Solutionism

I will define solutionism as the doctrine that all philosophical problems have solutions that are in principle available to us. It is the opposite of mysterianism. It characterizes an attitude or mindset with respect to the problems of philosophy—the solubility attitude or assumption. It deserves to be called an ideology. I can best explain it by way of example; so, let’s return to our beloved bats and their echolocation sense. Suppose we become interested in the abilities of bats and notice that they fly by echolocation. We hypothesize that they have sense experiences rather different from ours that involve echoes of their own shrieks—E-experiences. Intuitively, we regard these as mysterious—we suppose that we can’t (fully) grasp the nature of such E-experiences. They might even be cited by philosophers as examples of natural mysteries (possibly in the course of an argument against materialism). The mysterian philosopher will say that this is a genuine mystery: we just don’t know what it’s like to have E-experiences, adding that we may never know, or even will never know. He might regard this as a necessary truth—we must remain ignorant of such experiences. By contrast, the solutionist philosopher will reject such mysterianism (a mere meme, he will explain) and suggest instead some method by which we can know the nature of E-experiences. This method may vary, depending on the predilections of the solutionist: it may be because the experiences are actually just like our auditory experiences or our visual experiences or a combination of both; or because they are reducible to bat behavior; or because they are nothing but bat brain states; or because there are no such experiences in reality and hence there is nothing to know; or because the whole talk of “what it’s like” is just meaningless babble framing a pseudo-question. There is nothing mysterious about bats, he will insist. Nor, he will add, is there anything in sighted humans that is a mystery to blind people. Alien experiences, so called, are never mysteries; for we always have a solution to the (apparent) problem they pose. The question always has an answer, perhaps because to understand the question you must already be able to understand the answer and have it close to hand. The solutionist is ideologically committed to denying the existence of such alleged mysteries. He might even say that the infinite potential of natural languages guarantees that solutions can always be found. In any case, his attitude—his stance—is clear enough, and clearly distinct from that of the mysterian. If a problem can be formulated, it can be solved.

It is also clear that the solutionist response is unconvincing, indeed obviously false. It is unrealistic ideology. It is a dogma. The only real question is what explains the mystery of E-experiences: is it their intrinsic nature or is it something about us as knowers? It can’t be the former for obvious reasons, so it must be the latter; and clearly it has to do with the fact that we don’t share such experiences with bats. Bats don’t find them mysterious and neither do other echolocating creatures—the mystery is a relative mystery not an absolute mystery. Once this is understood we can generalize the point: it is often true that the experiences of others are mysteries to us; we might even say that the minds of other animals as a whole are mysteries to us, to one degree or another. In fact, other people are often mysterious to us: those of a different sex or a different age or a different culture or are differently motivated. Mystery is everywhere in inter-personal relations, a universal fact of life. I might even be a mystery to myself! Once this is accepted, we can move on to other things that seem mysterious: space and time, the nature of matter, causality, meaning, consciousness, knowledge, human voluntary action. A solutionist might propose a solution for each of these, thus producing a philosophical (or scientific) school: time is clocks, space is matter, matter is extension, causality is constant conjunction, meaning is conditioned response, consciousness is higher-order belief, knowledge is a faint copy of experience, voluntary action is causation by beliefs and desires, etc. Philosophy is full of such solutionist solutions: doctrines that are prompted more by ideology than by intrinsic plausibility—the need to have something to say, however unsatisfactory. The mysterian can live without solutions, preferring realism over forced intelligibility (to himself or humans in general). In truth, he finds the desperate contortions of solutionists somewhat comical. They are in denial, as psychologists say.

And now we reach a psychological question: what is the mindset of the solutionist—where does his solutionism come from? This is where I think we need to apply some tough love, otherwise known as a reality-check. For it is clear that some sort of psychological syndrome is at work here—some sort of phobia, in fact. A solutionist psychology is not a healthy psychology. It is impatient, self-centered, hysterical, narcissistic, unrealistic, needy, panicky, immature, primitive, anthropocentric, and rife with cognitive dissonance reduction. Sorry, but it’s true. It belongs with nyctophobia (fear of the dark), obsessive-compulsive disorder, an urge to control, a pathological reluctance to acknowledge ignorance. Animals don’t suffer from it; they don’t fret over their ignorance of nature, seeking to deny it. They are not constitutional know-it-alls. I speculate that for us it goes back to our childhood fear of the dark: we can’t see what is going on out there in the dark and it troubles us. There may be monsters lurking, prowling predators, waiting to pounce. This is perfectly rational: not being able to see is an obvious handicap. We don’t like the mysterious dark night with those dangerous beasts and sharp obstacles. Imagine living on a planet with no light at all only perpetual darkness! Terrifying. But ignorance is like darkness—dangerous, scary. We prefer the light of knowledge to the dark of ignorance. Thus, we are alarmed by the unknowable—the deep dark sea, outer space, aliens of various stripes, the foreign, black holes. The solutionist would rather accept comforting fictions than face alien facts; he is afraid of mysteries. The inscrutable bat gives him the willies, so he tries to render it familiar, a miniature version of himself perhaps. Better to think of E-experiences as familiar physical stimuli than inner mysteries. Better to think in terms of stereotypes than unfathomable individuals. Better to contemplate clocks than moments of pure time. Better not to think of infinite space at all. Mysteries must be kept at bay at all costs. Mystery-phobia thus leads to reality-underestimation.

This is where religion rears its falsely comforting head: it is solutionism at its most basic. Nature strikes early man as full of mysteries that threaten his well-being; he solves these problems with a religious theory. The sun is a god, etc. This takes the form of rampant anthropomorphism, which promises to relieve the fear and frustration of unknowing. It enables our ancestors to predict the future, to tell us what happens after death, to placate hostile forces. Religion is anti-mysterian in inspiration, if not in practice. Solutionist philosophers are like primitive religionists—desperate to find some sort of answer to life’s mysteries (maybe bats are the pets of the gods). We all have this tendency within us, tracing back to ancient times; it doesn’t just go away with modernity. We love the light and we hate the dark. We love transparency but not opacity (matter is so inscrutable, so hard to see through or into). Religion isn’t a type of mystery-mongering; it is a type of mystery-avoidance. The contemporary solutionist is deep down a religionist—a lover of comforting dogma. Socrates was the first anti-solutionist; for him everything was a mystery—he famously had no positive views of his own–but was only too happy to demolish the views of others. Popper too is properly seen as an anti-solutionist: no dogmatic solutions only cautious conjectures, hitherto unfalsified. Popper was a hard-boiled mysterian! Perhaps he was the ultimate mysterian (remember his views on the mind-body problem). For Popper, scientific theories are not solutions to tough problems, but acknowledgements of natural mystery; they can’t be known to be true, only known to be false when falsified. This is what epistemology looks like when you give up on finding solutions; nature is a vast ocean of mystery that we can only formulate conjectures about that may one day be refuted. It’s bat experience all the way down.

You might wonder why solutionism exercises such a hold on us, given that animals don’t suffer from it (they are immune to this human malaise). Why do we assume we can solve any problem we can recognize? This is an excellent question with no obvious answer (a mystery of biological nature?), but I have a theory which has not so far been falsified. Language. Languages give rise to illusions of omniscience: we think the infinite combinatorial potential of language will provide a sufficient resource for expressing everything about nature. If there are facts of the matter, our language is able to capture them intelligibly, even neatly (hands up who thinks this). But a moment’s reflection reveals the hollowness of this flight of fancy: do you think a blind man’s language will cure his ignorance of what color is? Do you think a person with mental retardation will be able to learn every lesson just because he can speak? Of course not (yet some people appear to believe this, unbelievably). It depends on the extent of the language’s lexicon and the intelligence of its speakers. Language is indeed a powerful instrument of thought, but it is not all-powerful; a child has language but is not capable of dispelling every mystery in the world. Still, it seems to give us delusions of cognitive adequacy. Animals don’t suffer from this source of error about the possibilities of knowledge, so they don’t parade around boasting of their cognitive supremacy. You have heard of confirmation bias; well, this is cognitive bias abetted by linguistic competence. We have an overly favorable opinion of our own cognitive capacities. Language has given us a big head (but not big enough). Solutionism has been encouraged by linguistic ability. Having a wordfor E-experiences is not enough for knowing what they are; knowledge isn’t the same as talking proper. Language expresses knowledge; it doesn’t create it. Language isn’t a magical searchlight into the darkness. I suggest pondering the question, “Am I a solutionist?”[1]

[1] To my surprise, I did not invent this word, nor the concept it expresses. It has a positive meaning and a negative one. Positively, it is someone who comes up with innovative solutions instead of being weighed down by hard problems; negatively, it is someone who wrongly thinks that all human problems have technological solutions. I have not seen it used in the way I do here, as a way of describing a certain philosophical attitude or stance. I came up with it by asking what the antonym of “mysterian” would be. It is interesting that our image of knowledge is that of a circle of light surrounded by darkness. The solutionist is someone who can’t bear the darkness and prefers to bask in false light.

Intellectual Impact

I am interested in the intellectual impact of this blog on the minds of its readers (who range from all over the world). What is it doing to your minds? I ask this as an educational psychologist manque. What you get here is a barrage of subversive thought, relative to received opinion, though highly disciplined. And it will not stop. Is it annoying, exhilarating, disturbing, amusing, infuriating? Is it changing the way you see things? Is it reshaping your mind? Does it come back to haunt you in the dead of night? I myself find it quite liberating and mind-altering, like a kind of intellectual LSD. So, readers, look within and report your findings to me. I will analyze the results.

Existentialist Metaphysics

I won’t attempt to explain, let alone justify, the existentialist philosophy laid out in Sartre’s Being and Nothingness; I will simply presuppose it. My concern is with the metaphysics that goes along with it (which Sartre completely ignores).[1] We have the in-itself and the for-itself. The in-itself is what it is; the for-itself is what it is not. The essence of the in-itself is inert matter; the essence of the for-itself is consciousness. The essence of inert matter is being; the essence of consciousness is nothingness. The essence of being is unfreedom; the essence of nothingness is freedom. So, the essence of the in-itself is unfreedom and the essence of the for-itself is freedom. The for-itself can be in bad faith, but the in-itself cannot. It is the essence of the in-itself (matter) to lack freedom; it is the essence of the for-itself (consciousness) to be free. Matter cannot be free; consciousness cannot be anything but free. This is because matter has no intentionality and consciousness is all about intentionality. The in-itself and the for-itself are categorically distinct—this is an irreducible dualism at the heart of reality (nothingness is real, all too real). Metaphysically, the in-itself and the for-itself are the opposite poles of the real. Being cannot be nothingness and nothingness cannot be being. Call this Sartrean dualism, analogous to Cartesian dualism.[2]

Now apply this system to panpsychism. Panpsychism says that matter is (partly) mental: the intrinsic nature of any material thing is mentality, i.e., consciousness. In addition to what we see of matter externally, matter also has an unseen inside—how it feels internally. Thus, matter is imbued with both being and nothingness, unfreedom and freedom, inertia and will. An electron, say, is both an in-itself and a for-itself, these being opposite types of reality: it both is what it is and what it is not. This makes it contradictory, which is impossible. Therefore, panpsychism posits a contradictory ontology. Existentialism doesn’t do this, since mind and matter are deemed separate things: one is free and the other is unfree. It is as if one is in jail and other isn’t. But you can’t be both. So, adopting Sartre’s ontology, panpsychism is a contradictory doctrine; it both affirms and denies that matter is free (a for-itself and an in-itself). That is, it says that matter is nothingness and that it is not nothingness (but is being).

How does Sartre’s system relate to the mind and body? The mind is consciousness, so it is nothingness (a for-itself); the body is inert matter, so it is being (an in-itself). Mind and body are therefore an irreducible duality. Human reality (as Sartre would say) is a double reality: we are all two things roped together–animals included. We are made of a free thing and an unfree thing, a thing of being and thing of nothingness. There is nothing contradictory about this, since body and mind are distinct existences (to borrow Hume’s indispensable phrase). There is no reason to think that Sartre would deny this; indeed, it is baked into his existentialist philosophy. Sartre is a metaphysical dualist with regard to mind and body. Fine, no problem about logical consistency. But not everybody is down with that; some folks want to retain a type of monism about human (animal) reality. How do they do this? They introduce a third category of thing, which they label the person or the self or the ego or the subject. This is commonly regarded as distinct from the mind and body, being instead an amalgam of the two—or better, something that has the other two aspects. That is, they talk this way, perhaps claiming that the concept of a person is primitive and not reducible to its physical and mental “aspects”. This sounds all well and good, given that we know what it means to talk of aspects of the same thing (e.g., the color and shape of a material body). Evidently, this third thing is neither an in-itself nor a for-itself—it isn’t pure matter and it isn’t pure mind, but a confluence of both (whatever that means—is it like two rivers joining together?). For want of a better label, let’s call it the “at-itself”, since the mind and body are both at a person—they are where a person is at. (It’s better than saying “up-itself” or “with-itself”.) The question then is whether the at-itself is real—can we quantify over at-itselves? I should bally well say not, as Bertie Wooster might phrase it; eff that, as others might put it. Because such a thing would involve a contradiction: for the at-itself is both free and not free, an in-itself and a for-itself, being and nothingness combined. What the flipping eff! The problem with the at-itself is that it isn’t real; it’s a myth dreamt up to avoid admitting dualism. This is why you can never quite put your finger on it (as Hume complained). The only realities here are the body and the mind, the in-itself and the for-itself; there is no third thing over and above these, acting as their bearer, their supervisor, their plus one. Look inside yourself: you are a body and a mind, and that’s it. There is no third thing lurking in the shadows and slouching around the premises—a homunculus or succubus. The person is a mythical creature, metaphysically. It is a handy way to talk, serving forensic purposes, but it is not a fundamental constituent of reality. Worse, it is bally contradictory—and we know what we say to that. In point of fact, Sartre never soils himself by introducing such an entity (he is a good empiricist); there are no persons in his ontology—no psychophysical hybrids. You are either an in-itself or a for-itself, no mixing or merging allowed. Here Sartre follows Descartes, who also eschewed the at-itself—the thinking-and-extended thing. We may talk this way for convenience, but in serious ontology we do better without it; once you have mind and body, you have covered the ground. Accordingly, Sartrean dualism and Cartesian dualism have no room for double aspect theories, these being deemed contradictory. This is not to say that they are all fine and dandy, only that they avoid a certain tempting move that ultimately leads nowhere. There are no metaphysical double agents, just a trick of language.[3]

[1] See my “Incompatible Minds”.

[2] We can label these views “French dualism”—firm distinctions not hazy continua (“Tibetan dualism”).

[3] Am I saying there are no people? Yes, I am saying that—no people in a metaphysically interesting sense. Of course, there are minds and bodies, but no third entity that has both a mind and body. There is no “I” but these. There are two things there not three. Similarly, there are no cats and dogs distinct from cat and dog minds and bodies. We can’t say, “Here is a cat mind, and there is a cat body, and over there there is a cat”. Nor can we say a cat is the mereological sum of its mind and body, as if they are cat parts. Ontologically, an animal is two things combined, not a third thing over and above the things combined—something like a zoological point or particle or spectral shadow. We can talk that way, but it is not serious metaphysics (like “sakes”). We should not be trinitarians about animal ontology (“the body, the mind, and the holy beast”). There is therefore really no such subject as the theory of personal identity, though there is certainly such a subject as body identity or mind identity. The person is nothing like a peg.

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.