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Very well then; just this once let us give [the mind] a completely free rein, so that after a while, when it is time to tighten the reins, it may more readily submit to being curbed.

—René Descartes, Meditations on First Philosophy

Tho’ the instance is so particular and singular, that ’tis scarcely worth our observing, and does not merit that for it alone we should alter our general maxim.

—David Hume, A Treatise of Human Nature

1

ABSENT BLUE WAX: ON THE MINGLING OF METHODOLOGICAL EXCEPTIONS

If philosophy involves the creation of concepts, it is the systematic character of philosophical thought that enables it to function as such. The statement and defense of a philosophical “position” through argumentation does not amount to the articulation of a philosophy, because every philosophy must construct not only arguments but the very concepts through which those arguments may be understood. Such construction requires a systematic determination of concepts, wherein the meaning and the functions any concept acquires relies upon and supports the meaning and functions of the other concepts that, together, constitute the singular thought of a philosopher. The positions of philosophers like Descartes, or Hume, or Spinoza, or Kant, or Hegel are not thereby incommensurable with one another, but their commensurability must itself be constructed through an understanding of each one’s thought which grasps the systematicity of its determinations, thus relating concepts to one another (for example, “idea”) through the specificity they acquire in each system, rather than through the assumption of a common terrain of positions they commonly inhabit. Philosophical systems must be made to communicate not so much at the interface of the common words they deploy, but through a paradoxical subsumption of our own thinking into the interior of their conceptual relationships, from within which we must think toward the interiority of another system that we must also inhabit. Philosophical communication suggests a strange topology wherein the exteriority of thought—the possibility that we may think one philosopher with another—is encountered within the deepest recesses of systems that would seem to shelter the specificity of their concepts from one another, that would seem to require us to remain within the immanent regulation of their terms in order to think those terms at all.

Alfred North Whitehead defines speculative philosophy as “the endeavour to frame a coherent, logical, necessary system of general ideas in terms of which every element of our experience can be interpreted.” Here “coherence,” he stipulates, “means that the fundamental ideas, in terms of which the scheme is developed, presuppose each other so that in isolation they are meaningless.” Thus, “it is the ideal of speculative philosophy that its fundamental notions shall not seem capable of abstraction from one another.”¹ This ideal involves the invention of concepts in the manner just discussed. It does not mean that they will be definable in terms of one another; “it means that what is indefinable in one such notion cannot be abstracted from its relevance to the other notions.” It is the indetermination haunting all individual words that finds its support, in the case of philosophical concepts, through the inter-determination of concepts that can never be wholly “defined” because they must be thought in their relational coherence. The term “applicable,” in Whitehead’s definition of speculative philosophy, “means that some items of experience are thus interpretable” (through the speculative scheme) while “adequate” means that “there are not items incapable of such interpretation.” So the speculative scope of philosophy is potentially applicable to all items of experience. Whitehead thus makes the important comment that his ideal of speculative philosophy “has its rational side and its empirical side”:

The rational side is expressed by the terms “coherent” and “logical.” The empirical side is expressed by the terms “applicable” and “adequate.” But the two sides are bound together by clearing away an ambiguity which remains in the previous explanation of the term ‘adequate.’ The adequacy of the scheme over every item does not mean adequacy over such items as happen to have been considered. It means that the texture of observed experience, as illustrating the philosophic scheme, is such that all related experience must exhibit the same texture.²

Thus not only the rational coherence of a scheme of concepts or “fundamental ideas” is at issue in philosophical systematicity; the very interpretation of our experience is bound up, insofar as we enter into the thinking of a philosophical system, with the intra-systemic determination of its concepts. The comparison of philosophical systems is in this sense not only an intellectual historical or analytical task; it is also a lived practice. We think and interpret the world that we inhabit through the ideas we have at our disposal, and insofar as these are philosophical they are systematically articulated. Thus our experience of the world enters into philosophical systematicity, and when we think across systems we also attempt to carry out the improbable (impossible?) task of carrying our experience from one system into another. What is the world that we pass through, at the crux of concept and experience, when we do so? Where is the extra-systemic space of philosophical reflection, or of thought, in which we think the compossibility or communication of philosophical systems? Where, and what, is the world we recompose as we do so?

Let me step away from what seem to me the vertiginous difficulties of these questions in order to approach the absence of their terrain from another angle, through another question, closely related: What is a philosophical exception? Or better, how are we to think the mutual exteriority of philosophical exceptions? Or at least, what happens when we encounter philosophical exceptions in their mutual exteriority, and when we invite them to encounter one another? Those are the kinds of questions I want to pursue in what follows. For an exception, in philosophy, would be an exception to systematicity: it would exemplify the positive power of a system of thought to intuit its outside from within its own parameters while retaining the sense of that exception as outside its parameters. When a philosophical system encounters and traverses an exception it encounters its own outside within the movement of thought, without thereby either absorbing or collapsing into that outside. What I would call an exemplary exception inhabits an extra-systemic yet intra-philosophical space, a space exterior and open insofar as it is unbounded by an envelope of conceptual systematicity, yet nevertheless determined in its contours by the edges of those philosophical systems that generate exceptions—that produce exteriorities by constituting a field of internal coherence. Such an exception is exemplary insofar as it shows what the system must exclude in order to constitute its own rule, yet it also shows what a system must somehow include by gesturing toward what it cannot. This is not a properly deconstructive analysis, but more simply an effort to show the strange appearance of two exemplary exceptions and to situate them in the structure of their exteriority. It is within such a structured yet exterior space that I want to situate rationalist empiricism.

The exemplary exceptions I consider are classic instances: Hume’s missing shade of blue and Descartes’s wax experiment. By linking them in an unfamiliar manner, I will argue that to think these exemplary exceptions together is to think the pre-Kantian chiasmus of rationalism and empiricism—the manner in which the representative “rationalist” and “empiricist” systems of Descartes and Hume produce and traverse key counter-methodological instances that can be thought within the space of methodological exteriority they inhabit.

EXEMPLARY EXCEPTIONS

In the texts of Descartes and Hume, both the wax experiment and the missing shade of blue are explicitly identified as exemplary exceptions, and both are disavowed as deviations from the main lines of the philosophical programs pursued by these thinkers. “But I see what it is,” writes Descartes, before taking up a piece of wax, “my mind enjoys wandering off and will not yet submit to being restrained within the bounds of truth. Very well then, just this once let us give it a completely free rein, so that after a while, when it is time to tighten the reins, it may more readily submit to being curbed.”³ Hume poses the question of whether an observer, confronted with a color progression from which a single shade of blue is missing, would be able to produce an idea of this shade without having seen it. Despite his own avowal that this would violate his epistemology, Hume decides that “the instance is so particular and singular that ’tis scarcely worth our observing, and does not merit that for it alone we should alter our general maxim.”⁴ Descartes demonstrates the cognition of res extensa by “purely mental scrutiny,”⁵ but he does so by temporarily indulging his sensory perceptions “just this once.” As a speculative counterfactual to his copy theory of perceptions, a “particular and singular” instance, Hume grants the mind’s capacity to construct the idea of an unperceived shade of blue, and then he immediately dismisses this example of an idea without a corresponding impression as “scarcely worth our observing.”

Both these exemplary exceptions effectively suspend the epistemological principles of their authors: Descartes permits himself an empirical method that interrupts the order of reasons; Hume grants himself a rationalist thesis that contradicts his theory of mind. The somewhat tenuous validity of these suspensions is suggested by the rhetorical conduct of both thinkers, who flatly assume the assent of their readers to the major premises of their respective arguments. “But does the same wax remain?” asks Descartes. “It must be admitted that it does,” he replies on our behalf; “no one denies it, no one thinks otherwise.”⁶ “Now I ask,” writes Hume, “whether ’tis possible for him, from his own imagination, to supply this deficiency, and raise up to himself the idea of that particular shade, tho’ it had never been conveyed to him by his senses?” “I believe,” he answers, “there are few but will be of opinion that he can.”⁷ So what is it to which we assent, we might ask—binding together these exemplary exceptions—when we affirm the identity and coherence of Absent Blue Wax?

Hume’s famous text appears toward the end of Book 1 of the Treatise and is reprinted nine years later in the Enquiry without significant alteration:

Suppose a person to have enjoyed his sight for thirty years, and to have become perfectly well acquainted with colours of all kinds, excepting one particular shade of blue, for instance, which it never has been his fortune to meet with. Let all the different shades of that colour, except that single one, be plac’d before him, descending gradually from the deepest to the lightest; ’tis plain, that he will perceive a blank, where that shade is wanting, and will be sensible, that there is a greater distance in that place betwixt the contiguous colours, than in any other. Now I ask, whether ’tis possible for him, from his own imagination, to supply this deficiency, and raise up to himself the idea of that particular shade, tho’ it had never been conveyed to him by his senses? I believe there are few but will be of opinion that he can; and this may serve as a proof, that the simple ideas are not always derived from the correspondent impressions; tho’ the instance is so particular and singular, that ’tis scarce worth our observing, and does not merit that for it alone we should alter our general maxim.⁸

The secondary literature on this missing shade of blue—let’s call it “Absent Blue”—is dominated in equal parts by efforts at damage control (on the part of orthodox Humeans) and by hindsight (on the part of doctrinaire Kantians).⁹ The problem for those devoted to sustaining the coherence of Hume’s copy theory of perceptions is that both the Treatise and the Enquiry unambiguously posit our ability to generate an idea of Absent Blue as a “contradictory phenomenon” demonstrative of the position “that it is not absolutely impossible for ideas to go before their correspondent impressions.”¹⁰ Why then, the scholars wonder, would Hume include this “proof” in his text, given that he asserts precisely the opposite immediately before and after? Is it an elaborate instance of Humean irony? A perverse effort to achieve notoriety through the generation of a conceptual scandal? How can it be rendered consistent with the so-called copy theory of perceptions? There can be no recourse to the theory of complex ideas here, since Hume is curiously adamant that not only different colors, but different shades of the same color “each produce a distinct idea, independent of the rest.”¹¹ Within the framework of the Treatise, then, Absent Blue is well and truly a simple idea, as irreducible to a combination of other simple ideas as it is to any impression. According to Hume himself, there is thus no way for his copy theory of perception to accommodate the putative power of the mind to “raise up” such an idea, other than to accord it the status of an “exception.”

Hence the satisfaction of the Kantian intellectual historian, for whom this exemplary exception encapsulates the difficulties encountered by empiricism pending a theory of synthetic a priori cognition. And indeed, though it is obviously not a mathematical judgment, the cognition of Absent Blue at least approximates the structure of Kant’s 7 + 5 = 12. We are given three terms—two contiguous shades and the perception of a blank between them—and we have to produce a new term on the basis of these relations. We can in no way arrive at Absent Blue by merely combining or analyzing the terms with which we are presented, just as “the concept of twelve is by no means thought merely by my thinking of that unification of seven and five.”¹² Rather, we have to go beyond the data we are granted in order to arrive at a real amplification irreducible to either analysis or experience—presumably through intuition. Kant credits Hume as the philosopher who came closest to the problem of synthetic a priori cognition, though he faults Hume for incorrectly believing he had proven the impossibility of such cognition through his analysis of causality. But perhaps the case of Absent Blue does affirm the possibility of such cognition—though, again, it is a possibility that Hume can affirm only as an exception and which he thus remains unable to theorize. For the Kantian, the anomalous status of Absent Blue in Hume’s system betokens the necessity of a transcendental idealism that would obviate the illusory opposition of rationalism and empiricism of which such an anomaly is symptomatic.

For anyone who seeks to obviate that opposition in a manner irreducible to transcendental critique, however, Hume’s exemplary exception opens a different opportunity for thought: the possibility of constructing a rapprochement between rationalism and empiricism without recourse to a transcendental subject. How is it possible to think—with Hume—the capacity of the mind to raise up such an idea while still—with Hume—thinking the genesis of the self as a bundle of perceptions (rather than “I think” of transcendental apperception)? This is not to ask how Absent Blue is consistent with Hume’s philosophical system. Rather, it is to ask how we can think such a capacity, such an idea, not as the rule of a subject or a system, but quite precisely as an exception.

Before returning to this question, let me take up our other exemplary exception: Descartes’s wax experiment. In the wax experiment, Descartes breaks with the order of reasons guiding his Meditations, as Martial Gueroult argues, in order to “deliver a verification” of the priority of the intellect by provisionally situating it “in the opponent’s point of view.”¹³ For Gueroult, the wax experiment “constitutes an anticipation of the general verification that the success of physics will bring to the entire set of metaphysical conclusions” arrived at in the Meditations.14 These conclusions are buttressed by the methodological devia tion of the wax experiment, since it is here that “common sense is … beaten on its own ground.”¹⁵ Via the anomalous empiricism of the wax experiment, “we rediscover here, by another means”—through indirection—”the conclusion obtained directly by following the genetic order of reasons.”¹⁶

So as to refute empiricism, we enter into it by way of immanent critique: “Let us take, for example, this piece of wax.”¹⁷ And as soon as we attempt to return to the order of reasons—as soon as we reenter rationalism by way of empiricism—we do so through an experience anticipating (in miniature) the default of synthetic imagination theorized by Kant as the sublime. “Let us concentrate,” writes Descartes,

take away everything which does not belong to the wax, and see what is left: merely something extended, flexible and changeable. But what is meant here by “flexible” and “changeable”? Is it what I picture in my imagination: that this piece of wax is capable of changing from a round shape to a square shape, or from a square shape to a triangular shape? Not at all; for I can grasp that the wax is capable of countless changes of this kind, yet I am unable to run through this immeasurable number of changes in my imagination, from which it follows that it is not the faculty of imagination that gives me my grasp of the wax as flexible and changeable. And what is meant by “extended”? Is the extension of the wax also unknown? For it increases if the wax melts, increases again if it boils, and is greater still if the heat is increased. I would not be making a correct judgment about the nature of wax unless I believed it capable of being extended in many more different ways than I will ever encompass in my imagination. I must therefore admit that the nature of this piece of wax is in no way revealed by my imagination, but is perceived by the mind alone.¹⁸

Following a subtractive method, itself following from an empirical demonstration, we arrive at the insufficiency of the imagination to grasp “an immeasurable number of changes” in their temporal unfolding, and we thereby accede to the power of the intellect to determine the supersensible identity of the wax, its nature, as a real idea. “That is sublime,” reads the decisive sentence of Kant’s analysis in the Third Critique, “which even to be able to think of demonstrates a faculty of the mind that surpasses every measure of the senses.”¹⁹

Already, then, just beneath the apparently placid surface of Descartes’s Second Meditation and his domestic piece of wax, we are implicitly embroiled in “the terrible struggle between imagination and reason,” the “tempest in the depths of a chasm opened up in the subject” that Deleuze locates in Kant’s Analytic of the Sublime.²⁰ Already we have the “Cogito for a dissolved self” evoked by Deleuze in Difference and Repetition: an “I” fractured by the form of time as the imagination, spurred by a sensible experience of quotidian alteration, filters through an immeasurable number of changes before the mind recovers itself in the stability of the intellect.²¹ “Time,” writes Deleuze, “signifies a fault or a fracture in the I and a passivity in the self, and the correlation between the passive self and the fractured I constitutes the discovery of the transcendental.”²²

Deleuze attributes this discovery to Kant, stating that Descartes could determine the thinking subject “only by expelling time, by reducing the Cogito to an instant and entrusting time to the operation of a continuous creation carried out by God.”²³ Kant, on the other hand, established through his critique of the Cartesian cogito that “my undetermined existence can be determined only within time as the existence of a phenomenon, of a passive, receptive, phenomenal subject appearing within time.”24 But in the Cartesian wax experiment we already encounter such a subject. Via the rationalist empiricism of Descartes’s exemplary exception, we encounter a retroactive genesis of the cogito irreducible to its initial formulation. We attain clear and distinct knowledge of our essence as res cogitans not through the punctual assertion of an act of thinking, but through a temporal experience of the imagination’s insufficiency and a concomitant re-emergence of the priority of the intellect. “I see that without any effort I have now finally got back to where I wanted,” writes Descartes as the meditation concludes.²⁵ But in the interim, we have quietly plunged into the “chasm opened up in the subject” that Kant will explore some one hundred and forty years after Descartes, and that Deleuze will excavate nearly two hundred years after Kant.

THE OUTSIDE OF PHENOMENOLOGY

Now, why does it matter that this retroactive, temporal genesis of the cogito occurs through an exemplary exception, during the sequence of his Meditations in which Descartes veers from the order of reasons through an empiricist deviation? It matters because the passive genesis of the cogito that unfolds through the wax experiment transpires as an encounter for which nothing in the order of reasons can account. This is what transcendental phenomenology is constitutively unable to grasp, unable to accommodate within its own Cartesian meditations. If the wax experiment is to perform an immanent critique of empiricism, it must really be empirical. And since it must be properly empirical—a true deviation from the order of reasons—it cannot operate within the purview of the phenomenological epoché. The phenomenological bracketing of experience is precisely what is itself bracketed by the “free rein” of Descartes’s exemplary exception. It is the fundamental incapacity of phenomenology to think the encounter that is betrayed by Michel Henry’s treatment of the wax experiment in his nevertheless extraordinary essay on Descartes, “Videre Videor”:

The entire analysis of the piece of wax or the people passing in the street with their hats circumscribes, characterizes, and elucidates precisely this “knowledge of the body” (as having its foundation in the ek-stasis of seeing as pure seeing, “inspection of the spirit,” the essence of videre): such an analysis, as we know, is precisely not that of the body, of this or that body, of extension, but that of knowledge of the body, that is, precisely of the understanding.²⁶

“As we know,” Henry assures us. According to an uneasy rhetoric of presumed assent, we have already agreed upon a methodological doxa that will guide our reading the text: Despite Descartes’s empirical procedure, the wax experiment does not really involve analysis of a body, but only inspection of the spirit. By the lights of Henry’s rhetoric, we should already have agreed that the phenomeno-logical epoché will secure us against a supposedly naive approach to the analysis of the piece of wax as an empirical experiment.

Certainly, as Henry argues, Descartes emphasizes the reduction of perception to thought, insofar as we can only truly affirm that we seem to perceive: “I certainly seem to see [videre videor], to hear, and to be warmed. This cannot be false; what is called ‘having a sensory perception’ is strictly just this, and in this restricted sense of the term it is simply thinking.”²⁷ But to follow Henry we have to ignore the equally clear establishment of the wax experiment as an exception to the circumscription of experience by this “restricted sense.” We have to ignore Descartes’s admission that the mind will “not yet submit to being restrained within the bounds of truth.” We have to forget that he thus posits the wax experiment as a temporary exception, “just this once,” to those limits, and that he explicitly declares a suspension of the epoché during which the mind will be given “a completely free rein,” so that “after a while, when it is time to tighten the reins, it may more readily submit to being curbed.” Regardless of such details, for Henry “the Second Meditation’s problematic develops entirely in an attitude of reduction.”²⁸ Never mind that Descartes emphasizes his consideration “not of bodies in general, but of one body in particular.” Never mind that he takes as his example “this wax.” As we know, according to Henry, the wax experiment is “precisely” not an analysis of “this or that body.”²⁹ Never mind that Descartes concedes, just this once, to “consider the things which people commonly think they understand most distinctly of all”; “that is, the bodies which we touch and see.” According to Henry, it is only “knowledge of the body”³⁰ that is analyzed, and thus only the understanding itself. Henry obviates the structure of the wax experiment, its unfolding in time as an alternation between empirical observations and epistemological statements, and he overlooks the particular order of reasons interior to this deviation from the order of reasons: First, we are offered a series of empirical observations (concerning the taste, scent, color, shape, size, consistency, and temperature of a particular body). These empirical observations are followed by a provisional summation of sensory data as possible grounds for distinct knowledge of a body (“In short, it has everything which appears necessary to enable a body to be known as distinctly as possible”). During this summation we descend back into empirical observation (“But even as I speak, I put the wax by the fire, and look …”), and then we question the grounds of our understanding (“So what was it in the wax that I understood with such distinctness?”). It is through the complex temporal unfolding of this alternating structure that we arrive at a subtraction of the empirical given (“Perhaps the answer lies in the thought which now comes to my mind; namely, the wax was not after all the sweetness of the honey”). And finally, it is after we have traversed this alternating structure, and following this process of subtraction, that we turn entirely inward toward our “knowledge of the body,”³¹ comparing the relative capacity of the imagination and the intellect to grasp the essence of extension, and thus understanding that we perceive the wax “by the mind alone.” But, according to Henry, we should ignore the dense structural articulation of the inductive process by which we arrive at such knowledge, working back and forth between empirical observations of a body and epistemological questions concerning those observations. “As we know,” after all, the Second Meditation “completely ignores the body and its supposed action on the soul.”³²

For Henry, in short, there is no exception. And for phenomenology there cannot be. So long as we abide within Henry’s “as we know”—so long as we do not depart the province of the phenomenological—we cannot follow the complex process through which the Meditations reenter rationalism by way of empiricism. Because phenomenology cannot sanction the encounter of thought and sensation, always-already folding them together, Henry has to fold the imagination and the understanding into a single unremitting “phenomenality” which, in turn, gives way to its essence as primordial auto-affectivity.³³ For Henry, nothing happens via the wax experiment, because (“as we know”) “this ‘knowledge of the body’ … originally and untiringly refers back to ‘knowledge of the soul,’ whose more original essence was exhibited in the cogito.”³⁴ It matters not at all that we are thus referred back to the cogito by way of an encounter with a particular body, and that it is through this encounter that a retroactive temporal genesis of the cogito unfolds. What phenomenology cannot encounter is the encounter itself, which always takes place outside its primary methodological imperative: not in the deepest recesses of the phenomenological epoché, but within its exterior.

RATIONALIST VS. TRANSCENDENTAL EMPIRICISM

“Something in the world forces us to think,” writes Deleuze in his chapter on “The Image of Thought.”³⁵ Descartes: “Let us take, for example, this piece of wax.” Hume: “’tis plain, that he will perceive a blank, where that shade is wanting.” Something, wax or blank, forces us to think, and according to the theory of transcendental empiricism, this “something in the world” is “an object not of recognition but of a fundamental encounter.”³⁶ Contra phenomenology, Deleuze offers an empiricism insofar as the encounter transpires through an experience of the sensible. But it is a transcendental empiricism insofar as what is encountered by way of the sensible is itself insensible: “not a sensible being but the being of the sensible.”³⁷ Spurred by the sensible mutability of a particular piece of wax, the imagination tests itself against the insensible essence of physical bodies and thereby gives way to the intellect. Activated by a sensible blank between proximate shades, the imagination raises up to the mind the insensible “idea” of Absent Blue.

But if the theory of the encounter we find in Difference and Repetition (unlike the theory of primordial auto-affection offered by Henry) enables us to grasp what happens in the case of our two exemplary exceptions, Deleuze himself seems to have failed to encounter their significance as exceptions. Hume’s missing shade of blue goes unmentioned in Empiricism and Subjectivity, wherein the metaphysical concept of ideas as virtual multiplicities is not yet fully operative in Deleuze’s philosophical itinerary.³⁸ In Difference and Repetition, just as Descartes’s expulsion of time from the constitution of the subject marks the subsumption of his philosophy by the figure of identity, his presumption of the identity of the wax over the course of his experiment (“It is of course the same wax which I see, which I touch, which I picture in my imagination, in short the same wax which I thought it to be from the start”)³⁹ marks the domination of his thought by the model of recognition. Just as Deleuze does not yet (in 1953) locate a transcendental empiricism in the philosophy of Hume, he does not register, in his discussion of Descartes’s Second Meditation, the manner in which the empiricist deviation of the wax experiment gives way to a retroactive temporal genesis of the cogito. Rewriting the First Critique in the wake of Nietzsche, Bergson, and Heidegger, Difference and Repetition recasts Kant’s transcendental idealism as transcendental empiricism. But what Deleuze misses—insofar as he misses Absent Blue Wax—is the opportunity to grasp the pre-Kantian exception to both rationalism and empiricism, a strange exteriority of these traditions that is not yet the exteriority of the transcendental subject. Absent Blue Wax, encountered through the chiasmus of our exemplary exceptions, incarnates the disavowed specters of an empiricist Descartes and a rationalist Hume within a single insensible idea. Unthinkable within phenomenology, and prior to the program of transcendental idealism, Absent Blue Wax delivers the outside of rationalism to the outside of empiricism and lets them mingle in their mutual exteriority. This exteriority is that of an encounter which never took place, and which has to be constructed. And the exteriority of this encounter to rationalism, to empiricism, and to transcendental critique is also the exteriority of philosophical systematicity itself.

We can thus answer, on our own terms, the scholar’s question regarding the mystery of Hume’s motives. Why does Hume include the missing shade of blue as a “contradictory phenomenon” within his theory of perceptions? He does so because the idea of Absent Blue indexes a profound intuition of the future of philosophy: not only a future that passes through Kant, but one that circles back behind him—through the work of such thinkers as Deleuze and Meillassoux—to the pages of Hume’s Treatise itself. And why does Descartes permit the mind “free rein” outside the ambit of his impeccably ordered method? He does so because the wax experiment expresses the radical capacity of the mind—in excess of Cartesian doctrine—to encounter the temporal genesis of the cogito even as it grasps the idea of substance. By including the outside of their philosophical systems within those systems—and thereby rigorously determining the conditions under which that outside is an outside—both Descartes and Hume unknowingly accede to the explosive vocation of philosophy, which perpetually redeploys the power of thought to think beyond its own conditions.

But what difference does it make to explore the possibility of a rationalist empiricism through these exemplary exceptions, and thus on the outside of both rationalism and empiricism, rather than through a direct invocation of Deleuze’s transcendental empiricism? It enables us, for one thing, to explicate certain problems within Deleuze’s system while remaining outside of it. Take, for example, the theme of “overturning Platonism.” How is it possible for an idea to be a simulacrum? Absent Blue provides us with a precise answer. For Plato, the idea is the model, while the impression is the copy; for Hume, of course, the impression is the model, while the idea is the copy. But, considered at once within and outside of Hume’s system, Absent Blue is an idea without a corresponding impression, and thus a copy without a model. In other words it is at once a simulacrum and a pure idea. If Hume thus anticipates an “overturning” of Platonism before Nietzsche or Deleuze, it is not through the copy principle of his theory of perceptions, but rather through an exemplary exception to that principle. We can thus think the possibility of overturning Platonism not as a philosophical program but precisely as the possibility of an exception to philosophical systematicity, which would be impossible from within the rule of any philosophical system. This would involve not an inversion of rationalism by empiricism, but rather a real transformation of both empiricism and rationalism introduced by the torque of their exceptional encounter.

But more important, rationalist empiricism differs from Deleuze’s transcendental empiricism insofar as it is not primarily concerned with the conditions of experience, whether understood as conditions of possible experience (Kant) or conditions of real experience (Deleuze). It is the interruption of experience by reason, and the extrapolation of reason from and yet beyond experience, that is at issue in the rationalist methodological pole, while it is the experience of reason and also the exposure, by empirical science, of what cannot be experienced that is at issue in our empiricism. Deleuze gives us a theory of the encounter—of what breaks with the synthesis of past and future—and this crucially informs our own thinking. But our account of rationalist empiricism is not oriented toward the construction of conditions as ground, but rather toward the groundless manner in which reason and experience propel one another without achieving synthesis. Deleuze’s theory of “asymmetrical synthesis” produces a concept of disparity as sufficient reason, and thus as the Urground that is deeper [profond] than the ground: disparity is the groundless ground breaking with the figure/ground distinction, and it constitutes a sufficient reason that rejects the principle of non-contradiction. We are interested, on the contrary, in pursuing an account of the relation between reason and experience that sustains the principle of non-contradiction while rejecting the principle of sufficient reason. Thus, we do not seek an account of the Urground that would be a condition of real experience, but rather the unconditional consequences of non-contradiction as that which overthrows, rather than sustains, the principle of sufficient reason. One works outside the transcendental by removing groundlessness even as condition and pursuing instead a thinking of how any rule of experience or reason, any condition, must be thought according to a displacement of sufficient reason itself. This coordination of the derivation of the principle of non-contradiction from groundlessness, and the displacement of the principle of sufficient reason by the principle of non-contradiction, is the burden of Quentin Meillassoux’s philosophical enterprise, addressed in detail in Chapters 2 and 4. For the moment we can say that Deleuze’s transcendental empiricism draws the outside of rationalism and empiricism back into the transcendental, as an account of conditions. Rationalist empiricism is concerned with sustaining the relational disjunction of rationalism and empiricism without drawing them back into the purview of the transcendental, without a sufficient reason that conditions both their disjunction and their relation.

THE PARADOX OF MANIFESTATION

Perhaps we could situate Absent Blue Wax within the “glacial world” evoked by Meillassoux in After Finitude, a world accessed by empirical science, yet refractory to any phenomenal experience, and thus explored through the rational formalization of technically registered indices.⁴⁰ For Meillassoux, the true Copernican revolution proper to the relation between modern science and modern philosophy resides in the power of mathematical formalization to determine the object as indifferent to givenness: the power to think what there would be if there were no thought. And “it is this capacity,” Meillassoux argues, “whereby mathematized science is able to deploy a world that is separable from man … that Descartes theorized in all its power.”⁴¹ Descartes’s wax experiment gives way, through the empirical, to that which can only be thought. What Meillassoux calls “the paradox of manifestation”⁴² is this operation, through which the given makes manifest that which is refractory to givenness, that which could never have been and has never been given to manifestation, though its very subtraction from manifestation has been made manifest. Thus the paradox of manifestation is also the recessed paradox of Descartes’s Second Meditation: to know a thing by the mind alone is also to know that its existence does not depend upon the mind. We can say that the wax experiment makes an exception, that it deviates from the order of reasons, so as to explore this paradox of manifestation, moving through empirical knowledge toward a pure res extensa that is thought by the mind as independent substance. The empiricist deviation within Descartes’s rationalist project matters because it registers the paradoxical nature of manifestation itself. In the wax experiment, givenness gives way to a world without givenness, to the “glacial world” that Meillassoux aligns with “the world of Cartesian extension”:

a world wherein bodies as well as their movements can be described independently of their sensible qualities, such as flavor, smell, heat, etc…. a world that acquires the independence of substance, a world that we can henceforth conceive as indifferent to everything in it that corresponds to the concrete, organic connection that we forge with it—it is this glacial world that is revealed to the moderns, a world in which there is no longer any up or down, center or periphery, nor anything else that might make of it a world designed for humans. For the first time, the world manifests itself as capable of subsisting without any of those aspects that constitute its concreteness for us.⁴³

The glacial world is a world that makes manifest its own subtraction from manifestation, but not from rational determination. This is the world into which Descartes’s wax leads us, but do we also enter into it through Hume’s Absent Blue?

Here we encounter the paradoxical idea of a secondary quality, the production, by the imagination, of an idea of an insensible shade, one that is not encountered through the senses and thus has to be thought. Perhaps the missing shade we call Absent Blue has a place in the world of Cartesian extension purely as the trace of our capacity to think it, as the trace of its subtraction from the given. Neither exactly a primary quality nor a secondary quality, but an exception—an insensible shade born of an encounter with the lacuna of the sensible—Absent Blue manifests the power of the mind to think the idea of an impression without deriving it from experience. Thus, if Absent Blue participates in the world of Cartesian extension, into which the wax experiment leads us, it does so only as the exposure of primary qualities, those of independent substance, to the hue of thought, to the shade of their subtraction from the given.

Absent Blue Wax, this compound exception mingling rationalism and empiricism within the space of its methodological exteriority, discovered disjunctively by Descartes and by Hume, is the curiously tinted substance of the glacial world, encountered at the crux of the paradox of manifestation.