Appendix A:

The Greimas Square¹

The relevance of these proposals for Greimas’s work turns on the whole matter of the so-called elementary structure of signification, or, in other words, the famous “semiotic square,” for many of us the supreme achievement of Greimassian semiotics. Here finally we find opened up the “black box” through which narrative is somehow “converted” into cognition and vice versa: finally we have the equations, we can witness the processes of transfer, which need no longer be posited mystically since it is “visible” before us. How this can be so, however, obviously demands yet another simplified exercise in the explanatory capacities of the “square,” whose canonical form is herewith reproduced (Figure A1):

The enumeration of the advantages of the square can begin at once with the observation that it is a decisive enlargement on the older structural notion of the binary opposition: S₁ versus S₂ is clearly just such a binary opposition, or in the language of philosophical logic a “contrary,” that is, a strong opposition (white versus black, male versus female), but one that the square now reveals to encompass far more than two available positions. It immediately implies, for example, the two supplementary slots of what logic calls a “contradictory,” where ₁ and ₂ are the simple negatives of the two dominant terms but include far more than either: thus “nonwhite” includes more than “black,” “nonmale” more than “female.” Meanwhile, the two compound or “synthetic” positions of complex and neutral offer still greater conceptual enlargements, the complex or utopian term, in which the opposition of “white” and “black” might be transcended (mestizo, for example), whereas the neutral term stands as the space in which all of the privations and negations are assembled (“colorless,” for example). Finally, the transversal axes map the place of tensions distinct from the principal or binary one, while the synthesis hypothetically proposed by uniting the two sides of the square (“white” plus “nonblack”) designates alternative conceptual combinations. The entire mechanism then is capable of generating at least ten conceivable positions out of a rudimentary binary opposition (which may originally have been no more than a single term, e.g. “white,” which proves to be internally defined by a hidden opposition we articulate by promoting the concealed pole “black” to visibility). I have suggested that other traditions may find this schema interesting if they entertain the hypothesis that it constitutes a virtual map of conceptual closure, or better still, of the closure of ideology itself, that is, ideology as a mechanism, which, while seeming to generate a rich variety of possible concepts and positions, remains in fact locked into some initial aporia or double-bind that it cannot transform from the inside by its own means.

However this may be, it seems appropriate to conclude this introduction with an outsider’s observations on the multiple uses and interests of this mechanism. A few initial remarks ought to concern its “proper use,” that is, to offer some warnings about what it can and cannot do. The square does offer, I believe, a kind of “discovery principle,” but of a special type, and it cannot be guaranteed to replace intelligence or intuition. Indeed, insofar as it can often be called on simply to map thoughts and interpretations arrived at in other (seemingly less technical) fashions, it is appropriate at the outset to stress its initial pedagogical function: one can, in other words, very properly use this visual device to map out and to articulate a set of relationships that it is much more confusing, and much less economical, to convey in expository prose, and these humbler pedagogical capacities of the semiotic square may not be the least index of its importance.

As for its heuristic value, however, experience testifies that you must blacken many pages before you get it right and that a number of key decisions intervene in the process. One lists a variety of entities to be coordinated; it is a list that must never be considered final, nor should the nature and nomenclature of the entities be foreclosed. It is desirable (even, in my view, necessary) that seemingly aberrant or marginal, minor, eccentric entities be enumerated, since it is their place in the scheme of things, and their very presence, which is the most interesting of the problems the square can be called upon to solve.

As for operative decisions or moments, I will mention three that seem to me crucial. The first is the inaugural decision, not merely about the terms of the binary opposition to be expanded and articulated in the square as a whole, but also, and above all, the very order in which those terms are arranged; it makes a fundamental difference, in other words, whether the founding binary is ordered as white versus black, or as black versus white. The square is in that sense not symmetrical but “temporal” or positional, and the placement of the terms (obviously this initial formulation will already imply something like dominant/subordinate, center/margin, self/other), like that of mathematical equations (or the lobes of the brain, or right and left hand), is not indifferent but actively determinant in astonishing ways (that very astonishment playing its own part in the unexpected lessons we find ourselves learning in this process).

The second important recommendation is that the four primary terms (S₁, S₂, ₁, ₂) need to be conceived polysemically, each one carrying within it its own range of synonyms, and of the synonyms of its synonyms—none of them exactly coterminous with each other, such that large areas of relatively new or at least skewed conceptuality are thereby registered. Thus, for example, in Hayden White’s conception of “metonymy” in Metahistory, two relatively distinct “semes” are encompassed—that of reduction (scientific or mechanistic explanation, determinism) and that of separation; this term thus includes a fruitful terrain for dialectical slippage, such that its “reductive” aspect may allow it to stand in opposition to the visionary and representational plenitude of “metaphor.”² Its other “identity”—as sheer disjunction or separation—then allows it unexpectedly to be coordinated with (or against) “synecdoche” as the reintegration of the separated and the construction of new wholes. This will to embrace the slippage within terms is here a practical recommendation, like handicraft rules of thumb or inherited wisdom, but it also opens up a dizzying perspective of the subatomic universes, a prospect of what a very different semiotician, Umberto Eco, following Peirce, calls “infinite semiosis,” in which each of the four primary terms of the square threatens to yawn open into its own fourfold system, down into the infinite divisibility of semiotic nature.

A final warning must be directed to the peculiar nature of the fourth term, the negation of the negation: ₂ This must be (when the operation is successful) the place of novelty and of paradoxical emergence: it is always the most critical position and the one that remains open or empty for the longest time, for its identification completes the process and in that sense constitutes the most creative act of the construction. Once again, it is simply a matter of experience that the first three terms are relatively “given” and demand no great acts of intellection, but that the fourth one is the place of the great leap, the great deduction, the intuition that falls from the ceiling, or from heaven. Yet this is something that here can be only mythically conveyed, as in that system of apocalypses foretold by Mayan religion, which, fourfold in a relatively universal fashion, only springs apart from Western paradigms unexpectedly in its fourth moment. The world, for the Mayans, will end in fire, as for us; a second time around, the world will be destroyed by water, as for us; yet a third time, and it will be destroyed by air (hurricanes). And it will also be destroyed a fourth time … by jaguars! (which, formerly the stars in the heavens, take on their new carnivorous form and drop upon the earth to devour the human race). So also with J. G. Ballard’s early and haunting end-of-the-world tetralogy: by water (The Drowning World), by fire (The Burning World), by air or hurricane (The Wind from Nowhere), and then … by turning into crystal (The Crystal World)!

The semiotic square is thus not static but dynamic: the significance of positionality within it is only one index of the way in which it can just as easily be considered to map a temporal process as to register a conceptual blockage or paralysis; indeed, the latter can most often be grasped as the very situation that motivates the former, namely, the attempt, by rotating the square and generating its implicit positions, to find one’s way out of the conceptual or ideological closure, out of the old or given—into which one is locked—somehow desperately to generate the novelty of the event, or of breakthrough, or of the Novum. Yet to see the square as the very image of closure itself tends to encourage some pessimism about the possibilities of escaping from it in any other way than the Hegelian one: one does not resolve a contradiction; rather, by praxis, one alters the situation in such a way that the old contradiction, now dead and irrelevant, moves without solution into the past, its place taken by a fresh and unexpected contradiction (which may or may not be some advance on the older aporias or ideological imprisonment).

Yet the very gestalt properties of the square—its capacity to be indifferently static or dynamic—are what accounts for its powerful mediatory capacity: it can, in other words, “reduce” a narrative in movement to a series of “cognitive” or ideological, combinatory positions; or it can rewrite a cognitive text into a desperate narrative movement in which new positions are generated and abandoned, and in which terms ceaselessly amalgamate in order to achieve the release of this or that ideal synthesis and release from their warring and antagonistic, structural-fragmentary nature.

I have offered elsewhere illustrations of possible “applications” of the square to problems of narrative analysis: these unorthodox efforts may serve to suggest ways in which the two planes of narrative—“characters” or, better still, systems of characters, and cognitive complexes or contradictions—can be coordinated and transcoded into one another.³ Here I will briefly sketch a sample of the analysis of a “cognitive” or theoretical text, Hayden White’s Metahistory, which is to be sure in a way preprepared, insofar as this text is itself already organized around a fourfold set of categories: the four tropes of Metaphor, Metonymy, Synecdoche, and Irony. This first system of categories is then multiplied by three more: a typology of world views, drawn from Stephen Pepper (Formism, Mechanicism, Organicism, and Contextualism); Frye’s “emplotments” (Romantic, Tragic, Comic, and Satirical); and finally Mannheim’s categories of ideology (Anarchist, Radical, Conservative, and Liberal). In practice, it may be suggested that this set of, as it were, vertical layers in fact tends to amalgamate into two groups of coordinated features: the tropes and Pepper’s “world hypotheses” function as alternate languages for the same characteristics, whereas the “emplotments” and the “modes of ideological implication” also tend to function synonymously. Yet within each of the two groups (which roughly correspond to the structure of a given history and to its metaphysical connotation, or reception, respectively), we already find that creative slippage I have referred to, the possibility of passing from one term to another by way of a shift in these levels (the earlier example of Metonymy illustrates a shift from the tropological sense of this “term” to its conceptual, or world-hypothetical, sense). What remains an open question is whether the two groups of categories need always function in unison, or whether one might not imagine a dissonance, that is, a contradiction, between say, the tropological mechanism and the emplotment or ideological message. This is something White seems to foresee, without, however, drawing any explicit conclusions from the possibility.⁴

White’s book seeks to do (at least) two things: first, to reassert the historical and cognitive claims of the so-called philosophers of history (Hegel, Marx, Nietzsche), who have, in the traditional canon of historiography, been assigned a lower and more amateurish status by the historians themselves, in contrast to “real” or practicing historiographers, of whom this book deals with four (Michelet, Ranke, Tocqueville, and Burckhardt). What Metahistory in fact achieves is a good deal less modest than this, since the thrust of the argument tends toward the assertion that in fact the philosophers of history are better historians than the historiographers. How the text generates this position will then be one of the questions an articulation by the semiotic square needs to answer.

The other function of Metahistory (which is specifically limited to the nineteenth-century “historical imagination”) is to demonstrate not merely the relevance of the conceptual typologies already enumerated but their cyclical function, in a rhythm that begins in naive Metaphor or Romanticism, passes through the negative or Metonymic, Mechanistic stage of reduction, begins to reclaim a larger totalizing construction in the new unities of Synecdoche, and finally, in the moment of Irony, comes to a self-consciousness of its own linguistic or tropological procedures that signals a new crisis of the historical imagination and may be expected, by way of the great Viconian ricorso, to swing around again into a fresh belief, a fresh Metaphoric or Romantic moment with which the cycle can begin all over again on a heightened level. Indeed, it is this rebirth of historiographic belief that White calls for in his concluding pages, which speak out of the moment of Irony and its crisis. What is peculiar, however, is that the moment of Irony, Metahistory, takes two distinct forms: the crisis of the nineteenth century reaches as it were two distinct paroxysms simultaneously—the “bad” Irony of Burckhardt, serene and aestheticizing (the “philosophy” of Croce is in effect a more elaborate double of this position), and the “good” or strong Irony of Nietzsche from within which Hayden White clearly speaks (even though Hegel and Marx were to have been “rehabilitated” more or less on equal grounds with the author of the Genealogy of Morals). These intricate moves are, however, not random ones, nor are they in any way the “mere” results of the personal opinions or ideological predilections of the metahistorian; the pattern is indeed a very logical one, which can be clarified and articulated by the operation of the semiotic square as the various possible terms and positions of Metahistory are mapped onto it.

The diagram attempts to respect as much as possible the combinatory richness and intricacy of the text, very specifically including what I have called the slippage within the terms, that is their multiple semic content or the copresence of various levels and codes within each:

What should be clear from this initial mapping onto the semiotic square is that the four historians each present, in all their differences, the spectacle of unison between all the levels, and that indeed it is this very absence of inner tension or contradiction that accounts for the author’s evaluations of them: itself a form of irony, not to say contempt, save in the case of Tocqueville, where a certain tragic honesty carries conviction, but where, it should be noted, this univocal position also ultimately disintegrates under its own momentum into a Burckhardt-type irony and nihilism, which itself—as yet another univocal ideological position—then is subjected to the full force of the metahistorian’s Irony. This last must therefore be of a different type, and it is precisely the advantage of the semiotic square to hold open other conceivable positions, which have not yet been secured in our diagram, and which are the so-called compound terms, the complex and neutral terms S and , and the deictic axes in which the lateral sides of the square also designate possible syntheses. Before demonstrating those, however, it is worth noting the strategic function, already referred to, involved in the choice of an initial binary opposition. The story, as anyone would naturally tell it, and as Hayden White himself initially maps it in his diagram of the levels in Metahistory, is one in which an initial Metaphoric consciousness disintegrates into a Metonymic or negative moment of determinism and random mechanistic causality.⁵ That negative crisis is then—on anyone’s stereotypical narrative paradigm—slowly overcome by Synecdochic reconstruction, only to be sapped and vitiated by a new kind of disintegration and a new kind of crisis—that of Ironic self-consciousness, and of the sense that even the Synecdochic solution was itself only fictional and linguistic—at which point, as I have already said, the entire system turns over and swings back into a new cycle of Metaphoric reaffirmation.

But this corresponds neither to the order of the chapters nor to the combinatory logic of the work itself, in which Romance is followed by Comedy, and Metaphor by Synecdoche, rather than by Metonymy. Thus, we have mapped the semiotic square around a quite unexpected binary opposition, not the familiar one of Metaphor versus Metonymy, but some new constitutive tension between Metaphor and Synecdoche—a tension that must necessarily be conceptualized as the antagonism between two forms of unity, an initial Metaphoric or representational one (Michelet’s great ecstatic moments of national unity in the Revolution and more specifically of the “fêtes de la Fédération” of June 1790) and a Synecdochic one, the construction of more “artificial” social unities, built up from their separate parts, in the form of Ranke’s institutions (church, nation, and so on). The point I wish to stress is that the square will not work any other way (the reader may now wish to test this assertion by experiment) and that only this arrangement of the terms will generate the essentials of Metahistory, a book about which we have therefore learned something new, namely, that its deepest subject, the fundamental contradiction it is concerned to resolve, is not that of meaning versus nonmeaning, or belief versus causality (Metaphor versus Metonymy: the traditional way of mapping the nineteenth-century “crisis of faith”), but rather the tension between two incompatible visions of the social, neither of which (ecstatic revolutionary spontaneousness and the slow permanency of the great social institutions) seems satisfactory.

I must also add a word about the question of the “fourth term,” also raised earlier. It is clear that, although the word itself is scarcely fresh or surprising, Irony is the great magical term on which the text turns and that its combinatorial mechanisms aim fully as much at producing this extraordinary “position” from across a wide range of meanings and uses (the slippage in this fourth term is far greater than in any of the others) as they simply register it as an object of study and one attitude among others.

We may now rapidly conclude the mapping of the square, whose complex and neutral terms can be loosely designated as historical Optimism and Pessimism respectively, a language whose slackness need not detain us long, since both are clearly logically impossible positions that the movement of the work rejects (S is a conceivable but impossible synthesis, is merely the empty wiping out of that content and the place of the global, mechanical negations of both terms of the initial opposition). It is therefore to the lateral (or deictic) syntheses that we turn our attention. Here indeed the great “philosophers of history” find their positions, which have been generated by the inner logic of the square itself. Both Hegel and Marx, White tells us, achieved syntheses of Tragedy and Comedy: history is a comedy, all of whose individual moments are tragic. Nietzsche, meanwhile, begins with an identification of Tragedy and Comedy, which luminously eclipse each other and in their indistinction give rise to something else, which will be an Ironic sense of the powers of language that now once again releases the great Metaphoric energies. (Note how it is very precisely the semiotic slippage between Romance and Metaphor that enables this ultimate moment to be something more than a mere synthesis of Romance and Satire.) With this, the combinational movement of the book is exhausted and a message emerges: the priority of Hegel, Marx, and Nietzsche over the “univocal” historians, and after that, perhaps, the more tentative priority of Nietzsche over the other two positions insofar as Nietzsche “includes” their moments of Tragedy and Comedy and then projects further new and original possibilities, Metaphor and Irony (properly linguistic or reflexive moments), out of the earlier pair (Figure A3).

Returning now to the nature of the semiotic square itself, it seems clear that its emergence from the dynamic of Greimassian semiotics betokens some profound spatiality in the system in general. What interests me is not the viability of this enterprise, nor how one might resolve this persistence of the irreducibly spatial within semiotics in some new and enlarged philosophical system, but rather the historical fact of its emergence in our society, where it is by no means the only example or symptom of a period intellectually given over to space in a way radically different from the preceding generation of the modernists, in thrall to temporality. All the structuralisms are deeply spatial in one way or another, and not merely in their rhetoric or modes of presentation (although the fact, previously mentioned, that we find these diagrams today more pedagogically convincing and persuasive than the corresponding linguistic expressions and developments of them is surely not insignificant either). Alone of the great philosophers, Henri Lefebvre has posited a genuine new philosophy of space, and this on a historicist basis, namely, the tendential spatialization of late capitalism (and, one might wish to add, using a concept not foreseen in Lefebvre’s work, of the postmodern). That Greimassian semiotics should be “true” in some sense (or at any rate, pragmatically, richly usable and full of practical development) and at the same time stand as a profound historical symptom of the nature of the age I find no difficulty in reconciling: the latter—the structure of the late capitalist global system—constituting something like the conditions of possibility for the conceptualizing and articulation of the new theoretical system.