The most concrete definition of the word paradox is as a statement that “contradicts itself,” that is, whose truth value cannot be determined because it entails its opposite, the simplest example being This sentence is false, where proposition p is “~p.” Such paradoxes are possible because, given that we experience in time the atemporal world of logic, in the course of processing a proposition we may be forced to pass from one state to a contradictory state.
This is more easily illustrated by means of the more complex paradox discussed in Chronicle 405. The “Barber Paradox” affirms that there is a barber in a town who shaves only the men in the town who do not shave themselves. This leads to a contradiction when we attempt to determine whether the barber shaves himself; for if so, then he belongs to the class of those he does not shave. I showed in that Chronicle that the statement of the paradox fetishizes into an ontological state what is a temporal contingency; if one simply takes “not shaving oneself” as not (yet) having shaved oneself on a given day, then the paradox vanishes, since the barber shaves himself at a moment when he has not yet shaved himself, after which he has shaved himself and need do so no longer. What this reveals is not sloppy formulation but the contrast between real-time situations and the logical propositions by which we pick out salient properties of these situations.
No doubt one can easily construct a context—for example, a sociological survey of shaving habits—in which it is reasonable to treat the categories of “shaving oneself” and its contrary as unchanging states. But this categorization produces a model, not a direct translation of reality. Dividing a population into those who shave themselves and those who do not, aside from eliminating those who may not do the same thing every day, passes over the temporal nature of shaving behavior: in order to “always” shave yourself, you have each day to perform the act, which means that you are for part of each day in the state of not-having-shaved-yourself.
The Barber Paradox is just concrete enough to make clear that it is the detemporalization inherent in the proposition that is the source of logical paradox. The categories that lead to paradox do not do so in the normal case where a proposition is used to understand the world, and this is true of empirical categorizations generally. In describing external reality, we decide what is important according to our needs; if millions of neutrinos are traversing our body every second, that does not mean that we are “distorting reality” to ignore them, nor is it relevant that the cat which is on the mat is a collection of atoms, quarks, dark matter, or for Quine, a collection of “undetached cat parts.” We use classifications for a practical purpose, not to exhaust the meaningfulness of things, which, whether one is a “Kantian” or not, cannot be known “in themselves” but only with respect to our ability and need to know them. (This does not, of course, imply that there is such a thing as a “thing-in-itself”; on the contrary, without human intentionality, “things” are just part of the massive world of Sartre’s en-soi, the “in-itself” without a self. Which is no doubt not all that far from Kant’s own view.)
What about “This sentence is false”? Just as the barber paradox is paradoxical because an empirical reality that is true or false at time t on day d (“X has/has not shaved himself”) is expressed as a permanent state (“X shaves/does not shave himself”), so the liar paradox is only paradoxical if the enunciation of the sentence is considered to take place instantaneously. Otherwise, when I say, “This sentence,” I am announcing a proposition, not enunciating one, so that there is as yet nothing to which a truth value can be assigned. Similarly in “This sentence is written in English” and “this sentence has five words,” although the empirical qualities (length, language) of the sentence allow for assignment of a truth-value, these grammatical sentences are not propositions in the sense of referring to a “state of affairs” in a reference-world separate from the world of the signs that represent it. Having five words or being in English is not a fact about the sentence until its enunciation has been completed; it cannot be tested against a model of the world that does not (yet) include the sentence. Which is why our first reaction to paradox is that we can avoid it by keeping language separate from what it refers to, and conversely, that self-reference is always paradoxical in that it breaks down the model-relationship between representation and its object, regardless of truth-value: “this sentence is true” is just as paradoxical as “this sentence is false.”
But to focus on self-reference, one risks forgetting what makes the configuration of linguistic communication originarily and essentially paradoxical. The first object designated by a sign must have been a potential source of a conflict that risked greater danger to the participants than the potential advantage to one who sought to appropriate it. The originary function of representation is to temporarily interdict appropriation of this object by setting it imaginarily on a scene that allows only for contemplation and representation. To exchange the (originary) sign is to accept this interdiction in exchange for the representation, that is, accept to contemplate the scene of representation rather than risk violent conflict by violating it through appropriative action.
In this case, we may say that significance is conferred on the object by the sign, but the object itself is experienced as the source of this significance. This is the originary paradox in an anthropological, not a logical sense. Here the temporality of paradox is concentrated in an instant: in representing the object, the “first” signer is the first to recognize it as significant, but this worldly significance, although clearly derived from the mimetically enhanced appetitive attractiveness of the object, is not reducible to it; it exists only in the human configuration that has just been created.
Language is paradoxical from its origin; logical language cannot eliminate paradox but has as its function to defer it. Paradox is not the product of the declarative form that allows sentences to “include” themselves, but just the opposite. The propositional world that allows for occasional anomalies such as “this sentence is false” is a mechanism designed for the deferral of paradox, the paradox that is at the origin of language.
Indeed, this statement itself appears paradoxical. But precisely, language itself is the greatest paradox of all. To come to designate an object of appetite as the object of representation, the sacred, God, when nothing had ever been “represented” before, to designate the object as always-already sacred/significant, as if discovering this quality in the object, when previous to this moment there was no place in the universe for the category of the sacred/significant or indeed for any category of thought as opposed to appetite, is to perform a gesture whose pragmatic impact is our very existence as a species. The possibility of playing around with self-referential “statements” such as “this sentence is false (or true),” “this sentence has five words—unless I decide to add a few more,” “this sentence has a great beginning but it,” and so on, is nothing but a trivial consequence of this primordial self-reference.
When I say the cat is on the mat, the priority of the reference world to the proposition is not in question, and yet it is only when I say it that my listener becomes aware of this “prior” shared reality—a phenomenon all the more obvious in the way the phrase is generally used, that is, as a fiction. In the world of esthetic experience, this oscillation between perception and representation is deliberately maintained over time, either itself temporally constructed as a “narration” in language and/or music or other performance, or in plastic art contemplated as a fictive object whose mental construction alternates with the examination of the work-as-representation. “Non-objective” art does not so much eliminate this oscillation as emphasize its paradoxical quality by removing the obvious associations between the constructed referent and real-world experience, making the contemplation of the artwork an anguished search for its “meaning.”
What we call the originary paradox of signification is nothing more than the fact, which not even the most gradualist anthropologist could deny, that the first word designates, points-to-as significant, a referent that cannot by definition have possessed this status before its designation. To point to God is less to “name” God than to indicate that he deserves to be so designated; yet however important he may be in the lives of the designators, he is only significant as the referent of a linguistic expression. This is not a flaw in the emergence and evolution of language; it is its very essence. Yet in the history of “linguistic philosophy” or “philosophy of language” or indeed of “philosophy” tout court, GA is the first theoretical perspective to recognize this. Which is no doubt why GA is at the center of philosophical and anthropological debate—except that the real purpose of the “debate” is to focus everyone’s attention on subjects of contention that allow them to avoid the center.
At the origin of language is the creation of a sign-world outside the temporal experience of the life-world. The simplest way to understand why accession to the sign-world defers conflict is that this accession takes place in lived time, in the world of appetite, yet the sign-world itself is outside lived time. Humans are the only creatures who have this second universe in which to dwell, divorced for the moment from the conflicts of the world. That this is true in no way prevents language and representation’s being used, like any deferral of worldly action, to store up energy for the sake of future conflict. Those who think naively that GA’s “deferral of violence through representation” means that language is always on the side of peace sometimes see in “violent language” a refutation of GA. But whether or not “violent language” exacerbates or substitutes for physical violence, the real human problem is that preparations for violence, including the sophisticated representations involved in building nuclear weapons, are also cases of “deferral of violence through representation.” Indeed, without language, there would be no violence in the human sense, only “nature red in tooth and claw”—cats eating birds, but not building gas chambers to exterminate them or bombs to obliterate them.
What remains indubitably true is that the sign-world emerges as a new, exclusively human phenomenon, and that the necessary naiveté of our expressed wonderment at the sacred interdiction that effects the separation of the sign-world from the life-world should not, as it seems universally to do within the intellectual community, allow us to think that the existence of language is simply one more result of the evolution of life and of the universe in general.
It seems to me that if one would not believe in God, one owes it to oneself to adopt a theory that allows one to understand, if not the fabulous miracles of the Bible, at least the everyday miracle that occurs when one participates in the human universe of representation. Paradox is one way in which the “miraculous” nature of language impinges on the taking-for-granted of everyday life, and this explains why it remains a thorn in the side of those who, as metaphysicians have always done, take the existence of language for granted in both theory and practice.