Logic of Scission



In Plato’s Phaedo, Simmias has the right of it:

I think, Socrates, as perhaps you do too, that in these matters certain knowledge is either impossible or very hard to come by in this life; but that even so, not to test what is said about them in every possible way, without leaving off till one has examined them exhaustively from every aspect, shows a very feeble spirit; on these questions one must achieve one of two things: either learn or find out how things are; or, if that’s impossible, then adopt the best and least refutable of human doctrines, embarking on it as a kind of raft, and risking the dangers of the voyage through life, unless one could travel more safely and with less risk, on a securer conveyance afforded by some divine doctrine.1

Knowledge not as a matter of certainty, but as an achievement,2 an adventure,3 a wager.4 But Plato never gives Simmias room. His challenges to Socrates’s arguments cannot be answered, only confounded, twisted. If not, the bar of metaphysics, that terrible wound in the real, might start to heal—and then what would be the use of a philosopher and his academy?


Plato’s divided line, the bar of occidental metaphysics, operates through scission, a machine for cutting, a knife for dividing. Through the logic of this scission, a “syntax” is elaborated, a “matrix” that grids the real.5 This is “philosophical decision,” the operation of “analysis,” the move whereby the real is thoroughly loosened, decomposed into constituents and reordered according to the will of the philosopher.6 What is needed instead is “vision,” a “scientific thinking of the One [that] excludes its dismemberment into a syntactical side and a real side.”7 There is only the real, the One, “a real singulare tantum [single as such, single only],” and it is because the real is the singular as such that science is possible, that nonphilosophical vision can become the beginning of our inquiry: look and see, there is the “individual implying the immediately absolute,” there, and there, and there.8

The effect of the One, the “real content” of this effect, is its “unilaterality” and “irreversibility,” the “de-jection” or “de-position of Being by the One” that presents to our vision the “extra-empirical multiplicity” of what is, the “non-positional” and “non-objectivizable diversity” of the real.9 This real cannot be “determined in an ontological mode,” is “in no way decidable, not even partially,” and indeed, has “no need of any criterion of choice nor of any critique.”10 Critique—krī́nō, to separate, divide, distinguish, decide—must always “justify or legitimate itself,” but for scientific vision “there is nothing to choose, no multiplicity of significations or interpretations of the One, no ontological or rational foundation that would be more powerful than” the real itself, the real given to our senses.11 Science is always already with what it studies. Our vision is presented with a myriad of indices to study and discuss, to see, and touch, and taste.

In science we discover the bar, the divided line, the syntax of the real, to be grounded in an “abyss” of “radical absurdity.”12 Our vision, our generic science, begins from this premise of absurdity, embracing “this diversity, radical that-ness or in itself … a diversity that is absolutely indifferent, [which] grounds … an absolute or indifferent choice.”13 There is nothing to choose, no need to choose, we are already with what we would choose, and this is the very “essence of choice, of absolutely any choice whatsoever without any limitation.”14 Our vision, our generic science, is, therefore, the practice of a “transcendental possibilization that frees choice as possible.”15

Plato would foreclose this choice, would deny the real, in favour of his decision—a “strategy,” a “logic,” and an “economy” performed and instituted with a single cut.16


Socrates asks, “do sight and hearing afford mankind any truth, or aren’t even the poets always harping on such themes, telling us that we neither hear nor see anything accurately?”17 Certainly, he continues, whenever the soul “sets about examining anything in company with the body, it is completely taken in by it.”18 To be a true philosopher, one must “undertake the hunt for each reality alone by itself and unsullied”—each reality, which is to say, each constituent of Plato’s syntax, each form, each decision.19 The true philosopher must be “separated as far as possible from his eyes and ears, and virtually from his whole body, on the ground that it confuses the soul, and doesn’t allow it to gain truth and wisdom when in partnership with it.”20 To know in this way is to be “pure,” to be separated “from the body’s folly,” and so to attain “through our own selves [to] all that is unsullied.”21 To know in this way is to decide against the real, to deny the absurdity of any such decision.

The cut in the real that Plato introduces is between “two kinds of beings, the one kind seen, the other invisible,” the seen “never constant” and the invisible “always constant,” the seen known by the senses, the invisible by the intellect.22 Syntax and soul are elevated above the real, attributed all of the terms that once belonged to the Eleatic One: “divine, immortal, intelligible, uniform, indissoluble, unvarying, and constant in relation to itself.”23 Plato inverts the unilateral, irreversible determination of cognition by the real, instituting a hallucinatory logic that makes it impossible for his students to do as Simmias advocates, to test, to learn, to find out how things are, trapping them in doubt and indebting them to the economy of his academy. A grand deception: to call freedom a “prison,” to call knowledge “ignorance.”24


Plato repudiates doxa, opinion, but in Heraclitus we see that doxa is the means whereby we might negotiate the uncertainty of all knowing. For Heraclitus, to “speak with intelligence [one] must stand firm by that which is common to all.”25 Unlike Plato, this “common,” that which is present to intelligence, to every intelligence, is not the invisible syntax of the real, the forms, but that which is “accessible to sight, hearing, apprehension.”26 We need not go to the master to have him explain the mysteries of the real, because the real is here before our eyes, and our opinions of the real may be checked against those of every other who looks and sees and forms opinions of their own. Indeed, for Heraclitus, all people have “the potential for self-knowledge and sound thinking.”27 The true intellectual danger is for one to “live as though they had private understanding,” to do as Socrates urges: the soul “to trust none other but itself.”28

Only through study and discussion can we come to know what “always was and is and shall be.”29 Not to “withdraw,” but to be with.30


Freedom as imprisonment; knowledge as ignorance. This is the logic Plato would have us accept, the cut of his metaphysical pedagogy.

In pedagogical logic, the ignoramus is not simply one who does not as yet know what the schoolmaster knows. She is the one who does not know what she does not know or how to know it. For his part, the schoolmaster is not only the one who possesses the knowledge unknown by the ignoramus. He is also the one who knows how to make it an object of knowledge, at what point and in accordance with what protocol. For, in truth, there is no ignoramus who does not already know a mass of things, who has not learnt them by herself, by listening and looking around her, by observation and repetition, by being mistaken and correcting her errors. But for the schoolmaster such knowledge is merely an ignoramus’s knowledge, knowledge that cannot be ordered in accordance with the ascent from the simplest to the most complex. The ignoramus advances by comparing what she discovers with what she already knows, in line with random encounters but also according to the arithmetical rule, the democratic rule, that makes ignorance a lesser form of knowledge. She is concerned solely with knowing more, with knowing what she did not yet know. What she lacks, what the pupil will always lack, unless she becomes a schoolmistress herself, is knowledge of ignorance—knowledge of the exact distance separating knowledge from ignorance.

This measurement precisely eludes the arithmetic of ignoramuses. What the schoolmaster knows, what the protocol of knowledge transmission teaches the pupil in the first instance, is that ignorance is not a lesser form of knowledge, but the opposite of knowledge; that knowledge is not a collection of fragments of knowledge, but a position. The exact distance is the distance that no yardstick measures, the distance that is demonstrated solely by the interplay of positions occupied, which is enforced by the interminable practice of the ‘step ahead’ separating the schoolmaster from the one whom he is supposed to train to join him. It is the metaphor of the radical gulf separating the schoolmaster’s manner from the ignoramus’s, because it separates two intelligences: one that knows what ignorance consists in and one that does not. It is, in the first instance, the radical difference that ordered, progressive teaching teaches the pupil. The first thing it teaches her is her own inability.31

This is the stultifying move of pedagogy, of philosophy, of the academy. The gulf, the split, the cut made between knowledge and ignorance, is the very scission that divides the real from itself and sets a logic over it to rule it, a logic into which students might be inducted, so long as they gain the favour of the master—and of course, so long as they pay the fee. What cannot be said, what must not be said, is that a student need only “observe[] what is before her, say[] what she has seen, and verif[y] what she has said,” and she will know what she did not know previously.32 As Simmias argues, find out, learn, test—that is all that one must do to know the real, that, and simply that.

The distance the ignoramus has to cover is not the gulf between her ignorance and the schoolmaster’s knowledge. It is simply the path from what she already knows to what she does not yet know, but which she can learn just as she has learnt the rest; which she can learn not in order to occupy the position of the scholar, but so as better to practise the art of translating, of putting her experience into words and her words to the test; of translating her intellectual adventures for others and counter-translating the translations of their own adventures which they present to her.33

Plato’s logic of scission is an “embodied allegor[y] of inequality,” a “distribution of the sensible, an a priori distribution of the positions and capacities and incapacities attached to these positions.”34 If we are to think, to set out on the adventure of thought, we must repudiate Plato’s decision, must unlearn the “inequality of intelligence,” must embrace the contingency of study, this emancipatory work whereby we might indeed be able to “change something of the world we live in.”35 There are no forms; in fact, there “is no more a privileged form than there is a privileged starting point. Everywhere there are starting points, intersections and junctions that enable us to learn something new.”36 Let us look and see together.


  1. Plato, Phaedo, trans. David Gallop (Oxford, UK: Oxford World Classics, 2009), 85c-d. 

  2. Isabelle Stengers, “Reclaiming Animism,” e-flux 36 (July 2012), https://www.e-flux.com/journal/36/61245/reclaiming-animism/. Stengers writes: “In experimental sciences, such achievements are the very condition of what is then, after they have been verified, celebrated as an objective definition. An experimental achievement may be characterized as the creation of a situation enabling what the scientists question to put their questions at risk, to make the difference between relevant questions and unilaterally imposed ones.” And before science, achievement characterizes sense perception itself. Alva Noë writes: “Seeing is an achievement, our achievement, the achievement of making contact with what there is. We can fail to see.” All sense experiences are achievements: “We make them. We don’t just have them. We manage them. If you think of living as a stream of doing, and undergoing, then the achievement of meaning and integration that is characteristic of our actual lived experiences is a thing of value.” See Strange Tools: Art and Human Nature (New York, NY: Hill and Wang, 2015), xi, 204. The achievement that is experience is not limited to scientific inquiry. It is generic, a generic science

  3. Stengers also characterizes the achievement of knowledge as an adventure, but here we can turn to Giorgio Agamben, The Adventure, 2015, trans. Lorenzo Chiesa (Cambridge, MA: MIT Press, 2018). The achievement of knowledge is an adventure of discovery, both the knight’s quest and the troubadour’s song, not passive but a matter of making, of poetry. Such adventure is always a “chance,” always “risky,” a “providential event” in which the “knight [has] an encounter with both the world and himself.” An adventure must be seized, and in so doing, it becomes more than “what happened,” but “also its narration.” An adventure must be seized and then recounted. See The Adventure, 21, 22, 24, 26. 

  4. I cannot find a specific reference but I believe this term comes to me from Richard Kearney. He always spoke of the wager of faith, of belief. More tangibly, and to bring these notes back around to the matter of science, Michael Polanyi considers all scientific inquiry, and indeed, “all novel thought” as necessitating an “existential commitment.” Indeed, for Polanyi, science is simply “a variant of sensory perception.” See The Tacit Dimension (Chicago, IL: University of Chicago Press, 1966), xix, xvii. 

  5. François Laruelle, Philosophies of Difference: A Critical Introduction to Non-Philosophy, 1986, trans. Rocco Gangle (London, UK: Continuum, 2010), 6, 11. 

  6. Laruelle, Philosophies of Difference, 196, 

  7. Laruelle, Philosophies of Difference, 196, 6. 

  8. Laruelle, Philosophies of Difference, 200. 

  9. Laruelle, Philosophies of Difference, 201, 202. 

  10. Laruelle, Philosophies of Difference, 204. 

  11. Laruelle, Philosophies of Difference, 205. 

  12. Laruelle, Philosophies of Difference, 206. 

  13. Laruelle, Philosophies of Difference, 206. 

  14. Laruelle, Philosophies of Difference, 206. 

  15. Laruelle, Philosophies of Difference, 206. 

  16. Laruelle, Philosophies of Difference, 206. 

  17. Plato, Phaedo, 65b. 

  18. Plato, Phaedo, 65b. 

  19. Plato, Phaedo, 66a. 

  20. Plato, Phaedo, 66a. 

  21. Plato, Phaedo, 67b. 

  22. Plato, Phaedo, 79a-b. 

  23. Plato, Phaedo, 80b. 

  24. Plato, Phaedo, 82d-e. 

  25. Heraclitus, F12, in The First Philosophers: The Presocratics and the Sophists, trans. Robin Waterfield (Oxford, UK: Oxford World Classics, 2000), 39. 

  26. Heraclitus, F28, in Waterfield, The First Philosophers, 41. 

  27. Heraclitus, F31, in Waterfield, The First Philosophers, 41. 

  28. Heraclitus, F6, in Waterfield, The First Philosophers, 38, and Plato, Phaedo, 83a-b. 

  29. Heraclitus, F36, in Waterfield, The First Philosophers, 42. 

  30. Plato, Phaedo, 83a. 

  31. Jacques Rancière, The Emancipated Spectator, 2008, trans. Gregory Elliott (London, UK: Verso, 2009), 8-9. 

  32. Rancière, The Emancipated Spectator, 10. 

  33. Rancière, The Emancipated Spectator, 10-11. 

  34. Rancière, The Emancipated Spectator, 12. 

  35. Rancière, The Emancipated Spectator, 11, 23. 

  36. Rancière, The Emancipated Spectator, 17.