In contemporary debates, the realist position (here speculative realism/materialism is of particular interest) not only implies a belief in what is real, but also allows us to ascertain a certain possibility of accessing reality, thus bringing about the question of correlation as it pertains to determination and subordination. This article borrows from Cornelius Castoriadis’ arguments regarding Georg Cantor’s set theory to criticize the primacy of mathematics in Quentin Meillassoux’s thinking. At the same time, it argues that there are three regimes of correlation. The first two senses of correlation imply determining subordination, whereas the third one invokes a new understanding of correlation: being is always related to the subject, but is never determined or subordinated by it. In this light, Castoriadis’s notion of radical imagination aims to maintain an emancipatory meaning – the call for an anamorphic procedure of change in perspective, to the gestures of constant re-determination, without any pretense to totality.
1 Introduction: realism and its questions
What does it mean to be a realist? In the contemporary debate, it is hardly possible not to invoke speculation as the approach for determining privileged relations to reality. The realist position not only implies a belief in what is real, but also allows us to ascertain a specific means of accessing reality. Thus, realism is positioned in the perspective of a long tradition, which could be formulated by two questions – “is there reality?” (ontology); “how can reality be accessed?” (epistemology).
As is well known, Quentin Meillassoux claims that this accessibility of reality is primarily associated with thought – more specifically, with the perspective of speculative thought, which enables the overcoming of correlative relations. In other words, speculative thought liberates reality from the necessity of being related to humans. He also describes his speculative materialism as the “pretension of thought to arrive at an absolute: that is, an eternal truth independent, on this account, of the contingencies (psychological, historical, linguistic) of our relationship to the world.” Therefore, it has become common for the movements of new realism and materialism, at least for the most part, to rely on speculative procedures that insist on the possibility of liberation from the human through thought, in order that reality can be disclosed independently from anthropocentric view.
However, in light of these polemics, Graham Harman has pointed out that realism is generally understood as the fusion of the following two claims: (a) that a world exists outside the mind, and (b) that we can gain knowledge of that world. Realism does not necessarily entail both claims at once, while the “type a” position does not automatically imply a conviction of the truth of “type b.” In virtue of such an alternative, even a free and critical relationship with forms of knowledge can express a certain realist position, regardless of whether such relations lay claim to the so-called zone of reality. On the other hand, even when questioning the claims of various methodologies, it is possible to remain a “type a” realist without thereby accepting the claims of the “type b” position. Moreover, “type b” realism permits one to raise the question of the modal characteristics of the various forms in which the liaisons with reality are established.
This makes it possible to argue for multiple types of relations with the real, including relations that are inexhaustible by the representation/correspondence framework that supposes a conformity between forms of knowledge and forms of reality. In this context, for instance, Harman speaks of “infra-realism,” in which the real is always a surplus beyond the possible knowledge of it, and traces this position to no less a figure than Socrates.
Interestingly enough, the problem of the status of mathematical determinations acquires the utmost importance in this regard. For instance, Meillassoux famously proposes to “reactivate the Cartesian thesis in contemporary terms,” by inviting us to return to the distinction of secondary and primary qualities – i.e., to those qualities of an object “that can be formulated in mathematical terms;” more precisely, they would allow us to think the thing-in-itself. Mathematics, as the most rigorous of all theories, is framed as a tool for activating speculative procedures of thought creating a privileged access to reality free of human contingencies.
This primacy of mathematics in Meillassoux’s work has frequently been questioned and criticized in various connections. Meillassoux usually dismisses the accusation that calculation is always correlated with human thought by referring to its formal characteristics. In fact, Meillassoux tries to avoid the ontologization of mathematics by saying: “My thesis on mathematics is a thesis on the scope of formal languages, not a thesis on Being.” And even though Meillassoux forswears any Pythagorean view on being – meaning that he does not ascribe any ontological status to numbers and theorems – he never takes seriously enough the complications of the role of mathematics in epistemic (scientific) processes. For instance, in proposing his famous idea of ancestrality (i.e., a state of reality which preceded the emergence of humans or any other life form), Meillassoux also claims as follows:
[A]n ancestral statement only has sense if its literal sense is also its ultimate sense. If one divides the sense of the statement, if one invents for it a deeper sense conforming to the correlation but contrary to its realist sense, then far from deepening its sense, one has simply cancelled it. This is what we shall express in terms of the ancestral statement’s irremediable realism: either this statement has a realist sense, and only a realist sense, or it has no sense at all.
The belief in a “literal sense” that leads to irremediable realism obviously implies a mathematical presupposition. However, unless taken critically, this demand for immediacy sounds like a version of naive epistemology. In this regard, it might be worth recalling a postphenomenological argument that questions the existence of purely empirical science. According to Don Ihde, incorporated technology affects the specificity of our perception. By being subjected to the trajectories that are predetermined by the functionality of an apparatus, the scientist’s body changes its experiential schemas. Thus, even mathematizable data of archifossils are determined through what Idhe calls the schema of an aberrant identity “(I-technology) – world.” Obviously, this also implies that a pure state of mathematics is impossible, since it is always found in sets of relations, and is subjected to the transformation brought about by the process of translation and mediation.
This insufficiently critical focus on mathematics was also criticized by Graham Harman who concludes that, despite his rejection of the charges of Pythagorization (or indeed because of it) Meillassoux remains within the perspective of the aforementioned “type b” realism, which focuses on the epistemological procedure of a “correct access” to reality.
We have seen that what Meillassoux means by “realism” is not primarily the existence of the real, but the mathematical knowability of it. Indeed, he much prefers the word “materialism” to realism, by which he simply means that there must be a Cartesian dichotomy between things that think (humans) and things that do not (dead matter). What is real in the things, though it is always fused with “dead matter,” is that which is cut to the measure of knowledge. There is no problem translating the real into the known; this can be done without distortion or energy loss of any sort. This is why I claim that Meillassoux’s supposed realism is not ontological, but merely epistemic. He defeats finitude and relativism only at the price of stumbling into idealism: which is the genuine enemy of the real even more than relativism.
What Harman calls “distortion or energy loss of any sort” encapsulates the problem in a nutshell. For continental philosophy the autonomy of mathematics represents a significant problem that can be formulated as follows: how can we do away with all the correlations that are brought about by even the most formal language possible? Mathematics remains a product of the human cultural imaginary and is always, at least in part, determined by the instituting choices of its founders. Here we might recall the duo of Husserl and Derrida in the latter’s Origin of Geometry, in which he discusses the origins of the status of ideal mathematical objects. In order to acquire an ideal status, geometry had to be verbalized: “the ideal Objectivity of geometry is first presented as a characteristic common to all forms of language and culture.” Mathematics, then, cannot be envisaged by using a naive Cartesian epistemology – by contemplating the melting wax and stripping it of its secondary qualities. Notwithstanding its formal character, the ideal ontology exists as a sphere of primary evidence and is accessible only to someone who speaks and writes – i.e., to someone whose existence is bound up with strong ties of correlationism.
This argument can also be paralleled with some considerations drawn from Cornelius Castoriadis, who critically discusses Georg Cantor’s set theory (which also has a great deal of influence on Meillasoux’s philosophy).
There is no mathematics without signs, and to use signs one must be able to posit that two different ‘realizations’ of x are absolutely the same x. Certainly, from the standpoint of formalized mathematics it will be said that this absolute identicalness of self to self-imposed upon what is ‘materially’ different is simply an equivalence modulo every relation that could be defined. Here we have the definition of identity in mathematics; it is the same as the one already given by Leibniz, when he said, eadem sunt quae substitui possunt salva veritate, ‘they are identical, those things that can be substituted the ones for the others while saving the truth’ – while saving all truths. But it is clear that one cannot substitute one thing for another while saving all truths; that would happen only if it were a matter of absolutely indiscernible things – in which case there could be no question of substitution.
In fact, even though he refuses a metaphysical theology, Meillassoux does not try to escape the logic of identity formulated in the principle of noncontradiction. Even though identities are not recognized as unchangeable substances of subjects, and do not entail any metaphysical essences, the primacy of contingency nonetheless requires certain identities to exist as its pillars of support. In this manner, according to Meillassoux, the ontological sense of the principle of noncontradiction expresses the necessity of contingency: “[T]he principle of unreason teaches us that it is because the principle of reason is absolutely false that the principle of non-contradiction is absolutely true.”
By rejecting any determination of reality that conditions it externally (i.e., sufficient reason, law, or rule) Meillassoux nevertheless leaves the inner determinacy of a thing as valid. It is absolutely necessary that something, by way of turning into something else, would already be something. In fact, the ontological meaning of the principle of noncontradiction grounds the omnipotence of hyperchaos as well as implicitly applying a hypercategory of determination. On this account, Meillassoux follows Leibnizian formula: the primacy of identity is registered through substitutability in relation to truth.
2 Subordination and determination
What does it mean – to be in relation to truth? Or, as reformulated by Castoriadis, to be “saving all truths”? It seems that this remark on the multiplicity of truth brings us above all to the determining character of relations. Truth can become a conditioning factor only insofar it establishes a grid of identification, thus providing the criteria of separation between true and false, identity and its contradiction. There is no identity without an externally instituted agency of truth that provides a basis for constituting the boundaries of identity. The diversity of truths, most certainly, endangers the stability of identities. Hence, the ironic remark by Castoriadis regarding the vicious circle of the situation: it is impossible to substitute one thing for another while saving all truths, unless we are dealing with “absolutely indiscernible things.”
Paradoxically, only absolute indeterminacy is the background for absolute identity, whereas every determination is, in fact, relational. It is the latter character of the dialectic between truth and identity that enabled Michel Foucault to propose the idea of a “regime of truth” which functions as a system of power relations subordinating the very possibility of true and false statements. According to Foucault, truth is produced and sanctioned by the mechanisms of power, which – in keeping with Leibniz’s idea – provides the means of the assignment of identities.
However, even without falling into the problem of power relations, we can return to the initial question regarding reality: what does it mean to escape correlation? Shouldn’t any truth-seeking realism start from the status of determination in its philosophy? According to Castoriadis, determinacy functioned in the history of philosophy as the essential and mostly implicit requirement of thinking based upon logic. It can also be understood as a hypercategory that grounds all other rules of logic. By reinforcing the foundational criteria of the logicality of logic itself, this operator of ensemblistic–identitarian logic is constantly maintaining its highest and implicit requirement, whose origins lie in the Greek attentiveness to the notion of the limit or peras. Only limited or determined things could have been spoken about, thought and treated as existing.
3 Set theory and Russell’s Paradox
As was already mentioned, a shared point of departure links the thought of Meillassoux and Castoriadis – namely, Cantor’s set theory. In one of his texts, Castoriadis reminds us of a line from Cantor’s letter to Dedekind, which highlights the presuppositions in the determination of the concept of a set: “Every multiplicity is either an inconsistent multiplicity or it is a set [ensemble].” Stated differently, the category of a set allows us to rein in the dispersed multiplicity by giving it a ground according to which it could be joined into an infinite albeit determined sequence. Nevertheless, as Castoriadis claims, “to say of a multiplicity that it is inconsistent implies obviously that this multiplicity is, it is in a certain fashion that remains to be specified and that Cantor does not specify.” In other words, this concept itself is the determining factor, circumscribing the ontological region in question, but not belonging to it and remaining external in respect to that region. With this determination we can group the elements composing a set and even assign them identities, although the totality never appears to be final and all grounding. Where only one type was thought to exist, set theory allows us to claim that there are different types of infinity, thereby evading those very principles of determination.
Cantor begins to formulate his conception of transfinitum precisely in relation between determination and indeterminacy. Transfinite infinity remains infinite, though it nevertheless exhibits the unique property that it can be extended. Therefore, in Cantor’s view, transfinite numbers can be understood in a certain sense as “new irrationals,” as numbers whose definition requires the establishment of the interrelations between different dimensions of mathematical ontology. By analogy with the definition of irrational numbers, which require infinite collections of rational numbers, the potential infinity should also presuppose an infinite collection of rationals, whereas the reality of transfinite numbers can be confirmed “directly by abstraction from the existence of infinite sets.” This means that the determination of a set is impossible within the domain of only one type of infinity: it is posited and affirmed by external parameters.
As is well known from the history of mathematics and philosophy, it was for precisely these reasons that Cantor’s set theory received reproaches of immaturity, and was sometimes even called “naive.” A famous counterargument, a paradox, was proposed by Bertrand Russell in his attempt to circumscribe the contradictory nature of the gesture at the center of set theory. Invoking Russell’s own example, this argument is usually illustrated with the so-called “barber paradox.” Let us assume that, “You can define the barber as ‘one who shaves all those, and those only, who do not shave themselves’. The question is, does the barber shave himself?” If he doesn’t, then the barber is not shaving all of them. If he does, then he shaves the beard of someone who shaves himself. According to Russell, this contraction can be lifted up only if it will be recognized that, “the symbol for a class is an incomplete symbol; it does not really stand for part of the propositions in which symbolically it occurs, but in the right analysis of those propositions that a symbol has been broken up and disappeared.”
This paradox finds itself at the heart of set theory: can that which determines also be the source of auto-determination? In other words, what is the nature of sets themselves, if in characterizing an ensemble of one kind, they themselves cannot belong to these ensembles? Is a particular set that has other sets as its elements its own element? If so, then it does not satisfy the criterion for its elements. If, however, it does not belong to itself, this would mean that the set is not fully complete.
As we know, the subsequent polemics on set theory took off in the direction of axiomatization, in which a ground for a set is sought, a ground that would permit us to derive it from the already known axioms. On the other hand, the situation disclosed with this paradox allows one to strike at the ontological nerve of Western philosophy, which appears in the considerations of both Castoriadis and Meillassoux. The origins of the problem of reality lie in the question of its determination, hence, in the question of the limit of the accompanying system of possibilities. In raising the question of reality, we are implicitly attempting to find and circumscribe the limits within which it can be valid.
That is to say, the question “what is real?” always contains within itself the question “can this be real,” with reference to the necessarily present fulfilled conditions, which allow for the identification of the possible variations of the set of reality. Thus, in raising the question of reality, we are trying to examine whether the instances under consideration could fall within the chosen set, even if they were never identified as actually being in it. A real occurrence does not need to have transpired. In this sense, reality always exceeds the finite totality of empirical facts: or rather, it can be understood as an infinity thought and imagined, which is the nature of a determined set. We characterize it not only as that which has occurred, but as conceivable events corresponding to the instances of the set.
The proposed emancipation of infinity from the single source of determination in Cantor’s theory becomes the basis to think of reality itself as the collision of different determining powers. On the other hand, keeping Russell’s Paradox in mind, it is precisely here that we can raise the question of how the factor determining the possibility of reality – which, furthermore, cannot be its own determination – is to be understood not only in the purely mathematical or logical dimension, but also as an ontological problem. Stated differently, what and how is the barber of Being shaving?
4 Three regimes of correlation
Hence, as we approach the problem of correlation – as understood by Meillassoux – we should question not only the relation between mind and world, but also the possible subordinate roles these poles might play. If according to Meillassoux reality is that which exists independently of human mind, then speculation remains the last correlate that still determines the version of reality that is being thought. In this way, it produces a certain dependency between the two. So how can we think the version of reality that has not already been conveniently conjured up by a human mind?
Before proceeding, I would like to reflect on correlation by proposing a scheme of 3 regimes:
The subject is a determining and subordinating factor. Correlation is understood in the sense of the world being subjected to the human mind. In this case, reality is subordinate to the mind. As the subordinating factor, the subject is in control of reality.
The world is a determining and subordinating factor. Correlation is understood in terms of human mind being shaped by natural, social, or technological reality (or subjected to genetic and biological givens). In this case, we end up in the context of natural (biochemical), evolutionary, social, technological determinism – humans are subordinate to nature, culture, technology, etc.
Determination is not subordinated to any factor, but remains correlationally open. Although an intense correlation is still found, it is established from polyphonic centers, while none of them acquires a dominant role. All action is distributed in a process of mutual determination.
5 Reality and imagination: liaisons dangereuses
How does the sphere of imagination fare in this context? Without a doubt, it counts as a problematic and ambiguous dimension. Even though the conventional opposition between reality and imagination only began to be drawn fairly recently, from both the ontological and the epistemological perspective imagination is marked by a long and complicated history, in which it was rarely given any merit by contrast with reality due to its inability to determine strong identities.
A number of prominent authors representing Modern Philosophy conceived imagination in terms of deficient reality or weak reproduction. For instance, Descartes intended to demonstrate the fundamental impurity of imagination: conceived as a power to visualize, i.e., to produce a mental image of an object, it appears as an “intermingled faculty” always entrapped in corporeal functions. By privileging the modalities of intellection and speculation, the Cartesian stance sees imagination through the lens of correlation – along the lines of Meillassoux’s thinking – as producing distortion and deviation.
In the Sixth Meditation Descartes provides a famous example:
To make this plain, I shall first examine the difference that exists between imagination and pure intellection. For example, when I imagine a triangle, not only do I understand it to be a shape enclosed by three lines, but at the same time, with the eye of the mind, I contemplate the three lines as present, and this is what I call imagining. But if, on the other hand, I wish to think of a chiliagon, I do indeed understand that this is a shape consisting of a thousand sides, no less clearly than I understand that the triangle consists of three: but I do not imagine the thousand sides in the same way, that is, contemplate them as present. And although at the time, because I am accustomed always to imagine something whenever I am thinking of bodily things, I may perhaps picture some figure to myself in a confused fashion, it is quite clear that this is not a chiliagon, because it is not at all different from the picture I would also form in my mind if I were thinking about a myriagon, or some other many-sided figure. Nor is it of any assistance in recognizing the properties by which the chiliogon differs from other polygons. But if I am dealing with a pentagon, I can certainly understand its shape, like that of the chiliagon, without the help of the imagination: but I can also imagine it, that is, by applying the eye of the mind to its five sides, and at the same time to the area contained within them; and here I observe very plainly that I need to make a particular mental effort in order to imagine, that I do not make when understanding. This further effort of the mind clearly indicates the difference between imagination and pure intellection.
Here Descartes tracks our mental effort in grasping a very complicated object. It is possible for me to form a mental image of a pentagon, even of an octagon, but the task becomes increasingly difficult with more sides. Finally, one must admit, an attempt to visualize a 1,000-sided figure is doomed to failure, as there is no optical certainty that an object possesses 1,000 sides, rather than 999 or 1,001 of them. Optically speaking, these different figures look almost the same. The identity of a chiliagon could be grasped only through thinking, with the intellectual aid of a geometrical definition of “regular polygon with 1,000 sides.”
One could say that the same epistemological weakness that discredits the power to picture things as they really are in the mind also produces the ontological dichotomy between imagination and reality. Since, epistemologically speaking, imagination is incapable of providing a clear and definite image of things, ontologically speaking it produces only distortions of truth and deviations from fact. In a nutshell, Descartes discredits the imagination for not being able to bring about the results of complete determination. The dichotomy between imagination and intellection is a correlate of the ontological polarity between illusion and reality.
As was beautifully noted by Fichte, this is exactly the function that should not be ascribed to imagination. The creative power of the mind can assume no stable position, and thus is subject to permanent oscillation – as it strives for determination, but never achieves it:
The imagination posits no sort of fixed boundary; for it has no fixed standpoint of its own; reason alone posits anything fixed, in that it first fixates imagination itself. Imagination is a faculty that oscillates in the middle between determination and nondetermination, between finite and infinite; and hence it does indeed determine A + B, both through the determinate A, and also through the indeterminate B, which is that very synthesis of imagination of which we were speaking just now. – Imagination designates this oscillation precisely through its product; it produces the latter in the course of its oscillating and through its oscillating as it were.
Personally, I hold this to be one of the most important and elegant quotes for encapsulating the complexity of the problem of imagination in a few phrases. Leaving aside the assumptions of Fichte’s philosophy (the famous dialectic of I and Not-I), the idea of the movement of “oscillation” (“Schweben”) remains valid whenever we try to describe the role of imagination as the power that aims at the reconciliation of seemingly irreconcilable opposites. Moreover, the power to create the liaisons dangereuses between contradictions nourishes the dynamics of imagination, by granting it a very particular role that cannot be performed by the intellect.
John Sallis’s remarks are illuminating in this respect: “Imagination has no fixed standpoint but the movement of displacement as such; it posits no fixed limits but circulates among the opposites so as to hold them together, its very displacement delimiting a space of opposition.” Perhaps this argument can be extended by analogy with the character of Stalker from Roadside Picnic, a science fiction novel by Arkady and Boris Strugatsky, adapted into a famous film entitled Stalker by Andrei Tarkovsky. The famous character breaks into the forbidden “Zone” to steal and smuggle artifacts with undetermined but seemingly supernatural properties. However, Stalker’s status remains suspended in an in-between state – he cannot settle down in the territory which he enters. Due to his hovering between the two spaces, he has no “fixed standpoint of his own.”
The Fichtean concept of imagination is conceived as a power that performs an intrusion into the territory of incomprehensibility without the possibility of laying any solid ground there. If anything, this approach toward indeterminacy is to be considered as a work of entering into the unknown with preliminary schematizations and smuggling back the semi-determined “artifacts” belonging to the alien state into what is known, and thus trying to inject the contradictory realms into each other. This amounts to the cultivation of the aforementioned formula A + B, which leaves no possibility of acquiring a fixed point of view based on a harmonious synthesis. A uniform view, neutralizing the contradictions, is left as a prerogative of intellectual function. Without any pretense of being definitive, imagination constantly amalgamates within its movement the fields of opposition, designating “this oscillation precisely through its product.”
Moreover, the possibility of performing this movement that is exercised between heterogeneous fields produces, according to Sallis, the effect of spacing: i.e., the transitory zone that allows oppositions to meet, but that also functions as a creative surplus that inevitably responds to intractable problems, not by eliminating or subsuming them in each other but by installing them into the field of necessary tension that keeps them in relation. As we are reminded by Sallis:
Imagination hovers in between opposites so as to hold them together in their opposition, so as to hold together in the finite and infinite, so as to hold together relation to a not-I and absolute self-positing. Imagination is the power of spacing those oppositions that can be neither dissolved nor eliminated from theoretical knowledge. Imagination is the spacing of truth.
This is a very strong claim that suggests truth needs imagination in order to gain comprehensible contours. Paraphrasing Leibniz’s formula, truth can be saved not by substituting identities, but by permitting the change of our perspectival relation to it to play out. The hovering power, through its instability, enacts the spacing of appearance of truth – namely, because it does not seek a full determination as a final goal. Once again, in-betweenness designates a very special performativity within the zone that requires constant motion, a choreography of approximation and distanciation, a constant forth and back, leaving no hope of attaining any clara and distincta perceptio, which is grounded in the freezing point of vision. Determination produces immobility, whereas imagination relies on blurred contours that are sketched out in action. This also concerns the fact that imagination, according to Fichte, plays a fundamental as well as paradoxical role in creating reality without coinciding with its ontological status:
In understanding alone (although first through the power of imagination) does reality exist; it is the faculty of the actual; the ideal first becomes real therein: (hence, to understand something betokens a relation to something that come from outside, without our assistance, but must throughout be merely indicated or intimated.) Imagination produces reality; but there is no reality therein; only through apprehension and conception in the understanding does its product become something real.
Leaving aside Fichte’s preconception of reality, stemming from sources in the ego without proper rights to autonomy, we can also return to an important characteristic of reality that is pertinent to numerous realist stances: its tendency to determination.
Reason, as a determinant factor, relies on what Fichte calls “stabilizing intuition,” which sets the limits to the wavering power of imagination and uses the resources of understanding in order to bring about stability. To speculate about reality in the first place implies the setting of a normative grid to define its limits. Hence reality is achieved through the process of stabilization, whereas the act of its production – ascribed to imagination – is subject to constant neutralization.
Ontologically speaking, the sort of realism that is both metaphysical and naive is grounded in the respective procedures of the delimitation of reality, achieved in the process of epistemological determination, which disqualifies the latent dynamism of liquid boundaries. This is why imagination tends to be identified with illusion – not because of its weakness in grasping what is real, but because of its inability to determine what is real by taking a fixed point of view. The oscillation fundamental to its nature blurs the boundaries and at the same time exercises a constant change of perspective.
The epistemological complication of this procedure was already individuated by Aristotle. There is a passage in On the Soul which admits its relations to procedures of truth: “If then imagination (φαντασία) is that in virtue of which an image (φάντασμα) arises for us, excluding metaphorical uses of the term, is it a single faculty (δύναμις) or disposition (ἕξις) relative to images, in virtue of which we discriminate and are either in error or not?”
However, according to Aristotle, the faculty of imagination is unique in the sense that it is not to be measured by truth or falsity. Yet “neither is imagination any of the things that are never in error: e.g. knowledge (ἐπιστήμη) or intelligence (νοῦς); for imagination may be false.” In other words, this very distinction does not hold for imagination, since its relationality is not of the same character as that of intellectual activity, in which the criterion of truth is essential. We may err in imagining, but this error can be ascertained only by applying external evaluation: that is, by submitting the given image to the verification of the intellect. It is precisely here that Aristotle also proposes the famous example of an erring imagination:
to imagine is therefore (on this view) identical with the thinking of exactly the same as what one perceives nonincidentally. But what we imagine is sometimes false though our contemporaneous judgment about it is true, e.g., we imagine the sun to be a foot in diameter through we are convinced that it is larger than the inhabited part of the earth.
What is explicated above delineates the trajectory of “unrealistic psychology” inscribed in the destiny of imagination. Epistemologically, it must be subordinated to intellect in order to be tested in the procedures of measurement, assessment, judgment, etc. This is how, since Aristotle, we tend to forget that the role of imagination is never exhausted by taking one perspective. On the contrary, in fixating its dynamism, we implicitly identify the same functionality in imagination that was recognized in the faculty of intellect. But the measuring of imagination by intellect ends up merely turning imagination into a weaker version of intellect. It is an easy way to reduce the process of oscillation into the lack of a stable position.
Imagination is not to be defined as the power of the production of images, i.e., of determined results. Its figurative expression is weak in relation to conceptualization, as was shown already by Descartes. Yet paradoxically, imagination does not yield images that compete with concepts to express a pretention of unilateral reality. Moreover, technically speaking, it does not generate images at all; these are only the outcomes of the process of wavering movement that tend to keep the contradictions in tension. This is why the meaning of imagination is concealed by noisy side effects – “the interplay of and with opposites that Fichte calls imagination.”
In this regard we are reminded of the special feature of determination indicated by Spinoza. In 1674 he wrote a letter to his friend Jarig Jelles that discussed, among other things, the status of figure as not being something positive. In trying to achieve apprehension through the figure one absolutely fails to do so, as figure is limited to the determination that does not pertain to the thing according to its being (juxta suum esse), but on the contrary it is its nonbeing (ejus non esse). Conversely, determinations produce the lack of being. This is why the figure is nothing but a determination (and the determination is a negation): it could not, as has been said, be anything but a negation. “Quia ergo figura non aliud, quam determinatio, et determinatio negatio est.”
Spinoza introduces a very clear separation between Being and the realistic intentions of determination. Figurative representations are nothing but determinations. Every determination is negation that demonstrates ontological weakness. Through the procedures of determination, being is eliminated. This point is then famously elaborated by Hegel, who proposes the reversal of its sense and recognizes the determining power of negation itself:
“Determinateness is negation” is the absolute principle of Spinozist philosophy; this true and simple insight is at the basis of the absolute unity of substance. But Spinoza stops short at negation as determinateness or quality; he does not advance to the cognition of it as absolute, that is, self-negating negation; therefore his substance does not contain the absolute form, and the cognition of it is not a cognition from within.
Hegel emphasizes that Spinoza’s discovery is bigger that he himself thought it was; partly because of that, he has been criticized for a “profound misreading of Spinoza.” Negation is to be characterized as absolute – namely as the negation of negation that grounds every relation as such: “The individual refers to itself by setting limits to every other; but these limits are therefore also the limits of its self; they are references to the other; the individual’s existence is not in the individual.” Hence, it would be relevant to say that determination is negation only insofar as we recognize the self-directedness of negation that enables us to exceed the realm of pure determination. In fact, negation is not the product of determination, but rather the converse: determinations are produced by negation.
However, it is less well known that in the famous passage cited above, Spinoza is criticizing Descartes’s concept of figuration in relation to the role of imagination. As Spinoza puts it:
The manner in which the imagination thus proceeds is evident here: to understand extension, it delineates it or it divides it, and it tries then to reconstitute it, to engender it, through the elements thus obtained. But this “genesis” can be nothing but fictive: it expresses nothing more than the powerlessness of the imagination to represent the infinite except by dividing it, in a strictly negative manner, thus inadequate to its essence. Determination does not pertain to a thing in regard to its being, on the contrary, it is its non-being.
Once again, it seems that Spinoza conceives of imagination as a very specific procedure of determination, not as the power which – for better or worse – never claims to exhaust infinity with its results. Since division is its main tool, we can always maintain the awareness of images being fictions with respect to infinity. However, this powerlessness of imagination does not provide an epistemic value, and hence it is conceived as its negative-potential: namely, an unstoppable activity that does not confide in its results: “it tries then to reconstitute it, to engender it, through the elements thus obtained.” With Fichte in mind, we might add: its powerlessness re-actualizes its power.
All these polemics brings us back to the philosophical meaning of imagination, which could be revalorized by reconsidering its perspectival origin. My hypothesis is that the problem of the real (Being) beyond determinations requires a revised concept of imagination that would not be subordinated to the logic of representation aiming at the contemplation of figures, images, or names. Determinacy stabilizes the imagination within the limits of one perspective. It is also a simple negation of its movement, a tranquilizer of its drive toward kinesthetic visions.
6 Anamorphic imagination
What would this oscillation of imagination look like if we were to go beyond a mere Fichtean project? What does it mean to overcome the weakness of imagination that was pointed out by Descartes – i.e., the failure to grasp adequately the forms of things in their clear and distinct determination? First of all, we need to consider a revised status for determinations. The logic of imagination defined as “A + B,” where determinate A is constantly played out through indeterminate B, is the logic of the validity of contradictions. Moreover, it is also the logic of a perspectivism, of mobility as the change of perspectives, of a paradoxical power to keep a few perspectives in relation.
If we return once more to the barber’s paradox, we can now invoke the definition of set as formulated by Cantor himself. Castoriadis reminds us of it: “A set is a collection into a whole of definitive and distinct objects of our intuition or of our thought. These objects are called the elements of the set.” Since a set is a sample, grasped by our intuition (Anschauung), then no set exists without intuition. Hence Cantor’s proposal, which might first have appeared naive, expresses “the indefinable within the definition of the definite, the ineliminable circularity within every attempt at foundation.”
One might add that Anschauung can be conceived as a certain taking of a position: one that requires the stabilization of sight in order to introduce the procedures of determinations. In the history of Western art, the primacy of first perspective was famously questioned by introducing the strategy of anamorphosis. As was outlined by Martin Jay, the validity of comfortable and static perspective introduced since the Renaissance was disputed during the Baroque epoch, by proposing the suspension of one dominant scopic regime. Hence vision itself turns out to be dynamized by the procedures of analysis and technological mediation. This occurs, for instance, by introducing the “anamorphosistic mirror, either concave or convex, that distorts the visual image or, more precisely, reveals the conventional rather than natural quality of ‘normal’ specularity by showing its dependence on the materiality of the medium of reflection.”
Technically speaking, anamorphosis is a deformed image that appears in its true shape when viewed by changing one’s initial perspective. According to Jurgis Baltrušaitis, anamorphosis, “plays havoc with elements and principles; instead of reducing forms to their visible limits, it projects them outside themselves and distorts them so that when viewed from a certain point they return to normal.” What appears as a monstrous image, projected on a plane or curved surface, is transformed by moving from an initial point of view and adopting the new perspective. By exercising this optical change (with the added help of a curved mirror or through a polyhedron) the regular proportions are regained and normal vision is reconstituted.
However, this procedure cannot keep both perspectives actualized and remain dependent on a constant vision that produces ruptures and dysfunctionalities and exercises the deformation of an image. One of the most famous anamorphoses, in Hans Holbein’s The Ambassadors of 1,533, requires a change of position in order to be seen. The contours of the human figures of the ambassadors are lost whenever a spectator chooses to change position and assume the vision of the skull. The initial image is then disrupted so that the distorted part can be seen. As Baltrušaitis notes, the mystery of The Ambassadors is presented in two acts:
Act One is played when the spectator enters by the main door and finds himself a certain distance away from the nobles, who appear at the back as on a stage. He is amazed by their stance, the display of luxury, the intense realism of the picture. He notes a single disturbing factor: the strange object at the ambassadors’ feet. Our visitor advances in order to have a closer look. The scene become even more realistic as he approaches, but the strange object become increasingly enigmatic. Disconcerted, he withdraws by the right-hand door, the only one open, and this is Act Two. As he enters the next room, he turns his head to throw a final glance at the picture, and everything becomes clear: the visual contraction causes the rest of the scene to disappear completely and the hidden figure to be revealed. Instead of human splendor, he sees a skull. The personages and all their scientific paraphernalia vanish, and in their place rises the symbol of the End. The play is over.
In Baltrušaitis’ description, the painting is scripted as a play for the spectator, who has to act by searching an appropriate position from which to gain a full view. The change in determining features of the image is performed by their moving from one room to the other. It is the spectator who has to re-determine what she/he is looking at. However, this is the moment when drama reaches its culmination, since it is impossible to find a holistic point of view that keeps both parts of the picture visually determined simultaneously. There is no place that enables us to see everything at once. Therefore, the change of perspective is doomed to constant motion.
This anamorphic procedure – an oscillation that keeps contrasting perspectives in tension – resonates with the idea of Fichtean imagination that does not reside in any given determination. In fact, the challenge of the anamorphosis unleashes the kinesthetic dimension that lies at the heart of the aforementioned formula, A + B: whenever a determination is produced, it technically remains a semi-determination, a partial image which is meant to lose its validity and enable the procedures of perspectival change. In this sense, every image is a precondition of movement; it engages the process of novel determinations and re-determinations that can be apprehended only in motu.
7 Magmas and the radical imaginary
On a related note, the idea that imagination can be conceived as a power of semi-determination is endorsed by Castoriadis, who invokes the category of magma as a special metaphor that helps to conceptualize the relation between imagination and the real in terms of determination. As is well known, magma is a geological term referring to the molten rocks found in the depths of the Earth. The chemical composition of magma is highly complex; moreover, it exhibits high temperatures: from 649°C to 1,200°C. Besides melted solids or suspended crystals, magma may also contain gas bubbles.
In light of these properties, Castoriadis conceptualizes magma as a form of contradictory multiplicity and conceives it as an ontological category. Already in The Imaginary Institution of Society he claimed as follows: “A magma is that from which one can extract (or in which one can construct) an indefinite number of ensemblist organizations but which can never be reconstituted (ideally) by a (finite or infinite) ensemblist composition of these organizations.”
The specificity of this magmatic reality inclines us not so much to sever relations as to radicalize them. “But could the living being organize an absolutely chaotic world? For the living being to be able organize, for itself, a world, starting from X, would still have to be organizable. This is the old problem of Kantian criticism, which one could never glide over.” As the thinker of the imaginary observes, this means that the forms immanent in transcendental consciousness and the logic underlying their structure has to be related to the material it forms. Differently put, this material, at least in its minimal form, should itself be something “formable.” Hence, “the idea of an absolutely disordered universe is for us unthinkable.”
It is important to note that the results of the radical imaginary are indeterminate in a specific sense. This nondeterminacy cannot be exhausted by the uncertainty regarding a specific concrete possibility, or by the question of which of the many concrete possibilities will actualize itself in a finite set. In the first place, the set of possibilities itself lacks determinacy. What is more, nondeterminacy for Castoriadis implies not only our own state of ignorance and uncertainty, but the radical possibility of creating a new state in which other determinations, new laws, and even new domains of lawfulness become possible.
Their function is understood, rather, as a constant process of self-determination irreducible to the results of this process. Magma is a state of the real that cannot be reduced to the sum of its constituent parts, even though it is capable of giving birth to a multitude of defined forms. Which is why, despite being constantly determined, magmas can never be fully grasped through determination and require the relationality of imagination.
The imaginary “is radical because it creates ex nihilo (not in nihilo or cum nihilo). It does not create “images” in the visual sense (though it does this as well: totem poles, emblems, flags, etc.). Instead, it creates forms that can be images in a general sense (linguists speak about the acoustic image of a word), but which in the main are significations and institutions (each of these being impossible without the other).”
In contrast with secondary (reproductive) imagination, the radical imaginary should be considered as a certain vis formandi – a force that both creates new significations and shapes itself. Castoriadis considers this force as “a-causal” – i.e., as something that breaks away from the causal chain and is therefore supernatural. However, its a-causality is not “unconditional” or absolute; relations and contexts always take part in the formation of new significations. Hence, the radical imaginary discovers its significations as “creations under constraints.”
However, the full radicality of imagination is grasped whenever both realms are maintained in the perspective: “Radical imagining is the positing, ex nihilo, of something that ‘is’ not and the connection (without previous determination, or ‘arbitrarily’ made) between this something that ‘is’ not and something that, in another sense [par ailleurs], ‘is’ or ‘is not’.”
8 Conclusion: correlationism beyond determination
Perhaps the most important thing is that the radical imaginary involves the binary gesture of creation out of nothing (ex nihilo). This implies that all determinations are permanently suspended, while all imaginary significations and the whole symbolic reality appear as fictitious, and can therefore be reshaped at any moment. The logic of magmas requires the logic of radical imagination, which reveals its fundamental character – to be a signifying procedure (of giving names, images, and structures) and to set an order in the “mud” by releasing creative representations upon what appears in the lack of order. Otherwise put, radical imagination requires anamorphic procedures that call into question the two senses of correlation that imply subordination. It never confides in the constructed version of the human world, which of course includes mathematics.
My argument is that the project of the return to the problem of the real necessarily passes through the radicalization of imagination, which technically speaking is performed as the perspectival change of anamorphosis. In my view, this procedure invokes the third meaning of correlation: Being is always related to the subject but never determined by or subordinated to it. In this light, the radical imagination aims to maintain an emancipatory meaning – the call to a constant anamorphic procedure, to the gestures of constant re-determination, by cultivating the change of perspectives without any pretense to totality.
In this sense, the radical imagination (with the void of Nothingness in its field of vision) emancipates us – almost on the empirical level – from the subordinating relation. It is nevertheless involved in the processes that create new determinations. Stated differently, the recognition of the groundlessness here should activate creativity that realizes autonomy, a creativity that would not turn any newly established form into an instance of the final law. Autonomy means that laws have to be re-created for oneself again and again.
One must admit that this fundamental creativity is a brutal intervention with respect to existing cultural coordinates and the preexisting anthropocentric horizon. However, it remains radical as long as the negativity of existence is kept within the horizon. Once again, signification is a production of what both is and is not simultaneously. Every name, every syntactical operation, every determination turns out to be a fiction (insofar as it is a creation), which establishes the horizon of potential opening and closure. Imaginary beings both exist and do not exist, because they are aiming at the real. That is why the radical imagination is a call for re-creation by returning to the state of creatio ex nihilo but also with the urgency of a novel systematization of reality. In the face of nothingness, we need both to reject the old and to invent new names. In this sense, we constantly need new possibilities that invoke new perspectives on the real.
This article is part of the European research project “The Future of Humanity: New Scenarios of Imagination” (Vilnius University). This project has received funding from European Social Fund (project no. 09.3.3-LMT-K-712-01-0078) under a grant agreement with the Research Council of Lithuania (LMTLT).
Aristotle. On the Soul. The Complete Works of Aristotle, Vol. 1. Princeton: Princeton University Press, 1984.Search in Google Scholar
Baltrušaitis, Jurgis. Anamorphic Art, trans. W. J. Strachan. Cambridge: Chadwyck-Healey, 1977.Search in Google Scholar
Castoriadis, Cornelius. The Imaginary Institution of Society, trans. Kathleen Blamey. Cambridge, MA: MIT Press, 1987.Search in Google Scholar
Castoriadis, Cornelius. “The Logic of Magmas and the Question of Autonomy,” In The Castoriadis Reader, trans. and edited by David Ames Curtis, 290–318. Oxford, Cambridge, MA: Blackwell Publishers, 1997a (1983).10.1177/019145379402000108Search in Google Scholar
Castoriadis, Cornelius. “Radical Imagination and the Social Instituting Imaginary.” In The Castoriadis Reader, trans. and edited by David Ames Curtis, 319–37. Oxford/Cambridge, MA: Blackwell Publishers, 1997b (1994).10.4324/9781315003528-8Search in Google Scholar
Dauben, Joseph Warren. Georg Cantor: His Mathematics and Philosophy of the Infinite. Princeton: Princeton University Press, 1990.Search in Google Scholar
Derrida, Jacques. Edmund Husserl’s “Origin of Geometry”: An Introduction, trans. John P. Leavey. Lincoln: University of Nebraska Press, 1989.Search in Google Scholar
Descartes, René. Meditations on First Philosophy, trans. J. Veitch. Toronto: Our Open Media, 2017.Search in Google Scholar
Fichte, Johann Gottlieb. In The Science of Knowledge, edited by and trans. Peter Heath, John Lachs. Cambridge: Cambridge University Press, 1982.Search in Google Scholar
Foucault, Michel. In Il faut défendre la société. Cours au Collège de France 1975–1976, edited by M. Bertani, A. Fontana, Paris: Seuil/Gallimard, 1997; Society Must Be Defended. Lectures at the Collège de France 1975–1976, translated by D. Macey. New York: Picador, 2003.Search in Google Scholar
Hegel, Georg Wilhelm Friedrich. The Science of Logic, trans. George Di Giovanni. Cambridge: Cambridge University Press, 2015.Search in Google Scholar
Ihde, Don. Technology and the Lifeworld: From Garden to Earth. Bloomington: Indiana University Press, 1990.Search in Google Scholar
Jay, Martin. “Scopic Regimes of Modernity.” In Vision and Visuality (Discussions in Contemporary Culture), edited by Hal Foster, 3–28. Seattle Washington: Bay Press, 1988.Search in Google Scholar
Meillassoux, Quentin. “The Immanence of the World Beyond.” In The Grandeur of Reason: Religion, Tradition and Universalism, edited by Peter M. Candler, Conor Cunningham, 444–79. London: SCM Press, 2010.Search in Google Scholar
Meillassoux, Quentin, Dolphijn, Rick, and van der Tuin, Iris. “There is contingent being independent of us, and this contingent being has no reason to be of a subjective nature: Interview with Quentin Meillassoux.” In Rick Dolphijn, Iris van der Tuin, New Materialism: Interviews & Cartographies, 71–81. London: Open Humanities Press, 2012.Search in Google Scholar
Sallis, John. Spacings—Of Reason and Imagination: In Texts of Kant, Fichte, Hegel. Chicago: The University of Chicago Press, 1987.Search in Google Scholar
Spinoza, Baruch. In Spinoza: Complete Works, trans. Samuel Shirley, ed. Michael L. Morgan. Indianapolis: Hackett, 2002.Search in Google Scholar
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