Circular Thinking

How to Think a Figure; or, Hegel’s Circles

by Andrew Cole 

The essay begins:

No philosopher better epitomizes circular reasoning, nor more fittingly embodies the logical fallacy of circulus in probando, than G. W. F. Hegel, because he loves talking about circles and his points often go in circles. This essay isn’t about Hegel’s endearing oral delivery, about which plenty has been said since the man himself was alive. Rather, this is an attempt to think philosophically about circles and rethink so-called Hegelian circularity.

Why we would even bother thinking about circles is on account of their “eternal” symbolism within philosophy and theory—the fact that the circle always stands for something, ever the symbol of this or that thing you don’t really like. Invariably, that something is Hegel, on the grounds that he typifies the circularity of thought. For example, Ludwig Feuerbach writes: “The circle is the symbol and the coat of arms of speculative philosophy, of the thought that rests on itself. Hegel’s philosophy, too, as is well known, is a circle of circles.” This is indeed one of those long-standing clichés about Hegel. So it’s no surprise that Louis Althusser—whose anti-Hegelianism can be forgiven in the knowledge that he’s really not a deep reader of Hegel—draws a circle around himself in order to step out of it, striding from ideology to science:

The whole history of the “theory of knowledge” in Western philosophy from the famous “Cartesian circle” to the circle of the Hegelian or Husserlian teleology of Reason, shows us that this “problem of knowledge” is a closed space, i.e., a vicious circle (the vicious circle of the mirror relation of ideological recognition). 

That’s a lot of circles, a lot of symbols. What do they mean? What do they really “show”?

These symbolic circles mean too much and not enough: call something a circle and the point about it is somehow immediately clear, but wait, how is something that’s not actually a circle like a circle or identical to a circle? Such symbolic circles mean what you want them to mean, which is exactly why all symbols are hopelessly bound up with the proverbial problem of meaning—tokens of the human need to line things up, to know where things go, ever since we first took soil for filth and polluted it accordingly. All the more reason, then, to think dialectically about our problem in an essay that both defends and extends Hegel’s thinking on this question of circularity and figures.

Our problem is this: Hegel rates figures below concepts but he needn’t always do so. In his mind, figures are just a bunch of numbers and lines annoyingly uncommitted to either Thought or Being. He also dislikes figures because they aren’t language, or are a lesser language. Hegel has his reasons for these positions. But those reasons may not be good enough, judging by the way he seems to equivocate about figures. Sometimes figures are so perfect as to figurate the very significance of his philosophy (and that’s no small feat!). And sometimes they are pretenders to proper conceptuality, conceptual thinking by other means. Hegel is all over the place on this question, as we’ll soon see. But if one applies even a modicum of mathematical wit to the figures Hegel does offer us—and most of them are circles, with triangles as a close runner-up—then we discover some rather interesting spaces in which dialectics might wander.

Here I propose that figuration (in my renewed Hegelian sense) is what Walter Benjamin tried to describe a century later as “dialectical images”—only Hegel’s figures are already in motion, are already an action, and already an “image of thought” that’s not static but dynamic. Figures are figures of thought because they move, just as thinking and the dialectic itself must move, according to Hegel. Figures both initiate and image the movement of thought. Figures are for thinking, whereas symbols are for reading and interpretation. Figures are dialectical. As such, they supply a way of practicing Hegel’s abiding ambition, as laid out in the preface to the Phenomenology of Spirit, “to bring fixed thoughts into a fluid state [festen Gedanken in Flüssigkeit zubringen],” so that we can apprehend “dialectical form [dialektische Form],” which is the representation of philosophical, critical thinking: in other words, Darstellung. Just what this thought process involves, the circle may help us grasp … and think. Continue reading …

In this essay Andrew Cole suggests that Hegel’s philosophy of the concept is also a philosophy of the figure, a demonstration of conceptuality by other means. Neither images nor symbols, Hegel’s figures—primarily, circles—initiate and image the movement of thought.

ANDREW COLE is Director of the Gauss Seminars in Criticism and Professor of English at Princeton University. Forthcoming works include Foundations of the Dialectic and Unmodernism.

Beginning with Aristotle

Fallacy: Close Reading and The Beginning of Philosophy

by D. Vance Smith

The essay begins:

The formal study of fallacies began, as have so many other intellectual disciplines, with Aristotle. In a short treatise called Peri Sophistion Elenchon (On Sophistical Refutations, referred to in the Latin Middle Ages as De Sophisticis Elenchis), he classified thirteen types of fallacious argument—six that depend on slippages of language and seven that do not. As with much of Aristotle’s work, this emphatic division belied a dense cluster of problems that later expositors would tease out, and which this article will explore in a moment, beginning at the primal level of what, precisely, “fallacies” are. The change in terminology from “sophistical refutation” to “fallacies” belies an immense epistemic shift—nothing less, really, than the emergence of medieval philosophy out of classical thought. The Latin Middle Ages assimilated Aristotle’s treatise into the logical curriculum simply as “On Fallacies” (De Fallaciis), from fallare, “to deceive,” or “to trick.” In William of Sherwood’s influential twelfth-century Introduction to Logic, which expounds five of Aristotle’s logical texts, De Fallaciis is the sixth and final chapter. On the face of it, the word fallacia in medieval logic retains the implication of deliberate misleading, the problem that motivates Aristotle’s treatise, which is essentially a manual on how to spot the tricks an opponent might use to derail one’s argument. But deception is used one way in medieval philosophy, another in Aristotle’s.

Aristotle’s definition of sophistical refutations itself is deceptively complex, beginning with what seems to be the plainest declaration of what they are. The very first sentence of his treatise defines them as what they are not: they “appear to be refutations but are really fallacies.” From the start, sophistical refutations involve a dialectic of appearance: they are what they do not seem to be, and are not what they seem to be. Medieval discussions swerve around this problem by arguing that fallacies have both “semblance” or “appearance” (apparentia) and, seemingly paradoxically, nonexistence (non-existentia). What they mean by nonexistence needs to be qualified: a fallacy exists, of course, in the domain of language, and to that degree has the same ontological status as a valid syllogism. As William of Sherwood says in his foundational Introduction to Logic, fallacy and valid syllogism appear to be the same because they share a verbal identity: the resemblance comes “ex identitate sermonis.” But what leaves the fallacy in the realm of pure appearance only is that it doesn’t mean anything real: it diverges from valid syllogism “ex identitate rei.” But William (and subsequent commentaries) doesn’t say that what a fallacy refers to doesn’t exist; it is the fallacy itself that doesn’t have existence. To put this definition more precisely: a fallacy must meet the condition of appearing to be a syllogism and of “its nonexistence” (“non-existentiam eiusdem”). It exists only in apparentia, and its existence only there means that it does not actually exist.

For Aristotle, the phainomenon of fallacies is elusive, but so is the language we use to speak of them. They are “really” fallacies, paralogismoi, statements that lie outside of reason or of rational discourse (para-, outside, beyond + logizomai, to think, to calculate, to consider; the word is from logos, the Greek word that means anything from word to reason to order). That is, not only can we recognize sophistical refutations only by what they are not; we also cannot use the term itself to describe them, since they occupy a position outside of discourse. Sophistical refutations are actually not refutations at all (ouk elenchon legomen). Strictly speaking, a treatise on sophistical refutation is a logical impossibility, the first deception in a treatise full of them. Continue reading …

This essay by D. Vance Smith locates the beginning of philosophy in Aristotelian syllogistic logic, where fallacy is the precondition of rationality. Smith then turns to medieval commentaries, which treat fallacy as a nonreferential discourse and develop what is essentially a theorization of fictionality and its practices.


D. VANCE SMITH is Professor of English at Princeton University. His current work includes the completed Arts of Dying, a study of logic and death in medieval literature, and a book on medieval Africa, Blood Flowers.


Badiou’s Paradox

Heideggerian Mathematics: Badiou’s Being and Event as Spiritual Pedagogy

by Ian Hunter

The essay begins:

This paper is an experiment in redescription and reinterpretation. It seeks to take a text that enunciates a Heideggerian metaphysics of the “event”—understood as an encounter in which a subject meets itself emerging from the “void”—and to treat this text itself as an event in a quite other sense: as an ordinary historical occurrence. I will thus be approaching Alain Badiou’s Being and Event historically, in terms of the publication of a written work, but of a highly particular kind. This is a work whose discursive structure programs a refined spiritual pedagogy, and whose composition and reception only make sense within the historical context of the elite academic-intellectual subculture in which this pedagogy operates.

If we consider that Badiou regards his text as a “metaontology” that enunciates the emergence of events and indeed of historical time itself from the domain of nonbeing, then to treat this work as a kind of writing that occurs wholly within a particular historical subculture will imbue our redescription with an indelibly polemical complexion. It should be noted at the outset, however, that this complexion arises from the choice of a particular intellectual-historical method, rather than from any normative contestation of the content of Badiou’s work. This method or stance treats even the most abstract objects of reflection as products of an open-ended array of historical intellectual arts: rhetorics of argument, formal and informal languages, mathematical calculi, “spiritual exercises,” pedagogical practices. As a result, even a mode of reflection that claims to apprehend its objects at their point of emergence from the “void” and the “unthought” will be described in terms of the contingent historical use of a particular array of such arts. These will be those arts through which a philosophical elite learns to fashion an illuminated self whom it imagines keeping watch at the threshold of the void for the emergence of things newly minted from nonbeing through their naming. It is the task of a certain kind of philosopher to fashion such a self. The task of the intellectual historian, however, is to describe the intellectual arts used in this “work of the self on the self,” and the historical circumstances and purposes governing their transmission and use. Continue reading …

This essay provides a historical redescription and reinterpretation of Alain Badiou’s major work, Being and Event. The work is approached historically, as a text that uses Heideggerian metaphysics to perform an allegorical exegesis of mathematical set theory and does so as a means of fashioning a supremacist spiritual pedagogy for a philosophical elite in the context of a national intellectual subculture.

IAN HUNTER is an emeritus professor in the Institute for Advanced Studies in the Humanities, University of Queensland, Australia. He has published a number of studies on early modern philosophical, political, and juridical thought, most notably Rival Enlightenments: Civil and Metaphysical Philosophy in Early Modern Germany (Cambridge, 2001). Professor Hunter has also published a series of papers on the history of “theory” in the humanities academy, including “The History of Theory,” Critical Inquiry 33 (2006), and, most recently, “Hayden White’s Philosophical History,” New Literary History 45 (2014).

Philosopher Catherine Malabou at Berkeley

Una’s Lecture
Photo of Catherine Malabou.

Monday, April 14, 2014 | 6:00 pm
Banatao Auditorium, Sutardja Dai Hall, UC Berkeley

French Philosopher Catherine Malabou teaches at the Centre for Research in Modern European Philosophy at Kingston University in London. She is the author of The Future of Hegel (2005), What Should We Do with Our Brain? (2008), Plasticity at the Eve of Writing (2009) and Self and Emotional Life: Philosophy, Psychoanalysis, and Neuroscience (2013)Her work has created the foundation for a wide range of current research focusing on the intersections between neuro- and biological science and the humanities. Her Una’s lecture, “Odysseus’ Changed Soul,” will offer a contemporary reading of Plato’s myth of Er (Republic, Book 10).

Professor Malabou’s short essay “The King’s Two (Biopolitical) Bodies” will appear in Representations 127, available in July 2014. In residence at Berkeley through the month of April, she will be a featured speaker in the interdisciplinary conference  “Animation/Reanimation” April 18, 2014 and participate (along with Representations editorial board member David Bates) in a two-day workshop April 11-12, entitled “Plasticity and Pathology: The History and Theory of Neural Subjects.”

Cartesian Robotics

In “Cartesian Robotics,” now available in Representations 124, David Bates looks at Descartes’s physiological theory, and especially his theorization of the nerves and the brain as an information-processing system, in order to offer a new interpretation of cognition within his philosophy. Rather than opposing mind and body, Descartes showed how the operations of the soul interrupted the automatic cognitive processes of the body to provide adaptive flexibility for the human organism as a whole. Bates is Professor in the Department of Rhetoric at UC Berkeley, where he teaches intellectual history.