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ProblemOfUniversals

Universals are either properties, relations, or types.  Last time I didn’t talk about types, but I should mention them now.  Now recall that last time I listed five different categories of being.  Of course, there are others.  Types are another category of being.  A human is a type of thing; a cloud is a type of thing; and so on.  An instance of a type is called a token of that thing; so I am a token of a human being; the letter "A" that I just uttered is a token of the first letter of our alphabet; the apple on the table is a token of the type, apple.

Remember now that one of the categories of being that I did list was classes.  Of course we can talk about the class of human beings, just as we can talk about the type, human being, or humanity.  But you might ask: how do classes differ from types?  Are these really two different categories of being?  Well I’m not sure; perhaps there isn’t any substantial difference.  But there is a difference in how we talk about types versus how we talk about classes.  Here’s the difference.  I say that I am a token, or an instance, of the type, human being.  But notice that I say instead that I am a member of the class of human beings.  We would not say that I am a "member" of the type, human beings.  I’m a token, or an instance, of the type.  So the difference is: types have tokens, or instances; classes, on the other hand, have members.  And if you think about it, to say that something is a member of something is different from saying that it’s an instance of something; that’s an intuitive way to put it, isn’t it?  That a member is different from an instance?  Anyway, whether or not types are definitely different from classes or they aren’t, I am going to treat them differently.  And I am going to consider types universals, along with properties and relations.  So universals include types, properties, and relations, as I said, but not classes.  However, I should add that all four items are generally considered abstract in the sense that I defined last time.

So let me give some examples of universals: there are types, like doghood; properties, like redness; and relations, like betweenness; those are all universals.  Not this particular dog, this particular red thing, or this particular object that is between other objects; those are all particulars, and instances of universals.  Doghood, redness, and betweenness are common to many different things.  So a universal is something that can have instances; but it doesn’t make sense to talk about an instance of a particular.

You can also think of universals as the referents of general terms.  In other words, they are what we refer to, when we use general words like "doghood," "redness," and "betweenness."  By contrast, we refer to particulars by using proper names, like "Fido," or definite descriptions that pick out just one thing, like "that apple on the table."  So I hope I have said enough to explain the difference between universals and particulars.

Now last time we asked, "What are objects?" and we gave two theories of objects.  We asked about the basic nature of objects, and we called that the problem of substance.  This time we are going to ask about the basic nature of universals.

So here is the problem of universals.  I’m going to try to explain what this problem is.  The problem of universals may be most briefly stated as a question: "What are universals?"  What are they in general?  Or, if you want it expanded a little bit: "What sort of beings are types, properties, and relations?"  This is, in a way, similar to our question from last time: "What sort of beings are objects?"  And remember that as far as metaphysics goes, we have no other way to describe objects than by their relations to their properties and relations.  When we tried to determine what was meant by this question "What are objects?" ultimately we interpreted that question as asking, "What are objects in relation to their properties and relations?"  OK, in the same way, when I ask what universals are, I am asking: "What are universals in relation to particular objects?"  So you might be able to see that the problem of universals is complementary to the problem of substance.  The problem of substance has you trying to explain what substances are in relation to universals; the problem of universals has you trying to explain what universals are in relation to objects.  So when we ask, "What are universals?" a clearer way of putting the question is this: "What is the relation of universals to particular objects?"

You might be wondering: Why is this a problem?  Well, I don’t expect you to see why it’s a problem just yet.  First let me list three facts about universals.  They will help you to see what the problem is.  These are similar to, but not the same as, the three points made on p. 354 of the reading.  These are facts that, no matter what our theory of universals is, if universals really are said to exist, then our theory about universals have at least to be consistent with, and even to explain, these facts.  In other words, you can take these three facts as background assumptions; and that means that if we come up with a theory which contradicts these background assumptions, we toss the theory out.  It’s no good.  Definitely we have to have some background assumptions, or else we wouldn’t have any tools to evaluate any theory of universals.

So here are the three facts.  Actually, I’ve already hinted at some of these, including the first.  The first fact is: Universals, if they exist, can be multiply instantiated.  What that means is that, if we’re talking about a universal, we’re talking about something that can have instances; if a universal has an instance, then we say it is instantiated.  For example: the type horse is instantiated by all the horses in the world; flying horse is a type of thing, though, that is not instantiated, which means there are no instances of it.  But the point is, it at least makes sense to speak of instances of horses, and of flying horses, whether or not there are any instances.  So universals, whatever else we think about them, have to be the sorts of beings that can be multiply instantiated.  This means a theory of universals has to make sense of the fact that universals can be multiply instantiated.  So for example if we come up with a theory of universals where the things that are supposed to be universals aren’t multiply instantiated, then the theory can be thrown out.

Here’s the second fact about universals: If universals exist, then we can form concepts of them, and when we do, we form a concept of something abstract.  In other words, when we think of, to change our example, dryness, we are thinking of something abstract.  Granted, when we conceive of dryness, we might imagine a particular dry thing, like the Sahara Desert.  But even though we imagine it, we understand that the Sahara Desert isn’t dryness itself.  It’s just an instance of dryness.  Whenever we have an example of a universal in mind, we know very well that the example isn’t the same thing as the universal itself; the Sahara isn’t dryness itself.  That doesn’t make any sense.  The point then is that to conceive of universals is to conceive of abstract things.  So what does this mean for theories of universals?  It means that if, according to some theory we’re looking at, universals aren’t abstract, then the theory should be thrown out.  Or if, according to a theory, it’s hard to see how we can even conceive of universals, then the theory should be thrown out.  Or suppose we come to the conclusion that, just as a matter of fact, we can’t conceive of abstract things; suppose we conclude that we can conceive only of particulars.  Then we should conclude that universals don’t exist.  So once again: If universals exist, we can form concepts of them, and when we do form concepts of universals, we are conceiving of something abstract, not particular.

Here’s the third fact.  If universals exist, then general terms, like "redness," "betweenness," and "doghood," refer to universals.  If there are abstract properties, relations, and types, then they are the sorts of beings that general terms refer to.  This makes perfect sense, once you understand it.  The word "redness" for example doesn’t refer just to the red apple here.  If abstract properties exist, then the word "redness" refers to an abstract property, not just one instance, because after all there are other instances of redness besides this apple.  Similarly, the word "dog," a type of object, doesn’t refer just to my mom’s dog Buffy; it refers to the type, dog, which can be instantiated in any number of our canine friends.  So general terms are supposed to refer to universals.  And if, according to a theory of universals, general terms don’t refer to universals, then that theory should hold that universals don’t exist.  That’s the proposal: according to this third alleged fact about universals, any theory which holds that universals really do exist had better have a way for general terms to refer to universals.  Really, what would universals be good for if we didn’t have them around for our general terms to refer to?  That might sound flippant but actually there’s some truth to it.

So there you have three basic facts that I am claiming are supposed to hold true of universals, if universals exist.  There might be other facts, other constraints we might want to put on theories of universals, but we’ll ignore them for now.

With these facts in mind, let’s see how we might update a statement of the problem of universals.  I said the problem in its simplest formulation was just the question, "What are universals?"  Now I’ll give you another way to put the problem.  Maybe putting it this way will make it more obvious how it’s supposed to be a problem.  Here’s the question: "What are these curious beings which can be multiply instantiated, which we conceive of when we conceive of abstract attributes of things, and to which general terms refer?"  Now remember also that I said the problem was explaining what the relation of universals to objects was.  So we can put the problem like this: "Can we give any sort of general account of what universals are, in their relation to objects, such that these three facts about universals come out to be true?"

If you still don’t understand what the problem is, you’ll get a much better idea of what it is after you have looked at some theories of universals.  So let’s now look at some theories of universals.  We are going to begin with the theory which was advanced by the ancient Greek philosopher Plato.

Plato’s theory of universals is also called "Platonism," or "Platonic realism about universals," or just "realism" for short.  But don’t confuse it with other doctrines called "realism" in philosophy.  The word "realism" is extremely ambiguous -- has a gazillion different senses in philosophy and also outside of philosophy.  I’m going to prefer the term "Platonism."  Anyway, according to Platonism, universals exist in a realm that is separate from space and time; universals have a sort of ghostly or heavenly mode of existence.  We never see or otherwise come into sensory contact with such Platonic universals.  They definitely do not exist at any distance, in either space or time, from your bodies.  Obviously they don’t exist in the way that ordinary physical objects exist.  Nonetheless these universals do, according to Plato, exist.  

Let’s call these sorts of universals, after Plato, forms.  They are also called ideas, but Plato’s universals certainly aren’t ideas in the mind; don’t be confused by that terminology; let’s just stick with calling Plato’s universals "forms."  Also, for simplicity we will use this word "form" only to mean Plato’s sort of universals.  That means that if you end up rejecting Plato’s theory of universals then you could say: The forms, Platonic forms, do not exist.  Or perhaps you should say instead: Talk of "forms" is nonsense.

Now let’s see how Platonism is supposed to solve the problem of universals.  Here’s the question to ask: What relation do the forms have to physical objects?  They aren’t spatially or temporally related to objects, right? -- No, the forms are not spatio-temporal items.  So what sort of relation do the forms have to physical objects?  Different views are possible here and Plato himself is hard to pin down.  We might say, first, that the forms are archetypes, meaning original models, of which particular objects and properties are copies.  So this apple is a copy of the form of applehood.  This particular redness here is a copy of the form of redness.  And so forth.  Particulars are then supposed to be copies of the forms.  (Whatever "copy" is supposed to mean here; we’ll discuss that in a little bit.)  Anyway, that’s one way that the forms might be related to particular instances of objects and properties and so on.  Another way they might be related, for Plato, is that particulars are said to participate in the forms, and the forms are said to inhere in the particulars.  This talk of "participation" and "inherence" is admittedly kind of mysterious.  What does it mean to say this apple participates in applehood?  What does it mean to say applehood inheres in this apple?  We don’t get very enlightening answers from Plato.  But we’ll talk a little bit more about that in a second.

Let’s consider how Platonism deals those three facts about universals that we listed.  First, are Platonic forms capable of being multiply instantiated?  Sure.  Plato did think that there were some forms that weren’t instantiated at all, but that doesn’t by itself mean that the forms couldn’t be instantiated.  On the one account, forms can have lots of copies -- or on the other account, they can inhere in lots of things.  On either account, the forms are capable of being instantiated by many different things.  But as we were just saying, it’s just not clear what either account of instantiation amounts to.  For example, what does it mean to say that this particular apple is a copy of the form of applehood?  Does it mean the apple is the same shape as the form?  Probably not; the form, after all, isn’t supposed to have a shape because it’s not spatial, remember?  And what does it mean to say that apple participates in applehood?  Is it like membership in a club or something?  It’s not clear.  Well, let’s not try to get into it very deeply.  I just want you to know that this is a basic problem for Plato’s theory: exactly how are we supposed to spell out Plato’s views on how particulars instantiate the forms?

How does Platonism do with regard to the second fact about universals?  The idea here is: if we can conceive of universals, then we have to be able to conceive of the forms.  When I think of redness in general, then according to Plato, I am thinking of the form of redness.  Well, OK, maybe that’s possible somehow; but this raises another problem: how on earth did we get the concept of something, a form, that exists neither in space nor in time?  The forms are supposed to exist in a special realm of the universe, apart from space and time.  How could I have any concept of them, then?  I didn’t get the concept via sense-perception.  You can’t see the forms.  I can see the apple, and its redness, but those things merely participate in the forms, or they’re just copies of the forms; and to conceive of this apple and this redness is not to conceive of applehood or redness-in-general.  We do not have any empirical evidence that forms even exist; in fact it’s hard to think of what such evidence could be.  So Plato ends up saying that our souls are born with the concepts of the forms, and we just have to be reminded of those concepts from back before we were born, back when our souls were in close contact with the forms in the Platonic heaven.  This theory is, however, very hard to take seriously.

Well, so far Platonism wouldn’t appear to be doing very well in accounting for these facts about universals.  So let’s see if it can do any better in explaining the third fact.  Would it make sense to say that forms are what general terms refer to?  Sure, I think so.  Platonism probably does best on this count.  Forms are just the perfect sort of items for our general terms to refer to.  When we speak of "applehood" or "redness" we are talking about something like Platonic forms: that sounds plausible, anyway.  In fact, some people have said that Platonism gets all its plausibility from the fact that when we talk about redness, for example, we seem to be referring to something that is apart from space and time, but which has lots of specific instances.

Still, problem like what participation is, and how we can have any concept of the forms, would appear to be very difficult.  I don’t want to give you the impression that Platonism is rejected by everyone now, because in fact it does still have its defenders.  But we would do well to consider some theories that aren’t quite so strange.

So next let’s consider Aristotle’s theory of universals.  Aristotle was Plato’s student.  And just as a historical tidbit let me add that Socrates was the teacher of Plato: so there is a very famous line of succession that included the three greatest ancient Greek philosophers.  It went: Socrates taught Plato, and Plato taught Aristotle, and the three of them together are responsible for the birth of Western philosophy as we know it.  The whole line of succession occurred between 500 BC and 300 BC. 

Anyway, to Aristotle’s theory of universals.  Aristotle disagreed with Plato by saying that universals do exist in space and time.  They exist all around us.  So then what is a universal, according to Aristotle?  Well, I’ll say something in reply to that question, but I won’t promise that you will find it enlightening.  Aristotle thought universals are simply types, properties, or relations that are common to a number of different instances.  Moreover, universals exist only where they are instantiated; they exist only in things (he said they exist in re, which means simply "in things"), never apart from things.  Beyond this Aristotle said that a universal is something identical in each of its instances.  So all red things are similar in that there is the same universal redness in each red thing.  There is no Platonic form of redness, standing apart from all red things; instead, in each red thing there is the same universal, redness.

Now let’s look at how Aristotle’s theory deals with those three facts about universals that we listed.

First of all, the universal is multiply instantiated, so it appears.  It is, after all, one and the same universal, applehood which appears in each apple.  But here I think you can see a problem: honestly, how can we make sense of exactly the same thing being in all of these different objects?  Because that’s what the theory says; to say that different deserts, the Sahara, the Atacama, and the Gobi are all dry places, is just to say that the exact same being, the universal dryness, occurs at each place.  Universals must be awfully strange entities if exactly the same universal can exist in many places and times at once.  Or so one might think.  But maybe that’s not so troubling; it seems troubling if you expect universals to be like physical objects, but remember, we’re talking about a totally different category of being.  Maybe it’s not so strange, then, to say that the exact same universal, dryness, occurs all over the earth at once; after all, there’s nothing strange about saying that different deserts can be dry at the same time.

OK, how does Aristotle’s theory deal with fact number two?  Are Aristotelian universals what we conceive of when we conceive of universals?  Perhaps.  Now let me explain something about how we form concepts, according to Aristotle.  Think of a little girl just forming the concept of human beings.  How does she do it?  Well, when we form the concept of a universal on Aristotle’s theory, we abstract from a lot of the instances we come across.  We as it were mentally extract from each thing the quality that they all have in common.  So how does the little girl get the concept of a human being?  She learns to ignore the details, tall and short, black and white, long hair and short hair, male and female, etc.; and she pays attention to the thing that they all have in common, namely, humanity.  On Aristotle’s view, the universal humanity is the same in all humans (i.e., all humans have that exact same property in common); and this allows us to form a concept of humanity that applies to all humans.

OK, the third fact: Are Aristotelian universals the sorts of things we refer to when we use general terms, like "redness" and "humanity"?  Again, perhaps.  The idea is that when we refer to humanity, we refer to the type, human being, that appears identically in each human.  We don’t refer simply to all the humans, but instead the type, human being, which is the same in each human.

Aristotelianism (that’s a fancy long word for "Aristotle’s theory"), on the whole, sounds pretty plausible, I think.  Except that there may be something peculiar in this talk of the exact same universal being in each thing.  So how might one think if one opposed both the views of both Plato and Aristotle on universals?

Well, the people who oppose both Plato’s theory and Aristotle’s theory tend to be rather hard-headed, intellectually speaking.  They don’t like all this spooky talk of "forms," which exist in some never-never land apart from space and time.  They don’t even like this talk of qualities that can exist in many different things at once, as Aristotle has it.  These people would prefer if we just talked about particular things, thank you very much, because that’s all there are -- particular things.

This view has a name: nominalism.  So nominalism is the view that universals don’t exist.  No abstract properties, relations, or types exist!  That’s what they say.  Since nominalists deny that universals exist, they don’t have to worry about explaining those facts about universals that I listed.  But that doesn’t mean that nominalists still have nothing to explain.  Because, clearly, they have lots of explaining to do.  Their position is really very strange!  I mean, consider this little argument: We do say, correctly, that this apple, lots of roses, and many sportscars are all "red"; so there is a property they have in common, namely redness; therefore there is a property; properties are universals, so universals exist.

How do nominalists reply to that sort of argument?  Whatever they say, they sure as heck do not want to admit that anything universal exists; everything that exists, they say, is located in space and time.  So we’ll just have to see if the nominalists have anything to say in reply to that argument.  Now, the word "nominalism" comes from from nominalis, which means, in Latin, "pertaining to names."  The first nominalists said that only general terms or names exist -- no general qualities exist for those terms to refer to.  Just the names.  So we can say the name "redness" exists, but there is no universal, redness, to which it refers.  What does the term "redness" refer to, then?  Perhaps any particular red thing, and perhaps the collection of all the red things.  This is called extreme nominalism: the view that universals do not exist, and that general terms (such as "humanity" and "redness") stand for either particular objects or collections of particular objects (such as "all humans" and "all red things").

Now if you’re a very worldly sort of person, who wants to say that whatever exists, can only exist in space and time surrounding us here and now, then nominalism might appeal to you.

But nominalism definitely has some problems; I’ll explain two of them.  So here’s the first problem.  If a universal is just a name, then all that the three humans, John, Mary, and Sally have in common, is that they are called "humans."  There is no property, humanity, that they have in common.  That seems very hard to accept!  After all, we need only ask: why are they all called humans?  We don’t just say that John, Mary, and Sally are all humans for no reason at all: we say so for some reason, don’t we?  But it is because each of them is an instance of the type, humanity, so you might say.  Or maybe you would want to say: each of them is called "human" because each is a rational animal.  But at any rate, they each appear to have some properties in common that make them all human!  For example: they all have highly-developed minds; they walk on two legs; they talk; and so on.  It certainly does look like there are some properties that John, Mary, and Sally have in common -- which are what we call universals.  And their having these properties in common is explains why they are all called "humans."

The point is that any nominalist worth his salt is going to have to come up with some way of answering the following: why is it that things that are described by the same general term appear to have many properties in common, even though in fact (as the nominalist says), they don’t have any properties in common?  I’m not saying that extreme nominalists haven’t tried to solve this problem, because indeed that have tried.  I’m just saying it’s a very hard problem for them to solve.

Let’s move on to a second problem for extreme nominalism.  According to extreme nominalism, general terms refer only to particular objects or collections of them, right?  That’s what I said anyway.  But surely when we talk about, for example, the redness of the apple, we don’t mean the apple itself, but instead a property of the apple, namely its redness.  Suppose extreme nominalism denies that that exists.  Then it seems to be denying that this apple has the particular shade of red that it obviously has!  That just seems insane.  It seems as clear as anything can be, that this apple has a certain color, which we call red; after all, we can see the color!  Or to take another example: if I say that B is between A and C, but I deny that between-ness exists, then I seem to be saying that B’s-being-between-A-and-C doesn’t exist; because that would be an instance of between-ness.  So it would seem we should reject extreme nominalism because it denies that instances of properties and relations can exist, when it is as obvious as anything that at least instances of properties and relations exist!  Even if we can’t see or otherwise experience abstract, or general properties, surely at least we can experience instances of them; and it’s pretty hard to deny the existence of something that appears to be staring you in the face!

So now let’s look at two less extreme examples of nominalism.  We won’t spend too much time on these two theories.  Now these two theories both deny that universals exist, which is why they are versions of nominalism.  But instead of saying that general terms refer to particulars, or collections of particulars, they say that general terms refer to something else -- namely, images, or concepts.  So let’s begin with imagism.  Imagism is the view that universals are mental images, pictures in the mind; or that general terms refer to such images.  So the general term "humanity" means an image of a human being in my mind.  "Redness" means a mental picture I have of a patch of red.  Now, notice that there is a distinction between mental images and concepts.  I can have an image of a thing in mind, but that doesn’t mean that I am conceiving of the type of thing it is: I can be imagining what a person looks like without thinking specifically of the concept of what a person is.  The image is different from the concept.  Images generally are different from concepts.  So then here’s the second version of nominalism, called conceptualism: this is the view that universals are concepts, or that general terms refer to concepts.  So triangularity itself is a concept -- of a closed, three-sided figure.  The universal, humanity, is the concept of a rational animal.  To be human, then, is to be an instance of that concept that you have in your mind.

I think you may see that these are initially plausible views -- especially conceptualism.  But there are various problems that can be raised for both imagism and conceptualism, and there is one objection which I think we can use to reject both views immediately.  Namely: images and concepts are of something.  So if I have an image of a triangle, or a concept of triangularity, it is an image or concept of that.  So we cannot identify images or concepts with what they represent.  What we want to know is the type, or the property, or the relation, that they represent.  So if I have an image of a triangle in my head, or if I conceive of triangularity, and I ask what sort of thing is the universal, triangularity, then I want to know what sort of thing this image is an image of, or what the concept is a concept of.  That image or concept in my mind can’t be triangularity, because the image or concept is supposed to represent triangularity.  So to sum up, we might have images, or concepts, of universals, but clearly the universals are different from any images or concepts we might have of them.

Nominalism, at least the way I have presented it to you, would appear to be generally a very dubious theory, after we consider the objections to it.  Now I’m going to ease our way into the final theory, which is called the resemblance theory, and which in my opinion at least has the best chance of being true.  I’m going to introduce some terminology and motivate the theory, before I present it.

Remember our second reason for rejecting extreme nominalism: we said that surely at least instances of properties and relations exist!  So this redness, this particular redness of this particular apple, or this instance of humanity, Mary, exists.  Why not then admit that much, that the instances exist: this instance of redness, this instance of between-ness, this instance of humanity.  Specific instances of types, properties, and relations are called tropes.  So tropes are particulars, because they aren’t multiply instantiated.  There just one instance of each trope.  Now although they are particulars, it’s hard to say that they are concrete.  Take Mary’s humanity: of course Mary is a concrete thing, located in a particular place in space and time, but Mary’s humanity?  It sounds strange to say that that is located at all; rather, it’s the type of thing she is, and it’s just strange to say that the type of thing she is is located somewhere.  Or take maybe a better example: London is north of Paris; so London’s-being-north-of-Paris is a trope.  Right?  It’s a particular instance of "being-north-of."  But where is that particular relation?  Is it at London?  At Paris?  Somewhere in the English Channel?  That’s just a strange question.  London’s-being-north-of-Paris doesn’t seem to be a concrete thing at all.  So even though it is a particular, it is, we might say, an abstract particular.  The redness of this apple is a particular, but it’s not concrete in the way that the apple is; so we say either that this redness is a trope, or more descriptively, that it is an abstract particular.  "Trope" and "abstract particular" are two different names for the same category of being.

So then the suggestion now is to say: tropes exist; but universals do not exist, if conceived of as something over and above tropes.  So the redness of the apple, the ball, and the flower each exist; but there is not something in addition to each of those things, some ghostly redness in general, which is somehow the same in each object.  Now in saying that tropes exist, we’re not quite done explaining the resemblance theory, but that’s an important part of it.  If the resemblance theory is a solution to the problem of universals, then we should still expect some answer to questions like this: What is redness itself?  Surely we aren’t saying that redness itself is any specific instance of redness.  Well then, what is it?

Try out this answer: "If I am not allowed to say that redness is any specific instance of redness, then I can still say that redness is the collection of all the particular instances of redness.  So the universal, redness, would be a collection, of all the particular rednesses in the world.  And, by the same token, humanity would be the collection of all the instances of humanity in the world."  Well, this answer might fly, but we still have a problem.  It is the same problem that was visited upon extreme nominalism: Sure, we can go ahead and say that the collection of all the redness tropes is what we mean by "redness in general"; but why do we call apple, the ball, and the flower all "red"?  We can say that each particular redness is a trope, and that those tropes exist; but why are they all tropes of redness as opposed to any other property?

Well, here’s a way to answer that question: we say that these three tropes, the redness of the apple, of the ball, and of the flower, resemble each other.  Moreover, we can simply look at the three side-by-side and see the individual colors, and see that the individual colors resemble each other.  Similarly in the case of John, Mary, and Sally: the reason we call all of them "humans" is that their individual properties resemble each other.  So in general here’s our theory: types, properties, and relations are particular attributes, or tropes, or abstract particulars, of objects; tropes are capable of resembling each other, and when a large number of tropes do resemble each other, we each formulate concepts and names which we use to apply to all of the tropes on account of the resemblance each of us sees.  But nothing genuinely universal exists; there are only (1) particulars including objects and their tropes, and (2) particular collections of tropes, and (3) particular resemblances between particular tropes, or between groups of tropes.  These three existence claims together make up the resemblance theory, which could also be called the trope theory.

Notice how the resemblance theory is different from Aristotle’s theory.  Aristotle said that a universal is the same in each object; but on the resemblance theory, each trope is quite distinct from each other trope.

The reading goes on to discuss this theory, but we are going to have to leave the discussion there.  A lot of philosophers these days do find something like the resemblance theory as presented here attractive.  But trust me, a lot more can be said on all sides.  In fact, it is not uncommon to find whole graduate-level courses just on the problem of universals.  But onto the next problem.