What is Nominalism?

This is part of a set of posts designed to show that realism with regard to universals can’t be true.  This post is just to clarify nominalism, what it is, and what it is not.

TL;DR

Nominalism is the philosophical position that only particulars exist, and that what we refer to as universals are just names for imaginary things that have no ontological being.  We talk about the names.

For example, a herd of cows is a bunch of particular cows, each having some essence of “cowness.”  We talk about a cow in the abstract, we really just mean collection of properties typical for those particulars, but abstraction itself has no other reality.  This is a classification problem.  There are two particular lumps of matter, and each has the features that denote a cow, and therefor I can put both animals in the same class, and say we have two instances of that class.

A circle is defined as the set of all points equidistant from the center point.  We can draw a particular circle on the board and it is far from perfect, yet still we use this as a symbol for the abstract, perfect circle.  We can talk about this perfect circle even though it does not actually have any ontological being.  The only thing that is important is that the people discussing a circle agree on what the properties of that abstract object would be if it existed.

Definitions

Wikipedia says:  In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels. There are at least two main versions of nominalism:

• One version denies the existence of universals—things that can be instantiated or exemplified by many particular things.
• The other version specifically denies the existence of abstract objects—objects that do not exist in space and time.

Classes and Classification

Consider a field with two cows.  Each cow is a particular, each having the essence of “cowness.”  We point to one, and say “that is a cow.”   Then we point to another and say “that is a cow.”    Clearly there are two cows, they appear to be two of the same thing, but what is the thing that there are two of?

When you tell someone to “look for a cow,” what is the thing they are looking for?  Before they see the particular cow, there is an image in the mind that represents an abstract cow.   In the sentence “look for a cow” the word “cow” is obviously standing for something, but what?   Can it stand for a cow that you have never seen?

We talk about a cow in the abstract, we really just mean collection of properties typical for those particulars, but abstraction itself has no other reality.

This is a classification problem.  There are two particulars, and each has the features that denote a cow, and therefor I can put both animals in the same class, and say we have two instances of that class.  There is no abstract cow holding the essence of a cow, which somehow appears twice in front of us.   Instead, there are two large lumps of matter with all the right features that we can classify them as cows.

Naming and Learning Meanings

It is obvious though that we can attach meanings to names.  In general, we can call those symbols or metaphors: one thing that stands for another thing.  When I talk about George Washington, how do we know that you understand what I am saying?  In a dialog, as one person speaks the listener is constantly evaluating what is said.  If I said that George had three heads, you notice jarringly that that does not fit you expectation, and that would raise a clarification question: which George are you talking about?  This sort of back and forth banter will clarify both our meanings with respect to the name George Washington.

The same thing happens with universals.  A you kid points to an animal and says “cow” and the mom then correct them:  “No dear, that is a goat.”  After a few cases of this the child learns to distinguish a cow from a goat.  This is how you learn all your words.

We make mistakes all the time, but when the mistake is large enough that it enters into conversation, it stands a chance of being corrected.  So back and forth we hone each others understanding to be the same as ours, and with luck the entire group holds the same meanings.

The class is just a name, and it is associated with a set of features that identify instances of the class.  “Cow” for instance is a largish animal, four legs, hoofs, sometimes horns, and shaped kind of blockish and lumbering.  This animal could never climb a tree, it makes a mooing noise sometimes, has furry skin, and so many other things we know about cows.  The class is just an association of these features.  The perceptual system represents these feature directly in neural circuitry, and any time we see a lump of matter that has the right features, we immediately recognize the cow.

When we see two cows, it is simply not a fact that you see two of the same thing.  You see two different things that fall into the same classification.

History

Roscellinus (1050 – 1125) and Abelard (1079-1142) wrote about rejection of universals in favor of nominalism.  William of Ockham (1287-1347) really put it on the world stage the idea that that universals are the products of abstraction from individuals by the human mind and have no extra-mental existence.

Ockham promoted a variation of nominalism known as conseptualism because he believed that within the brain there were concepts that were universal.  I am not sure how this is really different.  The concept that appears in your brain for, say, “cow” is clearly not exactly the same thing as what is in my brain.   This is, our minds do not share the exact same thing.   We both have concept for “cow” but they are probably not exactly the same.  These difference appear when we have different opinions on the topic.  If the concepts are different, then they are not universal.

I would say that the frame of neurons that form the concrete symbol for a subject is pretty much the same as what one means by a concept.  That frame is about something, and it is connected to other frames that are about other things.  As far as I can tell, these function in exactly the same way that Ockham said that concepts function.

Nominalism is given a big boost with the idea of embodied conception.  While it is clear that concepts in the brain build on other concepts, there is a difficult time explaining the bedrock concepts that everything has to be built on.  Embodied cognition explains that fundamentally everything is build on sensory-motor experiences.  We understand each other only because we have common sensory-motor experiences to build on.

1. The first objection to nominalism is usually: if we have a name for something, but there is no thing, then how can we be talking about the same thing?   You have your name “circle” and I have my name “circle” but no confidence that they are the same.

2. The second objection is that if only particulars (instances) exist, then there is no way to compare them.  Often they will say: if there is some sameness between the particulars, there must be some reality to that sameness for us to see they are the same.

Comparing Things

In order to compare two things, realism of universals insists that there must be some real thing that both particulars have in common.   Thus two blue 2018 Toyota Prius cars park near each other.  One sees them and thinks: “there are two identical cars.”   The universal realist says, in order to recognize that those cars are identical, there must be a universal blue 2018 Toyota Prius that you compare to.

Some say there is a set of properties in common: the color of the paint, identifiable details about the shape such as position and shape and size of windows, etc.   These properties by themselves and abstract from the particulars form a universal.

I have never found that satisfying.  First of all, we are equipped to recognize the color blue.  A particular network of nerves gets triggered when a light spectrum enters the eyes which is identified as blue.  Blue itself is just a name that we put to the frame of nerves that are activated when blue is perceived.  Though lessons when we were young, we trained those nerves to be associated with the word blue, the sound of blue being pronounced, and the visual look of the printed word “blue”.   We have associated the name Toyota with the car maker’s round symbol, and we have learned the general shape of the Prius model and have neural frames associated with each of these.

Thus, when we look at a car, our perceptual systems decodes what is being seen.  It effectively does a comparison to all the features we have seen on all cars, and picks out the features that are present, and those are mapped to a make and model.  This is how the perceptual system works.  It does not leverage any real universals that are floating around.

All we do is measure.  The car is a certain size.  The windows are a certain size within that.  The shape of the windows are another feature that is measured.  These measurements are “features” and we compare to other features (measurements and ratios of measurements) that are stored in neural frames.  Matching proportions causes those frames to activate, and when they do, they activate connected frames.  Thus from the shape, we remember the make and model.  I am saying that two identical cars can be recognized as identical just because we measure them and find them to have the same measurements.

Only What is Important

We accomplish this with precision only in areas that we have trained to do so.  For example, while driving, I notice the make and often the model of every car that passes.   I am not in a jam of cars, I am in a jam of Fords, VWs, BMWs, Toyotas, Hondas, Dodges, Teslas, etc.   I remember before about third grade, I did not do this.  I saw that cars had different shapes, but I would never have known the make and model.  Cars are common conversation for boys.  My wife clearly does not see cars the same that I do — there are just many cars should could not tell you the make and model of.  This simply reflects a different training that I got, a different interest.  The tables are reversed when we talk about shoes:  there are many types of shoes that all look the same to me but I am tolk they serve entirely different functions.

What I am trying to reflect on here is that we all parse reality differently, the details of what we see are constructed differently, but the concept maps overlap in large areas so that we do in fact communicate.  A group of people working together will develop a unique vocabulary specialized to their area of work.  Outsiders find that jargon hard to understand, but an outsider can join the group, learn the vocabulary, and quickly become fluent in that jargon.  The words you know are the words that are needed to communicate about those things and with those people.

Variation of Meaning

Within nominalism it is perfectly understandable that people will have differing understanding.   Take this:  Alex points to a car and says “see that Toyota there” and Bob says “I see a VW there”.   One of them is mistaken and this kind of mistake is common.

With Plato’s universals which exist in a special universal realm, the real world objects are “shadows” of the universals.   Plato insists that there is a real universal showing through.    What it can’t explain is why one person sees the shadow of a Toyota, and the other a shadow of a VW, because reality can let only one universal shine through.

Aristotle’s hylemorphism fall prey to the same thing.  He says that the object has the form of a universal Toyota appearing in the form of the thing, however if it is really a Toyota, then there is no way to explain how Bob saw a VW.

The advantage of nominalism is that this situation is perfectly explained: Bob’s map of features to makes of car was not complete.  His perceptual system attempted to decode the blobs of color that entered the eye into a particular kind of car, and for some reason picked up on features that got him to activate the VW frame.   The eye has to take these patterns of light and detect the features, and it is fallible.  It might be that Bob is not familiar with Toyota.  Or it might be that a glint flashed and Bob detected a feature that was not there.  Whatever it was, nominalism can explain how different people recognize different things, while universal realism can’t really explain this.

To be fair to universal realism there is an aspect that Plato and Aristotle say that you need to wander the world in order to learn the universal forms, but they don’t explain how this association works.   Plato felt you get “better” at reaching into the realm of forms, but where exactly is that learning taking place?   It has to be in the mind/brain, and so this implies some kind of recognition frames in the mind, and essentially you end up with all the mechanisms you need such that universals are no longer needed to explain behavior.

Only a Name

Critics of nominalism obsess about how there is only a name.  A “cow” is only a name.  But there seems to be a universal cow.   I say the word cow to you, and some kind of image appears in your head.  What is that that you see?   It is not a particular because there is no guarantee that any real cow exactly matches that image.  The image might even be a cartoon of a cow.  It just feels like there is something there.

There is a real frame of nerves which are activated any time you see or hear of a cow.  This is a real thing in the brain.  That frame was constructed through learning.  If you lived on a planet without any cows, there would not be a frame for that.  Frames are formed by the brain in the act of remembering things.  The forming of frames is how you remember things.

As you learn more and more about cows, that frame gets connected in more and more ways to other things.  Maybe the name of the local dairy that runs ads featuring cows.  Maybe there is a hike you took where cows on the trail frightened you.  Maybe you saw a western movie where cows stampeded. Maybe in language class you learn that “vache” is the French word for cow, and “kuh” is German, and those also are linked in to the frame.  There complex and subtle interconnections.  A cow in a an alpine situation feels different from a cow in a western situation and these subtle nuances come with the memory.

It is worth mentioning that remembering a concept is at some level in the brain exactly like experiencing it.   Thus when you see a cow, that neural frame is activated, and with it all the things that come with cow, and you experience the cow.   Similarly, when someone says the word cow, the exact same frame is activated, and all the things that come with it are activated.  Saying the word, or imaging the cow, is in many ways exactly the same as experiencing the cow.  I believe it is this experience that occurs just by thinking that makes it feel that a new universal cow must exists.  You seem to be experiencing something, and saying that there is just a name there is unsatisfying.

Arguments against Nominalism

• One over many argument.  Consider a large set of triangles, different colors, drawn using different matter, equilateral, scalene, etc.  “In spite this diversity of triangles, there seems to be something in common that they share, even though they are nevertheless particular.  THAT they share something in common is quite clear because we recognize them as instances of something, particularly triangle.  . . . it is not the case that they have nothing to do with one another.  There seems to be something in common.”  “The universal is common to all the individuals.”

This is tough because he states that it “is quite clear” that they have something in common.  But turn of phrase “have something in common” simply means that they have similar features.  Two people might both have blue eyes, and we say they have something in common, but that does not in any way mean that there is some real thing that is part of both of them.

If I measure two building to have the same height, both are 35 meters tall exactly, then we say they have this measure in common, that does not mean that there is any real thing that they they share.   We just measure both of them, and they came to the same measure.   The language “they have height in common” does not say that there is a universal representing 35 meters, and it is a real thing that is in both.  Yes, they have the same measure, but that does not mean that there is any real thing that is “in” both of them.  Measuring is a thing anyone can do: take a unit, like a meter, and see how many of them fit in the space defined.

I have had people respond: wait a minute: a meter is a universal.  Yes, it is a unit of length.   I hold a stick next to something that is a meter long, and I cut the stick to be the same length.  (look at that, the stick just acquired one-meterness!)   Now I can measure things using my stick.  There is no magic.  If you were to say that the X, Y, and Z dimensions are universal that would be a different argument.  I am willing to accept that the fundamental dimensions of space might in fact be universal, but of course real space is not Euclidian and we have to consider that real space is stretchy.  I could buy that positive and negative charges are universals, but again that is far from what we normally talk about with universals.

In summary, this guy is arguing that because two thing have the same measure, they “have something in common” but that is linguistic prop.  We visualize universals as if they were objects.  We talk about universals as if they were objects.  But they are imaginary: they simply don’t exist.

• “The universal triangularity is not simply reducible to the sum of the individuals within the class.  All triangles could go out of existence, and the universal triangle would still exist, because new triangles could be created again.  The universal for the triangles can not be the particular.

If a universal is just a set of features, then there is no dependence upon instances to support it.   A triangle is defined as three (non-colinear) points, and the lines that connect the three points.  You could theoretically get rid of all triangle instances, but this definition still exists.  Notice that the definition is not a universal.  The definition is the words in the second sentence to this paragraph.  Those words exist, but those words are not a triangle.  Get rid of all triangles, and the words that define the triangle still exist.

Similarly, you could recognize a cow.  One might make all the cows disappear, but the neural circuits that recognize a cow could persist (for a while).  The fact that the set of features that denote a instance of a class does not depend on instances of the class.  This should be obvious.

• The universal triangle does not have color or matter that it is drawn with.  Because the universal triangle does not have these, there is no way that it can be the same as the particular triangles we see.

Thinking that the universal might be the same as the particular is a by product of thinking that universals are things.   They are not, instead there is simply a set of rule that detect features of the object in order to classify it as a member of that class.

Universals don’t exist, so it is not surprising that a universal is not the same as the particular.  What does exist is a set of feature-specifications (rules) that identify an instance as being in the class.  This specification of course is not a triangle, and not in the particular triangles.   It is strange that one might suggest that there is something “in” each triangle particular

• Because the universal exists without any particulars, means that it must exist in its own.

They don’t exist at all except as a collection of rules.  The collection of rules certainly exist separate from the particular.  The illusion of universals gives people the feeling that they exist, and as a consequence ask this rather silly question.

For instance, I could look for a “Chinese pizza” — I don’t know what one is, however I feel certain that if I saw one I would recognize it.  A Chinese pizza will be a set of rules that select for some things pizza-like and some things chinese-like.   For example, maybe a pizza dough with sweet and sour pork on it.  No universal is needed, all I need is the rules.

• Mathematical knowledge.  If there were no universals, as the anti-realist claims, we would never have any knowledge about mathematical things like triangularity as such.  Only individual triangles.  And mathematics would be turned into a sort of physics, where instead of being able to absolutely prove theorems, we would only be able to hypothesize about particular right triangles and make probabilistic statements.   We have knowledge of triangularity as such.  The anti-realist has to be incorrect; there must really be universals like triangularity.

Once again, the assumption that there exist universals drives the conclusion that there exist universals.   So, we define a triangle as a set of three lines connecting three points.   Given that definition, we can propose a hypothetical pure triangle.  It does not exist, but if it did exist, we could measure the interior angles and they would add to 180 degrees.  We can say this about a hypothetical without it actually existing.

We do this again by using more rules.   A complete circle is defined as 360 degrees.   Given this definition, we can prove that the sum of the angles is the same as half a complete circle.  Neither triangles, nor degrees, nor circles need to exist.  It all comes from the rules that we make up about these abstract objects.

We can have knowledge about things that do not exist.   How did James Bond like his martini?  Shaken not stirred.  However, James Bond does not and never did exists.  Knowledge about something does not require that they exist.

• The logical necessity of such knowledge rules out conceptualism, which would say that these abstract objects are just merely constructs of our mind, which they cannot be because our minds are contingent and changing, and are not necessary in their nature.

This argument is that because minds are contingent, they can’t possible have a set of rules to recognize a triangle.  Obviously, we teach these rule sets to each other, and so the fact that one person dies does not mean the end of all triangularity.  Because many many people have internalized there rules, and also they are written down in books.   The argument that contingent minds can’t know something that is eternal is silly.

• Physics talks about particles, like an electron.  This is a property not only of a single electron, but of all electrons.  These abstract theories owe their predictive power by the ability to go above and beyond the particular.
• The anti-realist position, particularly the nominalistic position, in the way that denies universals and that things are radically individualized I claim is quite hostile to reason.

Notice the use of “radiacally individualized” which is an emotional persuasive argument designed to imply that nominalists so no commonality in things.  That is far from the truth.  There is no radical individualization.  Individual cows are individual cows, and they have differences, but we recognize them as cows because we have rules to do so.

• 1. self refutation by a punative universal.   Nominalism is incoherent.   What is this name stuff the nominalist is talking about?  Seems like it is something in common across all the particulars.  If we slap the name “man” across Plato, Aristotle, and Socrates, it has to be the “same” man used in all cases.  What is this same stuff if not a universal, something in common shared over and above the particulars.  There is no way the nominalist can not say that the name “man” is not the same “man” when applied to the three individuals.  Seems like they smuggle in a universal for this.

The term “man” is defined in a number of ways, and it is really just a set of rules that recognize a man.   A head, two eyes, two ears, a body, two arms, to legs, and of course a penis.  That definition certainly exists on its own.  Apply the rules individually to Plato, Aristotle, and Socrates and you find they all fit the class.  Otherwise, there need be nothing else in common.

Of course, the name “man” applies to the rules, and when you see three individuals you recognize each as a member of the class.   No magical universal is needed.

• infinite regress by similarities.  Nominalists never explain why it is that when I see three individuals I slap the same name on each of them.  Why name them all men?  There is obviously something in the individuals that makes me do that.  Nominalist says I recognize a similarity.   But what is this similarity, if not a universal?  A similarity might just be another name, but this higher order naming does the nominalist no good and simply pushes the problem back.

This is strangely the “third man” argument that works against universals.

In Summary

Nominalism says that when we talk abut universals, such as “cow”, we have a symbol that represents something “the ideal cow” that does not actually exist.  The symbol itself holds everything we know about the subject precisely because the neural frame has connections to every frame that represents things we know about.   Learning is the act of building and wiring these frames.  All thoughts and language can be explained in terms of these frames.   The activation of a frame “feels” like we are experiencing something, and in the case of abstract objects, we feel like we are experiencing a universal.   But it is an illusion, they simply don’t exist.