Modern Platonic Realism

Someone has asked me to discuss the Problem of Universals. The trouble is, I don't see a problem. Universals quite obviously exist, although we ought to give credit where credit is due and return to calling them Forms. The basic phenomena philosophers who talk about Universals are trying to explain are the similar properties shared by objects. For example, this computer screen is white. My refrigerator is white. All the walls in my apartment are white. In fact, it has a sort of institutional feel to it. But what is this “white” that surrounds me? Well, it's a color, an abstract property that many things share. These abstract properties are called “Universals” or “Forms”.

There are three basic strategies to dealing with these abstract ideas – Realism, which accepts that these similarities between concrete items as really real; Nominalism, which accepts that there are similarities between concrete items, but denies that these similarities are real things themselves; and Anti-Realism, an extreme variety of Nominalism that denies that these similarities even exist.

1.a The Nominalist (Austere flavor)

Nominalism is often characterized as an attempt to respond to the supposed problems of Realism. This is rubbish. The Austere Nominalism of the modern philosopher rejects Plato's forms as unnecessary. It is enough to say that there are similarities between things – no further explanation is necessary. What I perceive with my senses is enough. It was specifically this viewpoint that Plato responded to in the Theaetetus (with Socrates conversing with the title character):

THE: Well, Socrates, after such encouragement from you, it would hardly be decent for anyone not to try his hardest to say what he has in him. Very well then. It seems to me that a man who knows something perceives what he knows, and the way it appears at present, at any rate, is that knowledge is simply perception.
SOC: There's a good frank answer, my son. That's the way to speak one's mind. But come now, let us look at this thing together, and see whether what we have here is really fertile or a mere wind-egg. You hold that knowledge is perception?
THE: Yes.
SOC: But look here, this is no ordinary account of knowledge you've come out with: it's what Protagoras used to maintain. He said the very same thing, only he put it in rather a different way. For he says, you know, that 'Man is the measure of all things: of the things which are, that they are, and of the things which are not, that they are not.' You have read this, of course?
THE: Yes, often. (151e-1521

Socrates then goes on to analyze precisely what this claim must mean, and shows conclusively that what we know is not our mere perceptions, but beliefs. And we can only have correct beliefs if we are willing to embrace the Forms – without them we literally cannot speak of anything because our only guiding principles are our own perceptions. As soon as we begin to discuss anything we tacitly acknowledge them. I can think about “my walls being white” and deny that the thought has any connection to a reality outside of myself. As soon I communicate the idea to you, I am appealing to a third thing – a set of ideas that we share in common – in this case, we are mutually accessing the ideas of “wall” and “white”.

Austere Nominalists are usually stubborn folk, however, and one may persist in insisting that these similarities and resemblances between concrete things are mere brute facts and not larger connections. One could explain that this is just how the universe works, and it bears out no further explanation. It is perhaps mysterious that one could acknowledge that the white of my walls is the same as the white of my neighbor's walls without ever acknowledging that that “white” is thing itself. But people can, and do. These holdouts, one must presume, are not interested in learning about the Theory of Gravity either, content as they must be to simply explain “shit falls when I drop it”.

1.b The Realist (Platonic flavor)

Although the conclusions that Plato would draw from his Theory of the Forms are sometimes complicated, off base, or just plain wrong – the theory itself is beautifully simple, explanatory, and does not carry nearly the metaphysical or ontological baggage that later philosophers ascribe to it. The Forms are present in all of Plato's dialogues, but their inclusion is often so innocuous and uncontroversial that the average reader will agree with Plato's argument while denying that s/he believes in something as silly as “Platonic Forms”! As a preface to a larger argument (to be dealt with below), Socrates explains the forms to Cebes in the Phaedo:

We are altogether agreed then, he said that an opposite will never be opposite to itself.–Entirely agreed.
Consider then whether you will agree to this further point. There is something you call hot and something you call cold.–There is.
Are they the same as what you call snow and fire?–By Zeus, no.
So the hot is something other than fire, and the cold is something other than snow?–Yes.
It is true then about some of these things that not only the Form itself deserves its own name for all time, but there is something else that is not the Form but has its character wherever it exists.

This bit about the Form existing for “all time” allows Plato to argue for the immortality of the soul, but also provides the impetus for many of the objections raised to the theory. It is, strictly speaking, unnecessary to the Theory of the Forms itself, although it is necessary for many of the arguments Plato constructs based around them.

1.c The Anti-Realist (Metalinguistic flavor)

There are also some who dismiss the idea of similarities between objects entirely. Some claim that when we discuss universals, we are really discussing words. Any talk of universals is mere human projection of beliefs we create onto reality. There are many ways of making this argument, but the basic point they all share is the refutation of realism by linguistic analysis. This is an intuitive view, which one expects would be favored by those seeking the least necessary components of a coherent belief system. We already have words, so why invent more abstractions? But sometimes simplicity's razor cuts too deeply.2

In the Cratylus, Socrates is discussing etymology with Hermogenes and the title character. They reach a point of accord, where all admit that names are properly determined by rule-makers and taught to students based on the definitions provided by these rule-makers, just as modern semantic philosophers might determine that names mean what they mean by their proper usage within the linguistic community. But Socrates continues:

SOC: Come now, consider where a rule-setter looks in giving names. Use the previous discussion as your guide. Where does a carpenter look in making a shuttle? Isn't it to that sort of thing whose nature is to weave?
HER: Certainly.
SOC: Suppose the shuttle breaks while he's making it. Will he make another looking to the broken one? Or will be look to the very form to which he looked in making the one he broke?
HER: In my view, he will look to the form.
SOC: Then it would be absolutely right to call that what a shuttle itself is. (389a-b)

Socrates and his interlocutors continue their discussion, but the point is made – it is not the name of a thing (“Shuttle”), or the thing (the broken shuttle), but the form of the thing which is the thing itself.

If the meta-linguistic types were to persist, I might remind them of the actions of a dog – any dog can distinguish between humans and dogs and trees and rain and the like. If similarities between concrete particulars are mere linguistic ephemera, how can a being with no language detect them?

2 Platonic Realism: Problems and Solutions

The preceding section was meant to explain the general impetus for believing in Universals, and discussed some competing views in an obviously biased manner. The following section will address some specific criticisms of Platonic Realism.

2.a Aristotle and The Third Man

The greatest challenger to Plato's Theory of the Forms during his lifetime was not Nominalism – it was Aristotle's version of Realism. Due to Raphael's painting, The School of Athens, Plato's forms are usually characterized as being transcendent, existing in “Plato's Heaven”. Aristotle, on the other hand3 is said to have believed his forms were “down here”, “in the things themselves”, or “immanent”. Aristotle's Realism was actually fairly similar to Plato's, in that both of them believed the forms were completely abstract. Where they parted ways was in Aristotle's system of categorization of the Forms, and his belief in the interplay between Form and Matter. While the primary virtue of Aristotle's system is that it lends itself very well to analogies regarding bronze statues, he may also have created his taxonomy with an eye towards the “Third Man” argument in the Parmenides (indeed, Plato named one of the characters in this dialogue after Aristotle). The argument is too long to excerpt (131-133b), but the basic point that Parmenides makes is that Socrates's immature theory of the forms could fall prey to a recursive loop.

Say, for example, that I have a thing y that has the property x. So, y has x-ness. Now there is a relationship “having x-ness” in addition to the property of x. So y has “x-ness” and “y has x-ness” has “having x-ness”. Soon enough we will discover that y has “x-ness”, and “y has x-ness” has “having x-ness” and has “'(y has x-ness) has having x-ness' having 'having x-ness'”, and so on, ad infinitum. Plato clearly did not find this argument convincing, writing it out in his own dialogue and leaving it as a lesson for the student to solve. He later went on to write several more dialogues featuring the older Socrates and his fully formed Theory of the Forms.

There are two easy answers to this puzzle, and many more that are being endlessly discussed somewhere by people who like to play word games. The first reaction is to punt – the instantiation relationship between a thing and the form of that thing may be a form itself, the form of instantiation. This form could determine the proper relationship between things and forms and ensure that no monkey business of this sort was taking place. The second reaction is to say “so what?” Abstract ideas are by their nature limitless. Trying to limit the amount of Forms we can perceive is like limiting the amount of numbers we can perceive. The “Third Man”4 might be an interesting wrinkle in the Forms, but it certainly doesn't disprove them.

2.b Humean Paradigms

One of the more Anti-Realist responses to Realism is David Hume's theory of Paradigm resemblances. To refer back to the selection from the Phaedo above, Hume would argue that “cold” and “hot” are not distinctive things operating in the ether without snow and fire, but rather that they are examples or paradigms that we hold in our memories due to our exposure to the aforementioned physical objects. In the Problems of Philosophy, Bertrand Russell showed that Hume's argument has an obvious flaw because the relationship between our memory of a paradigm and new things we experience is itself a universal. For some reason Russell tries to appear clever and claims that this idea of a relationship as a universal is a new idea. It isn't, in fact it appears all throughout Plato's dialogues.

The real question then, is why did Hume bother with such an obviously flawed argument? One answer could be that the conclusions drawn by the Forms were too much for him. In the Phaedo, after Socrates has established that cold exists for “all time” with or without snow, he uses that to prove that he too will live on as a soul in the afterlife. This was problematic for Hume, but it is even more problematic for us, since we are beginning to learn the materialistic mechanisms by which the human brain associates ideas – and an immortal soul does not appear to be part of the equation.

2.c Recollection? Not a Problem.

One of the more questionable components of Plato's theory of the Forms is the doctrine of recollection, as expressed in the Meno. But look at the actual objection that Meno makes to Socrates's ability to discover what virtue is:

MENO: How will you look for it, Socrates, when you do not know at all what it is? How will you aim to search for something you do not know at all? If you should meet with it, how will you know that this is the thing that you did not know?
SOC: I know what you want to say, Meno. Do you realize what a debater's argument you are bringing up, that a man cannot search either for what he knows or for what he does not know? He cannot search for what he knows—since he knows it, there is no need to search—nor for what he does not know, for he does not know what to look for. (80d-e)

To be sure, the idea that we were once all immortal baby souls in heaven, knew everything, and are just trying to remember what we once knew is a bit ridiculous (especially in the light of modern science). But that isn't the point! The argument that takes up the rest of the Meno is Socrates teaching a slave boy geometry, to prove the point that people can learn. We can easily abandon the silly metaphysics of the “Platonic Heaven” in favor of modern physics and biochemistry, but the arguments for the Forms themselves, those non-physical objects of knowledge, those ideas are still valid.

3 Austere Realism

It should be clear that my own view of “Universals” matches up closely with the view expressed by Plato two and a half millenniums ago. But my view is different from his in two important ways.

Firstly, I value metaphors. But it is important, especially when discussing the “really real”, to draw a distinction between the actual and the elaborative. To the extent that Plato's arguments for the forms rely upon supernatural metaphors, be it the recollection of the Meno, or the transcendent enlightenment of the Philosopher-Kings in the Republic, I regard these as merely metaphors. And any conclusions he draws from those particular supernatural fables (such as the immortality of the soul, or the superiority of an Oligarchic Government) are suspect.

The second difference I have with Plato is his belief that the forms are eternal. The fundamental property of the Forms, as Plato describes them himself, is that they are abstract. They are not tangible. Most people can understand that this means they lack dimension – height, width, and depth. What most forget is that time itself is merely a fourth dimension. The Forms exist outside of spatial reality – this means that they exist outside of temporal reality as well. This does not mean that they are eternal, it means that time is a meaningless concept when one is considering the Forms. They are objects of knowledge that assist us in better understanding physical reality – but they are fully apart from it.

With a few minor alterations, Plato's Theory of the Forms can survive the harshest of criticisms, both Ancient and Modern. The granddaddy of all metaphysical theories is still the king, baby.

1. John M. Cooper, editor, Plato Complete Works (Indianapolis: Hackett Publishing Company, 1997)
All subsequent citations are also from this source.

2. William of Ockham, I'm looking at YOU.

3. Literally, check out the painting:
For 500 years, their philosophical differences have been caricaturized by hand gestures.

4. But why is it called the “Third Man” Argument? Because every time you have the thing and the form, you're sticking a third guy on there. Also, Aristotle usually used the form of “man” to illustrate the argument.

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