Kip Canfield

Dept. of Information Systems
University of Maryland
canfield@icarus.ifsm.umbc.edu

I. On (Pure) Rhetoric

 

Peirce (Buchler 99) says that the task of pure rhetoric is “to ascertain the laws by which, in every scientific intelligence, one sign gives birth to another, and especially one thought brings forth another.” Sign models are metaphors that evolve to support any constellation of ideas, and as de Man points out, “metaphors are much more tenacious than facts” (“Semiology and Rhetoric” 123). Any critique of current ideas dealing with human cognition and symbolic behavior must therefore address the metaphoricity of sign models.

 

In what follows, we will explore a remarkable parallelism in stories about the sign, between the discourse of the humanities and of cognitive sciences. This exploration will be conducted in the form of close readings of two works, “Linguistics and Grammatology,” Chapter 2 of Of Grammatology by Jacques Derrida, and “On the proper treatment of connectionism” by Paul Smolensky. The purpose of these readings is not to apply results from one field to another or to hypothesize direct influence, but rather to investigate two rhetorical strategies that develop in the face of the same metaphoric impasse. Both of the works in question come out of a rejection of structuralism–in philosophy and cognitive science, respectively–and although their arguments are basically the same, they take different paths away from structuralism.

 

Derrida stakes out a skeptic’s position, one that shows the aporias and contradictions inherent in the dyadic sign model used by structuralists. He explicitly denies that there is any way around these contradictions. Smolensky, by contrast, has the scientist’s typical aversion to skepticism, and he tries to reconceive the sign model that underlies his theory of connectionism in order to resolve those same contradictions. The parallels between these two works, I will argue, may be attributed to a similarity in the historical moment of each author, even though the works themselves are twenty years apart and their authors are of different nationalities.

 

Derrida stakes out his territory in opposition to Structuralism, with its linguistic model of rules and grammars for atomic units of meaning. Oversimplification of Structuralism can be dangerous (see Culler 28), but in essence, Structuralism was an empiricist reaction to the interpretive projects of the New Criticism, and it explained referent meaning as the center of a symbolic system or structure. In “Linguistics and Grammatology,” Derrida demonstrates the problems that such an autistic view of human signification entails, and suggests that the dyadic sign model of Saussure is in fact responsible for generating the aporias of Structuralism.

 

Smolensky’s work is an oppositional response to traditional Cognitive Science, that uneasy mixture of Cognitive Psychology and Artificial Intelligence. Cognitive Psychology, in turn, began as a reaction to the empiricism of Behaviorism and its inability to refer to Mind as a theoretical construct. The relatively humanistic models employed by Cognitive Psychology came under attack after the field became heavily influenced by computer-based Artificial Intelligence in the 1970s, and it became fashionable to value cognitive models only if they had a computational implementation. The state of this modeling led to very simple and brittle models of human cognition and, in effect, dragged Cognitive Psychology back towards Empiricism. For example, a recent work by Alan Newell Unified Theories of Cognition) proposes a theory of cognition that is based primarily on production rules (rules of the if/then type). The complex problem of how the antecedents and consequents of these rules arise cannot be addressed in such a limited architecture: in fact, Smolensky sees this sort of dyadic sign model–the kind of model that is easily implemented on a serial computer–as the basic problem for objectivist Cognitive Science.

 

Both Smolensky and Derrida, then, object to a tradition that presents a simplistic, deterministic view of human signification, and both elaborate a new vision of semantics and dynamics for their sign models. Each author offers a vision of human cognition that is more complex, more mysterious, and less deterministic than the traditions they oppose.

 

II. Sign Models

 

Though the discourse of any given historical moment is governed by certain metaphors, it is often the case that changes to those metaphors are generated by the very discourse they govern. Structuralism and Cognitive Science use a static, dyadic model of the sign, but the syntactic orientation of dyadic sign models makes such explanations of meaning unsatisfying, both logically and contextually. Authors such as Sheriff have tried to rescue meaning by applying the triadic model of Peirce, with its interpretant, but this solution is largely unsuccessful because it simply inscribes pragmatics in the interpretant, leaving the connection between pragmatics and meaning obscure. The critiques of Structuralism and Cognitive Science described below rely on more flexible, dynamic sign models: Smolensky tries to change the architecture of the dyadic sign model fundamentally, while Derrida explores that model’s inability to account for the gap between the signifier and the signified. Both authors employ an organic, dynamic, systems model which unifies the oppositions that arise in static accounts of the sign.

 

Smolensky’s Model

 

Cognitive Science was carved out in academia during the mid-1970s to create an interdisciplinary home for various scholars who took an information-processing approach to cognitive modeling. Two major critical responses to this objectivist cognitive science are cognitive semantics (Lakoff, “Cognitive Semantics”) and connectionism (McClelland Parallel Distributed Processing vol. 1). George Lakoff is one of the more polemical writers of this critique. He has identified two definitional aspects of what he calls objectivist (mainstream) cognitive science. They are:

 

(1) The algorithmic theory of mental processes: All mental processes are algorithmic in the mathematical sense, that is, they are formal manipulations of arbitrary symbols without regard to the internal structure of symbols and their meaning.
 
(2) The symbolic theory of meaning: Arbitrary symbols can be made meaningful in one and only one way: by being associated with things in the world (where "the world" is taken as having a structure independent of the mental processes of any beings).("Cognitive Semantics" 119)

 

Lakoff goes on to propose a “cognitive semantics” (he also calls it experientialist cognition). In so doing, he challenges two major characteristics of the objectivist account. First, he counters the arbitrariness of the sign with a new theory of categorization related to the prototype theory of Rosch; second, he lambastes the syntactic orientation of algorithms in the information processing model:

 

The most essential feature of objectivist cognition is the separation of symbols from what they mean. It is this separation that permits one to view thought as the algorithmic manipulation of arbitrary symbols. The problem for such a view is how the symbols used in thought are to be made meaningful.("Cognitive Semantics" 125)

 

Lakoff’s language here revolts against the arbitrary nature of the sign and the syntactic character of algorithms. Its criticisms strike at the dualistic definition of the sign and therefore at the foundations of structuralism.

 

The connectionist approach to cognitive modeling accepts Lakoff’s critique, but connectionism is primarily concerned with model architecture:

 

Connectionist models are large networks of simple parallel computing elements, each of which carries a numerical activation value which it computes from the values of neighboring elements in the network, using some simple numerical formula. The network elements, or units, influence each other's values through connections that carry a numerical strength, or weight.(Smolensky 1)

 

The connectionist architecture supports distributed processing, in which each parallel processor is doing only part of a larger process that perhaps cannot be modeled as a series of steps in an algorithm (as with a Turing machine). In the connectionist models, representation is achieved by looking at an entire network of individual unit values. These models are often called parallel distributed processing (PDP) models (Rumelhart and McClelland).

 

The connectionist model is largely incompatible with the traditional cognitive science framework, which is symbolic and based on language. This rejection of the traditional structure of the sign (signifier/signified) makes allies of Lakoff and Smolensky. Smolensky’s article offers what he calls “the proper treatment of connectionism” (1). The article sets out to define the goals of connectionism, and it explicitly advocates a specific set of foundational principles. Smolensky’s first task is to establish the purview of his analysis, which he calls the level of the subsymbolic paradigm. This level lies somewhere between the symbolic level of traditional structuralism or cognitive science and the neural level of basic biological processes:

 

In calling the traditional approach to cognitive modeling the "symbolic paradigm," I intend to emphasize that in this approach, cognitive descriptions are built of entities that are symbols both in the semantic sense of referring to external objects and in the syntactic sense of being operated upon by symbol manipulation. . . . The mind has been taken to be a machine for formal symbol manipulation, and the symbols manipulated have assumed essentially the same semantics as words of English. . . . The name "subsymbolic paradigm" is intended to suggest cognitive descriptions built up of entities that correspond to constituents of the symbols used in the symbolic paradigm; these fine-grained constituents could be called subsymbols, and they are the activities of individual processing units in the connectionist networks."(3-4)

 

Smolensky has dispensed with the signifier/signified dyadic structure of the sign (where symbol=sign). He was forced to do this by the intractable space (gap) between the signifier and the signified. This space caused brittleness in the artificial intelligence systems–inflexibility in the face of a changing environment. By contrast, Smolensky’s architecture for the sign is very malleable. A sign (concept) has no simple internal structure that contains the big problematic gap: instead, a sign is conceived of as a network of very simple elements that allows context to intrude into (be contained in) the sign. Dreyfus and Dreyfus put it thus:

 

What Smolensky means by a complete, formal, and precise description is not the logical manipulation of context-free primitives--symbols that refer to features of the domain regardless of the context in which those features appear--but rather the mathematical description of an evolving dynamic system.(31-32)

 

Smolensky says: “the activities of the subconceptual units that comprise the symbol–its subsymbols–change across contexts” (15). He states the principle of context dependence as follows: “In the symbolic paradigm, the context of a symbol is manifest around it and consists of other symbols; in the subsymbolic paradigm, the context of a symbol is manifest inside it and consists of subsymbols” (17). At this point Smolensky has described a network structure that claims to have more powerful explanatory capabilities than the traditional dyadic model of the sign because context can intermingle with content.

 

Derrida’s Model

 

Derrida has precisely these same objections to the traditional structure of the sign. Whereas Smolensky responds with the network metaphor, Derrida’s critique is governed by the metaphor of generalized (arche) writing. Writing is the structure and process which makes possible the dynamic character of language, according to Derrida, but it is (commonly) considered to be exterior to language. He discusses this exteriority at length, arguing that

 

[t]he exteriority of the signifier is the exteriority of writing in general, and I shall try to show later that there is no linguistic sign before writing. Without that exteriority, the very idea falls into decay.(Of Grammatology 14)

 

The problem is that once you enforce the distinction between the signifier and the signified, reference is confused, and you continually get the “eruption of the outside within the inside” Of Grammatology 34). The nature of the confusion surrounding reference in a static, dyadic account of the sign is clear in the following:

 

The system of writing in general is not exterior to the system of language in general, unless it is granted that the division between the exterior and the interior passes through the interior of the interior or the exterior of the exterior, to the point where the immanence of language is essentially exposed to the intervention of forces that are apparently alien to its system.(Of Grammatology 43; my emphasis)

 

This notion of penetration is parallel to Smolensky’s observations about brittleness, since including context inside the sign is an example of the exterior intruding on the interior. Under a dyadic sign-model, such an interpenetration of context and the sign is not allowed, and this prohibition, in turn, is one factor that generates critique.

 

III. Movement and Meaning

 

Both Derrida and Smolensky object to dyadic sign models because of their naive simplicity and semantic problems. This naivete is a consequence of Structuralism’s and Cognitive Science’s view of the sign as static. Both Derrida and Smolensky elaborate a dynamics in their critiques. Derrida’s mechanisms for including movement in the sign-model are differance, trace and presence, which are discussed below. Smolensky uses the mathematical theory of dynamic systems to put movement into his network structure. The semantic problems are, at root, the same as the hoary old mind/body problem of philosophy. Smolensky thinks that his sign model, in the framework of connectionism, goes some distance in solving that problem. Derrida despairs of a solution and, in fact, states that a solution is impossible. Let us look first at the semantic aspects of each critique and then at the dynamics. SEMANTICS

 

Structuralism and most flavors of cognitive science are forms of rationalism or introspectionism (see Chomsky, Knowledge of Language). Both Derrida and Smolensky oppose such rationalism. Smolensky proposes an intuitive processor (which is not accessible to symbolic intuition), and a conscious rule interpreter:

 

What kinds of programs are responsible for behavior that is not conscious rule application? I will refer to the virtual machine that runs these programs as the intuitive processor. It is presumably responsible for all of animal behavior and a huge proportion of human behavior: Perception, practiced motor behavior, fluent linguistic behavior, intuition in problem solving and game-playing--in short, practically all skilled performance.(5)

 

The programs running on the intuitive processor, then, are not composed of symbols which have a syntax and semantics similar to language. This idea is not mainstream in cognitive science, which takes an artificial-intelligence or information-processing view of cognition and posits exactly the intuitive/linguistic correspondence Smolensky rejects.

 

Smolensky translates subconceptual processes into mathematics, which are not accessible to intuition. Derrida describes the traditional rationalism as logocentrism, a fundamental effect of the atomic structure of the signified. In the course of his polemic on speech, Derrida says:

 

The affirmation of the essential and "natural" bond between the phone and the sense, the privilege accorded to an order of signifier (which then becomes the major signified of all other signifiers) depend expressly, and in contradiction to the other levels of Saussurian discourse, upon a psychology of consciousness and of intuitive consciousness. What Saussure does not question here is the essential possibility of nonintuition. Like Husserl, Saussure determines this nonintuition teleologically as crisis.(Of Grammatology 40)

 

The appeal to nonintuition by both authors is a necessary break with traditional representation, and it recalls Lacan’s barrier between the signifier and the signified (Noth 303), where there is no “access from one to the other.” One can no longer retain traditional models built with now-discarded tools: the new models require a new metaphysics.

 

It is intriguing that both authors appeal to levels to justify the apparent difference between usual interpretations of the sign and the novel view taken in these texts. Smolensky’s appeal is to physics:

 

The relationship between subsymbolic and symbolic models is more like that between quantum and classical mechanics. Subsymbolic models accurately describe the microstructure of cognition, whereas symbolic models provide an approximate description of the macrostructure.(12, my emphasis)

 

This comparison jumps right out of his three-level architecture. The lowest level, the neural level, is closely modeled with the subsymbolic (=subconceptual) level. The highest level, the traditional symbolic (=conceptual) level, is only an approximation of the lower levels. It is an approximate language that developed to allow us (the subject) a way to talk about cognitive matters. He says:

 

The relation between the conceptual level and the lower levels is fundamentally different in the subsymbolic and symbolic paradigms. This leads to important differences in the kind of explanations that the paradigms offer of conceptual level behavior, and the kind of reduction used in these explanations. A symbolic model is a system of interacting processes, all with the same conceptual-level semantics as the task behavior being explained. . . . [whereas, u]nlike symbolic explanations, subsymbolic explanations rely crucially on a semantic ("dimensional") shift that accompanies the shift from the conceptual to the subconceptual levels.(11; my emphasis)

 

Derrida has to resort to a similar tactic in the face of our inability to escape metaphysical talk:

 

What Saussure saw without seeing, knew without being able to take into account, following in that the entire metaphysical tradition, is that a certain model of writing was necessarily but provisionally imposed . . . as instrument and technique of representation of a system of language. And that this movement, unique in style, was so profound that it permitted the thinking, within language, of concepts like those of the sign, technique, representation, language.(Of Grammatology 43)

 

The dyadic structure of traditional structuralist sign models has proven unacceptable for both authors. Smolensky responds by conceiving of a new structure (a network) and Derrida by exploring the problems in the old structure (the gap between signifier and signified).

 

Smolensky’s Intuitive Processor

 

A recurring theme in these stories about levels is the inaccessibility of the lower levels to symbolic intuition. Traditional theories of the sign assume that intuition can penetrate anything cognitive. By contrast, semantics in Smolensky’s model involves the mysterious “shift” from numeric to symbolic representation, a shift described in his “subsymbolic hypothesis”:

 

The intuitive processor is a subconceptual connectionist dynamic system that does not admit a complete, formal, and precise conceptual level description. . . . Subsymbols are not operated upon by symbol manipulation: They participate in numerical-- not symbolic--computation.(7, 3; my emphasis)

 

Furthermore, the unit processors in the model do not correspond to conceptual-level semantics at all. They do not model words, concepts, or even distinctive features as described in linguistics. Smolensky proposes the following subconceptual-unit hypothesis:

 

The entities in the intuitive processor with semantics of conscious concepts of the task domain are complex patterns of activity over many units. Each unit participates in many such patterns. . . . At present, each individual subsymbolic model adopts particular procedures for relating patterns of activity--activity vectors--to the conceptual-level descriptions of inputs and outputs that define the model's task.(6-7)

 

A complete description of cognition is numerical and therefore not available in our native symbolic language. Subsymbolic computation in a dynamic system is cognition, and the asymptotic behavior of trajectories in the system is somehow approximately mapped to symbolic language. This explains the nonintuitive character of the intuitive processor and presumably explains why symbolic theories like those in linguistics always seem to almost formalize language, but ultimately fail on the fringes.

 

Derrida’s Origins

 

We have noted above that Smolensky links the subsymbolic and symbolic levels with a “semantic shift.” The Derridean concepts of trace and differance parallel these levels. These concepts operate within the metaphor of writing in a way that allows Derrida’s system of signs to move and be dynamic. For our purposes, the problem of the origin and the dynamics of differance are the salient topics in Derrida’s theory.
Because the signified is “always already in the position of the signifier” Of Grammatology 73), origins become problematic. As Derrida puts it,

 

Representation mingles with what it represents, to the point where one speaks as one writes, one thinks as if the represented were nothing more than the shadow or reflection of the representer. A dangerous promiscuity and a nefarious complicity between the reflection and reflected which lets itself be seduced narcissistically. In this play of representation, the point of origin becomes ungraspable.(Of Grammatology 36)

 

This attention to the problem of origin indicates an uneasiness with semantics. Derrida uses the image of track or trace to express this uneasiness. What he says (in Smolensky’s terms) is that there is no origin because we attach a semantic purpose to origins and at the point of origins, there is no semantics. The (pure) trace is not semantic:

 

The trace is not only the disappearance of origin-- within the discourse that we sustain and according to the path that we follow it means that the origin did not even disappear, that it was never constituted except reciprocally by a nonorigin, the trace, which becomes the origin of the origin. . . . The (pure) trace is differance. It does not depend on any sensible plenitude, audible or visible, phonic or graphic. It is, on the contrary, the condition of such a plenitude. Although it does not exist, although it is never a being-present outside of all plenitude, its possibility is by rights anterior to all that one calls the sign. . . . The trace is in fact the absolute origin of sense in general. Which amounts to saying once again that there is no absolute origin of sense in general.(Of Grammatology 61-62, 65)

 

This recalls Smolensky’s “semantic shift” problem, in which he sets up a system where all computation is purely numerical and has no symbolic-level semantics. He must then finesse a “shift” to our human realm of signs, something Derrida says is impossible:

 

This arche-writing, although its concept is invoked by the themes of "the arbitrariness of the sign" and of difference, cannot and can never be recognized as the object of a science. It is that very thing which cannot let itself be reduced to the form of presence. . . . There cannot be a science of differance itself in its operation, as it is impossible to have a science of the origin of presence itself, that is to say of a certain nonorigin.(Of Grammatology 57,63)

 

Derrida, like Smolensky, emphasizes the nonintuitive or unconscious character of cognitive acts like language. Derrida calls this the “fundamental unconsciousness of language” Of Grammatology 68) and says that “Spacing as writing is the becoming-absent and the becoming-unconscious of the subject” Of Grammatology 69). But while Derrida says of the trace that “no concept of metaphysics can describe it” Of Grammatology 65), Smolensky has presented a mathematical metaphysics. Smolensky’s attempt has yet to tackle the precise point that Derrida has tried to show cannot be described: the point at which the non-semantic origins of signification become semantic.

 

Dynamics

 

In the terminology of engineering mechanics, statics is the study of forces on structures, and dynamics is the study of forces on structures in motion. All critiques of structuralism reflect a passing from statics to dynamics; the dynamic view of structuralism has always existed in structuralism but was not mainstream (see Piaget). Post- structural discourse emphasizes movement and temporality. Smolensky uses models taken from dynamic systems theory to achieve this, while Derrida defines a cluster of terms (differance, trace and presence) for the same purpose. Both authors use this dynamism to argue for an organic sign model that integrates form and function.
Smolensky explicitly uses the models and mathematics of dynamic systems, as studied in physics. He views the architecture of his model in this way:

 

The numerical activity values of all the processors in the network form a large state vector. The interactions of the processors, the equations governing how the activity vector changes over time as the processors respond to one another's values, is an activation evolution equation. This evolution equation governing the mutual interactions of the processors involves the connection weights: numerical parameters which determine the direction and magnitude of the influence of one activation value on another. The activation equation is a differential equation. . . . In learning systems, the connection weights change during training according to the learning rule, which is another differential equation: the connection evolution equation.(6)

 

He elaborates a “connectionist dynamical system hypothesis” in which the connection strengths (weights) of the network embody the data, and differential equations describe the dynamic process within which these data become knowledge. The state of this intuitive processor (the network) is defined by a vector which contains the numerical state of each unit processor in the network. For our discussion, the important aspects of this description are the global control over the process of signification given by the systems idea, and the semantic anomalies presented by the numerical character of the model.

 

Smolensky’s Global Control

 

The systems idea is very important in Smolensky’s discourse. It becomes possible to describe the connectionist version of cognition by using a mathematical dynamic system as a model (my discussion is informed by Rosen). A dynamic system in mathematics depends on two kinds of representation: one must represent every possible state of the system (statics), and also the behavior of the system (dynamics). The static description uses the concept of a state space, which contains an instantaneous description of every possible state of the system. These states can be described as measurements on a system. For example, in Newtonian mechanics, all particles can be described in a system with six dimensions: three for position in 3-dimensional space and three for a momentum measurement in each of those three dimensions. It is important that the number of dimensions chosen give a complete description of the state of the system. In such a model, all states that have the same values in all dimensions are identical to each other. Each dimension is a state variable and the n-tuple (or vector) of all the state variables is a representation of the (instantaneous) state of the system. The mathematical set of all possible unique vectors is the state space of the system. Therefore, most systems will be multidimensional and cannot be visualized in Euclidean space.

 

In order to provide a dynamic description of a system, one must know how the state variables change with time. Mathematically, this means that each state variable (dimension) is a function of time. If each of these functions is known, the dynamic behavior of the system is a trajectory in the state space through time. It is usually impossible to know these functions exactly, but since the rate of change of a single state variable depends only on that state in the state space, we can give conditions that these functions must follow. These conditions constrain the trajectory of a behavior but do not uniquely determine it. The constraint is modeled as the derivative of a function which gives the rate of change at a point (state). The derivative of a function (with respect to time) is analogous to the slope of a tangent line to a curve; the slope reflects how fast the points on the curve are changing in the neighborhood of the state. A dynamic system, then, is described by a set of simultaneous differential equations where differential equations are functions of the state variables and their derivatives. Systems described with differential equations represent infinitely many possibilities that are constrained by the (dynamically changing) structure of the system.

 
Dynamic systems impose a global effect on the state space. For example, in the plane of this paper, all points (positions) can be described with two numbers–the coordinates in the xy plane (a vector with two elements). The intuitive processor’s state space, however, is multidimensional: its state space is the set of all possible vectors that describe all activation values of all unit processors in the system. The global effect occurs (most simply) because a differential equation sets up conditions on every point in the state space. For example, a differential equation with a function in two dimensions involves derivatives which set up a direction field that constrains the trajectory of any curve that goes through a point in it. The direction field is a condition that attaches itself globally to every possible point, and it is what makes possible a global, system-level description of a multitude of separate interacting agents.

 
The modern scientific concept of fields–such as electric fields, magnetic fields, or even magic force-fields in science fiction–are examples of this kind of global effect. They are something usually unseen but considered to be real (i.e., they effect material reality) and they operate globally, albeit mysteriously, in an area of space. Smolensky sees reference as the asymptotic behavior of a trajectory in a dynamic system, and his scientistic assertion of the possibility of global control contrasts with Derrida’s exasperated skepticism, seen below.

 

Derrida’s Differance

 

The early Derrida is conducting a guerrilla war against structuralism from within the metaphysical terrain of structuralism. He only has whatever is at hand there for the fight. While Smolensky is free to use exotic weapons from his experience (he was trained as a physicist), Derrida must work within the tradition of the dyadic sign. He considers the dyadic sign constitutive of human thought, even as he shows its inadequacy for explaining meaning. Notwithstanding these differences in tradition and precept, there are many points of contact between Smolensky’s dynamic systems and Derrida’s trace and differance.

 
Derrida conceives of the operation of the trace as a field in the sense described above, but has no language to justify such a global and actively structuring concept. In exasperation, he calls it “theological”:

 

The trace, where the relationship with the other is marked, articulates its possibility in the entire field of the entity [etant], which metaphysics has defined as the being-present starting from the occulted movement of the trace. The trace must be thought before the entity. But the movement of the trace is necessarily occulted, it produces itself as self-occultation. When the other announces itself as such, it presents itself in the dissimulation of itself. This formulation is not theological, as one might believe somewhat hastily. The "theological" is a determined moment in the total movement of the trace. The field of the entity, before being determined as the field of presence, is structured according to the diverse possibilities-- generic and structural--of the trace.(Of Grammatology 47, my emphasis)

 

The reader should compare this description with the global structuring impact of dynamic systems on state- space, described above. At all times, Derrida presents the trace as dynamic. It is the “movement of temporalization” Of Grammatology 47), and “[t]he immotivation of the trace ought to be understood as an operation and not as a state, an active movement, a demotivation, and not as a given structure” Of Grammatology 51). The shift from statics to dynamics is, of course, a key feature of contemporary discourse on the sign.

 
Derrida responds to accusations that differance is negative theology with an essay in “How to Avoid Speaking: Denials.” Frank Kermode summarizes the argument well:

 

The purpose of Derrida's pronouncement is to claim that differance is not negative in the same measure as the God of negative theology; for it is so in much greater measure--indeed it cannot properly be thought of as negative at all; it is outside negativity as it is outside everything. Only by an intellectual error-- induced by a sort of metaphysical paranoia, a fear for the security of that "realm"--could anybody suppose that differance has a design on us, or a desire to make itself into some sort of presence.(Kermode 75; my emphasis)

 

Informed by a reading of Smolensky, one might conclude that differance is desire, and that “metaphysical paranoia” is completely justified. Where structuralists and objectivist cognitive scientists assume “meaning” as a concept around which structure is built, Derrida and Smolensky use ideas of process and structure to produce “meaning.” The main rhetorical strategy both authors use to do this is to deny a hard distinction between form and function. This conflation gives reality to a field of signification. This is explicit in Smolensky’s mathematical metaphysics; in Derrida, it is implicit in the movement of the trace.

 

Derrida’s treatment of presence is interesting in relation to these metaphysical ideas. Culler, in On Deconstruction, invokes Zeno’s paradox to explain Derrida’s insistence on the impossibility of presence. The present moment is never really present, but always marked with the past and the future. The present is then not real, as difference is not real. Trace “does not exist” and differance is “nothing.” Time and absence conspire to destroy any phenomenology.

 

Arche-writing as spacing cannot occur as such within the phenomenological experience of a presence. It marks the dead time within the presence of the living present, within the general form of all presence. The dead time is at work. That is why, once again, in spite of all the discursive resources that the former may borrow from the latter, the concept of the trace will never be merged with a phenomenology of writing. As the phenomenology of the sign in general, a phenomenology of writing is impossible. No intuition can be realized in the place where "the whites indeed take on an importance."(Of Grammatology 68)

 

One might be tempted to regain presence by an appeal to the idea of a field of signification, proposed above, but presence fails for both authors at the point where its phenomenology must be intuitively accessible to the subject. Both authors set up a metaphysics which describes a mechanism for presence, but both place that mechanism in the inhuman realm of numbers or (pure) traces.

 

Derrida’s insistence, then, on presence and difference as “nothing” might be understood as referring only to the realm of human consciousness, the only realm describable in structuralist terms. Derrida’s nullification of presence and differance recall a funny story, an old chestnut, that I have most recently seen reincarnated in a book by Arbib In Search of the Person): it seems that there was this mathematician who wished to prove something for Riemann geometry. He disappeared into a room and filled a blackboard with Dirichlet integrals and other mathematical arcana. After a time, a cry was heard from the room, “Wait! Wait! I’ve proved too much! I’ve proved there are no prime numbers!” The nullification of differance is a funny idea when one considers such that this nullification might be the global control that produces cognition. Smolensky might accuse Derrida of having been inattentive in his calculus classes. On the other hand, Derrida would probably apply a quotation from Barthes (Noth 313) to Smolensky: “I passed through a (euphoric) dream of scientificity.”

 

IV. Conclusion

 

I would like to reiterate that this has been an exploration of rhetorical strategies that arose in two similar historical moments. My discussion ignores any justification or evaluation (scientific or otherwise) with regard to the works by Smolensky and Derrida, and it proposes no direct influence of one on the other. Most importantly, this is not a “methodological” paper that proposes something ridiculous like a “dynamic systems approach to everything.”

 
Both Derrida and Smolensky want to give a fuller, more complex vision of the signifying human. Structuralism and objectivist Cognitive Science present a syntactic picture of human meaning that is unsatisfying. Each author tries to breath life into the dyadic sign model by regaining presence. Smolensky explicitly appeals to presence as a field in dynamic systems theory. Derrida precisely defines such a field with the terms trace and differance while denying their reality because he rejects the concept of global control. The genesis of these critiques is the static character of structuralist or objectivist accounts of signification, theories which relegate all process to the gap between a signified and a signifier, a gap which is “nothing”: Derrida and Smolensky rush in to fill this void. Both authors note a semantic problem for sign models that requires a mysterious “semantic shift” from the unconscious to the conscious. This semantic anomaly does not allow intuitive access to the basis of the sign model. Derrida sees this as an insurmountable mystery, while Smolensky thinks it can be accounted for.

 
Spivak uses Levi-Strauss’ term bricolage to contrast modern discourse with engineering: “All Knowledge, whether one knows it or not, is a species of bricolage, with its eye on the myth of engineering” Of Grammatology xx). Smolensky and Derrida are doing similar odd jobs, but with different tool boxes. Smolensky, with his “eye on the myth of engineering,” is a bricoleur with a full quiver of metaphor: he can play Ahab (“That inscrutable thing is chiefly what I hate”). Derrida doesn’t have much faith in his weapons: he can love the whale.

 

References

 

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