The “world” contains no paradoxes; paradox is a property of systems of representation. And humans alone possess systems of representation, or simply language, in contrast to the signaling systems of animals. Pavlovian “paradoxical states” are not paradoxes in our sense; hesitating between incompatible actions, like Buridan’s ass between two bales of hay, or overreacting to a stimulus out of frustration, do not possess the defining quality of paradox, which is the necessary incompleteness of self-inclusion. Once one has a system of representation, it cannot be prevented save by artificial means from representing itself. Self-representation is indeed always paradoxical, even when it involves no contradiction with logic in the strict sense. Thus the sentence “This sentence has five words” is “true” enough, but a paradoxical construction nonetheless, since what it represents is not independent of the representation itself—whence for example, the substitution of equivalent terms, such as “The present” for “This,” can falsify it, which is not compatible with the rules of logic. And if you are allowed to say that, you then can say, “This sentence is true,” which is meaningless, and then graduate to “this sentence is false,” which will be called self-contradictory if we allow sentences to tell about themselves. Yet how can we not? Passing legislation only imposes an outside authority; what is going to prevent me from writing or speaking such sentences? Which is to say that the attempt to legislate paradox out of existence, as via Russell’s Theory of Types (which, as is well known, can itself be used to construct paradoxes), is useful only in the context of a specific sub-system of representation, not in that of representation, or language, itself.
Yet to take the problem a bit farther, we discover that all language is paradoxical in that its representations are unavoidably included in the universe they represent, and more concretely, in the ethical sense that the language of the representation cannot be segregated from the human universe it describes. No doubt the moons of Saturn do not care what we say about them, which is why natural science is generally safe from paradox. Thus I am skeptical about physical theories that imply that our knowledge of something (rather than the disturbances we cause in attempting to obtain it) somehow affects its existence. Scientists aren’t very sophisticated as anthro-philosophers (or anthropoeticians), and I don’t trust them not to introduce ghosts into the machine; talking about “information” being retrieved from a black hole makes me nervous regardless of the IQ of the physicists involved.
But in any case, as I have been trying to make clear for the past 35 years or so, language is in the first place ethical; its representations concern in the first place human matters, or “divine” ones that are revealed only as counterparts of the human. It is the insertion of our representations into the human situation that matters, and here even a statement about a remote galaxy, however little effect it might have on that galaxy, has one on the human world to which it is addressed.
Logic and mathematics are human-made systems of representation with internal constraints. As a result of our awareness of these constraints, we are tempted to take a “Platonic” view of these systems as existing independently of our will and even of our existence. Many will say (the word believe begs the question of whether one can consistently “believe” such statements) that even if all humans and any other hypothetical intelligent beings vanished from the universe, that the “truths” of mathematics would remain. And no doubt this is correct if what is meant is that given the postulates that define arithmetic, etc., the conclusions we have drawn from them, from the multiplication table to Fermat’s Last Theorem, could all be proved by any hypothetical creature capable of performing the operations of the system—forgetting about the necessity of such a creature to formulate the hypothesis in the first place. And no doubt if there were some other life-form capable of understanding language, it would come up with the same truths: there is no system of representation in which, given the usual definitions, 2+2=5, or a fifth-degree polynomial can be solved by radicals.
But this in no way demonstrates the independence of these systems from the human act of representation. That constraints are inherent in systems independently of the will of their constructors is a truism, ultimately a tautology. Just because one can deduce conclusions about these systems that were not explicitly given in their definition is no proof that the systems somehow “exist” independently of humanity, any more than the constraints of an internal-combustion engine have somehow resided for all time in a Platonic realm of Ideas. No doubt the manipulation of numbers seems so basic to the universe that we can’t imagine that any intelligent being would not be drawn to devise a homologous system, even if it preferred base 12 to base 10. But given that outside of science fiction there are no other known examples of “intelligent,” representation-using creatures in the universe, our imagination concerning such creatures is wholly gratuitous. Perhaps we can conceive nothing else, but the proverbial man searching for his keys under the streetlight is in precisely the same position.
More germane to the subject of paradox is the conundrum that since every statement made within the generalized scene of representation of human communication modifies the minds of those who hear it (including the speaker), every statement about the world is implicitly paradoxical. The world after I have made my statement, or someone hears it or reads it a second or a hundredth time, is not the same as the world about which I originally made the statement. No doubt the reception of most statements does not modify the world sufficiently to make them false or deprive them of factual content, but the point is that the model of a “vertical” representation or language-world that represents the “real” world is never truly self-consistent.
That mathematics itself is vulnerable to “external” representation is the burden of Gödel’s famous theorem, which shows that, given a system homologous to arithmetic, one can make true statements about the system that cannot be demonstrated using the axioms from which the system is constructed. Whether this is a coincidence or a direct homology between ethics and mathematics, or whether such a question itself can ever be “scientifically” answered, fortunately need not be decided here.
For it is the ethical, communicative nature of representation that concerns us. The fact that the natural world is unaffected by representation (if not by its real-world manifestations), so that we can use language and its offshoots to study its regularities and develop technologies that make use of them— in a word, Enlightenment—should not blind us to the original purpose of language and to the consequent impossibility of explaining the emergence of language as a simple product of “cognitive” development. Knowing the world and even to some extent predicting and anticipating its processes, as the more intelligent animals do, in no way “gives rise” to language.
Even if we stipulate that “double-scope blending,” the ability to think of an idea in two different contexts at the same time, is a specifically human cognitive capacity, the following declaration illustrates cognitive science’s surprising blindness to the foundational reality of human language:
- The indispensable capacity needed for language is the capacity to do double-scope blending.
- The development of double-scope blending is not a cataclysmic event but, rather, an achievement along a continuous scale of blending capacity . . .
- Language arose as a singularity. It was a new behavior that emerged naturally once the capacity of blending had developed to the critical level of double-scope blending. (Fauconnier and Turner, The Way We Think, Basic Books, 2002: 181)
Since “blending” is a mode of thought it is difficult indeed to conceive of it in the absence of language; but above all, it is an extraordinary category error to describe language as an individual “behavior” “emerging naturally” from our cognitive capacities rather than as a new form of communication that ipso facto could appear only in a collective situation. At least Terrence Deacon proposed a marriage ritual as a hypothetical scenario for language origin.
Language can only be understood as a communicative phenomenon that arises in order to prevent conflict by deferring “instinctive” appetitive action. Jacques Derrida explained his revolutionary notion of différance by the hesitation implicit in the use of a (linguistic) paradigm, for which the user must decide which member to choose. But independently of the dubious psychological basis for this explanation (when we see something red, do we really determine this only after rejecting [which?] other colors?), what he was really aiming at was the indubitable fact that any use of language is a stepping back from “instantaneous” or “instinctive” reaction to its referent. Whence the importance of Sartre’s notion of the néant that separates (human) consciousness from its intended object, even if Sartre himself never refers to language in this context.
I find it hard to understand the failure of the cognitivists to recognize the importance of either the deferring or the communicative features of language. Nor do they get any argument from today’s humanists, who devote to their works the same rapt attention they formerly gave to “French Theory.” The “two cultures” dichotomy C. P. Snow wrote about in 1959 has clearly been resolved in favor of the scientists. Rather than defending the cultural essence of language, professors of humanities “on the cutting edge” invest their energies in the victimary disrespecting of culture as such. Indeed, this was already central to the deconstructive project, but Derrida was too subtle a thinker to reduce deconstruction to victimary resentment.
The scene of representation, in particular that of language, is paradoxical en puissance because it purports to be an extra-worldly “space” in which the world can be represented, yet in the literal, physical sense it remains within the world, like a map that cannot represent itself without falling into mise-en-abyme. Language is not in the first place a mechanism for the rational modeling of reality but for deferring the appetitive, and using it for “rational” purposes however defined is the product of a discipline guaranteed by its peace-making effects and not simply inherent in language-users’ “cognitive” competence.
The key point of human as opposed to animal cognition is precisely that an intelligence that makes use of the models of the world available to animal capacities of perception and appetite is incommensurable with one that can step back from the world’s immediacy into a scene of representation whose “objectivity” is guaranteed by the fact that it is shared with a language community. Language, even when used in private, is a collective phenomenon, and the sharing of other forms of representation is analogous.
For example, the idea of creating iconic figures that reproduce the patterns of perception to create recognizable images is available only to the species that possesses a scene of representation. Why, after all, don’t other animals, even our “closest relatives,” draw pictures? They don’t need advanced “cognitive” abilities for this, nor do they (appear to) need language. Yet they are not interested in representation, and the reason for this is that they lack a scene of representation whose reproduction in the brains of human individuals is derivative of its public existence. Once this scene exists, we can have the idea of reproducing on it not merely the (linguistic) signs by which we have learned to communicate in public but other representational acts, including iconic signs whose recognition by others one can presume without their being the products of a prior convention.
But given that it is difficult to think of language, representation, culture as essentially paradoxical, it is the cultural function of religion to reconcile us to the paradoxical nature of the human. As individuals, we experience this paradox most crucially as a contradiction between the permanence of representation and our individual mortality—we do not simply fear death, but experience it as incomprehensible. Because our words and thoughts are not mortal, the knowledge of our physical mortality strikes us as scandalous. The idea of an “immortal soul” is the natural corollary of the “immortality” of our representations. The sacred is the domain within which this element of human paradox is thematized.
Not that religion and the sacred were created in direct response to this conundrum. The originary hypothesis situates the first use of the sign as a communication of desire/signification/sacrality implicit in the abortion of what we conceive of as a common gesture of appropriation toward the central object. This life-saving deferral of appropriation as a result of the “impossibility” of individual action confers sacrality on the object, which appears to exist in “another” sphere that is for the moment inaccessible to us. Because this deferral of the appetitive through the sign keeps us alive in the moment of crisis, we are driven to invoke it in other moments of danger, from which such deferral may not suffice to save us.
To speak of the “verticality” of the sign in reference to its object, its existence in “another world” (Karl Popper’s “World 2”) reflects our theoretical understanding of representation, but for the originary participants, the sign appears as the result of the existence of its (sacred) referent in “another world.” This sacred existence turns what had been appetite into desire, not simply because it is mimetic of the desire of the others, but because the resultant of this collective mimesis is the object’s inaccessibility.
The “absurdity” of the sacred object’s being on the one hand simply before us and on the other inaccessible in “another world” is the experiential foundation of paradox. If it is in our world, why can we not appropriate it? If it is in another world, how can we see it as physically proximate and in principle appropriable? This contradiction inherent in the notion of the sacred historically precedes the paradoxes of logic. It may be restated as what I call the fundamental paradox of signification:
The sign confers signification on its referent as already significant.
For the significance of the object is experienced not as conferred by the sign but as its motivation. Yet at the origin there can have been no prior notion of “significance”; originary signification defines significance as the equivalent of sacrality, which is necessarily experienced as independent of one’s will.
In short, the religious sphere, the sphere of our dealings with the sacred, is the cultural locus where paradox is manifest, where the human reveals to itself, in terms that can never be fully rationalized, its paradoxical nature.
As I tried to show a propos of the Mahayana philosopher Nagarjuna’s writings on language (see Chronicles 515 and 516, which together comprise a paper on Nagarjuna and Zeno delivered at the Nagoya GASC in June 2016), this school of Buddhism makes linguistic paradox much more central than Western thought. Examining Zeno’s paradoxes as counter-examples, it is not difficult to interpret them as conundrums pointing to not-yet-available scientific formulations in terms, for example, of infinite series or calculus—”transcendental” but surely not paradoxical supplements to arithmetic and Euclidean geometry. But for Nagarjuna, these same paradoxes do not point to improved scientific representations. They are put forth in great number to indicate that what we consider rational thinking necessarily raises problems it cannot solve, that rational thought is in itself illusory, and that the only escape from illusion is to empty one’s mind of representations to contemplate a reality that cannot be thought, that is, the (paradoxical) empty scene of representation.
Buddhism, less appreciative than Judeo-Christianity of the central role of violence-deferral in the human project, is for that reason more open to the direct association of paradox and the sacred. Its project of emptying the mind is clearly less “dialectical” than that central to the West, which defines sacred paradox by the coexistence of human and divine personhood in the crucified Jesus. Here, in contrast to the empty scene sought by Buddhism, the “logos” is incarnated in the exemplarily suffering human. Girard was fully justified in noting the more sharply anthropological bent of the Christian mystery, which renews “pagan” sacrifice to/of the deity as the revelation of the sinfulness that we must ever defer through identification with the victim. The paradoxality of this identification is very different from that of Nagarjuna’s “the traverser does not traverse.” The two can be seen as broadly homologous only if we are willing to accept GA’s understanding of language as primarily not a way of stating facts but of deferring human mimetic violence.
Clearly this subject cannot be exhausted in a single Chronicle. The recently discussed paradoxes of antisemitism as well as those of liberal democracy deserve elaboration in their own right. Yet it seems useful to sum up in a word, or two, the specificity of human culture. The cognitivists’ willful ignorance of the nature and function of religion, as exemplified by Michael Tomasello’s recent foray into human morality (see Chronicle 519), cannot be divorced from their obliviousness to what is unique about human language and the human in general.
Let me stress in conclusion that I am not a religious “believer.” René Girard certainly was, and I respected him for this and admired the refusal to deny the relevance of his faith to his theoretical work that was the source of his greatest intuitions. For my part, I have tried to understand religious belief as far as possible in the rational terms of anthropology. My ultimate aim would be to reach the point at which paradox and faith are understood as synonyms, a point that cannot perhaps be lived, but that these Chronicles exist above all to approach.