Generic Science, 2

Parmenides, Anaxagoras, Badiou

2021-04-12

Why begin with void? After drawing our continuity between the abstract ontologies of Anaximander, Pythagoras, and Heraclitus, we can now return to Alain Badiou and his peculiar beginning, using it as a staging area for engaging with Parmenides of Elea and Anaxagoras of Clazomenae. This progression of essays has allowed us to separate the traditional pair of Heraclitus and Parmenides, so keeping us at a distance from Plato’s treatment of the two thinkers and allowing their philosophies to stand on their own. This should, in turn, put us on a better footing for returning to Badiou as promised and engaging with the motive for his philosophical project.

In Badiou’s lecture, “How to Begin with the Void,” he does not dive into building his ontology out of sets of nothing right away.1 Rather, Badiou spends a significant amount of time setting up his ontology in its historical situation, specifically with respect to the “concept of the infinite.”2

For Badiou, the philosophical moment in which we find ourselves is that of an “irrational struggle” between a “reactive classicism” and a “reactive romanticism.”3 The “rational struggle” between science and religion at the end of the sixteenth century and the beginning of the seventeenth century has given way to a new “dominant contradiction,” a contradiction that, in this mode of reaction, strikes backward at the fusion of the One and the Infinite that can be understood as the abstract foundation of the West.4

In an earlier lecture in the series, “A History of Finitude and Infinity: Romanticism and Modernity,” Badiou locates the genesis of Western modernity in the Judaeo-Christian supersession of the finite Greek One by the infinite One—the “new God.”5 Infinite possibility becomes thinkable, and significantly, it becomes thinkable as transcendent. The mediation between finite existence and infinite Being is thus a kind of miracle, a miracle which is figured in the person of Jesus Christ, the first dialectical mediation, and thus fusion, of the One and the Infinite.6

Classicism, the thought of classical antiquity, maintains the One as finite, and perfection as the realization of the finite possibilities of the One. Romanticism, on the other hand, maintains the One as infinite and transcendent, and perfection as the creation of radically new possibilities by way of an eruption of infinite possibility in the finite.7

We find ourselves today at the far end of this subsequence, in the “third sequence,” the dialectic of the classical and the romantic nearing its terminus.8 Two thousand years of mixture have brought us here—but for what? Badiou’s presentation of “reactive classicism” and “reactive romanticism” is difficult and vague, providing us with little help in answering this question. What Badiou makes clear, however, is that both positions are characterized by the proposition of the “impossibility of a new access to the infinite.”9 Reactive classicism seeks to make a world with the “finite possibilities” available to it while reactive romanticism seeks dissipation in and of the world—for both, the world is “something like a terrible necessity,” that which is utterly, finally closed.10

It is challenging to pin down which thinkers or schools of thought Badiou has in mind when he describes these two modes of reaction, but what is more important is understanding Badiou’s chief concern in framing this struggle: his concern over the possibility of a future, over the possibility of something new emerging in the world. If the infinite is, truly, foreclosed, then “there is no mediation between concrete life and something like an opening to the infinite,” and “if there is no mediation, in some sense there is no future, no real future.”11 Badiou continues:

There is a small future inside the present, something like the movement of the present, but this movement is not exactly the representation of the future, but the present itself. Every day the world changes, but this change is the change of the same, it is a change inside the same, because our world is a world that’s law is to change. It is a law: that we must change. If change is the law of the situation, it is not a true change, but a continuation. A true change would be much more to stop all that, and not to continue. But it is not possible to stop, because the law of the world is to continue absolutely, to continue to produce, to continue in different modes of capitalism, to continue the banks, and so on. To continue is the law of the world as it is … When there is no mediation between our world, finite existence, and something infinite, what exists is by necessity always the same thing, because there is no mediation for something really different.12

Though I find Badiou’s utilization of “reactive classicism” and “reactive romanticism” ultimately unproductive, it does serve to bring us to the point of asking the vital question of the possibility of newness, a question which, for our purposes here, also brings us face to face with Parmenides and his profoundly singular vision. In constructing this new dialectic, we can short circuit the dialectic of classicism and romanticism that has culminated in reaction and exhaustion, and so attempt to begin again.

Wherein the prior thinkers we have been considering have all included change by some mechanism or other in their ontologies (soul, motion, god, limit, or the logos itself), Parmenides concludes that change is impossible, and thus unreal. The Parmenidean paradigm is distinguished by this denial, a denial to which we have already seen Badiou, at a distance, respond.

We are told that Parmenides “would not agree with anything unless it seemed necessary,”13 and Parmenides himself writes that it is “well-rounded truth,” and not the “beliefs of mortals,” that he seeks.14 Like Heraclitus, Parmenides asserts that the “point from which I start is common; for there shall I return again.”15 We have already cast this philosophical posture as that of a Laruellian “generic science,” which stands in a “direct or radical” relation to the real.16 Indeed, like Laruelle, Parmenides begins his inquiry before the “paths of night and day,” his vision described by Waterfield as “transcend[ing] the polarity of light and dark.”17 In other words, Parmenides begins in Laruelle’s “black universe”—that which is always already before the scission of philosophical syntax, and always already after, “opaque and solitary,” “deaf and blind,” unreflected, groundless, and “entirely interior to itself.”18 This is the “hyperspace” in which Parmenides’s education by the goddess occurs.19

Parmenides is known for his “two ways”—the way “that it is and it cannot not be” and the way “that it is not and that it must not be.”20 The first is the “path of Trust,” the second “an altogether misguided route.”21 These gnomic statements can be somewhat difficult to parse, but what we see in each is a proposition about a state of affairs linked with a modal assertion. That it is is necessary; that it is not is impossible.

As in Heraclitus, what is, for Parmenides, is “what can be spoken and thought,” because what can be spoken and thought “is there for being.”22 Waterfield is careful to note that by this “Parmenides cannot mean, literally, that thinking and being are identical, but that they are co-extensive: thinking is thinking of a thing as it is.”23 We can nuance this position, however, and say that thinking and being are not co-extensive in Parmenides, like two distinct planes superimposed, but rather are parts of the same continuum—as in Heraclitus, thought stands firm by being. As we have remarked previously, this direct and radical relation of thought to the real echoes the phenomenological dictum that “[a]ll consciousness is consciousness of something” or the externalist dictum that consciousness is identical with its contents and not a theatre of representations.24 To this citational play we might add the semiotic dictum, that the “matter segmented in order to express something expresses other segmentations of that matter.”25 Parmenides later confirms this reading, contending that the “same thing both can be thought and is that which enables thinking. For you will not find thinking apart from what-is, on which it depends for its expression.”26 Thought is secondary, unilaterally determined by being.

It is this unilateral determination that leads Parmenides to the necessity of his conclusions. Allow me to quote at length:

what-is is unborn and imperishable, entire, alone of its kind, unshaken and complete. It was not once nor will it be, since it is now, all together, single, and continuous. For what birth could you seek for it? How and from what did it grow? Neither will I allow you to say or to think that it grew from what-is-not, for that it is not cannot be spoken or thought. Also, what need could have impelled it to arise later or sooner, if it sprang from an origin in nothing? And so it should either entirely be, or not be at all. Nor ever will the power of trust allow that from what-is it becomes something other than itself …

Thus birth has been extinguished and perishing made inconceivable. Nor can it be divided, since all alike it is. Nor is there more of it here and an inferior amount of it elsewhere, which would restrain it from cohering, but it is all full of what-is. And so it is all coherent, for what-is is in contact with what-is. Now, changeless within the limits of great bonds, it is without beginning and without end, since birth and perishing have been driven far off, and true trust has cast them away. It stays in the same state and in the same place, lying by itself, and so it stays firmly as it is, for mighty Necessity holds it in the bonds of a limit which restrains it all about, because it is not lawful for what-is to be incomplete. For there is no lack in it; if there were, it would lack everything …

Now, since there is a last limit, what-is is complete, from every side like the body of a well-rounded sphere, everywhere of equal intensity from the centre. For it must not be somewhat greater in one part and somewhat smaller in another. For, first, there is no such thing as what-is-not, to stop what-is from joining up with itself; and, second, it is impossible for what-is to be more here and less there than what-is, since it all inviolably is. For from every direction it is equal to itself, and meets with limits.27

Just like in Heraclitus, being is our teacher, “single” and “continuous.”28 And indeed, Parmenides’s argumentation here reads much like a development of Heraclitus’s common logos. For what is to truly be single, it must be alone, complete, together, alike, full, coherent, and inviolable. And if what is meets these criteria, it also necessarily entails the fact that what is not cannot be because what is would as such have to have a beginning and an end, and what need could impel something to arise from nothing? This is Parmenides’s answer by way of an absolute affirmation to the arche-philosophical question: why are there beings at all instead of nothing?29

What I find most striking about this long passage, however, are the generic, scientific questions that animate it, questions that animate cosmological research to this day. If we read Parmenides through Laruelle, his inquiry quite clearly becomes a matter of direct, radical relation to the universe. Where earth is the old autochthony of human being, and world is the horizon of human possibility, universe is the “how” and “according to” of thought, the abstract substance of the real.30 Such a mode of thought is what Quentin Meillassoux means when he invites us “to get out of ourselves, to grasp the in-itself, to know what is whether we are or not.”31 Waterfield finds Parmenides’s attention to physical questions “remarkable,” given that his “chief intention was utterly to repudiate the world of the senses.”32 This seems a poor reading. Rather, Parmenides wants to get out of himself, not to repudiate sense data but to repudiate mortal belief. As we have tried to demonstrate in the thought of Anaximander, Pythagoras, and Heraclitus, and now in Parmenides, reason is real, and human reason, when correct, is unilaterally determined by this reason that is common.

If so viewed, the questions to which Parmenides is responding are questions to which we can attempt to propose actual answers. For instance, the cosmological principle dictates that everywhere the universe is equal in intensity in the sense that it is homogeneous and isotropic at a large scale. However, this principle requires us to nuance our understandings of Parmenidean togetherness and fullness in order to properly understand the homogeneous but structured distribution of matter throughout the universe and the more abstract vacuum energy of the universe, which is signified by the cosmological constant. The universe remains single, but what this singleness looks like is transformed. We could pursue similar lines of inquiry in order to respond to the questions of aloneness, completeness, alikeness, coherence, and inviolability in Parmenides, and even to the question of the beginning and end of the universe—the possibility of which Parmenides denies due to lack of sufficient reason.33 Our generic and radical scientific posture does not, as such, deny philosophical questions, but rather restores philosophy to its proper footing. To do philosophy is to attempt to say what is.

If we continue in this mode to Anaxagoras of Clazomenae, we see that Eleatic thought is not some mystical school requiring dogmatic adherence but a posture inviting inquiry, challenge, and innovation. As with Heraclitus, “one ought to follow what is common” and not the word of the master handed down from his “private universe.”

Anaxagoras, unlike Parmenides, proposes a beginning, at which point “[a]ll things were together, with no limits set on either number or smallness; for there were in fact no limits set on smallness. And while everything was together the smallness of things meant that nothing was distinct.”34 He continues:

separation would have taken place not only here with us, but also elsewhere. Before there was separation, while all things were together, not even any colour was distinct, because the mixture of all things made that impossible—the mixture of the moist and the dry, the warm and the cold, the bright and the dark, with a great deal of earth among them, and an infinite number of seeds quite dissimilar to one another.35

Importantly, Anaxagoras’s beginning is separation, a “dispersal,” and not “creation.”36 Thus, in a Milesian move, Anaxagoras introduces phase or becoming into the singularity of being, a nuance of the Parmenidean singularity that does not violate the criteria defining that singularity. What is remains inviolable—separation does not come from outside, but is intrinsic to what is. Just as we might say of phase changes in water that it does not at any point pass into nothingness, but only through different structures or forms of organization, so too does being, in Anaxagoras, never depart from itself—simply, “everything grew as it was dispersed.”37

The separation, for Anaxagoras, is “prevailed over” by air and aither (that is, fire), and these are “separated off from the vault of the surrounding matter, which is limitless.”38 What we see here in this first phase of being is an infinite density, from which first air (a Milesian principle of change) and aither (fire, the Heraclitean concretion of the change intrinsic to the logos) are separated out, and from which in turn are separated all the other seeds or “homoeomeries.”39 Growth happens not out of nothingness, so preserving the Eleatic denial of what is not, but “as a result of things that already exist.”40 Thus, we see a kind of fusion of Anaximander and Parmenides in Anaxagoras wherein the boundless containing opposites separated off by motion is preserved as the singularity of infinite density containing all things.

To tie all of this together, Aëtius remarks that, for Anaxagoras, the “effective cause” of the separation is “mind,” thus preserving another term from the Milesian framework.41 Indeed, for Anaxagoras, mind is “independent,” “on its own and by itself.”42 Mind is “responsible for initiating the rotation,” and as Aristotle writes, the rotational separation of the homoeomeries is a “unique event,” the “source” or “single principle” of the phase transition.43 Certain statements on Anaxagoras’s part can lead to a spiritualization of this principle, but if we retain a rigorous generic and scientific posture toward him, as he does toward Parmenides, Anaxagoras’s mind presents itself as a fairly obvious continuation of the Presocratic realism with respect to reason that we have been tracing. Dualism itself is avoided by Anaxagoras’s rigorous Eleaticism—while “mind” is independent, the universe is “one,” and mind cannot, therefore, be transcendent. Though Anaxagoras’s mind is not as elegant as motion in Anaximander or limit in Pythagoras, it is at worst a repetition of Thales’s soul, and we have already seen how the Milesian positing of a dual at the origin of individuated being is in fact one of the most useful Presocratic intuitions available to us today.

What is more, this posture helps us refigure Anaxagoras’s homoeomeries from the macroscopic scale of “flesh, bone, and so on,” to a much more fundamental scale.44 If we do so, we find a remarkable counterpoint to the four classical elements of Empedocles (which Aristotle also notices), with Anaxagoras’s mixture providing us with a logical template for a universe that is single but full of structure. We cannot claim that Anaxagoras somehow intuited the standard model of particle physics, but if we were to try and explain the standard model to Anaxagoras and Empedocles, it seems likely that Anaxagoras would be the first to assent to the proposition.

But what of the void? Why begin with Badiou? This dialectic has been necessary for us to understand the stakes of the Judaeo-Christian supersession of the finite Greek One, but also to short circuit the reaction and exhaustion of the classicism-romanticism dialectic.

Badiou contends that our philosophical moment is one of reaction because the new is foreclosed. The Judaeo-Christian transcendence of finitude encounters the death of god and is caught fast. Either one accepts finitude, or one delays and dissipates it through the “imaginary and tragic infinite of translation.”45 Both paths are ultimately a “nihilism.”46 And yet, the death of god cannot be denied because the god of philosophy is no true god, only some “ultimate being.”47 The fusion that Badiou locates in the historical figure of Jesus itself appears foreclosed.

What, then, is to be done? Is there a possibility of a new access to the infinite? Badiou would argue that there is, and this argument finds its basis in modern mathematics. To get there, we must examine the four possible orientations to the infinite that Badiou identifies.

The first hypothesis is that the One is Infinite and Transcendent. This is the hypothesis of the New God, and so an anatheism, god after the death of god, a “creation,” a “new vision.”48 The second hypothesis is that the One is Infinite and Immanent, which Badiou identifies as the “modern vitalism, a new philosophy of life.” The third hypothesis is that the One is Finite but is yet “something divine,” a “Weak God” or a “modern paganism.” However, for Badiou, this perspective also ultimately is a “dispersive law,” effecting a “dissemination” of the One by the dissemination of the divine. The powerful intuition of the universe as single is lost. The fourth hypothesis, then, is that the One is Finite and Neutral—it is “indifferent”; it “does not work for our satisfaction.” The “clarification” of this final hypothesis is what leads Badiou to the void.49

To begin a philosophical inquiry, we begin in nothing, like Descartes, like Socrates. The alternative is to begin by the infinite, but this Badiou rightly identifies as the “religious way,” the way of revelation, which saps philosophical questions of their force because these questions find themselves already preempted by an answer. To do philosophy we begin in nothing, but to begin in nothing “we must affirm that nothingness exists.”50 This is the Badiousian bootstrap, his subtle shift from “knowledge” to “use.”51 We affirm the “existence of the fact that it can be said that I know nothing,” like Socrates and Descartes, and we affirm the existence of “nothing as an experience,” like Kierkegaard, Heidegger, and Sartre.52 These are the two modes of the “subjective possibility” of nothingness, but for Badiou, this possibility is predicated on a further possibility, the “possibility of a trace, of a pure ascription of nothingness,” a “pure beginning, a name for nothing, the smallest thing possible,” and “it will be for us the beginning.” This is how we begin with void, but also this is why we begin with void, the modern mathematical basis for the reinstantiation of the infinite.53

Without rehearsing Badiou’s argument already covered in “Pure Indetermination,” let us try to be precise here, following through on our dialectic. In Parmenides, being is, alone, complete, and inviolable. But his denial of the possibility of birth or perishing denies the existence of the real structures that tell a different story, indeed, which necessitate a different story. Anaxagoras sees this difficulty, and with resources drawn from Anaximander inverts Parmenides, allowing for what is to remain alone, complete, and inviolable, but now also as without limit. Anaxagoras thus opens Eleatic thought to the Milesian intuition that allows not only for being but the becoming of being, the equiprimordial dual which we interpreted with help from Gilbert Simondon and his theory of the preindividual (being) and its individuation or dephasing (becoming). Finally, Badiou’s positing of the “trace” of nothingness is the very framing that allows us to look back on the individuation, as individuals, and understand its basis in an inaccessible, unrecoverable prior phase, the pure indetermination and infinite density or saturation of preindividual being. Short circuiting classical and romantic thought in this way, we (re)discover a properly generic and radical scientific thought that stands in direct and groundless relation to the real. The framing, the trace, the individuation—a sort of cosmic microwave background for our philosophy—remains neutral, unjustifiable and unreasonable, but in this factiality of what is,54 we also recover the Parmenidean assertion that it is and it cannot not be in its truest sense as the pure affirmation of that which does not require and is utterly indifferent to the affirmation of its existence.


Notes

  1. Alain Badiou, “Infinity and Set Theory: How to Begin with the Void,” European Graduate School Video Lectures, YouTube, January 12, 2012 [2011], https://youtu.be/I1G_SI1-W-4

  2. Badiou, “How to Begin with the Void,” n.p. 

  3. Badiou, “How to Begin with the Void,” n.p. 

  4. Badiou, “How to Begin with the Void,” n.p. 

  5. Badiou, “A History of Finitude and Infinity: Romanticism and Modernity,” European Graduate School Video Lectures, December 17, 2011, https://youtu.be/DyZmXPLeT2Q

  6. Badiou, “A History of Finitude and Infinity: Romanticism and Modernity,” n.p. 

  7. Badiou, “A History of Finitude and Infinity: Romanticism and Modernity,” n.p. 

  8. Badiou, “A History of Finitude and Infinity: Romanticism and Modernity,” n.p. 

  9. Badiou, “How to Begin with the Void,” n.p. 

  10. Badiou, “How to Begin with the Void,” n.p. 

  11. Badiou, “How to Begin with the Void,” n.p. 

  12. Badiou, “How to Begin with the Void,” n.p. 

  13. Eudemus in Simplicius, Commentary on Aristotle’s Physics, in The First Philosophers: The Presocratics and the Sophists, trans. Robin Waterfield (Oxford, UK: Oxford World Classics, 2000), 56. 

  14. Parmenides, F1, in Waterfield, The First Philosophers, 57. 

  15. Parmenides, F2, in Waterfield, The First Philosophers, 57. 

  16. Alexander Galloway, “Superpositions,” Culture and Communication, October 11, 2014, http://cultureandcommunication.org/galloway/superpositions. 

  17. Parmenides, F1, in Waterfield, The First Philosophers, 57, and Waterfield, The First Philosophers, 55. In his “On the Black Universe,” François Laruelle writes: “Black is anterior to the absence of light, whether this absence be the shadows that extinguish it, whether it be it nothingness or its positive opposite. The black universe is not a negative light.” See Laruelle, “On the Black Universe: In the Human Foundations of Color” (1988), http://www.recessart.org/wp-content/uploads/Laruelle-Black-Universe1.pdf, 4. 

  18. Laruelle, “On the Black Universe,” 2, 3, 4. 

  19. Laruelle, “On the Black Universe,” 6. 

  20. Parmenides, F3, in Waterfield, The First Philosophers, 58. 

  21. Parmenides, F3, in Waterfield, The First Philosophers, 58. 

  22. Parmenides, F5, in Waterfield, The First Philosophers, 58. 

  23. Waterfield, The First Philosophers, 51. 

  24. Jean-Paul Sartre, Being and Nothingness: An Essay on Phenomenological Ontology (1943), trans. Hazel E. Barnes (London, UK: Routledge, 2003) and Riccardo Manzotti, The Spread Mind: Why Consciousness and the World Are One (New York, NY: OR Books, 2018). 

  25. Umberto Eco, Semiotics and the Philosophy of Language (Bloomington, IN: Indiana University Press, 1984), 45. 

  26. Parmenides, F8, in Waterfield, The First Philosophers, 60. 

  27. Parmenides, F8, in Waterfield, The First Philosophers, 59-60. Syntax adjusted for readability. 

  28. Parmenides, F8, in Waterfield, The First Philosophers, 59. 

  29. Martin Heidegger, Introduction to Metaphysics (1953), trans. Gregory Fried and Richard Polt (New Haven, CT: Yale Nota Bene, 2000), 1. 

  30. Laruelle, “On the Black Universe,” 2. 

  31. Quentin Meillassoux, After Finitude: An Essay on the Necessity of Contingency (2006), trans. Ray Brassier (London, UK: Continuum, 2009), 27. 

  32. Waterfield, The First Philosophers, 55. 

  33. Waterfield, The First Philosophers, 53, note 7. 

  34. Anaxagoras, F1, in Waterfield, The First Philosophers, 122. 

  35. Anaxagoras, F5, in Waterfield, The First Philosophers, 122-123. 

  36. Elias of Crete, Commentary on the Speeches of Gregory of Nazianzus, in Waterfield, The First Philosophers, 123. 

  37. Elias of Crete, Commentary on the Speeches of Gregory of Nazianzus, in Waterfield, The First Philosophers, 123. 

  38. Anaxagoras, F1 and F2, in Waterfield, The First Philosophers, 122. 

  39. Aëtius, Opinions, in Waterfield, The First Philosophers, 123, and Aristotle, On the Heavens, 302a28-b4, in Waterfield, The First Philosophers, 124. 

  40. Aëtius, Opinions, in Waterfield, The First Philosophers, 123. 

  41. Aëtius, Opinions, in Waterfield, The First Philosophers, 124. 

  42. Anaxagoras, F10, in Waterfield, The First Philosophers, 125. 

  43. Anaxagoras, F10, in Waterfield, The First Philosophers, 125; Aristotle, Physics, 187a23-b7, in Waterfield, The First Philosophers, 125; and Aristotle, Physics, 203a16-33, in Waterfield, The First Philosophers, 127. 

  44. Aristotle, On the Heavens, 302a28-b4, in Waterfield, The First Philosophers, 124. 

  45. Badiou, “How to Begin with the Void,” n.p. 

  46. Badiou, “How to Begin with the Void,” n.p. 

  47. I will not delve into theology here, but there has been much recent writing re-litigating this conception of god. See Yujin Nagasawa, Maximal God: A New Defense of Perfect Being Theism (Oxford, UK: Oxford University Press, 2017) and Jeff Speaks, The Greatest Possible Being (Oxford, UK: Oxford University Press, 2018). Jonathan Kvanvig has reviewed both for Notre Dame Philosophical Reviews. See Kvanvig, NDPR, May 1, 2018, https://ndpr.nd.edu/reviews/maximal-god-a-new-defense-of-perfect-being-theism/, and Kvanvig, NDPR, January 4, 2019, https://ndpr.nd.edu/reviews/the-greatest-possible-being/

  48. Richard Kearney, Anatheism: Returning to God After God (New York, NY: Columbia University Press, 2011), and Badiou, “How to Begin with the Void,” n.p. 

  49. Badiou, “How to Begin with the Void,” n.p. 

  50. Badiou, “How to Begin with the Void,” n.p. 

  51. Badiou, “How to Begin with the Void,” n.p. 

  52. Badiou, “How to Begin with the Void,” n.p. 

  53. Badiou, “How to Begin with the Void,” n.p. 

  54. Meillassoux, After Finitude, 79. Factiality is Meillassoux’s term for the “principle of unreason,” the principle that precedes or is beneath the principle of sufficient reason (which Parmenides invokes), which dictates that there is “no reason for anything to be or to remain the way it is.” See After Finitude, 60.