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The Problem of Universals

Richard Bielawa

Ancient Philosophy

Term Paper

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The problem of universals is a metaphysical problem. This means that the problem of

universals is dealing with a problem about the nature of reality. Specifically, the problem of

universals is a problem about commonality in our world. It asks how we understand the same

type of thing appearing in multiple instances. To better understand this idea, I would like to

provide an example. My friends and I like to play pool. I look down at the pool table and I see a

bunch of balls. I see things that these balls have in common. I see that all the balls have a similar

shape, roundness. I see some of the balls share a color, redness. I see that some balls share

patterns, being striped or solid. I see that one of the balls is green and it share its greenness with

the color of the felt on the table. I start thinking a little philosophically (maybe after a few

drinks) and I notice that not only do some balls and the table share colors, but that the table and

balls have the common feature of shape. Seeing commonality between distinct instances is the

motivation behind the problem of universals. The problem of universals asks: what explains this

commonality? The goal of this paper is to: explore the problem of universals, see how Plato

answers the problem of universals, look at some problems with Plato’s answer, and explain why

a theory of modes may be a better answer the problem of universals.

Plato puts the problem nicely in Parmenides when he says, “Whenever some many

things seem to you to be large, perhaps there seems to be some one character –the same-… and

from that you conclude that the large is one thing” (Cohen, 647 line 132). Plato is talking about

seeing different instances that share common properties. Since these common properties all

appear to be the same, he wants to call them by one name. Here we can also talk about types and

tokens. A type would be a property, like the property of red that is attached to the billiard ball.

We can talk about the tokens, the instances of the type, the redness we experience in both the

striped and solid billiard ball. Another helpful idea in understanding universals is looking at the

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way we form sentences. When we form descriptive sentences (the billiard ball is red), these

sentences include a subject and a predicate. The subject of the sentence being the billiard ball,

and the predicate being “is red”. The predicate of the sentence, in this case, is pointing out a

common feature of reality. This means that the way we describe our world points out certain

commonalities in order to make the world more intelligible. If predicates kind of imply the

existence of universals, is our way of describing the world accurate, or is separating the subject

and predicate just a manner of speaking? This is not to say, however, that our way of talking

about the world gives us a direct vein to the way the world really is, just that we need examine

why we speak as we do in order to see if that manner of speaking is an accurate description of

reality.

In answering the problem of universals, there are two ways of going about it. The first is

the realist perspective. The realist holds that universals are indeed real. They believe that the

predicates in the subject-predicate distinction are in fact something distinct from that which they

are attached to. Then, there is anti-realism, the anti-realist denies the existence of universals.

There are two different types of anti-realism I will explain in this section, all with a different way

of explaining commonality.

First, let’s look at extreme realism. Extreme realism holds that the universals exist

independently from there instances. They believe that there is an individual, and there is a

quality. The quality is the universal. This universal is exactly the same in all of its instances.

There are the individual substances that are unique (or numerically distinct), and then there is the

universal along with that substance. Since the extreme realist believes the universal is one entity,

which attaches to multiple substances, the instances of this one universal are strictly identical.

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Then there is the strong realist. The main difference between strong and extreme realism

is that the strong realist denies independently existing universals. “A universal on this view is

just the quality that is in this individual and any other qualitatively identical individuals”

(MacLeod and Rubenstein pg. 5). For the strong realist, if I were to remove all instances of the

universal, the universal would cease to exist. This would not be the case for the extreme realist,

however, since the universal exists separately from the substance. Now that we have looked into

the two realist views we can see some opposing anti-realist views.

The first anti-realist view we’ll be looking at is predicate nominalism. The predicate

nominalist completely denies universals. They say universals are just a manner of how we

describe the world. This makes commonality purely a function of how we describe the world. So,

the green in the billiard ball and on the table’s felt, are only both called green. We just call them

by the same name. For the predicate nominalist, there is no true way reality is that makes us

recognize this shared feature. In fact, the predicate nominalist takes our seeing commonality as

an unanalyzable brute fact. It is just that some ways of describing the commonality are okay

while others are not; they give no further analysis than that. (MacLeod and Rubenstein pg. 6)

A little less harsh, but still under the anti-realist umbrella is the resemblance nominalist.

“Resemblance Nominalists explain individuals shared qualities by talking only about

resemblance relations” (MacLeod and Rubenstein pg. 5). For the resemblance nominalist, then,

we only call things the same merely because they resemble each other. Since the word

resemblance is employed, this means there isn’t strict identity between two objects, just two

things that are similar enough that we recognize a resemblance, a similarity, and call them the

same. For the resemblance nominalist, resemblance is a brute unanalyzable fact. In other words,

we can’t understand why two things resemble each other, they just do.

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Now we must examine the problem with saying things share commonality in virtue of

resembling each other. This is a problem for the nominalists. It will also become an apparent

problem for the theory I will posit later, modes. The resemblance nominalist talks about set

membership. Things are put into sets when they resemble each other more than they resemble

non-set members. Take for example the “set” game. We put football and soccer into the set,

game, because they resemble each other more than they resemble cooking or shoemaking. By

organizing sets by resemblance, however, you end up including members in the sets that are

completely dissimilar from other members. We have the red billiard ball, which is in the set (red)

with the stop sign and red apples. Since things resemble each other in various respects, the red

billiard ball is in the same set as the green billiard ball. The green billiard ball clearly has no

similarity to the stop sign, but they are stuck in the same set since they both resemble the red

billiard ball. I believe for someone who solely posits resemblance relations this problem is

overbearing. (MacLeod and Rubenstein pg. 5) Now we understand the problem of universals.

We understand some of the major ways to answer this problem. We now need to see if Plato’s

answer to this problem is better than nominalism. I will give an account of Plato’s theory of

forms, and then explain which of the categories listed above Plato falls into.

Plato’s Theory of Forms is one of the most famous theories in all of philosophy. It

can be found predominantly in The Republic, although it is brought up in many of his works. It is

used to answer the problem of universals, but for him it also answers ethical and epistemological

questions. The forms are qualities of a substance such as: roundness, triangularity, and

goodness. The forms are supposed to be perfections of qualities that exist independently from the

physical world we experience. The forms exist in a place that is sometimes called the platonic

heaven. Plato is an Extreme Realist. To better understand the forms and how Plato is an extreme

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realist, it is important to be familiar with all of the forms important qualities. In an article entitled

Plato’s Theory of Forms, David Banach explains six important properties of the forms.

The first important property is that the forms are transcendent. Banach explains this as

meaning “the forms are not located in space and time”. Another way of putting this is that the

forms are non-physical. This is why people say that there is a “Platonic Heaven”. They are

saying that the forms do not exist in the physical world which we exist in. They are located

outside of time and space. The forms do not exist at one particular time. The forms also do not

exist in one particular space. By virtue of being transcendent, the forms are also immaterial.

Materiality is a characteristic of objects that are located in time and space. While material objects

are subject to alteration and destruction because they are made of physical stuff, the forms are

unchanging because change is a property of material substances.

The next important property of the forms is that they are pure. Banach explains this as

meaning that “The forms only exemplify one property”. This means the forms themselves do not

have multiple properties, they only exemplify one property. Let’s go back to the billiard balls.

The billiard balls have multiple properties: redness, sphereicity, hardness etc. For each of these

properties there is a corresponding form. There is no one form that contains both redness and

sphereicity. There is one pure form of redness and one pure form of sphereicity. These forms

themselves have no other quality except for the quality which they represent in the physical

world.

Another important property of the forms is that they are archetypes. To be an archetype

means to be a perfect instance of that which it is exemplifying. I often hear people talk about

archetypes in relation to people. For example; people often talk about the archetypical male, and

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talk about someone like George Clooney as being that archetype. They say George Clooney

because they think of the qualities that represent a male, such as being handsome and suave.

They see him as being a perfect representation of these qualities. Now let’s take this example to

the forms. We have the billiard ball and one of its qualities, redness. The form, Redness, is a

perfection of the quality redness. It is perfectly red; it couldn’t be anything other than this

because the forms are pure. If the forms were not perfectly red, that would mean there is some

other quality at work.

Banach’s next important quality he ascribes to the forms is that they are Ultimately Real.

This quality is given to the forms because they are unchanging. The instances of the forms in the

physical world are subject to change and therefore, not ultimately real. Since the forms are

fundamental, they are not subject to destruction like that of the physical world. The material

objects we experience are mere copies of the forms.

Also important is that the forms are Causes. This quality is given to point out that the

forms are the causes of all things. The forms explain why anything is the way it is, this is

because the forms are the source of being for all things. According to Plato, if the forms did not

exist, no other things could exist. This means that the forms precede the physical world. The

instances in the physical world did not cause the creation of the forms. The existence of the

forms caused the existence of the physical world.

The last important property of the forms is that they are Systematically Interconnected.

This means that the forms are connected to each other as well as to the physical world. From

some forms other forms can be drawn. As I will show, I think this property of the forms is the

source for a major problem for the forms called the third man argument.

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Using the properties of the Forms, and what we know about extreme-realism, we can see

how Plato was an extreme realist. The defining mark of the extreme realist is that he believes that

the universal exists independently of the instance. This is certainly what Plato believed and is

shown in the transcendence of the forms. The extreme realist also believes that the universal is

the same in all of its instances. By virtue of the forms being archetypal and pure, they are not

going to be different in their instances.

Problems with the Theory of Forms

I will be putting forth two problems with the theory of forms. The problem of divisibility

and the third man argument come by Plato’s own hand in Parmenides. I will describe these two

problems and I will provide a counter argument against the problem of divisibility. The first

problem that is presented in Plato’s Parmenides is what I will be calling the problem of

divisibility. In Parmenides, Plato uses Parmenides as the scrutinizer of the forms. Parmenides

asks “So does each thing that gets a share get a share of the form as a whole or a part of

it?”(Cohen, pg. 646 line 131a). In other words, does each billiard ball get a whole of the form of

sphereicity, or a part of sphereicity? Plato’s answer to this would be that the forms are wholly

present in each one of their instances. How can something be wholly present and be in more than

one place? Certainly, sphereicity is seen in both the cue ball and the eight ball. This, however,

means the form of Sphereicity is in more than one place at the same time. If the forms were not

wholly present in each of their instances, that would mean parts of the form exist in each

instance. If the forms were parts, and the parts existed in their instances, then once the instances

(the parts) go out of existence then the whole too would go out of existence. Plato’s aim is to

prove that the forms precede their instances. If the instances compose the forms, then this

certainly cannot be the case. I do not believe this is a true problem for Plato because of the

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property of Transcendence. By virtue of the forms being transcendent, they are immaterial. “It

seems to be the mark of materiality that that things can only be in one place at one time”

(MacLeod, Rubenstein pg. 3). Since the forms are immaterial, they are not constrained to being

in one place at one time. The problem of divisibility is not a problem for the theory of forms

because they are transcendent. This does not mean, however, that the forms are unproblematic.

Let’s move on to the next problem, the Third Man Argument.

The Third Man Argument also comes from Parmenides. It is a very brief section of the

book (only from 132a-132b), but it is a very famous argument and a devastating blow to the

theory of forms. Vlastos argues that three important things must hold true for the Theory of

Forms to be refuted. The third man argument proves that Plato’s theory leads to vicious infinite

regress. It is called a vicious infinite regress because the forms are supposed to provide an

answer to how things are the way they are. A vicious infinite regress leads to no answer. From

the forms, other forms can be derived (because they are systematically interconnected). When

you try to explain the nature of a form, say Largness, you end up explaining Largness with

another form Largness. This process continues to infinity and you never get the explanation that

was originally sought. I will now explain the vicious infinite regress more in depth.

I’m walking around in New York City. I see a bunch of buildings and say “gee, these are

all rather large”. Plato would say “Of course you say they are all large! They all participate in the

form of Largness!” I will use F to represent the form of Largeness and a and b to represent the

buildings. So, a and b both participate in F. Since the forms are archetypes, F is itself large. Now,

we have 3 large things a, b and F. We now need a form to represent the largeness of these three

things known as, F2 (form of Largeness 2). Now we have a, b and F participating in F2. Again,

since the forms are archetypes F2 is itself large. So now we need F3 to explain the largeness of a,

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b, F, and F2. Next there would be a Form F4 to explain a, b, F, F2, and F3. This vicious regress

would continue to infinity. You would end up with F100 ,F10000, an infinite number of forms of

largeness. This is vicious because we never get an explanation. Vlastos points out important parts

in the third man argument that must hold true for the vicious infinite regress to occur.

Firstly, is what is called One Over Many. This is referring to that from many we can

derive one. This is the problem of universals. The forms are posited precisely to take many

instances and provide a one that derives from these instances. In the mentioned example, there

were buildings; these buildings are large according to Plato because they all participate in the

form largeness. The one (Largeness) is derived from the many (buildings, large things). The next

important part of the criteria is self-predication. This means “any form can be predicated of

itself” (Vlastos 324). Self-predication must be true because the forms are archetypes, George

Clooney represents the archetypal male and himself is a male. The forms are perfect examples of

that which they represent. The last important part of Vlastos’s criteria is the Non-Identity

Assumption. Vlastos describes this as meaning “If anything has a certain character, it cannot be

identical with the form in virtue which we apprehend the character” This criteria is the hinge of

the forms. If the forms were identical with their instances, they would just be the instances. If the

forms were identical with their instances, there would be no forms. Since the forms themselves

have a property, they must themselves have a form over them to describe that property.

So let’s reword the argument in Parmenides using Vlastos’s terms. We have a and b

which are both large. Since One-Over-Many is the heart of the forms, from a and b we derive the

form of Largeness (F). Now Self-Predication , since the forms are archetypes, they have the

property of the instances which they represent. The Form of Largeness (F) is itself large, it must

be. Lastly, the Non-Identity Assumption. If something has a property, that property is not derived

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from itself, but from another form. Since F has the property of largeness and, it needs another

form of Largeness (F2) in order to describe it .These same steps happen for F2, which leads to an

F3. This regress happens to infinity. We never get a description of the property. This is a fatal

blow to the theory of the forms.

The answer to the problem of universals I would now like to propose is called a theory of

modes. It comes from John Heil’s book entitled The Universe as We Find It. A mode is a

particular way a particular substance is. This is how Heil accounts for properties. He says

“properties are ways substances are” (Heil 4). Heil never comes out and says what he thinks the

substance(s) is (are), but some other philosophers who have posited modes have done so. Locke

suggested modes. His substance was called corpuscles. The corpuscles arranged in a particular

way gives rise to various properties to make the billiard ball. To better understand how properties

can arise from arrangement, think of a water molecule. A singular water molecule is not itself

wet, but when several water molecules come together the property of wetness arises. Heil holds

that properties and substances are inseparable. If you have a substance, it’s going to be a

particular way and thus have properties. It is important to note that for Heil things like tomatoes

are not substances that properties attach to. To treat the billiard ball as a substance is to treat it as

an indivisible unit. For Heil substances must be simple (indivisible). This is because the

substance must have an infinite number of potential properties, in order to account for all the

various properties. I believe this is because properties arise from arrangement. If a tomato (non-

simple) was a substance it could only give rise to certain properties (redness, sphereicity). If we

take something like the most basic constituents of atoms as basic (simple), we can account for all

of the objects and properties we encounter in the universe.

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Now, we need to see how modes answer the problem of universals. In other

words, how do modes explain commonality? I would like to call a theory of modes, resemblance

nominalism analyzed. This means that we experience commonality in virtue of the two

properties resembling each other, but for someone who posits modes the story is deeper than

that. For the resemblance nominalist, resemblance was an unanalyzable fact of the world. The

mode theorist can analyze the resemblance. The mode theorist says resemblance occurs because

the two objects with resembling properties have similar or identical substance arrangements. Let

me give an example. We have a red billiard ball and a red tomato. Let’s just assume there is one

substance: atoms. The atoms are obviously arranged very differently in the billiard ball and the

tomato. The tomato is soft, juicy, and delicious, and the billiard ball is hard, dry, and would kill

me if I ate it. The atoms in both, however, are arranged in such a way that they both absorb

certain wave lengths and reflect the red wavelength. The arrangements of atoms in both the

tomato and the billiard ball make it so a particular wave-length is reflected. The structure of the

substance in similar enough ways gave rise to similar properties. Resembling structures is one

way that the mode theorist can explain commonality, but perhaps not a sufficient way to explain

commonality.

I mentioned earlier that at face, this theory encounters the same problem as the

resemblance nominalist. To reiterate, when you say things are in the same set by virtue of

resemblance you end up putting dissimilar things into the same class. The green billiard ball and

the red stop sign are in the same class because the green billiard ball resembles the red billiard

ball, and the red billiard ball resembles the red stop sign. This is an apparent problem for the

mode theorist as well because two dissimilar things could be in the same class. The structure of

the red billiard ball has a similar structure to the red stop sign, but the red billiard ball also has a

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similar structure to the green billiard ball. This makes it so two dissimilar things ( the green

billiard ball, and the red stop sign) are in the same class. I believe Heil, however, gives a feature

of structure that allows this problem to be avoided.

In order for the mode theorist to avoid this problem they must reach beyond mere

resemblance. The mode theorist must posit something identical among instances to explain

commonality. Heil suggests that “properties are powerful qualities”(Heil 61). This allows a

change in the answer to the problem of universals from how the structure is to what these

structures do or would do. Back to billiard balls, a given structure makes a billiard ball look red,

and it makes the billiard ball roll. These words (look, roll) are referring to actions of the billiard

ball. Without the ability to act no commonality could be experienced. The experiencing of

commonality is what the problem of universals is all about. If the billiard balls’ structure did not

give the billiard ball the power of looking red, no red would be experienced, hence no

commonality would be experienced without powers. Using the model of powers we can see why

we place objects in the same sets. We can place objects in the same set if they have the same

power. Commonality is now based off of what these structures actually do, as opposed to how

these structures resemble each other. Resembling structures produce identical actions, therefore

have identical powers. We move from set placement based off resembling structures to set

placement based off identical powers. This allows the mode theorist to avoid having dissimilar

members in the same set. The green billiard ball is not in the same class as the stop sign and red

billiard ball because it’s structure doesn’t give it the power of looking red. Using powers on a

theory of modes to answer the problem of universals provides an unproblematic way to explain

commonality.

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In this paper, we have explored the problem of universals. We have looked at it from

several viewpoints. We saw how Plato answered this problem and then saw problems with his

theory. This led us to a view I find particularly convincing, modes.

Works Cited

Banach, David. "Plato's Theory of Forms." 1 Jan. 2006. Web. 15 Nov. 2014.

<http://www.anselm.edu/homepage/dbanach/platform.htm>.

Cohen, S. Marc. Readings in Ancient Greek Philosophy: From Thales to Aristotle. 4th ed.

Indianapolis: Hackett Pub., 2011. Print.

Heil, John. The Universe as We Find It. Print.

MacLeod, Mary, and Eric Rubenstein. "Universals." Internet Encyclopedia of

Philosophy. Web. 15 Nov. 2014. <http://www.iep.utm.edu/universa>.

Vlastos, Gregory. "The Third Man Argument in the Parmenides." The Philosophical

Review: 319. Print.