No More Learning

Marx did not employ the term "constant" that I borrowed from Le? vi- Strauss, but a genial expression: "tendential law," capable of inflecting (not contradicting) the primary tendential law, which means that a ten- dency does not possess the form or figure of a linear law, but that it can bifurcate under the effect of an encounter with another tendency and so forth to infinity. At each intersection, the tendency can take an unfore- seeable form, just because it is aleatory. 18
This is the very issue that Althusser tackles head-on at the end of the essay on Cremonini.
ART AS REVOLUTIONARY WEAPON
According to Althusser, Cremonini's "radical antihumanism" took him down the same road as
the great revolutionary, theoretical and political thinkers, the great mate- rialist thinkers who understood that the freedom of men is not achieved by the complacency of its ideological recognition [reconnaissance], but
by knowledge [connaissance] of the laws of their slavery, and that the "realization" of their concrete individuality is achieved by the analysis and mastery of the abstract relations which govern them. (LP 240-41; EPP 584; translation modified)
Althusser is unyielding (and currently rather unfashionable) on this point, as he had been in the "Letter on Art": art is on the side of knowledge, of science, not on the side of ideology, of which it gives a knowledge, however different in form from that which is given in sci- ence. On an Althusserian account, art provides a means by which to discover the true nature of the world, the structure of its social rela- tions, and the possibilities it holds for realizing human emancipation.
If this were the end of the matter, if materialist aesthetic practice were to be limited in its effects to this essentially critical function in re- lation to ideology, the charge Althusser offhandedly hurls at Brecht-- that "there is an aspect of the enlightener in Brecht, the theme of 'theater in a scientific age,' etc. " (EPP 553)--would double back on Althusser himself (although one should add that there are many worse fates than to be an enlightener). The couplet ideology/knowledge would in principle be immediately and permanently dissolved, for who would continue to subscribe to an ideology having attained a knowl- edge of it? But, as always, things are not so simple. 19
The specific relation that works of art establish with ideology is the subject of Althusser's final reflections in the Cremonini essay. If we say that this relation is akin to but distinct from that of the sciences (in- cluding politics), it is only to indicate the specificity, the unique materi- al modality of art. Art matters by virtue of the effects it produces, ef- fects manifested precisely in ideology. Here, one last time, is Althusser on the relationship between art and ideology:
Every work of art is born of a project both aesthetic and ideological. When it exists as a work of art it produces as a work of art (by the type of critique and knowledge it inaugurates with respect to the ideology it makes visible) an ideological effect. . . . like every other object, including instruments of production and knowledges, or even the corpus of the sciences, a work of art can become an element of the ideological, that is to say it can be inserted into the system of relations which constitute the ideological. . . . Perhaps one might even suggest the following proposi- tion, that as the specific function of the work of art is to make visible (donner a` voir), by establishing a distance from it, the reality of the ex- isting ideology (of any one of its forms), the work of art cannot fail to
Art and Ideology 43
44 Michael Sprinker
exercise a directly ideological effect, that it therefore maintains far closer relations with ideology than any other object, and that it is not possible to think the work of art, in its specifically aesthetic existence, without taking account of this privileged relation with ideology, that is to say without taking account of its direct and inevitable ideological effect. (LP 241-42; EPP 585-86; translation modified)
Scandalously--but with complete consistency--Althusser insists that the ideological (and therefore the political) effectiveness of artworks derives from their aesthetic power, namely, from their production of an "internal distance" in relation to the ideology that they present. The presentation of ideology in art, as it were, estranges ideology from it- self, creating the possibility for, not only identification with or interpel- lation by the ideology presented, but a knowledge of it, a knowledge that the audience can then put to use in transforming the conditions that produced the ideology in the first place. Art's aesthetic power is the source of its pedagogical, scientific function. The key interlocutor, not mentioned by name here, is obviously Brecht.
Consider, for a moment, Brecht's career and posthumous fate. Forced into exile during the Nazi period, his postwar return to the German Democratic Republic saw him attain a transformative power over dramatic practice, in Germany and beyond, that had eluded him during the Weimar period. Not only were his plays performed around the globe, his dramaturgical writings exercised an influence so wide- ranging as to make him, arguably, one of the most significant figures in world literature during the 1950s and 1960s. 20 What one might call "the Brecht-effect" was among the most astonishing developments in postwar culture, not least because the political program he espoused could, during the Cold War, be so easily dismissed with the epithet "Stalinist. " Nor has this "Brecht-effect" remained unchanging, frozen in time as the singular model for revolutionary theater. In the post-Cold War era, books like John Fuegi's debunking biography and widespread attempts to "liberate" Brecht from the "burden" of his Marxism are only to be expected.
Yet there remain alternatives, many of them skillfully set forth by Fredric Jameson, whose brief for Brecht's contemporary relevance to Marxist politics is entirely salutary. 21 One that ought to be more fully explored is the very opposite of those aesthetic practices that have con- ventionally been termed Brechtian and are powerfully associated with Brecht's German disciples such as Heiner Mu? ller, in filmmaking with
the French nouvelle vague (Godard, Straub) and the German New Wave (Fassbinder in particular), and in British drama with Stoppard and Caryl Churchill, among others. Far from being revolutionary today, in the age of MTV, the Simpsons, and Beavis and Butthead, what was once alienating in Brechtian theater has become a staple of the culture of consumption. 22 In this ideological conjuncture, then, the truly Brechtian project may just be the reinvention of realism, in the theater certainly, but more importantly in film and video, the dominant media of late-capitalist culture. Not Quentin Tarentino or David Lynch, but Ken Loach and Mike Leigh--the latter are the authentic Brechtians of this moment, the ostensible conventionality of their films notwith- standing. 23 But that would be the subject for another paper, one in which the matter of art is more programmatically linked to the project of revolutionary politics. The latter is still very much on the agenda, however distant the horizon of its realization may seem just now.
NOTES
This essay is a substantially emended version of a paper delivered at the "Culture and Materiality" conference held at the University of California at Davis April 23-25, 1998. The original included lengthy exegeses of texts by Brecht, Althusser, and Benjamin that are of marginal interest in the present context of Paul de Man's later writings on aesthetics and ideology. To conform better to the occasion, I have omitted this other material and expanded the section that directly addresses de Man's writings.
1. Louis Althusser, "A Letter on Art in Reply to Andre? Daspre," in Lenin and Philosophy and Other Essays, trans. Ben Brewster (New York: Monthly Review Press, 1971), 222-23; hereafter, cited parenthetically as LP. The French original was first published in La Nouvelle Critique 175 (April 1966). I cite from the text as it appears in Louis Althusser, E? crits philosophiques et politiques, vol. 2 (Paris: Stock/IMEC, 1995), 561; hereafter, EPP. I have occasionally modified the standard English translations of Althusser.
2. Stefano Rosso, "An Interview with Paul de Man," in Paul de Man, The Resistance to Theory (Minneapolis: University of Minnesota Press, 1986), 121.
3. Paul de Man, Aesthetic Ideology, ed. Andrzej Warminski (Minneapolis: University of Minnesota Press, 1996), 56; hereafter cited parenthetically as AI.
4. On Locke's (unsuccessful) attempt to discipline language and subject it to rational principles, to eliminate the abuses to which it is put in discourses of eloquence (namely, rhetoric), see de Man, "The Epistemology of Metaphor," in AI, 35- 42.
5. Paul de Man, The Resistance to Theory (Minneapolis: University of Minne- sota Press, 1986), 11; cited by Warminski in his Introduction to AI, 8.
6. Louis Althusser, "Ideology and Ideological State Apparatuses (Notes towards an Investigation)," in LP 162; in French, "Ide? ologie et appareils ide? ologiques
Art and Ideology 45
46 Michael Sprinker
d'E? tat," in Sur la reproduction (Paris: Presses Universitaires de France, 1995), 296; hereafter SR.
7. The phrase "en sujets" is characteristically rendered "as subjects," but it might better be translated "into subjects," namely, into subjectivity. Ideology takes that which is not a subject (individuals) and subjectifies (or subjectivates) them, al- though it should be said that the ubiquity of ideology makes it impossible to con- ceive anything like a (nonideological) nonsubject; hence, Althusser's scandalous as- sertion that "individuals are always-already interpellated by ideology as subjects [en sujets], which necessarily leads us to one last proposition: individuals are always-already subjects" (LP 176; SR 306-7).
8. At least one other commentator on de Man has drawn a similar comparison between the Althusserian concept of ideology and de Man's account of tropes; see Andrzej Warminski's Introduction to Aesthetic Ideology, 9-12. Warminski takes up the relationship between de Man's extant texts and The German Ideology in his "Ending Up/Taking Back (with Two Postscripts on Paul de Man's Historical Materialism)," in Critical Encounters: Reference and Responsibility in Decon- structive Writing, ed. Cathy Caruth and Deborah Esch (New Brunswick, N. J. : Rutgers University Press, 1995), 11-41.
9. Cf. the following: "The point is that the neoclassical trust in the power of imi- tation to draw sharp and decisive borderlines between reality and imitation . . . depends in the last analysis, on an equally sharp ability to distinguish the work of art from reality. . . . The theoretical problem [of the aesthetic], however, has been dis- placed [between its original formulation by Schiller and its presentation in Kleist's apologue "U? ber das Marionettentheater"]: from the specular model of the text as imitation, we have moved on to the question of reading as the necessity to decide be- tween signified and referent, between violence on the stage and violence in the streets" (Paul de Man, "Aesthetic Formalization: Kleist's U? ber das Marionettentheater," in The Rhetoric of Romanticism [New York: Columbia University Press, 1984], 280).
10. Cf. de Man: "the political power of the aesthetic, the measure of its impact on reality, necessarily travels by way of its didactic manifestations. The politics of the state are the politics of education" (ibid. , 273)--a formulation that Plato would have heartily endorsed.
11. As de Man elsewhere observes: "Thus Kant would have forever ended the play of philosophy, let alone art, if the project of transcendental philosophy had succeeded in determining once and forever the limits of our faculties and of our freedom" (ibid. , 283). Notoriously, Kant's project was a failure, the principal evi- dence for which is the Critique of Judgment itself, the text to which de Man turns to disclose this other Kant.
12. In the discussion following her own presentation, Judith Butler contested this formulation, asserting that in this instance materialism for Kant (and presum- ably for de Man as well) was not a concept at all. That there could be something like a "materiality without materialism" (as Jacques Derrida perspicuously put it in his paper), I would not wish to deny. But to the extent that Kant is attempting in the passage cited to define a representational modality ("seeing as the poets do it") and thereby to make it available to the understanding, what he writes necessarily pos- sesses a conceptual dimension, or else it would not be readable at all. Materiality (that to which Kant refers or that which he posits) may not be conceptual, but a
theory (the mode of Kant's referring or positing) of the materiality of art, of seeing "as the poets do it," cannot do without concepts, empty or not. This is the same, ele- mentary, distinction insisted upon by Althusser between the "real-concrete" and the "concrete-in-thought"; see the latter's "On the Materialist Dialectic: On the Unevenness of Origins," in For Marx, trans. Ben Brewster (1969; rpt. London: NLB, 1977), 188-89.
13. Even famous limit cases like John Cage's performances of silence require the appearance of the composer/performer on stage sitting motionless for a certain number of minutes before the piano. The silence requires this minimal phenomenali- zation for the composition to be realized. The point is evident in the passage on the sublime from Kant's third Critique cited by de Man, but it is slightly obscured in de Man's translation. The standard English rendering discloses the necessity for even the most rigorously anti-aesthetic practice to exhibit itself in phenomenal form: "we must regard [the sublime], just as we see it [bloss wie man ihn sieht], as a dis- tant, all-embracing, vault. Only under such a representation can we ranage that sublimity which a pure aesthetical judgment ascribes to this object" (Immanuel Kant, Critique of Judgement, trans. J. H. Bernard [New York: Hafner, 1951], 110; quoted from Rodolphe Gasche? , The Wild Card of Reading: On Paul de Man [Cambridge: Harvard University Press, 1998], 101).
14. This is the burden of Gasche? 's exposition of de Man's theory of reading; see especially chapter 3, "Apathetic Formalism," in The Wild Card of Reading, 90-113. 15. Gasche? discusses de Man's anti-Hegelian, that is, anti-aesthetic, theory of reading in relation to the passage from Hegel's Aesthetics on silent reading in ibid. ,
115-16.
16. One of the anonymous referees who evaluated the present volume for the
University of Minnesota Press took my essay to task for "its old-fashioned com- paratist strategy," characterized by its "presentation of 'parallels' between the work of de Man and Louis Althusser," and for failing (in contrast to Ernesto Laclau's contribution) "to demonstrate how de Man can help us to read history and politics. " The reader also complained that my paper "lack[s a] conclusion" but "'concludes' with a discussion of Brecht that fully 'forgets' de Man. " I would have thought that the point of the pages that follow is clear: to contrast Althusser's ex- ploration of the political and ideological effects of artworks and to show how it cashes out de Man's provocative, but practically underdeveloped, assertions. That I have recourse to the example of Brecht to illustrate Althusserian theory is hardly fortuitous. I do not so much "forget" de Man as I suggest that his critique of aes- thetics culminates in a gesture toward art's politicality, rather than in any determi- nate politics of art. My aim is therefore quite different from that ascribed to Laclau's text: it is not "to demonstrate how de Man can help us to read history and politics," but rather, to examine the potential for and the limits of a political prac- tice of art. These are not, in my view, de Manian questions; hence, my turn away from de Man at the end.
17. Warminski, "Ending Up/Taking Back," 34.
18. Louis Althusser, Sur la philosophie (Paris: Gallimard, 1994), 45; my trans- lation. On the continuity between the early Althusserian concept of the overdeter- mined conjuncture and the later program to develop an "aleatory materialism," see Gregory Elliott, "Ghostlier Demarcations: On the Posthumous Edition of Althusser's
Art and Ideology 47
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Writings," Radical Philosophy 90 (July-August 1998): 27-28. That there may be a deeper theoretical affinity between Althusser and de Man connecting the former's "aleatory materialism" with what Gasche? identifies as de Man's object of defining the "absolutely singular," an affinity that would involve their respective commit- ments to nominalism (noted by Fredric Jameson in the case of de Man, and by Warren Montag in the case of Althusser), is a topic requiring detailed examination of the entire corpus of both thinkers. Such a project clearly exceeds the scope of the present occasion, which is devoted to a more restricted inquiry into the relation of aesthetics to ideology, and to the political effects of art.
19. Althusser explicitly rejects the Enlightenment concept of ideology in the ISAs; see LP 163-64.
20. The claim is argued more fully by Fredric Jameson in Brecht and Method (London and New York: Verso, 1998). See also, inter alia, Michael Patterson, "Brecht's Legacy," in The Cambridge Companion to Brecht, ed. Peter Thompson and Glendyr Sacks (Cambridge: Cambridge University Press, 1994), 273-87; and the essays by John Willett (on Brecht's reception in Britain), Bernard Dort (on Brecht in France), Karen Laughlin (on Brecht's assimilation by American feminist playwrights), Renate Mo? hrmann (on Brecht's influence on women's cinema in West Germany), and Thomas Elsaesser (on Brecht's incorporation by film theory and practice in France, Britain, and Germany), collected in Re-interpreting Brecht: His Influence on Contemporary Drama and Film, ed. Pia Kleber and Colin Visser (Cambridge: Cambridge University Press, 1990). A more specialized but highly in- formative study is George Lellis, Bertolt Brecht, Cahiers du Cine? ma, and Contem- porary Film Theory (Ann Arbor: UMI Research Press, 1982).
21. See Jameson, Brecht and Method, especially the two concluding sections, titled "Actuality" and "Historicity. "
22. See the concluding pages of Thomas Elsaesser's essay on Brecht and con- temporary film, cited in n. 20 above.
23. The Loach-Leigh connection is commonplace in accounts of contemporary British cinema; see, for example, Michael Coveney, The World according to Mike Leigh (London: HarperCollins, 1996), 13-14; and the introduction to Leigh's inter- view with Cineaste 20:3 (1994): 10-17. But just as quickly as the connection is as- serted, it is disavowed, or heavily qualified (not least by Leigh himself). Despite no- table differences in political affiliation, their shared commitment to realism as an aesthetic mode is of the utmost importance, as are each director's methods of preparing cast and narrative for production. Both practice that form which Fredric Jameson argues was Brecht's preferred vehicle for dramatic realization: the work- shop or master's class (see Brecht and Method).
Algebra and Allegory: Nonclassical Epistemology, Quantum Theory, and the Work of Paul de Man
Arkady Plotnitsky
The "nonclassical epistemology" of my title refers to the epistemology defined by a particular configuration, to be assembled in this essay, of the concepts of materiality, phenomenality, formalization, and singu- larity. These concepts would be naturally associated with de Man's work by his readers, as would be the concept of allegory, which is, I shall argue, correlative to the epistemology and the conceptual configu- ration in question. 1 The appeal to "algebra" is somewhat more eso- teric. It is, however, far from out of place, especially in the context of the question of formalization and given the relationships among de Man's work, nonclassical epistemology and quantum theory, which I shall also discuss here.
It would indeed be difficult to circumvent de Man's work in consid- ering these subjects or such figures as Kant, Kleist, and Shelley, to whom a significant portion of this essay will be devoted. 2 In particular, nonclassical epistemology has fundamental connections to aesthetic theory, beginning (at least) with Kant and Schiller, and to the practice of literature and art, such as of Kleist, Shelley, and other Romantic au- thors, or, as T. J. Clark's "Phenomenality and Materiality in Ce? zanne" (in this volume) suggests, that of Ce? zanne. These connections are cen- tral to de Man's later works, specifically Aesthetic Ideology, where Kant's third Critique, The Critique of Judgment, and aesthetics and (the critique of) aesthetic ideology, are given a special place. 3 The history of the particular aesthetic-ideological (mis)reading of the third Critique in question in his work is seen by de Man as beginning with and still gov- erned by Schiller's encounter with Kant. By contrast, the work of, espe- cially, Kleist and of some among his Romantic contemporaries appears
49
50 Arkady Plotnitsky
to mark for de Man the opening of a different aesthetic theory. This opening also leads to a very different type of reading of the third Critique (which may be closer to the spirit, or indeed the letter, of the work) by de Man and such authors as Jacques Derrida, Jean-Franc? ois Lyotard, Jean-Luc Nancy, and several others. This difference is, I argue, defined by the set of, in terms of this essay, nonclassical concepts-- in particular, "formalization," "materiality," "phenomenality," and "singularity"--to which I now turn. I begin with formalization and what I call radical or nonclassical formalization.
Paradoxically, or so it may appear, the radical character of radical formalization, and of its formal laws, is defined by the fact that they allow for, and indeed entail, that which is irreducibly unformalizable, irreducibly lawless; that is, whereas the "algebra" of any formalization may be seen as defined by a set of (specified or implicit) laws, here the configuration or ensemble of configurations of elements governed by these laws entails that which cannot be comprehended by these laws or by law in general, and furthermore, that which cannot be conceived by any means that are or even will ever be available to us. Accordingly, the irreducibly lawless in question is not something that is excluded from the domain or system governed by formalization, is not an ab- solute other of the system, but is instead irreducibly linked to it. 4 This is in part why radical formalization may appear paradoxical, and it does lead to an epistemology that, while technically free of contradic- tion, is complex and difficult (and, for some, impossible) to accept.
The particular version of radical formalization that I shall now in- troduce appears to be epistemologically the most radical yet available. But then it may also be the only available (or even possible) model of the configuration of the formalizable and unformalizable just defined. Accordingly, from this point on, by either radical or nonclassical for- malization I refer to this version. The complexities and implications of the concept are many and far-reaching. The configuration itself defin- ing it, or constituting the point of departure for it, is, however, simple to formulate: the representation of the "collective" may, in certain circumstances, be subject to formalization and law; that of the "in- dividual" is irreducibly nonformalizable and lawless; and the overall efficacity of both types of effects, formalizable and nonformalizable, is inaccessible by any conceivable means. 5
This formulation does not merely mean that formalization or law in this case does not apply in certain exceptional situations. Instead, every individual entity (element, case, event, and so forth) that belongs
to the law-governed ("organized") collectivities in question is in itself not subject to the law involved, or to law in general. More accurately, one should speak of what is "seen" (is phenomenal) or represented as such an entity or such a collectivity. The qualification is important to the relationships between "materiality" and "phenomenality" in non- classical epistemology. I shall consider these relationships in detail later. It may, however, be useful to offer a preliminary sketch here, be- ginning with this qualification.
Although law here does apply only at the level of certain collective, rather than individual, effects, both types of effects, lawful and law- less, are manifest, materially or phenomenally. Accordingly, when in- volved, material strata of such effects may, at least, be treated as avail- able to phenomenalization, representation, conceptualization, and so forth, for example, for the purposes of formalization. By contrast, the ultimate efficacity of these effects cannot, in principle, be so treated (even though, as will be seen, this efficacity may, at a certain level, be considered as material). In other words, this efficacity is irreducibly inaccessible not only to formalization and law--to "algebra"--but to any representation, phenomenalization, and so forth. Nor, ultimately, can we think of it in terms of any properties or qualities that, while in- accessible, would define it. It is irreducibly inaccessible by any means that are or, conceivably, will ever be available to us; any conception of it is, and may always be, impossible, ultimately even that of the impos- sibility of conceiving it. As will be seen, it would not be possible to ac- count for the coexistence of both types of effects (collectively lawful and individually lawless) in question otherwise. The presence of both types of effects is logically possible if and only if we cannot conceive of their efficacity at all: the peculiar character of the effects makes one infer the even more peculiar character of the efficacity. It follows that all conceivable terms are provisional, suspect, and ultimately inade- quate in describing this efficacity, including efficacity or ultimate, both quite prominent here. It is worth, however, registering more specifically some of the terms that need to be suspended.
First, although this efficacity manifests itself through the effects of both types, it cannot be thought of in terms of an underlying (hidden) governing wholeness, either indivisible or "atomic," so as to be corre- lated with manifest (lawless) effects, while subject to an underlying coherent architecture that is not manifest itself. Either type of under- standing would (classically) reduce the (nonclassical) "counterposition" of the manifest effects of collective lawfulness, on the one hand, and of
Algebra and Allegory 51
52 Arkady Plotnitsky
individual lawlessness, on the other. This efficacity is neither single in governing all of its effects (individual and collective), nor multiple so as to allow one to assign an unambiguously separate efficacity to each lawless individual effect.
Second, an efficacity of that type cannot be seen in terms of inde- pendent properties, relations, or laws, which, while unavailable, would define a certain material entity that would exist in itself and by itself, while, in certain circumstances, giving rise to the (available) effects in question. Instead, it must be seen as reciprocal with and indeed indi- visible from its effects: it can never be, in practice and in principle, con- ceived as isolated, separate from them. Nor, however, can it be seen as fully "continuous" with these effects either. All individuality or, con- versely, collectivity in question appears (in either sense) only within the manifest strata of such indivisible configurations. These configura- tions, however, also contain the inaccessible strata that cannot be iso- lated and hence cannot appear, either as accessible or even as "inacces- sible. " It is irreducibly inaccessible and yet, indeed as a corollary, equally irreducibly indissociable from that (part of the overall configu- ration) which is accessible--is subject to phenomenal representation, conception, knowledge, and so forth. One might say that, while the in- accessible in question is indeed inaccessible absolutely, it cannot be seen as something that is the absolutely inaccessible. It follows that nonclassical epistemology does not imply that nothing exists that, in certain circumstances, gives rise to the effects in question. Instead the point is that this efficacity or the corresponding "materiality" (which also designates something that exists when we are not there to observe it) is inconceivable in any terms that are or perhaps will ever be avail- able to us. Naturally, "existence" or "nonexistence" are among these terms, along with the possibility or impossibility to "conceive" of it, or "possibility" or "impossibility," or "it" and "is," to begin with.
As will be seen, these conditions are the conditions of both quan- tum epistemology and allegory in de Man. It is true that de Man often associated allegory (or irony) with discontinuity (in earlier work in juxtaposition to the continuity of symbol). We may, however, more properly think of this relation as neither continuous nor discontinuous, or in terms of any conceivable combination of both concepts, or, again, in any given terms, as just outlined. De Man's emphasis on disconti- nuity of allegory appears strategically to point in this direction, away from the continuity of the symbol or of classical thought in general, for example, aesthetic ideology. Both continuity and discontinuity are re-
tained at the level of "effects," and the effects of discontinuity are in- deed more crucial to allegory (or irony).
In the circumstances in question, then, formalization and laws apply only to certain collectivities, but in general not to individual ele- ments composing such collectivities. (I am not saying that they fully describe the latter, since, as follows from the preceding discussion, how the "workings" of the efficacity just considered make lawless individu- al elements "conspire" to assemble into lawful collectivities is ulti- mately inconceivable. ) Accordingly, the (lawless) individual effects in question can no longer be seen as a part of a whole, so both are com- prehended by the same law, or by a correlated set of laws. This possi- bility defines classical systems and classical formalization, and I use the term classical accordingly. A classical formalization may and often must apply within nonclassical formalization. Within classical limits, however, nothing is, in principle, lawless, even though, in practice, laws may be difficult or, as concerns the ultimate laws, impossible to apply. In the latter case, an underlying lawfulness, however unknown or even unknowable, would be presupposed. By contrast, nonclassical, radical formalization not only figures as lawless the manifest individu- ality of certain effects involved, but rigorously suspends even the possi- bility of ascribing any structure, law-governed or not, or properties to the efficacity of all manifest effects, lawful or lawless.
Under these conditions, individuality becomes not only uniqueness but also singularity. Indeed, "singularity" may be defined by this prop- erty of manifest lawlessness in relation to a given law, or to law in general, perhaps especially when this property arises in a point-like, "singular," fashion--spatial or geometrical; algebraic or analytical (a "singular" point of a function or a "singular" solution of an equation in mathematics); temporal or historical; and so forth. To some degree, one might see the inaccessible efficacity of the singular (or indeed all) effects in question as itself "singular," as Rodolphe Gasche? appears to do in his reading of de Man in The Wild Card of Reading. 6 Historically, however, the term singularity has been associated with the (manifest) point-like configurations or with a relation to the inaccessible, and it is, I would argue, in de Man as well. In addition, the efficacity of such singular events in de Man is indivisible from its effects (in accordance with the analysis just given). Accordingly, it cannot be conceived of as an independent entity severed from them and, hence, as isolated from them either materially or phenomenologically, as the appeal to "singu- larity" in describing it might suggest. By contrast the singular effects in
Algebra and Allegory 53
54 Arkady Plotnitsky
question can be isolated phenomenologically, although, in view of the same reciprocity, ultimately not materially or efficaciously. Indeed, they are phenomenologically defined by this "isolation" from their (ul- timate) history and (both materially and phenomenologically) from each other. 7
Given the features just outlined, however, nonclassical formaliza- tion and nonclassical epistemology are indeed singularly radical episte- mologically or, as the case may be, antiepistemologically, as well as anti- ontologically. The view just outlined equally disallows any ultimate ontology and any ultimate epistemology--any possibility of knowing or conceiving how that which is at stake in it is ultimately structured, or is ultimately possible. For example, it would not be possible to pre- dict which information will become available at a later point. Hence, unknowability is not certain either, any more than knowability, except, again, at the ultimate (efficacious) level, where the unknowable be- comes irreducible. At this ultimate level, we may adopt Gasche? 's for- mulation, "any [ultimate] knowledge, even that of the impossibility of knowledge, is . . . [indeed] strictly prohibited" (The Wild Card of Reading 182)--but only at this level, hence I insert "ultimate" here. One would be reluctant to say, especially in the context of de Man's work, that nonclassical epistemology disallows materiality, although at the ultimate level no given concept of matter can apply any more than any other concept. One might say instead that one needs the kind of conceptual architecture here discussed in order to argue for the ne- cessity of a certain form of "materiality," in particular as "materiality" without an ultimate epistemology and an ultimate ontology. 8 De Man specifically associates this radical materiality with both Nietzsche and Derrida (161-62), and earlier Kant and Hegel, although such thinkers as Bataille, Blanchot, and Lacan are pertinent here. De Man also as- sociates this materiality with the "textuality" of Kant's and, by im- plication, other radical texts. He speaks of "the simultaneous [with idealism] activity, in his [Kant's] text, of a materialism much more radical than what can be conveyed by such terms as 'realism' or 'em- piricism'" (AI 121). I shall return to de Man's understanding of textu- ality later.
The qualifier "ultimate," which recurs throughout this essay, is cru- cial. For it is not that no account or knowledge is possible, which is not an uncommon misunderstanding of nonclassical theories, specifically de Man's or certain interpretations (such as that here considered) of quantum mechanics. On the contrary, rigorous and comprehensive ac-
counts of the situations in question only become possible once the epis- temological circumstances in question are themselves taken into ac- count. Specifically, at the level of "effects," classical ontology, episte- mology, and phenomenology become possible and necessary. Indeed, these are the effects that make us conclude that their emergence entails something that is ultimately inaccessible to us in that it may not toler- ate an attribution of any properties, terms, conceptions, and so forth, including, ultimately, any conception of the ultimate. For, at the very least, the sum of these effects is unaccountable for classically, even when they are subject to classical knowledge, as at a certain level they must be, since they would not appear to us otherwise. Nonclassical knowledge does not offer us a better knowledge of the irreducibly in- accessible in question in it than classical knowledge does. But it does allow us to infer this inaccessible from its effects and to account for these effects themselves, retaining the irreducibly inaccessible as part of this account.
The overall epistemological situation may, again, appear paradoxi- cal and (ideologically? ) unacceptable to some, in the case of quantum physics, Einstein, among them. It is, however, consistently defined and free of any logical contradiction, as Einstein indeed admitted in the case of quantum mechanics in his debate with Bohr. Do such configu- rations actually exist, or need to be constructed in certain situations? Do we need radical formalization to account for anything, even if it is conceivable and technically free of contradiction? Yes, such configura- tions do exist, or need to be constructed, both in literature (where they may be more expected as "inventions" of poets) and life (where one may expect them less). They appear to be necessary in facing the "dead nature" as well, at the level of its ultimate constituents, as we under- stand these constituents now, that is, in terms of quantum physics.
Indeed, in order to make "phenomenality" more rigorously appli- cable in nonclassical circumstances, we may, following Bohr, define "phenomenon" in terms of the reciprocal or indivisible relationships between the effects in question and their nonclassical efficacity, and, accordingly, recast these relationships in phenomenological terms. A "phenomenon" is a representation of a specific (material or already phenomenal) configuration where such relationships are found.
In quantum mechanics, such configurations are defined by the physi- cal interaction between quantum objects and measuring instruments, while manifesting, in a trace-like manner, the effects of this interaction only in the latter. In contrast with classical physics, the role of measuring
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instruments is irreducible in quantum physics. 9 The behavior of mea- suring instruments is described by means of classical physics and in terms of classical epistemology, since classical physics may be treated as epistemologically classical, in particular causal and realist. In these arrangements there "appear" traces (say, on silver bromide photo- graphic plates) of quantum objects, such as elementary particles (or what is so called by convention)--photons, electrons, and so forth. Such traces emerge as the effects of the interaction (itself quantum) between the latter and the measuring instruments. Both the physics of measuring instruments and of the traces in question are available to us, while quantum objects themselves cannot be ascribed physical (or perhaps any) properties, for example, such conventional "quantum" properties as discontinuity, or of being "objects" in any given sense.
The mathematical formalism ("algebra") of quantum mechanics applies to some of these effects, specifically to certain collective effects, found within one type of phenomena, and does not apply to other such effects, specifically certain individual effects, found within the other type of phenomena. Both types of phenomena can never be combined, or be seen as derived from a single efficacious situation, however hid- den. Nor can we have both types of effects within a single phenome- non. If we are to "see" each effect of a formalized (lawful) collectivity as lawless, this collectivity has to be (re)phenomenalized so as to be di- vested of both collectivity and law--either through a single phenome- nal collectivity of lawless individual (singular) effects or through a col- lectivity of singular individual phenomena. In other words, the lawful collectivity and lawless individuality in quantum mechanics, or in any radical formalization, require different phenomenalizations, even when dealing with the "same" set of effects. Accordingly, both the sets of ef- fects and the efficacity of such phenomena will be different by virtue of the different material or mental agencies of phenomenalization in- volved. This is in part why this efficacity can never be seen as an entity isolated from its effects but instead as that which is irreducibly recipro- cal with and indivisible from its effects. It may of course be stratified as to the "location" of some of its strata, while retaining the radically in- accessible character of each such stratum.
These circumstances manifest themselves most famously in the ap- pearance of either the ordered or patterned wavelike effects (which pertain only to collectivities of such traces) in some circumstances and the particle-like effects (in general not subject to law in quantum me- chanics) in other circumstances. The presence of both types of effects is
essential to and defining for quantum physics, even though (and be- cause) it is impossible to ever combine the two types of phenomena together or derive them from a single common configuration. The cir- cumstances of their emergence and hence the phenomena that corre- spond to them are always mutually exclusive or, in Bohr's terms, com- plementary. The latter fact is primarily responsible for Bohr's choice of the term complementarity for his overall interpretation of quantum mechanics.
"Quantum objects" or, more accurately, that which makes us speak of such entities can be assigned an independent existence as something that may be assumed as existing when we are not there to observe it. That "something," however, cannot be assigned any conceivable inde- pendent physical (or other) properties, for example, those defining (classical) particles or waves. Nor can it be isolated from their inter- action (itself quantum) with measuring instruments so as to establish their independent impact and hence ascertain their independent prop- erties on the basis of the effects of this interaction. Classical physics fails to describe the sum total of these effects and can be shown to be rigorously incapable of doing so: the possibility of a classical-like de- scription would be in conflict with the experimental data of quantum physics. Quantum theory is able to account for both types of effects and for their complementarity. It does so, however, in a nonrealist and noncausal way. As I said, quantum theory (at least in Bohr's interpreta- tion) does not describe the properties and behavior of quantum objects themselves but only (in a statistical fashion) certain phenomenal effects of their (again, quantum) interaction with measuring instruments. This is why, in contrast to classical physics, in quantum theory this inter- action can never be neglected or compensated for, while entailing the irreducibly inaccessible efficacity of the effects constituting the data of quantum physics. "Quantum objects," detected in any given experi- ment, are part of this efficacity. In general, however, the latter involves other agencies, such as measuring instruments, perhaps in turn ulti- mately quantum (in view of the ultimate quantum constitution of all material objects).
Bohr's interpretation of quantum mechanics, as just outlined, is, I argue, generalizable to all nonclassical epistemology, and the nonclas- sical phenomenology it entails, in particular those found in de Man's work. We must, of course, rigorously adhere to the specificity of the workings of the general scheme here presented in different situations, even when we can leave aside technical aspects of modern mathematics
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and science, including in their connections to each other, such as, in the case of quantum mechanics, making experimentally well-confirmable statistical numerical predictions, or sometimes even exact numerical predictions concerning certain information, say, the position or the momentum of a particle, but never both together. (Hence, from the classical viewpoint, such information is always partial. The laws of quantum mechanics disallow us to assume a wholeness, however un- knowable, behind this information, hence making it complete, as com- plete as any information than can, in principle, be obtained in any experiment performed on quantum objects, or, again, what we infer as such from this information. ) In nonscientific nonclassical situations, the nonclassical effects would emerge through such entities as (materi- al) signifying structures of the text (de Man's "materiality of the signi- fier"); material texture (in either sense), such as that of Ce? zanne's paintings; the materiality of historical occurrences or events; or certain "mental" configurations of the same joint (classical-nonclassical) type. (At bottom, [material] materiality may be irreducible even in the last case, even though, given the epistemology in question, there is no ulti- mate bottom line here, and the concept itself of materiality is affected accordingly. ) Also, we now deal (or so it appears) with "macroscopic" human subjects (in either sense) rather than the ultimate (microscopic) constituents of matter (seen as material) of quantum physics. The epis- temology of quantum mechanics and nonscientific epistemology here considered do, however, (re)converge at certain points, including, from both sides, on the latter point. In particular, they share the supplemen- tary (Derrida) or allegorical (de Man) production of phenomenaliza- tion and indeed, as Bohr stressed, idealization from "technomaterial" marks. This term may be applied to such marks with "writing" in Derrida's sense in mind. In quantum mechanics, or already relativity, this application would involve certain parts of the (material) technology of measuring instruments, where the scientific data in question in these theories appear in the form of certain material marks or traces. The situation may be rigorously shown to correspond to Derrida's "econo- my" of trace, supplement, writing, and so forth. 10
More generally, in all situations here in question, the key nonclassical features are brought about by the irreducible role of "technology" (in the broad sense of techne ? ) in them. From this perspective, we may de- fine as "nonclassical" situations those in which the role of technology is irreducible. The technology of measurement in quantum physics, or of techne ? of "writing" in Derrida's sense, and the techne ? of "linguistic
materiality" in de Man's sense (which I shall discuss later), make the situations in question nonclassical. By contrast, in "classical" situa- tions techne ? is, at least in principle, reducible, as, for example, in the case of measurement in classical physics, since measuring instruments play only an auxiliary role there so as to allow us to speak of the inde- pendent properties and behavior of classical objects. One can view analogously certain forms of reading or textual processing and produc- tion in general, insofar as the role of "writing" may be neglected there. Thus, classical textuality is not only possible but is necessary within certain limits. By definition, we depend on it even in nonclassical situa- tions insofar as (as in the case of measuring instruments in quantum physics) nonclassical effects appear through classical textual processing.
These connections are not coincidental. Although physics played the most decisive role, the ideas of Bohr and other key figures in the history of quantum physics may be traced to nonclassical aspects of the nineteenth-century philosophy, literature and the arts, and then to modernism. Conversely, the relevance of, among other mathematical and scientific fields, quantum mechanics to de Man's work is hardly in doubt. Nor is it surprising in view of the significance of new science for modern intellectual history, even leaving aside that de Man was edu- cated in science and engineering. Relevant elaborations are found throughout de Man's works, if often reconceptualized or allegorized so as to function independently of their scientific frames of reference. "Pascal's Allegory of Persuasion" offers more direct connections to mathematics and science. In particular, de Man's analysis there may be linked both to mathematical formalization and to its role in physics. As will be seen, both subjects are significant for Aesthetic Ideology and related work. The connections to physics, from optics to quantum me- chanics, could be traced throughout de Man's work. The interplay of optical tropes of "reflection" (admittedly a customary trope in such discussions), "translucence," "transparence," and so forth in de Man's essay "The Rhetoric of Temporality" may be read as metaphorically shuttling between geometrical (linear), wave, and quantum theories of light. "Quantum-mechanical" themes emerge in most of de Man's "optical" tropology and in his epistemological arguments. The connec- tions between both is a more complex question, since nonclassical epistemology does not always govern the architecture of optical tropes, although de Man's essay "Shelley Disfigured" suggests more direct connections of that type. It may, however, be argued that most radical and most significant forms of "blindness" and "insight" in de Man are
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"quantum-mechanical," even when they relate to the blindness and insight of reading. The latter is not surprising, given the technological and material character of textuality as considered by de Man, and the fact that for de Man epistemology is indissociable from reading. A massive deployment of "optics" is found in "Shelley Disfigured," where it is also especially justified, given Shelley's own deployment of optical theories in The Triumph of Life and elsewhere. 11 The essay also con- tains a number of formulations of a general epistemological, rather than specifically "optical," nature (although in this case they can be brought together) that are parallel and perhaps indebted to quantum epistemology. Thus, de Man writes at the outset, virtually defining his analysis: "The status of all these where's and what's and how's and why's is at stake, as well as the system that links these interrogative pronouns, on the one hand, to questions of definition and of temporal situation and, on the other, to questions of shape and figure. "12 This is strikingly reminiscent of and is epistemologically parallel to Bohr's in- augural definition of complementarity (1927): "The very nature of quantum theory thus forces us to regard the space-time coordination and the claim of causality, the union of which characterizes the classi- cal theories, as complementary but exclusive features of the description, symbolizing the idealization of observation and definition respectively" (PWNB 2:54-55).
More interesting at this point, however, is not the influence of mod- ern mathematics and science on de Man's and related work, but the conceptual reciprocity between both domains and the deployment of that work in our approaches to, at least, epistemological, conceptual, and aesthetic aspects of mathematics and science. I shall here consider two such examples--the allegorical character of quantum mechanics, and the relationships between formalization in science and the radical (materialist) formalism that de Man finds in the Kantian sublime.
Complementary phenomena are common in and peculiar to quan- tum physics. Those related to "wave" and "particle" effects and their complementarity are the most famous. Arguably the most significant, however, are those related to the measurement of physical variables, such as position and momentum, or time and energy, correlative to the complementarity of "the space-time coordination and the claim of causality," mentioned earlier. According to Bohr, such variables and the overall quantum-theoretical description can only be applied to quantum objects themselves provisionally or, in his terms, symbolically. For, as we have seen, even though we often (by convention) speak of
such variables in relation to quantum objects, in actuality we can only measure the corresponding physical quantities (either position or mo- mentum, or time and energy, but never both together) pertaining to the classically described measuring arrangements; that is, we measure clas- sical physical variables pertaining to certain parts of such arrange- ments, rather than to the quantum objects themselves, but describe the relationships between the mathematical variables corresponding to these physical variables in terms of quantum-mechanical, rather than classical, formalism. Classical physics can only describe each such physical variable in a corresponding experimental arrangement, but never both together, since there is no experimental arrangement that would make it possible. This situation can be numerically represented by Heisenberg's uncertainty relations, which, thus, become mathemati- cal correlatives of this situation. 13 The rigorous impossibility of ac- counting for this situation in terms of classical physics makes it neces- sary (a) to infer the existence of quantum objects and (b) to introduce a different, quantum, theory, including a different mathematical formal- ism or "algebra," which provides such an account. It does so, however, in a physically and epistemologically nonclassical way.
Now, I would argue that the situation is rigorously allegorical in de Man's sense, thus linking "algebra" and "allegory" within physics itself. The formulation from "Pascal's Allegory of Persuasion" is espe- cially fitting here: "the difficulty of allegory is rather that this emphatic clarity of representation does not stand in the service of something that can be represented" (AI 51). 14 Indeed, this clarity may be said to stand in the service of that which cannot be represented by any means. Thus, classical physics can offer us only incomplete and partial--and spe- cifically complementary--allegories of the quantum world. Nothing appears to be able to offer us more. Accordingly, Bohr's "symbolic" means "allegorical" in de Man's sense, for this "symbolism" in fact rigorously prohibits the classical epistemological features of "symbol" (as analyzed by de Man), in particular any possibility of deriving "alle- gorical" representations from any original or primordial unity. The formalization of collectivities in quantum mechanics does not offer a classical (or classical-physics-like) description of quantum behavior or, again, allow one to claim any primordial unity behind it. It only statis- tically predicts the emergence of certain collective patterns, but never of individual events or effects. If the mathematical formalism, algebra (no quotation marks are necessary), of quantum theory represents any- thing at all it represents this nonclassical and (with respect to using
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conventional concepts of classical physics) allegorical situation. 15 Inso- far as one can apply this formalism to quantum objects themselves, ei- ther by correlating it in some ways with classical physics and its mathe- matical formalism or otherwise, it can only be done allegorically.
We can have a further and deeper sense of these connections be- tween quantum mechanics and de Man's work, and the reciprocal theoretical possibilities they offer, by considering the question of the mathematical formalization of physics. Even beyond "Pascal's Allegory of Persuasion" (which would require a separate treatment), the subject of mathematical formalization is significant in Man's work, specifically in his analysis of Kant's sublime. It has, of course, a major significance for Kant's own analysis of the sublime (or of the beautiful) and in his work in general. In de Man's reading it acquires a special prominence not in Kant's treatment of the mathematical sublime, but as Kant's analysis enters the question of what Andrzej Warminski, in "As the Poets Do It: On the Material Sublime," aptly terms "the material sub- lime. " In this case we (must) "find" the sublime, if we regard, for ex- ample, the ocean, "as poets do, merely by what the appearance to the eye shows [or points] [was der Augenschein zeigt]. " (I modify de Man's translation [AI 80]; a stable, or any, translation may not be possible, only a reading, as Warminski's essay suggests as well. ) According to de Man, "Kant's [phenomenal? ] architectonic world is not a metamor- phosis of a fluid [material? ] world into the solidity of stone, nor is his building a trope or a symbol that substitutes for the actual entities" (AI 82; emphasis added). "Flat" and "the third person" as it is, this archi- tectonic world may be seen as a certain configuration of phenomenal "effects" produced by a reciprocal and yet inaccessible efficacity. "The only word that comes to mind," de Man says, "is that of a material vision" (AI 82).
The nature of this materiality and of the formalism that, de Man ar- gues, accompanies it is complex. Indeed, de Man immediately adds: "but how this materiality is then to be understood in linguistic terms is not, as yet, clearly intelligible. " This understanding will bring with it further complications of the concepts of the sublime, materiality, and formalism (or formalization), and a more radical dislocation of aes- thetic ideology than those entailed by the material vision, qua vision, as here described by Kant and de Man--or at least as this vision has been described so far. This vision may entail more radical limits in this respect, which become more apparent through an understanding of its materiality "in linguistic [or/as textual] terms. " The analytical and tex-
tual pressure put upon Kant's text both by Kant himself and by de Man becomes extraordinary indeed, since we have already come quite far. For, as de Man writes:
The critique of the aesthetic ends up, in Kant, in a formal materialism that runs counter to all values and characteristics associated with aes- thetic experience, including the aesthetic experience of the beautiful and of the sublime as described by Kant and Hegel themselves. The tradition of their interpretation, as it appears from near contemporaries such as Schiller on, has seen only this one, figural, and, if you will, "romantic" aspect of their theories of imagination, and has entirely overlooked what we call the material aspect. Neither has it understood the place and the function of formalization in this intricate process. (AI 83; emphasis added)
It is not altogether clear whether the term formalization here refers only to the radical formalism in question at the moment; or whether it is seen more generally so as to encompass other forms of formaliza- tion, specifically those analogous to radical formalization; or whether, especially once understood in linguistic terms, the radical formalism of the material vision, qua vision, of the sublime entails something like radical formalization. It is also not altogether clear whether "ends up" refers to this particular moment of Kant's and de Man's analysis or anticipates de Man's final elaborations in the essay. The question, then, is whether this linguistic understanding of the materiality involved is "deconstructive" or even (in Kant's text) "self-deconstructive" in some sense (i. e. , whether Kant's text inscribes this understanding against its own grain); or whether this understanding is an actual outcome of Kant's analytical rigor; or whether a yet more complex space of read- ing is at stake. It would be difficult and perhaps impossible to give a fully determined answer. For one thing, what poets "see" or "do" in finding the (material) sublime, how we understand this materiality in linguistic terms or how poets do so (possibly at the moment of this vision), and the movements of Kant's argument appear to be already ir- reducibly entangled in Kant's text. Both the material vision in question and its understanding in linguistic terms (and by implication radical formalization) may be brought together by the kind of reading of Kant and de Man offered by Warminski in "As the Poets Do It. " According to Warminski's reading, what "poets" in fact find in finding the sublime is the radical linguistic materiality that we find in Kleist and, via Kleist, in the end of de Man's essay. Even so, certain differences between the
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materiality (and phenomenality) of the sublime and those involved in radical formalization may remain, especially as concerns what does and does not appear to the eye. The radically inaccessible in question in radical formalization cannot be "seen" in any conceivable sense. It would also be difficult to disregard the fact that Kant parallels, if not identifies, "[to find the sublime] as the poets do it" and "what the ap- pearance to the eye shows. " These complexities do not diminish the radical implications of de Man's analysis, and may be a virtue insofar as it offers new epistemological and aesthetic possibilities, even "insur- mountable possibilities. "
It appears that, in all circumstances, in order to reach the limits of materiality here at stake we need Kleist's aesthetic formalization, as radical formalization, through which de Man develops the linguistic understanding in question, rather than only Kant's radical formalism, as it emerges prior to this understanding. In particular, the latter corre- sponds to and, in a certain sense, is the mathematical formalism of classical physics, specifically, "the mathematization or geometrization of pure optics" (AI 83), rather than to the radical formalization of quantum physics, as is the aesthetic formalization of Kleist or de Man's linguistic understanding. 16 We recall that de Man closes "Kant's Mate- rialism" by suggesting that Kant's radical formalism (formalism, in question at the moment, rather than radical formalization) may not ul- timately be "formalistic enough" (AI 128). He may well have had Kleist's aesthetic formalization in mind, which, along with de Man's essay of Kleist itself, is invoked at the end of "Phenomenality and Materiality in Kant," and something similar is intimated in the end of "Kant's Materialism" (AI 89-90; 128).
The question of the mathematization of science, here specifically optics, enters at the point when the (purely) formal character of the (purely) material vision is ascertained. De Man writes:
The sea [of the material sublime] is called [by Kant] a mirror, not because it is supposed to reflect anything, but to stress a flatness devoid of any suggestion of depth. In the same way and to the same extent that this vi- sion is purely material, devoid of any reflexive or intellectual complica- tion, it is also purely formal, devoid of any semantic depth and reducible to the formal mathematization or geometrization of pure optics. (AI 83)
Beyond the more immediate reference to vision--here, moreover, a vi- sion of the sea as "mirror"--the role of optics has, as I said, a special place in de Man's thought, extending to the connections to quantum
physics, the ultimate optics, at least for now. The latter, however, al- lows for no mathematization and particularly geometrization of its ul- timate "objects. " Instead it entails radical formalization and, with it, both a materiality that is available to phenomenalization and (limited) formalization, and a materiality that is unavailable to any formaliza- tion, representation, phenomenalization, and so forth, and hence to any vision. The latter could still be seen as "material," insofar as any conceivable term could apply.