Universals and Realism: Plato’s Theory of Forms

While Plato’s Theory of Forms ultimately faces intractable problems, it raises interesting questions. Specifically, it is an excellent introduction to the idea of “universals.” What follows is a very condensed summary (skipping over certain bits and pieces) of the instructive outline Edward Feser presents in The Last Superstition.

Consider an object of our ordinary, everyday experience, like a triangle. Better yet, consider a set of triangles. Some are written on paper, some are displayed on a computer monitor, another one is written in the sand. Some are written in blue ink, some red, some are made up of black pixels, and the one written in the sand is just made up of the impressions left by someone’s finger. We call every one of these things “triangles”. Why? What do they have in common that warrants us classifying them all as the same, despite being different individual objects? In the case of triangles, it is the fact that they are closed-plane two-dimensional geometric figures made up of three straight lines. All of the aforementioned triangles, despite being different colours and sizes and being displayed on completely different mediums, have these essential features in common. Let us call that set of essential features “triangularity.” Each particular triangle instantiates (is an instance of, or represents) “triangularity.” That is what is common to each of those triangles, and it is why we label them all with the same name. Simple enough? Now this is where things get interesting.

Consider now how each particular triangle is going to have features that are not essential to triangularity. Being red or blue, big or small, written on paper or scrawled in sand - each of these is not a necessary part of triangularity. Each of these particular triangles will also be missing features that are an essential part of triangularity. The triangle drawn in the sand will likely have crooked lines and breaks in the figure. Even the triangles drawn on paper may have imperfectly closed corners or crooked lines. The triangle displayed on the monitor is likely to be the most perfect of all, but even it will not be comprised of truly straight lines, as closer inspection will always reveal imperfections (in this case due to the fact that the lines are actually comprised of pixels). Every physical triangle we ever encounter is going to have features that are not a part of triangularity, and is going to be missing features that are an essential part of triangularity.

What follows from this, according to Plato, is that whenever we grasp the essence or nature of triangularity, what we are grasping is not something material or physical. No particular physical triangle can actually be triangularity for the reasons outlined above. For example, let us consider a triangle drawn on paper with red ink. Is the colour red a necessary part of triangularity? Nope. Is being drawn on paper a necessary part of triangularity? Nope. Is the triangle going to be comprised of perfectly straight lines? Again, no. Any particular, physical triangle we consider cannot, in principle, actually be triangularity itself. Yet, if triangularity itself didn’t in some sense exist, then we would have no reason to consider all of those different objects as being similar in any way at all. “Triangularity” as an ideal must exist over and above any particular triangle in order for us to be able to relate and compare all of those objects to some common reality.

It follows, therefore, that triangularity not only must exist, but also that it cannot be material or physical. For if it were material or physical, then it would be a particular object in a particular place and time, and therefore could not have the universal applicability it does. Triangularity must be something immaterial. It is also what could be called a “universal”, as opposed to being particular. It is the “universal” that is instantiated by particular triangles, applying to each one of them universally but not being exactly the same as any particular one. Triangularity as we have just described it is what Plato would call a “Form.” Triangles are not the only things that instantiate forms. Trees, dogs, human beings, justice, virtue, etc., are all what they are insofar as they instantiate the form over and above the particular instance.

Plato’s Forms are not material. But their existence is not limited merely to the mental realm either. While we grasp them with our intellect, they have an existence that transcends our own. We don’t invent them - we discover them. The truths that flow from the essence of being a triangle (or a human being, dog, chemical compound, etc.) are what they are, and we cannot change them. We cannot one day decide that triangles will now have four sides while having all angles add up to 180 degrees. Logically impossible. We cannot decide that human beings will now have 56 chromosomes instead of 46. Even if we could create such a thing, it wouldn’t be the same species anymore, and therefore would be the instantiation of a different form. The forms existed before we did, and will exist after we’re gone.

So if these forms are not material, and if they are not merely mental, then what/where the hell are they? Plato situates them in a “third realm” of abstract objects. When we grasp the essence of anything – dogs, trees, justice, beauty, etc. – we are grasping something that is universal, extra-mental and immaterial. We are grasping the “form” of that thing. This third realm, being comprised entirely of immaterial objects, is essentially nowhere. Being somewhere implies spatial location, which implies a material presence (forms are immaterial) and being in a particular place at a particular time (forms are universal).

According to Plato, the forms, though beyond our mere senses (being grasped via the intellect), are more real than the material things which instantiate them. The form of the “good” has a unique and especially elevated place among the other forms. This is due to the fact that any particular instantiation of a form is going to be a better or worse one depending on how well it conforms to the ideal (Consider two triangles, for example. One drawn slowly and carefully, and one drawn quickly and sloppily. One will be a better triangle than the other.) The form of the good permeates everything in a certain sense. This is farther than we needed to go for my purposes, however. Enough said for now.

  

Plato’s theory faced objections (see the “Third Man Argument”), and was therefore refined and modified by subsequent thinkers. For philosophers like Aristotle, whose approach to the existence of universals is said to be much more “sober and down-to-earth,” there are no forms as Plato would understand them. Universals do not have an independent existence in a third realm. Rather they exist only in the things that instantiate them, and in the intellect that grasps them. Augustine held the view that the universals we grasp pre-exist in the mind of God. I suppose his view is somewhere between Aristotle’s and Plato’s; the forms do not have an independent existence of their own, but still exist outside of the things themselves and outside of our intellects – in the intellect of God. I am not all that familiar with the details of his view, however, so I won’t comment any further. Regardless, each one of them holds that the “forms” or “universals” we grasp with our intellect must have some sort of real existence. If they did not truly exist, then there would be nothing tying together the various objects of our experience. We would have no way to account for the fact that many different objects can in a certain sense be “one.” There would be no reason to call those objects “triangles”, “human beings”, etc., if there were not a universal that each particular object was instantiating.

I mentioned at the outset that the Theory of Forms is a good introduction to the idea of “universals.” Philosophers who believe that universals have a real existence (whether Platonic or otherwise) are called “Realists.” Those who deny the real existence of universals are called “Nominalists.” The line of reasoning involved here is foundational for many topics in philosophy. The intellectual activity of the mind – more specifically the use of propositions in logic and mathematics – is a phenomenon that many philosophers argue cannot be understood in terms of purely material operations. Mathematicians who take an interest in the philosophical underpinnings of their discipline often lean toward some version of Platonic Realism as well. Within the field of Ethics, an understanding of universals is one of the building blocks required for the Natural Law and Virtue Ethics theories of morality.

If you are going to study philosophy, even as nothing more than an amateur such as myself, you are best to start at the beginning! Understanding a conversation that has spanned millennia will be much easier if you start where at all started – with the Greeks. Only then will you get a grasp of what the philosophers of the middle ages were saying, and only then will the significance of the debates between moderns and the classical/scholastic philosophers be adequately appreciated.