not
individuals, what are they? Some philosophers contend that universals
are too strange to accept into our world view. In a similar vein, it
has been alleged that any philosophical work done by universals can be
done just as well without them; whether they are strange or not, many
argue, universals are simply unnecessary. Of course, it would need to
be shown that universals really can be dispensed with, and we'll
return to this controversy. But first we will examine competing
Realist conceptions of the nature of universals.
a. The Nature of Universals

In fundamental debates in metaphysics, it can be useful to understand
the type of entity or concept in contrastive terms. For instance, it
is helpful to understand universals by contrasting them with
individuals. What then, is an individual, or a particular, in the
philosophical or metaphysical sense of the term?

Traditionally, the term "individual" is used to pick out members of a
certain category of existents, each member of which is said to be
unique. More precisely, individuals are said to be nonrepeatable (not
multi-exemplifiable), which means that they can't be in more than one
place at a time. Examples include the familiar objects of
sense-experience, such as chairs or tigers. A room may contain many
chairs that are virtually alike in their intrinsic qualities, but each
chair is nonetheless a distinct thing in one place at one time. By
contrast, the universal "chair" is repeated around the room.

The individuals familiar from experience are also said to be material:
they fill regions of space with impenetrable "stuff," and are
locatable in space and time. Some philosophers are committed to other
types of individuals, as well: immaterial ones (such as souls and
sense-data) and even ones that are also outside space and time (such
as numbers and God.) The crucial contrast for our purposes, however,
is between what are repeatable (universals) and what are not
(individuals).

Although individuals are nonrepeatable, universals can serve their
characteristic functions only if they differ from individuals in this
respect. In order to ground relations of qualitative identity, for
instance, universals must be multi-exemplifiable (or repeatable,) able
to be here and there at the same time. My apple and yours are both
individuals, and this implies that each can be in only one place at a
time. But if the redness they share is a universal, then the redness
they share is a real non-individual, literally in both. The apples are
similar in virtue of sharing this universal, redness. And if redness
is shared in this way, then it is in at least two places at once.

As we proceed we will get more precise about these characterizations,
and explore variations that have been defended in opposing Realist
accounts. But we can appreciate already why some philosophers balk at
the existence of universals. For, as just noted, all defenders want to
say that universals are repeatable. It seems, however, that defenders
of universals must also say that universals are wholly present in each
of the places they exist.

To explain, suppose we were to destroy one of the apples considered
above. We'd have one fewer individual, to be sure. Would there be a
diminishment of redness itself? It doesn't seem so, since redness is
held to be an entity in its own right. Nor does it seem to make sense
to say that redness increases when another apple ripens and turns red.
These considerations suggest that a universal is wholly present in
each of its instances, and that the existence of a universal at one
place is unrelated to its simultaneous existence at any other place.
It's not clear, however, how universals could be both wholly present
in each of the places they exist, and, at the same time, present in
many different places at once. This certainly would make them unusual,
to say the least.

Moreover, it seems to be a mark of materiality that a material thing
can be in only one place at a time. If so, then universals cannot be
material. This in turn creates a problem when it comes to causation.
For as we usually understand causal relations, one thing affects
another by interacting with it, say by colliding with it. But that
seems possible only if the entities in question are material. For
these reasons it is difficult to explain how universals interact with
other things that exist. The puzzle becomes more acute when we wonder
how we can know universals at all. Don't they have to interact with
our brains for us to know them? If they are not material, this
interaction is quite mysterious.

In summation, we've seem that universals are quite different from
individuals, and in ways that make them odd. Philosophers with low
tolerance for strangeness tend to dismiss them for these reasons. Why,
then, do some philosophers continue to believe in them, despite their
unusual natures?
b. Reasons to Postulate Universals

Universals are called on to serve many philosophical functions. For
most of this article, we'll focus on one particularly famous one – the
role universals play in professed solutions to what has come to be
called "The Problem of Universals."

First, a word or two about postulating entities is in order. Here we
might compare the philosophical enterprise of deciding whether
universals exist with the scientific enterprise of deciding whether
strange unobservable entities, like quarks or neutrinos, exist. The
scientific case it itself controversial, but many scientists and
philosophers believe in the existence of unobservables, provided the
theories that postulate them best explain the observable phenomena
under study. For example, many believe the universe contains what
physicists call "black holes," in part because the best (perhaps only)
way to explain a range of stellar phenomena is to suppose that black
holes are responsible. Again, this is controversial, but if the
explanation provided is the best (or only) explanation, many
scientists and philosophers claim a right to believe the postulated
unobservables exist.

In parallel, we now ask, "Are their any philosophical puzzles or
problems that can best be solved by believing in universals?" In fact,
universals have been called on to answer a range of philosophical
questions. Recall our points about subjects, predicates and reference.
Prima facie, a name wouldn't be a name if there weren't something for
it to refer to. Some philosophers think that the meaning of a name
just is its referent. What about general terms, terms that can be said
of many things, such as "red" or "wise"? What gives those terms
meaning? Some have said that predicates must have referents to be
meaningful, and universals fit the bill.

Universals have also been called on to solve problems in the theory of
knowledge. Plato, for instance, said that for us to know something,
that which is known must be unchanging. Since material individuals are
subject to change, Plato argued, there must be things that don't
change, suitable as objects of genuine knowledge, not just belief.
Universals might fit the bill here, too.

Relatedly, some philosophers have argued that we need universals to
understand the stable, unchanging laws of nature that govern
individuals' changes. Indeed, it has been argued that a law of nature
just is a relation among universals, by which one universal brings
about, or necessitates, others.

Our focus in this essay concerns another role for universals, perhaps
the most famous one. They are said to answer what seems a very simple
question, but which turns out to be one of the most famous and
long-standing issues in Philosophy. This returns us to the so-called,
"Problem of Universals."
c. The Problem of Universals

Often we predicate properties of individuals. When we say that both
cherries and rubies are red, for instance, we seem to say individuals
share common properties, those that make cherries cherries, those that
make rubies rubies, and those that make both red. Predicates are said
of many subjects, then, but is there anything in reality to match the
linguistic one-over-many? Are there general truths? Is there
commonality in nature, in reality; or is commonality imagined and
illusory, perhaps a mere product of language? If the latter, how can
we accommodate the intuition that it is the world, and not our
conventions, that make predications true or false? The Problem of
Universals arises when we ask these questions. Attempts to solve this
problem divide into three broad strategies: Realism, Nominalism, and
Conceptualism. We'll take these in turn, and consider the pros and
cons of each.
2. Versions of Realism

We'll begin by examining versions of Realism, all of which claim that
yes, there are universals; yes, there are truths about the general;
yes, there is commonality in nature. Unless we accept universals into
our world view, the Realist argues, we will be unable to explain a
fundamental and apparent fact, namely, that there is genuine
commonality and systematicity in nature. Again, experience suggests
that the individuals we encounter share properties with other
individuals. Some are red, and some are not; some are blue, and some
are not; some are emeralds, and some are not. Realists claim what
makes it the case that these individuals seem to share properties is
that in fact they do. There is an entity, a universal, present in each
of these individuals at once, which in turn explains our right to say
that they are qualitatively identical.
a. Extreme Realism

The oldest, and most famous variant of Realism comes from Plato.
Plato's position is that in order to explain the qualitative identity
of distinct individuals, we must accept that there is another entity
besides the resembling individuals, an entity we've called a
universal, and which Plato would call a Form. If two apples, for
example, are both red, this is because there is a Form of Red that is
able to manifest itself in both those apples at once.

Really there are three different components in this picture. There is
the individual, a particular apple; there is the red of that apple –
which exists right "in" or with that apple; and finally, there is the
Form of Red, which manifests itself in the red of this apple (and of
course, the red of other apples.) What, then, is the nature of the
Form itself, which provides for the bit of red we see in this apple or
in that?

On Plato's view, Forms are immaterial. They are also outside of space
and time altogether. They are wholly abstract, we might say. Of
course, for the Form of Red to make an individual apple red, the Form
must somehow be related to the apple. Plato postulates a relation of
participation to meet this need, and speaks of things "participating"
in Forms, and getting their qualities by virtue of this relation of
participation. One last point about the nature of Forms proves
crucial. For the Form of Red to explain or ground the redness of an
apple, the Form of Red must itself be red, or so it seems. How could a
Form make an apple red, if the Form were not itself red?

As we noted, Plato's account of generality was the first one, and it
has held great appeal ever since. But it is also subject to serious
criticisms. Interestingly, one of the most devastating objections to
the theory of Forms comes from Plato himself. We will return later to
this famous objection, which has come to be known as the Third Man
Argument. Because of the power of this argument, many philosophers
sympathetic to Realism have looked elsewhere for a solution to the
Problem of Universals. We'll explore one alternative now.
b. Strong Realism

Although the first position is credited to Plato, this next one is
widely thought to be inspired by Aristotle. The key in this position
is its rejection of independently existing Forms. As we noted in
Section 2a., Extreme Realists posit an explanatory triad involving an
individual, the quality of this individual, and the Form that grounds
the quality of this individual (and that one, and others). Strong
Realists, in contrast, resist this triad. When an individual has a
quality, there is simply the individual and its quality. No third,
independent thing is needed to ground possession of the quality. A
universal, on this view, just is the quality that is in this
individual and any other qualitatively identical individuals. The
universal red, for example, is in this apple, that apple, and all
apples that are similarly red. It is not distinct and independent from
the individuals that have this color. Because it is a universal it can
exist in many places at once. According to Strong Realism, the
universal red in my apple is numerically identical to the red in
yours; one universal is in two individuals at once. It is wholly
present in each place where it exists.

As we'll see, Strong Realism is immune to the Third Man Argument. It
also reduces the strangeness of Realism. We need not have Forms that
are abstract, in the sense of being outside of space and time,
mysteriously grounding the qualities of material individuals. The
Strong Realist's universals are in space and time, and are able to be
in many places at once. Multiple exemplification may be considered
strange, but it not as strange as existence outside space and time.
c. Objections to Realism

We turn now to objections. We've already seen what might be called the
Strangeness Objection. This is the intuition some philosophers have
that universals are just too oddly natured to be accepted into our
world view. These philosophers typically countenance only what is
material, spatiotemporal, and nonrepeatable; and universals just don't
fit the bill. Philosophers who believe in only individuals are known
as Nominalists. We'll return to them later. We should note, however,
that there are other versions of Realism in addition to the two we've
discussed. Medieval philosophers spent much time exploring these
issues, and formulated many versions of Realism. This introduction to
the Problem of Universals will not explore these other variants,
though they too are vulnerable to the objection that closes this
section.

Extreme Realism is challenged by the Third Man argument. Recall the
essentials of that position, in particular, what is said about the
nature of the Forms. For any given quality had by an individual there
is a Form of that quality, one that exists separately from
individuals, and also from the quality found in each particular
individual. There is the apple, the red of this apple (and the red of
that apple), and the Form of Red. By participating in the Form of Red,
the apple gets its particular bit of redness. And finally, as we saw,
the Form Red must itself be red. Otherwise it couldn't provide for the
redness of the apple. Suppose we now ask, "What explains the red of
the Form of Red, which itself, as we said, is red?" Coming to believe
in the existence of Forms begins with the urge to explain the redness
of apples and other material individuals, but once this step is taken,
the Extreme Realist is forced to explain the redness of the Form of
Red itself.

To explain the redness of the Form of Red, in Extreme Realist fashion,
we will have to say that the Form of Red participates in a Form. After
all, a fundamental tenet of Extreme Realism is that possession of a
quality always results from participation in a Form. Presumably, a
Form cannot participate in itself. Therefore, if the redness of the
Form of Red is to be explained, we'll need to say that the Form of Red
participates in a higher order Form, Red 2 . Moreover, participation
in Red2 will explain the redness of Red1 only if the higher order
Form, Red2, is itself red. Of course, now we will have to explain the
redness of the Form of Red2, and that will require us to introduce yet
another Form, in this case, the Form of Red3, which the Form of Red2
participates in to get its redness.

It is clear that this will go on indefinitely. So it seems that we
will never have an explanation of why or how the Form of Red is
actually red. That means we'll never be able to explain why our
original apple is red. That was what we wanted initially, and so it
seems that Plato's theory is unable to provide an answer. This has led
many to reject Plato's theory. (There is, not surprisingly, a large
body of secondary literature which explores whether Plato's theory can
survive this objection and what Plato himself thought about it, since,
as we've seen, it was Plato himself who first raised the objection.)

The Third Man Argument threatens only Extreme Realism. Strong Realists
do not rely on independently existing Forms to explain the redness of
individuals, and so they need not explain why an independent existent
– the Form of Red – is itself red. Instead, Strong Realists can simply
note that the universal present in each apple is itself red, and the
red of this universal explains the red of each apple, and also their
similarity with respect to color.

However, the objection to which we now turn threatens all variants of
Realism. This final objection is not so much an argument that Realism
is intrinsically flawed, but rather that Realism is unnecessary. A
general principle governing many metaphysical debates is that, all
things being equal, the fewer types or kinds of entities in one's
ontology, the better. Those opposed to Realism argue that they can
meet the explanatory demands we've discussed without relying on
universals. If qualitative resemblance and identity can be accounted
for without universals, and if any other work done with universals can
be done as well without them, then, the opponents of Realism argue, we
should do without them. We will then have fewer categories in our
ontology, which, all things being equal, is to be preferred.

For this reason, opponents of Realism try to solve the Problem of
Universals without universals. The question we will track is whether
such solutions are in fact adequate. If not, perhaps commitment to
universals, however unpalatable, is necessary.
3. Versions of Anti-Realism

We'll call any proposed solution to the Problem of Universals that
doesn't endorse universals a version of "Anti-Realism". Anti-Realists
divide into two camps: Nominalists and Conceptualists. Nominalists
maintain that only individuals exist. They argue that the Problem of
Universals can be solved through proper thinking about individuals,
and by appeal to nothing more than the natures of, and relations
among, individuals. Conceptualists, in contrast, deny that individuals
suffice to solve the Problem, but they also resist appealing to mind
independent universals. Instead, qualitative identity and resemblance
are explained by reference to concepts or ideas. We will explore this
Conceptualist strategy at the conclusion of our discussion of
Anti-Realism. First we will survey a range of Nominalist theories.
a. Predicate Nominalism

How can we explain the qualitative identity of distinct individuals
without relying on universals? One strategy begins by giving an
account of what makes a single individual, which we will call "Tom,"
red. A minimal, but perhaps sufficient answer is to say that Tom is
red because the predicate "is red" can be truly said of Tom. As for
the predicate "is red" itself, it is just a particular string of words
on a page (or this screen), or else a string of spoken sounds.
Expanding this strategy we get the view that two individuals, say Tom
and Bob, are red simply because the linguistic expression, the
predicate "is red," is truly said of both. We account for commonality
in nature by reference to individuals–in this case the individuals Bob
and Tom, and also linguistic expressions such as the predicate "is
red."

On this view then, all that exist are individuals and words for
talking about those individuals. This seems metaphysically innocuous,
but many philosophers charge that Predicate Nominalism ignores the
Problem of Universals, and does not solve it. Why is it true to say
that both Bob and Tom are red, for instance, and not green or blue?
What is it about the world, the individuals, that explains why they
are that way and not some other way? What explains their similarity?
Predicate Nominalists just leave it as a brute fact that some things
are red (or blue, or green.) More precisely, what they leave brute is
the fact that, for any given individual, some predicates correctly
apply and others don't. But when it comes to explaining these facts,
Predicate Nominalism will go no further. This refusal to take the
Problem of Universals seriously has even landed Predicate Nominalism
the label "Ostrich Nominalism."
b. Resemblance Nominalism

Another Nominalist strategy is to collect individuals into sets based
on resemblance relations, and then account for qualitative identity
and resemblance by appeal to commonalities of set membership. An
individual's redness, for example, is explained by the fact that it
belongs to the set of red things. The fact that two individuals are
both red is explained by their both belonging to the same set of red
things. A given set, such as the set of red things, is constructed by
adding to it individuals that resemble each other more closely than
they resemble any nonmembers, that is, the individuals that aren't
red. In this way, Resemblance Nominalists explain individuals'
supposed shared qualities by talking only about resemblance relations.
Things that resemble each other belong to a common set. Membership in
a certain set defines what it is to have a certain property, and two
members of a set can be said to share a property, or be qualitatively
identical, in virtue of simply belonging to the same set of resembling
individuals.

In the course of trying to account for two distinct properties,
however, Resemblance Nominalists can end up constructing the same set
twice. If two distinct properties were to pick out the same set,
however, this would cause a serious problem. For instance, it is
thought that everything that has a heart also has a kidney. If so, the
set of individuals constructed for the property "has a heart" will
have the same members as the set constructed for the property "has a
kidney." Two sets with the same members are really just one set, not
two, by the very definition of "set," so Resemblance Nominalists are
forced to say that having a heart is one and the same property as
having a kidney. But that is clearly false.

A second problem for the Resemblance Nominalist arises when we wonder
about the method of set construction. Accounting for an individual's
redness requires building a set with that individual and other
resembling individuals as members. But, unfortunately for Resemblance
Nominalism, some members of the red set actually turn out to not be
red at all. To explain, remember that the construction of the set
proceeds by grouping particulars that resemble each other, and,
importantly, things can resemble each other in various respects. Our
red apple resembles other red apples, red stop signs, and red books,
and all those things would thus get into the set. But our red apple
also resembles a green apple, of the same type, which isn't ripe yet.
So that green apple would go in the set. Other things, too, will
resemble our apple, but not by being red. As such, it seems that
Resemblance Nominalism "explains" our individual's being red by
reference to a set containing non-red things, which is just to say it
doesn't explain it at all.

The tempting reply here is, "Sure, the green apple does resemble our
red apple, but not in the right way. If you stop building sets with
the wrong kinds of resemblance, you won't let non-red members into the
set." The problem with this reply is that the only way to stop these
"bad" resemblances is to include in the set only things that are red.
But remember, being red is what the Nominalist is trying to explain in
the first place, and so we can't use being red to guide set
construction. To do so would be circular.

A third objection arises when we consider the resemblance relation
itself. Resemblance Nominalism cannot succeed without this relation;
it bears most of the explanatory load. Arguably, then, the position is
committed to the existence of resemblance relations. This seems to
generate a serious problem. Individuals resemble one another, of
course, but resemblance itself is not an individual. So, if the
position is committed to resemblance relations, and if resemblance
relations are not individuals, then it seems that Resemblance
Nominalism is a misnomer. Upon close inspection, the position looks to
be a kind of Realism. Suppose three things (a, b, and c) resemble one
another, and belong in the same set. We have three individuals in this
case, but what about the instances of resemblance that hold among
those individuals? Are they the same kind of resemblance? They had
better be, if the previous objection is to be avoided! Resemblance
Nominalists, then, need to posit instances of, and kinds of,
resemblance, all of which suggests we actually have a universal
here–namely, the resemblance relation that holds between a and b,
between b and c, and between a and c. If resemblance itself is a
universal, Resemblance Nominalists are committed to at least one
universal. Perhaps they should make life easier (if not simpler) and
let them all in!

The above objections have moved some Nominalists to develop
alternative accounts. Many have turned to Trope Nominalism, which we
will discuss next. Trope Nominalism is committed a new kind of entity,
tropes. This may seem surprising, since Nominalists insist on
ontological simplicity. But while Nominalists allow only individuals
into their ontology, this doesn't preclude explanatory appeals to
tropes. For tropes, as we will see, are a class of individuals.
Perhaps with this innovation Nominalists will fare better.
c. Trope Nominalism

Though they were known to Medieval philosophers, tropes are relatively
new to contemporary metaphysics, and have been called on to address a
number of very different philosophical issues, including the Problem
of Universals. Trope theory can be understood, somewhat paradoxically,
as making properties into particulars. Tropes are a type of
individual. While ordinary individuals are qualitatively complex, a
trope is qualitatively simple, and is, in fact, a particular property
instance. The blue of the sky is a particular trope numerically
distinct from the blue trope of your T-shirt, even if the two tropes
are qualitatively identical.

For the tropist, ordinary individual objects can be conceived as
bundles or collections of tropes; and an ordinary object, which is a
complex particular, has a certain quality in virtue of having, as a
member of the complex, a particular trope, which is that particular
character. An apple thus is a complex of tropes–a red trope plus an
apple-shape trope, plus a sweet trope, plus a crisp trope, and so
forth. If the apple is red, that is because there is a red trope, a
red individual, that is a member of that bundle or complex. Red is not
a property the trope has; rather, the red trope is the red itself.
(Instead of treating an ordinary object as nothing more than a bundle
of tropes, another option is to treat an individual as a substance
that possesses a bundle of tropes. For simplicity, we will set that
option aside. Whether an object is, or instead has, a bundle of
tropes, the coming points hold.)

Trope Nominalism explains qualitative identity between two distinct,
ordinary individuals by saying that the first individual has a
constituent trope that is qualitatively identical to, but numerically
distinct from, a trope had as constituent by the second individual.
Two apples are red, for instance, because each has a red trope "in"
them, and these tropes themselves are individuals that exactly
resemble each other. Importantly, because this is a version of
Nominalism, we don't say the tropes resemble each other because they
share a universal. Instead, they simply resemble each other. If we
like, we can expand on the claim that red tropes resemble each other
by constructing sets of resembling individuals. In this case, we would
have a set of red tropes, the members of which resemble each other
more closely than they resemble any other tropes. In summary, then, by
appeal to qualitatively identical, but numerically distinct tropes, we
can explain qualitative similarities among ordinary objects, all
without reliance on universals.

How is this better than Resemblance Nominalism? Remember that
Resemblance Nominalism was vulnerable because it explained qualitative
identity of individuals by reference to sets of resembling
individuals. The trouble was that the individuals collected into sets
are ordinary objects, ones that have many properties, so they can
resemble each other in many ways. For this reason, no noncircular
criterion of set construction could exclude members with the wrong
property. Tropes, however, have only one property, so if individual
tropes are collected into sets, there won't be members that don't
belong. The set of red tropes will have only red tropes in it. Trope
Nominalists can now make unproblematic appeal to "resemblance among
individuals." This has convinced many that Trope Nominalism is a
serious contender against Realism.

As well, recall that Resemblance Nominalism faced the charge that only
a resemblance universal could account for resemblance relations among
individuals. Trope Nominalism has a reply here too. (As always, in any
complex philosophical discussion, there are various ways to reply to
objections, just as there are many objections. We outline here just
one of the ways Trope theories have responded to this objection.)
Whereas Resemblance Nominalists seemed forced to countenance a
resemblance universal, Trope Nominalists can appeal to resemblance
tropes! Should we have, for example, three identical red tropes, then
there will be a resemblance relation between a and b, a similar
relation between b and c, and a similar relation between a and c.
Trope Nominalism can treat each of these resemblances as distinct
tropes. When three red tropes are mutually resembling, then, in
addition to the red tropes themselves, there are three resemblance
tropes. And just as the resemblances among the three red individuals
is a basic fact, so too is the resemblance among these resemblance
relations. Not all resemblances are alike, of course, but in this case
they are. All properties are tropes, and properties include not just
ones like "red," but also ones like "resembles."

But there are still problems, perhaps, for Trope Nominalism. Recall
that we began by wondering how distinct, ordinary things could be said
to be qualitatively identical without introducing a universal common
to both. Tropists instruct us to view ordinary particulars as
complexes of tropes, and allow that there can be qualitatively similar
but numerically distinct tropes present in different complexes.
Qualitative similarity among ordinary objects is explained by the
qualitative similarities of their constituent tropes. Finally, the
qualitative similarity among distinct tropes is explained by the fact
that some (for example, red) tropes resemble each other more closely
than other (for example, non-red) tropes. The last point is the
crucial one. We are told that it is simply a brute fact that some
tropes resemble each other, and that others don't. That is just the
way things are, and there is no further explanation to be given. But
tropes were meant to do explanatory work; so, at the level of tropes,
we want and expect an account of generality. If trope theories are
presented as a solution to the Problem of Universals, they should
explain how there can be truths to explain the appearance of
generality in reality. What we end up with, though, is brute and
ungrounded qualitative identity among distinct tropes. In essence
then, the tropist dismisses, but does not solve, a question about the
nature of generality, by making generality a brute fact. Unlike
Predicate Nominalism, the tropist goes to great lengths to develop a
theory, but in the end seems to offer no more explanation of
generality. We know that our original objects resemble each other.
Why? Because they have tropes that resemble each other. But the latter
resemblance is not explained. And so it seems we've not gone very far
in explaining our original resemblance. What we want is an explanation
of qualitative similarity. Accounting for it in terms of qualitative
similarity–now at the level of tropes–does no more than relocate the
question. The very relation we sought to understand reappears as our
answer.

Again, qualitative similarity across ordinary particulars is explained
by the relation of qualitative similarity holding among the tropes
that constitute those particulars. But that seems either to postpone
answering the question, or to answer it by appealing to the very fact
we wanted explained. At best, this explanation is unsatisfying; at
worst, it is circular. We are left with qualitative identity as a
brute, unexplained phenomenon, triggering the reasonable question:
What then have we really gained with trope theories?
d. Conceptualism

A final strategy for avoiding universals comes by making generality
not a feature of reality, but instead a feature of our minds and the
concepts or ideas in minds. Conceptualism thus seeks a third way, as
they see it, between the excesses of Realism, and the unilluminating
resemblance relations of Nominalism. Because many individuals can fall
under the same concept, Conceptualism hopes to accommodate the
intuition that qualitative identity and resemblance are grounded in
the sharing of something, but in a way that doesn't appeal to dubious
items such as universals. According to this view, individuals a and b
are red because the concept of redness applies to both. The concept
red is general, not because it denotes a real non-individual, but only
because many diverse particulars fall under, or conform to, that
concept.

As tidy as this seems, it too suffers from obvious problems. To see
this, we need simply realize that concepts can be misapplied in some
cases, such as when we say of a cat that it is a dog. And of course,
misapplied concepts explain nothing deep about generality.
Conceptualism's appeal to concept application must concern only
correct concept application. As such, it is fair to ask, "What makes
it the case that the concept red is rightly applied to both a and b,
but not of some third individual, c?" To treat this fact as brute and
inexplicable is to revert to problematic Predicate Nominalism. So it
seems the Conceptualist must say that the concept red applies to a and
b, but not c, because a and b share a common feature, a feature c
lacks. Otherwise, the application of red is unconstrained by the
individuals to which it applies. But simply noting that a and b
resemble each other isn't going to help, because that just is the fact
we originally sought to explain, put differently. The Conceptualist
might now say that a and b share a property. But if this isn't to
amount to a restatement of the original datum, it must now be
interpreted as the claim that some entity is in both a and b. That, of
course, turns our supposed Conceptualist strategy back into Realism.

Critics say Conceptualism solves no problems on its own. In trying to
ground our right to predicate the concept red of a and b, we are
driven back to facts about a and b themselves and that leaves
Conceptualism as an unstable position. It teeters back and forth
between Realism, on the one hand, and Nominalism, on the other.
4. Concluding Thoughts

As with many issues in Philosophy, we started with a fairly simple
question and found it difficult to reach a satisfactory answer.
Qualitative similarity is a seemingly undeniable feature of our
experience of the world. And there seems to be every reason to expect
an explanation for this common fact. But upon closer inspection we
find that we must either accept some rather unusual items into our
world view, or go through some fairly elaborate theorizing to reach an
answer. And that elaborate theorizing itself seems full of problems.

Perhaps this explains why the Problem of Universals has had such a
hold on philosophers for all these years. We sense that there must be
an adequate solution to be found, but our failure to find one prods
our reason and imagination. Of course, we've only skimmed the surface
of this debate in this essay, and nearly every move we've discussed
has been debated, reformulated, argued for and against, analyzed,
accepted as obviously true and rejected as obviously false. A
consensus does seem to be emerging though, as one of the main
contributors to the debate in recent decades has articulated, that two
genuine contenders are left– Strong Realism and Trope Nominalism. As
always, there is much work to be done on this issue, despite its
distinguished heritage. We hope this introduction to the problem has
inspired you to seek a new path, to find a flaw in our reasoning, to
note what hasn't been noted before. You might turn out to be the next
Plato.
5. References and Further Reading

* Armstrong, D.M. Universals: An Opinionated Introduction.
(Boulder: Westview Press, 1989).
o An excellent survey of nearly every position in the debate
over universals, by one of the most important contributors to this
century's version of the debate.
* Armstrong, D.M. What is a Law of Nature? (Cambridge: Cambridge
University Press, 1983).
o An overview of the debate over the laws of nature, with a
defense of univerals as the required elements in an adequate account.
* Campbell, K. Abstract Particulars. (Oxford: Basil Blackwell Ltd., 1990).
o An important introduction to theory of tropes, showing the
versatility and potential of this metaphysical category.
* Loux, M. Metaphysics: A Contemporary Introduction. (London:
Routledge, 1998).
o Covers foundational debates on a number of areas, with
particular attention to the Problem of Universals.
* Simons, P. "Particulars in Particular Clothing: Three Trope
Theories of Substance" Philosophy and Phenomenological Research. 54
(1994), pp.553-75.
o A sophisticated explorations of various trope theories
with important proposals for advancing this theory. Reveals the
potential power of this position as an alternative to Realism.
* Spade, P.V. (trans.) Five Texts on the Mediaeval Problem of
Universals. (Indianapolis: Hackett Publishing Co., 1994).
o Indispensable collection of important Medieval texts with
useful guides and comments.
* Vlastos, G., "The Third Man Argument in the Parmenides,"
Philosophical Review. 63 (1954) pp. 319-349.
o A landmark article on Plato's Third Man argument, one that
rekindled widespread interest in Plato's metaphysics.