Plato, Ockham's Razor, and the Spectrum: Finding Universals

 Plato's Theory of Ideas looms like a cliff face on the frontier of philosophy: his belief that every meaningful word is the shadow of a pre-existing, perfect, and unchanging entity in a World of Forms. Everything we know, whether abstract or concrete, is a debased copy of a perfect model accessible to contemplation but obscured by material existence. All learning is remembering because all truths pre-exist. 

         When I was a nineteen-year-old philosophy student, Plato's dialogues read as nonsense because they assumed this. Socrates would ask an interlocutor to define an abstract word--the kind of word that, even at nineteen, I knew meant different things in different contexts--and then he would change the context as if that invalidated the definition. Plato assumed that a word like justice, goodness, or tree has a single fixed, universal meaning.

Aristotle disagreed. He saw justice, goodness, and tree-ness as mental constructs abstracted from particular examples and existing only our understanding of them. All knowledge begins with observation. We know a tree, not as an approximation of ideal tree-ness, but by recognizing similarities between various trees. Of course, abstraction is prone to ambiguity. People often misclassify plants--calling a mature bush a tree and a young tree a bush. 

In his Categories, Aristotle enumerates ten kinds of things that can be subjects or predicates in propositions. Notably, substances are of two kinds: (1) particulars such as a given tree and (2) universals such as the category tree. Though knowledge of trees as a universal is real, it is secondary or derivative. True conclusions can be drawn from universals--for instance, a Prime Mover deduced from principles of motion--but Aristotle disagrees with Plato by teaching that universal truths are derived by persons based on their experience with particular truths. In this sense, he denies the reality of universals: they are not transcendent pre-existing forms.

In the initial flowering of Christian theology with Tertullian, Origen, Augustine, and Boethius, the dominant philosophical school was that of Plato--specifically the mystical Neoplatonist tradition that culminated in Plotinus--so the reality of universals was taken for granted, particularly intangibles such as the Trinity that had the authority of scripture. Plato's forms were thoughts in the mind of God. For Augustine in the Latin world, and even more for the Pseudo-Dionysius in the Greek, Platonism represented a world-view so harmonious with Christianity that it was thought to demonstrate that pagans guided by "reason" alone could know true scriptural principles. The soul was like a room without a ceiling, lit from above.

In the 13th Century, eight centuries after Augustine, the works of Aristotle, finally available in Europe, swept across the new universities in a movement called Scholasticism. The greatest Scholastic, of course, was Thomas Aquinas, who balanced Aristotle's experience-based rationalism and what he called the "mysteries" of the faith--making large claims for natural reason, which he used to prove doctrines such as the existence of God. Scholastics did not deny the reality of universals. Aristotle's ten categories were not just grammatical items, but categories of being. Overemphasis on Aristotelian principles among arts faculty in the University of Paris, a perceived threat to the faith, led to their condemnation four years after Aquinas' death. His massive Summa Theologica still dominates Catholic theology, but a 14th Century decline in Aristotle's authority had radical consequences in the work of a British friar, William of Ockham.

Ockham chooses a razor

Ockham is famous for insisting that systems should be pared down to the smallest number of necessary elements--a principle known as Ockham's Razor--which prompted him to dismiss most of Aristotle's Categories as redundant. In secular metaphysics, he reduced ten Categories to two, substance and quality--in other words, objects and their traits--from which everything else was derived. Universals such as tree-ness and justice were not entities in the mind of God or a world of Forms, but names for concepts formed by observing particular things. 

         Called nominalism in contrast to Platonic realism, this restored naturalistic reading of Aristotle was a revolution in metaphysics, sometimes seen as the beginning of modern secular relativism. If general truths are only words, then where is their authority? Ockham was not, in fact, a pure nominalist. Understanding universals to be grounded in our rational understanding of the world, he is more accurately called a conceptualist. For him, universals aren't merely names, but words for valid concepts. Tree-ness isn't a form in an eternal la-la-land, but neither is it a vocalization arbitrarily created.

Plato mystified me on first encounter because I was a nominalist without knowing it. The world of Forms seemed (and still seems) lunacy. A would-be proof of the Forms appears in Plato's Republic: "What about someone who believes in beautiful things, but doesn't believe in the beautiful itself…? Don't you think he is living in a dream rather than a wakened state?" (476c). This sounds fine until its logical form is exposed. Am I "dreaming" if I believe in a turd but not universal turdiness? In zippers but not zipperness transcending time and space? Must I define the essence of absolute Silliness? Just because a fine-sounding word exists in language doesn't mean it is privileged over less elegant words: tree over turd, chair over zipper, or Beauty over Silliness. Just because some words have grand connotations so we can sell them to listeners as metaphysical givens doesn't make make them more than mouth-sounds for human concepts. I can perfectly well enjoy a slice of lemon pie without believing in a pie in the sky.

This said--even if all human language is, well, human language rather that a magic window into timeless world of forms--that need not mean that concepts are arbitrary, that we are free to invent names free of reasonable constraints. The pure nominalist idea that we invent the world by naming, that there are no clear extra-mental givens, is wrong. Concepts and their names are tools for managing daily experiences of trees, turds, zippers, chairs, beauty, and silliness--for surviving in that reality--and if we construct a tool box of inch-sized wrenches in a world of metric nuts, we're screwed. Even if there are no eternal pre-existing forms for words to name, it is still the business of words to model as usefully as possible the patterns we see in the world.

A universal is something of which is possible to give examples, such such as the color blue. I point to blue in the sky, in my denims, and in my navy blazer, and call them the same, but this is an oversimplification: one is azure, another indigo, and the third almost black. The human eye is capable of discriminating millions of colors, but there are twelve popular color names (such as blue) in industrialized languages, fewer in most nonindustrial languages. The concept blue abstracts a fact, an approximate band of spectral light frequencies, from many dissimilar experiences, creating an abstract object, a "color," transcending any particular time or place. This is the grain of truth in Platonism. But, blue is a manufactured object created by our collective conceptualizing of it. It exists as a separate thing only because it is named.

I selected the blue because, according to the Brent Berlin's and Paul Kay's classic survey, Basic Color Terms: Their Universality and Evolution (1969), world languages have as few as two simple color words and as many as twelve, and, in the normal evolution of color systems, blue is a late addition. Many cultures have no idea of blue, no such "universal," but distribute it between green and black. The eye can distinguish millions of colors, but when I look at the spectrum above, I see color bands corresponding to English color names--as predicted by the Sapir-Whorf hypothesis that language shapes how we see the world. Most universals are socially constructed.

But there may exist universals "remembered" by all people, even if not based in Plato's timeless world for Forms. Berlin and Kay found that, when languages have only two terms for color, those are always black and white--corresponding to dark and pale, unreflective and reflective, night and day. These are universal universals--given more than invented. If a third color is added, it is red, the color of blood, but, after that, even though they use universality in their title, the rest of their proposed color evolution is far from universal. Nevertheless, if dark-light (and maybe red) are human givens, not linguistic inventions, there presumably are others.

One place to look is at Carl Jung's archetypes of the collective unconscious. Jung's theory, though grounded in psychology, not metaphysics, is Platonic in spirit and supposes that identical mental patterns--called archetypes--exist unconsciously in everyone and are consciously expressed in a variety of ways extrapolated from their deep structure. Archetypes often occur in pairs, such as dark-light. Names may indeed be arbitrary, but some universals seem to be named in every culture. Among these are good-bad, mother-father, warm-cold, and friend-enemy. Jung concluded that the archetype he called the Self, our deepest and most unitary sense of being, was the archetypal idea of God. Coming to know it was the ultimate religious quest.

Credit: my flyover of ancient and medieval thought is indebted to to Thomas Williams' course, Reason and Faith: Philosophy in the Middle Ages, published by The Teaching Company (2007).