Circles of Being

Circles of Being

Let’s take analytical philosophy to a place it has never been before—into the heart of darkness. We have been up sunlit rivers into low-lying bush (necessary and sufficient conditions etc.), but now we must venture into the depths of the jungle to seek out new life and new forms, the basic structures of existence. Have you ever noticed the prevalence of the sphere and circle in nature? Stars and planets, orbits, atoms, raindrops, plant and animal parts, the wheel, balls, geometrical figures—there’s a whole lot of circularity going on. Here I mean to include not just the strict circle and sphere but also ellipses and polygonal approximations to the circle (e.g., a thousand-sided figure). Not everything is round—there are a lot of jagged irregular shapes in the world—but the round thing is ubiquitous (from testicles to the sun and moon). One can imagine a grizzled pre-Socratic announcing, “All is round”. If an object isn’t round, it is composed of round things (atoms), or on the way to being round (you just need to keep adding sides to a square to reach something looking round). The circle looks like the preferred geometric form of nature. There is nothing necessary or a priori about this; the universe could have been irregular and sharp-angled through and through. But in fact, there are spheres everywhere, or circular cross-sections. The Mona Lisa has a round face, and other parts of her body are round too. Humans have round heads (and roundish brains). Ontology is extremely round. Could it be that conceptual analysis reveals the pervasiveness of the circular? Is our conceptual scheme built on the notion of roundness? Kant thought space was everywhere in the phenomenal world; could roundness be a necessary attribute of both our reality and our conception of it? Is roundness the basic category or rule of being?

What is a circle? It is a closed figure whose edges are equidistant from a center. We all remember the geometry of the circle from our school days: circumference, diameter, radius, chords, tangents, quadrants. It is etched in our consciousness (and unconsciousness). The sun and moon are striking exhibits in the museum of the round. They have been striking the human (and animal) mind for millions of years. We later discovered that the earth is round too—just one more sphere in a world of spheres. There can be spheres within spheres; concentric circles. The circle has been regarded as the perfect figure, the epitome of harmony, symmetry, and wholeness. It has a godlike status (like the sun for our impressionable ancestors). We can imagine an artistic movement, analogous to cubism, that privileges the circle (“sphericism”)—pictures populated with spheres, circles, and ellipses—and not much else. If asked what shape God is, we might if pressed say spherical—certainly not cubical or shaped like Great Britain. There is something holy about the circle, mystical. Observable space is spherical. The sky is dome-like. The form of circularity would occupy a high place in Plato’s hierarchy of forms. What I want to know is whether the circle is central to philosophy; it is central to the natural world, but is it central to the philosophical world? This is where the dark jungle begins, because here the circle is not staring us in the face. We have to dig deep for it, cut through the dense vegetation. Do the central concepts of philosophy harbor circles at their heart? And I don’t mean concepts of the spatial natural world but of the world of morality, mind, knowledge, truth, and beauty: is the concept of the circle implicated in these areas?

On the face of it, no: how can goodness be spherical? We might begin with a Platonic thought: goodness is a thing, an object, the primary Form. What kind of thing? We might picture it as like the sun: a radiant orb illuminating and benefiting all before it. Plato’s idea of the Good is based on the Greek gods, evidently, and they are in turn derived from ancient sun worship—that massive disc of blinding light and soothing warmth we observe every day in the sky. The sun is a circle and it provides the model for the Platonic concept of the Good; if the Good has a shape, it is going to be a circle not the shape of a walnut or a scorpion. It is an iridescent ball of some sort. Perhaps this is exactly how Plato pictured it in his imagination and our remote ancestors believed it to be (“Good is Sun”). But we have got beyond such primitive thinking and don’t fall for ancient myths, so has our moral thinking left the circle behind? Not quite: for we still invoke the circle in our moral thinking in our conception of the “moral circle”. We think of the sphere of moral obligation in geometrical terms (as witness that word “sphere”). This idea goes back two thousand years and it has cropped up repeatedly in the history of moral thinking. First, there is the family circle[1] surrounding the individual; then the extended family; then the local community; then the country; then humanity; then animals. A set of concentric circles within which a kind of moral equality obtains, with a radius and a circumference; it tells you who is in and who is out. It is critical to morality because it defines who is, and who isn’t, of moral concern. This is prior to any consideration of what is right or wrong, or what right and wrong consist in. It is like the physical notion of territory. The longer the radius the less the moral concern. Equality is part of it because the distance of each point from the center is always identical for any given circle. There is moral equality within the moral circle. The circle may expand, recognizing new circles of moral concern; morality admits of such expansion. Morality thus has a geometry. It is one example of geometrical thinking, more general than ordinary spatial geometry. There is a moral “space” and it has a circular form.[2]

That wasn’t so hard, was it? Now mind: is it made of circles? Again, not physical circles but circle-like structures. The head is a sphere with a midpoint and a radius and a surface. We have the (roughly) spherical brain with its (roughly) spherical cerebral areas. The neurons have spherical components: the nucleus and the encircling fibers. We have phrenology (or we did). But what about consciousness and the soul? Here things go blurry, but the circle is not left completely behind. What shape is the soul? If you had to choose, I conjecture you would say it is round (that’s what disembodied minds look like on Star Trek anyway). The sphere is the shape of the spirit in traditional iconography. When the soul ascends to heaven it takes on the appearance of a globular cloud not an anvil or coffee cup. The circle is the closest shape to the mind. We also have the idea of a center and a periphery—the self and its faculties laid out as if on a platter. The senses are like points on a circumference at some distance from a central point. We can’t help trying to fit the mind into our geometrical conceptions, with the circle as the dominant form. The circle seems like the most natural form for the mind to be. It might even be that we think of circles by analogy with minds; we psychologize them. The idea of a border, of inclusion, of distance—the ego with its surrounding mental structures. The abstract architecture is common to both.

What about knowledge? Here again we have clues in ordinary thought: the widening circle of knowledge. Knowledge grows outwards forming an expanding circle, outside of which ignorance prevails. It is like a bright disc in a dark night. Kant’s phenomenal world is like a sphere of knowledge surrounded by a noumenal world about which we know nothing. Human knowledge in toto is spherical; it forms a sphere. To come to know something is to move outwards from a center, thus enlarging the sphere. It grows to form a sphere, like a growing plant (think apples and oranges). Science comprises a circle of knowledge.

Truth is a more challenging case, and here we must resort to ingenuity not ordinary thought. But I think the rewards are palpable if not easily digested. Truth is correspondence to reality (facts, the world). What is this correspondence and what things do the corresponding? Evidently, there is some similarity of structure. Let’s go full Tractatus on this: the correspondence is isomorphism and the correspondents are geometric entities (complexes of things standing in certain relations to each other). We can lay one beside the other and see the geometric relation—the similarity of form. Is it like parallel lines? But parallel lines don’t touch—they make no contact. We want truth to involve some sort of contact or overlap, joining up with reality, embracing it. What does this better than a circle? The picture, then, is that truth is like two halves of a circle mirroring each other with no firm break between them. They merge and mirror. If the top half is the proposition and the bottom half is the fact, then truth is the top half mirroring the bottom half. They each replicate the other and truth is the result. The two halves are isomorphic and joined together they form a truth. If there is no corresponding fact, there is no whole circle just a semi-circle, an incomplete figure. Thus, truth has the form of a circle; it is made of a pair of isomorphic halves. That, at any rate, is how we naturally conceive it, if not consciously and explicitly. The world is the totality of these truth-making circles. For a proposition to be true it must be one half of a truth circle. The link between them is continuous not disjoined; they are organically compounded. Proposition and fact flow into each other forming a unity. There is a symmetry and harmony between them. The geometry of truth is a circular geometry.

Finally, beauty: here not much heavy lifting is required. Beauty and the circle belong together. The portrait is the summit of this coincidence: the face is a circle, more or less. The head is a sphere. The circle is the prototype of the face; once you have drawn a circle a face is easily sketched in. The nude is a collection of fleshy spheres, among other things. The eyes are orbs. The mouth is a round orifice. Still lives abound with round objects. Eliminating the circle from art would rob it of its charm (that may be the point). The dome is an architectural feature. The sun and moon are beautiful objects. Novels are about social circles. Circular thinking is never far away in aesthetic matters. Geometry itself is beautiful, or was so to Euclid, Pythagoras, and Plato. Apples and peaches are beautiful (bananas and carrots not so much). Philosophy of art should have a journal dedicated to the philosophy of the sphere. Jagged, misshapen, irregular things are lacking in beauty. Babies are nice to look at. We like the feel of a ball in our hand.

It is important to see that geometry as a department of mathematics is not the only kind of geometry. We also have folk geometry and what I will call general geometry. General geometry is the field of abstract geometrical relations like inclusion and exclusion, closed and open, inside and outside, distance and proximity. Everything has a geometry in this sense, as everything has a logic. It lies at the heart of all concepts—a kind of map. Arithmetic has a geometry: parts and wholes, size, the successor relation, series. Logic has a geometry; just look at how a logical argument is laid out in a logic text. The circle is at the center of geometry and it generalizes into non-mathematical areas. It is tempting to suggest that all this derives from the sun (with a little help from the moon), but that too may be more an instance of roundness than its original source. Somehow the human mind constructed the idea of the circle and allied concepts; it seems archetypal, part of the collective unconscious. It is surely innate. It shapes our whole way of looking at things (literally). We have Being and Time and Being and Nothingness; how about Being and Roundness?[3]

[1] The OED gives as its second definition of “circle” the following: “a group of people or things forming a circle”—such as the Vienna circle. This may well be a fundamental aspect of our concept of a circle. Being invited to join “our circle” may be considered an honor and gift. This is all part of conceptual analysis, broadly understood.

[2] The halo is also circular, as is Jesus’s crown of thorns. Wedding rings are circular and indicate fidelity, a virtue. They are usually costly and much-valued. Necklaces and bracelets are similarly viewed.

[3] All being divides into the round and the not-round, the smooth and jagged. The former is deemed superior to the latter (recall Kant’s “crooked timber” of mankind). It may also be deemed more real. There are intermediate forms like polygons, which arguably lean in the direction of the circle—degenerate circles, it may be said. Presumably, there could be a universe in which everything is a variant on the circle, a perfect universe; but ours is a fallen universe in which the perfect lives cheek by jowl with the imperfect. The circle gives us the idea of the perfect, which guides our judgements of imperfection. (Or is this fanciful metaphysics?) Our conceptual scheme is a convoluted thing and does not easily reveal its secrets. The circle of our conceptual scheme is infused with the concept of the circle.