FOUR

Signs Becoming Mind
Becoming Signs:
A Topological View

I. THE BINARY MACHINE’S FEET OF CLAY. One of the recent infatuations with binarism has been the right-left brain hemisphericality. Admittedly, this dichotomy departs somewhat from customary binary thinking, since the right brain already represents, by definition, holistic, synthetic, nontemporal or multitemporal, and nonlinear processes.

FIGURE 3

Consider, in this light, and for the mere sake of schemata, the brain to be compartmentalized according to figure 3. Area 1 is the sinister brain, 2 the dexterous brain, and 3 the whole brain, whose domain includes 1 and 2 in addition to the zone it exclusively inhabits. In other words, we have (1) the “skillful” and “adroit,” plus (2) the “pernicious” and “destructive,” plus (3) “Nirvana” and “oblivion,” the composite of which yields the self, or better, self-consciousness, which is neither absolutely individual and disjoined nor fused and conjoined, but somewhere in between. Area 2, according to stock interpretations of the split-brain phenomenon, is analytic, linear, sequential, causal, atomistic, and so on. Underlying all those rather sterile categories with which we are familiar such as male/female, outside/inside, logic/intuition, rationalism/empiricism, it entails essentially a binary mode of intellection, somewhat comparable to Saussurean-based binarism.

In this regard, 1 is not simply the opposite of 2. Rather, as the pre-Socratic philosophers—especially Heraclitus—interpreted such dualities, 2 and I shoyld be understood in terms of what they are not. That is to say, in terms not of differences but of the interplay between different differences—or as Gregory Bateson (1972) was prone to put it, of differences that make a difference. Area 1 is 2 in the sense that dualities shape differences and differences combine to form wholes. And it is also not 2 in the same manner that 2 is 2. That is, 1 brings 2’s sequentiality into an atemporal framework. Poststructuralist thinking, inspired by Nietzsche and propagated by Derrida, Foucault, and Lacan, among others, sets 1 + 2 off against traditional Platonism. Area 1 + 2 + 3, in addition, reveals a possible move outside the normal channels of thought and intuition found in 2, 1, and 1+2, toward the final self-referential, self-sufficient, self-confirmatory interpretant, which is inexorably destined to remain approximate rather than consummate.

The circle girding 3, 2, and 1 is significantly an icon of pre-Firstness. It is the beginning before the beginning, before the first cut, mark, sign. The ordinary generative progression is: o => 1 => 2=> 3. But since 3 is never final, there must needs be the possibility of reversion (by way of a Peircean de-generacy of signs) from 3 back to o, which in, by, and for consciousness, is then mediately filled with the sequence of ciphers. And the ongoing cycle continues.

In his extensive commentary on Peirce, Hartshorne (1970:100-101) places a set of “metaphysical contraries” in two columns, the first corresponding to Seconds and Thirds, and the second to Firsts, the more relevant of which I have with certain variations reduplicated:

Hartshorne observes, and rightly so, I believe, that what appears at the outset to be a set of dichotomies is actually enclosed in triadicities. In this he follows Peirce’s implicit injunction: “Think in triads, not mere dyads.” The latter are crude and misleading; the former, though indeterminate, are always evolving toward something. Regarding trinarism and binarism, merely to oppose concreteness and abstractness is fallacious. Both concepts are universals, and their very juxtaposition as a dichotomy tends to obscure the fact that concreteness is itself an extreme form of abstraction, and that an instance of concreteness is by no means the concept reiterated, but something new and richer.

Let us, in this light, redefine the ciphers, 0, 1, 2, and 3, in consonance with Hartshorne’s formulation, to yield figure 4. Initially notice that the rectangle topologically evinces the construction of a Mobius strip. If we cut it out, double it, and give it a twist, thus connecting the o corner to the 1 corner and the 2 corner to the 3 corner, we have a two-dimensional surface warped in three-dimensional space such that at the junctures 0-1 and 2-3 “inside” becomes “outside,” and vice versa. This is not insignificant, as we shall see, since in addition, at these same junctures, continuity becomes discontinuity, or the other way round, as the system finally doubles back and takes a gander at itself. The arrows of the two-way transformations represent the pathways of least semiotic resistance (de-generacy, embedment, automatization, confirmation, entropy) as well as the general push against the current (generacy, de-embedment, de-automatization, novelty, surprise, negentropy). The curved arrow from o to 1 represents a leap from what we may call the “greatest lower bound” to the simplest of cuts-signs, from the empty mind to thought-signs, from nothingness to somethingness.

Then, semiosis (generacy) can proceed from o = > 1 = > 2 = > 3. The self-returning loops around each sign type depict recursive reiteration of the same sign folding back on itself (111, 222, 333). The arrows depict the function booting sign generacy up a notch toward the “least upper bound,” to yield the natural classes of signs (112, 122, 222), though it can proceed directly from 1 = > 3 to yield special sorts of higher sign types (113, 133, 333). And so on.¹ From 3, the culmination of a cycle, sign generacy can then be elevated to 1 at yet a higher level—it becomes another sign of a more developed type in the hierarchy. On the other hand, it can de-generate to a lower type, into either 1 or 2. Or, by a “catastrophe,” so to speak, it can be canceled entirely to fade back to o, into “oblivion” or “nothingness”—the empty sheet of assertion. The process then once again begins anew.

Very significantly, the Möbius strip is a necessary characteristic of figure 4, because the rectangle is radically asymmetrical. In contrast to the Aristotelian square of oppositions, the so-called semiotic square (Greimas and Courtés 1982:308-11), or Piaget’s (1953) psychological group, the three operations depicted by the horizontal, vertical, and diagonal arrows are not entirely symmetrical, reflexive, and two-way, but chiefly unidirectional, though not entirely irreversible. In other words, signs tend toward semiosis—sign generacy at increasingly complex levels—or they tend to de-generate, to gravitate toward a natural “sink”: o.² Hence the one-way arrow from 1, 2, 3, to o, and from o to 1. And hence the radical asymmetry they imply.

FIGURE 4

Figure 4 takes on further import, given its particular topology, and especially in light of Jacques Lacan’s theory of the unconscious (see Clément 1983; Turkle 1978). I refer to the so-called Schema R, a rectangular figure drawn on the flat page, which must be read, Lacan warns, in three dimensions, like the Mobius strip (Lacan 1966:531-83). J.-A. Miller (1966:175-76) adds that the Mobius quality of the schema renders apparent heterogeneity homogeneous. What would otherwise be a catastrophe is, so to speak, smoothed out. In short, discontinuity becomes, from another vantage, continuity, and symmetry becomes asymmetry. Elsewhere, Lacan (1977:155-56) uses another two-dimensional figure, called the “interior 8,” which doubles back into itself. That is, the “interior 8” is continuous only up to a point, where the surface is folded in upon itself in three-dimensional space such that there are two intersecting fields:

Lacan places the libido at the point of the intersection as the field where the unconscious develops. This point is, Lacan claims, a void. It is commensurate with a mathematical point: imaginary. Potentially everywhere and yet no-where, it can be at one of an infinity of locations along the inner loop. We are told that this line, containing potentially an infinity of points, is the “line of desire” lying between “the field of demand, in which the syncopes of the unconscious are made present.” More significant still, this “line of desire” is metonymous, that is, linear and asymptotic, since desire cannot be totally fulfilled (Lacan 1977:156). And here we note an obvious commonality between the point of intersection in Lacan’s “interior 8” and a given point on the initial sheet of Peirce’s “book of assertions.” Moreover, the “interior 8” is comparable to what Peirce in his “existential graphs” calls a “scroll” (MS 450), which can be constructed in four operations (Roberts 1973:34n):

My introducing Lacan is not for the sake of defending or debating the value of his theory but to reveal the nature of his figure: its import for the present purpose lies in its abstract quality as a topological form, rather than in its substance or figurative meaning. Like the topology of Lacan’s “interior 8,” Peirce’s “scroll,” as one cut within another, represents a cut severing an area from the sheet of assertion and hence enacting a second severance. Thus a scroll:

can be read “P scrolls Q.” It is the graph of material implication, “If P, then Q.”³ Q is the inner cut of the scroll, a second enclosure or area on a flat plane—the sheet of assertion. It implies something more than an imaginary sheet of infinitesimal thickness, however. It essentially includes two sheets (i.e., an additional dimension), since the cut allows a view of the successive page in the book of assertions. And with successive self-enclosing scrolls, an indefinite number of sheets (dimensions) become necessary (see appendix 1).

This is, I believe, significant. Neither is the scroll nor the “interior 8” merely symmetrical, reflexive, or reversible. They are, rather, like the Möbius strip embodied and enfolded in figure 4 by which the observer, traveling along his two-dimensional path, can alternate from “inside” to “outside.” At the Spencer-Brownian level of pure form, the transformation “in” and “out” of dimensions renders the continuous discontinuous and the reversible irreversible. But unlike Spencer-Brown’s marks, in the living context of particular “semiotically real” worlds, with each transformation there is never absolute reiteration. Something is always different: the difference that makes a difference. Here, as we shall observe in more detail in the next section, we have a model, or perhaps a microcosm, it would appear, of the essence of movement, change, novelty, and perhaps even time. As signs are piled upon signs, and erasure of signs (embedment, submergence into consciousness, memory loss) upon erasure, our navigation toward the ultimate interpretant in the universal sea of signs within which we find ourselves as immanent travelers has no end point short of infinity.

Nor can we enjoy the comfort of retrievable origins: signs are an infinite regressus as well as an infinite progressus (we are always caught in the void of Lacan’s “interior 8” along the “line of desire”). In other words, denied complete knowledge of where we are in the signifying fabric, we have no recourse but to enter an imaginary state, the equivalent of Spencer-Brown’s (1979) imaginary value, √—1, which, he suggests, is the generator of time in its most primitive form. Within this domain what is not enjoys its rightful place at the side of what is—Peirce’s knowledge by virtue of error—as a guiding principle. Mere blind or animal-like reiteration is “truth” (what is) with instinctive or computerlike consistency, while awareness of difference, and above all of error, entails awareness of “falsity” (what is not). Pure reiteration is obliviousness regarding time; awareness of difference and error requires time, since at some point in the then, there was a rupture of the flow. For example, according to the “universe ≈ machine” model, with embedment there is an accompanying loss of awareness that a machine is in certain important respects different from the universe—the icon is tacitly taken for the genuine article, as if it were an absolute icon. Time is of no consequence; there is no difference that makes a difference. On the other side of the ledger, becoming aware at a particular point in time that the universe is in certain important respects not machinelike entails the process of de-embedment, a becoming of conscious awareness. The flow has been ruptured; something in the now is not what it was. Thus memory comes into play.

But how can smug instinctive, computer determinacy—or Deleuze and Guattari’s paranoid “this then that”—potentially become worrisome, uncertain knowledge—the schizophrenic “either . . . or . . . or . . . n” ? When blind habit becomes consciousness of habit, the semiotic machine can then become aware of the error of its ways in order to bring about a change in its “semiotically real” world. Such switches or dissipations pattern the asymmetry, transitivity, and irreversibility manifested in figure 4. And they lie at the heart of Peirce’s dictum: signs, and especially symbols, grow. However, since the “real” can be no more than approximated asymptotically, a given community of knowers is ipso facto limited to one or another of the myriad possible “semiotic realities” of their own making—recall that Peirce was an “objective idealist” (i.e., a methodological realist but an epistemological and ontological idealist). Rather than the “real” and “truth” per se, we are forced to consider, so to speak, topology and relations per se. Awareness of this all-important feature of semiosis breeds awareness of myriad possibilities rather than tunnel-visioned assurance.

Fallible fledglings that we are, there can be no absolute provability, only refutability, as a result of error-awareness (of course, we have here once again the Peircean counterpart to Popper’s “falsification” [see Freeman 1983; Freeman and Skolimowski 1974]). In the open space of truth there is no fulcrum point; but in the overpopulated jungle of error, a starting point can be found virtually anywhere, followed by a tenuously charted path hewn toward some unknowable end. Therein rests the beauty of Peirce’s notion of cuts of variable size and shape made anywhere in the initial empty sheet of assertion according to one’s whims, and Spencer-Brown’s equally arbitrary marks and indications in conceptual space separating this from that.⁴ Ultimately, relations—between cuts or marks—are paramount, especially regarding the necessity of time to Peirce’s general scheme of things, which calls for irreversibility.

However, another rather random walk will be necessary in order further to illustrate the thesis of process, of irreversibility, being presented here, which will include a few words on Peirce as semiotician-mathematician-logician. Some commentators find in Peirce a unique contribution to the study of mind and language paralleling and at the same time illuminating the work of Frege, Russell, Wittgenstein, and others, and, in addition, a general framework for an integrated theory of culture (for example, Apel 1981). However, Peirce was actually far removed from the logical atomism generally prevalent during the first decades of this century. Though Christopher Hookway (1985:157-80) expresses worries about Peirce’s outmoded, classical theory of perception, Hartshorne (1983:88-92) assures us that with his theory of mathematico-logical relations, the “logic of relatives,” Peirce took a step toward superseding classical subject-predicate logic (see MSS 516-17, 532-37, 544-45, 547-48). To say “P is Q” implies a dyadic relation, which is sufficient in the event that the copula is taken to be the equivalent of identity. But where relatives are concerned, dyadic relations are inadequate. “P is sad,” “P sees,” and “P gives” are clearly incomplete. “P” is saddened by what? What does “P” see? What does “P” give and to whom? Such predicates imply dependence or relativity, especially in light of Peirce’s pragmatic maxim, as discussed above.

Russell, Hartshorne (1983:88) remarks, “took over the logic of relatives, largely from Peirce, and neatly missed the ontological point.” For Russell the subject of a relational proposition is not relative but absolute: the only logical requirement is the subject and its own monadic predicate. Russell followed Hume insofar as for both of them “reality” consists of a succession of fragmented and stationary states, each being what it is at its particular moment and independent of all other states. Two states, A_l and A₂, are logical absolutes; they are related symmetrically. Each is a Peircean First to the other, hence there is no concept of linear, irreversible progression from one to the other. The relations are entirely reversible (a notion which, interestingly enough, Borges [1962:217-34] takes up, with the aid of Hume and Berkeley, and extrapolates to the extreme in his celebrated “The New Refutation of Time”).⁵

This static notion of relations allows no Secondness or Thirdness. Secondness offers at least an initial introduction to asymmetry, thus excluding two radical doctrines: Hume’s and Russell’s perceptual atomism or absolute pluralism, and an extreme form of monism in the sense of Francis Bradley. Secondness is the actualization of a possibility, of Firstness, and it points toward Thirdness. Firstness as what might be becomes what is, which will invariably have some successor drawn from it by Thirdness, or conditionality, what would be under certain circumstances. In this light, Hartshorne (1983:88-89) concludes:

It seems close to obvious that without Secondness there can be no understanding of what it is distinctively to be a caused or conditioned phenomenon, and without Firstness there can be no understanding of what it is distinctively to be a cause or condition, and that without a third and intermediate relation between sheer dependence and sheer independence there can be no understanding of time’s arrow, the contrast between the already settled, decided past, and the not yet decided, needing-to-be-decided—yet not merely indeterminate—future.

Russell’s perceptual atomism also entails immediate “knowledge by acquaintance,” a form of pure intuitionism by way of a dyadic relation between knower and known, which was the focus of repeated attacks by Peirce (Bernstein 1964:167-68). Moreover, the Kantian flavor of Peirce’s work—i.e., that the mathematically “real” is the ontologically ideal—coupled with a lack of sympathy for the logician’s program of reducing mathematics to logic, sets him apart from the analytical school (Rescher and Brandom 1979:104-25).

But above all, and as I have suggested, Peirce’s notions of vagueness and generality, which roughly coincide with inconsistency and incompleteness in the sense of contemporary logic and mathematics (Rescher and Brandom 1979), render him highly suspect from the vantage point of those hotly in pursuit of certainty. Vagueness, for Peirce, is “the antithetical analogue of generality.” A sign is general in that it “leaves to the interpreter the right of completing the determination for himself,” and it is vague in that it leaves its interpretation “more or less indeterminate, it reserves for some other possible sign or exception the function of completing the determination” (CP:5.505).⁶

In this sense, to repeat, vagueness defiles the purity of the principle of noncontradiction as generality does that of the excluded-middle principle. This is the inverse of Russell’s view that the excluded middle rather than noncontradiction is restricted by vagueness (Cohen 1962; Gallie 1952). Analytic philosophers and logicians are prone to agree that natural languages are vague, thus their interest in constructing a precise ideal language. In contrast, those with a desire to encompass a more general sign system within their purview find it essential, usually after a number of fits and starts, to entertain the idea that vagueness is implicit in any and all forms of semiotic representation (Nadin 1983:159-64).⁷

Following Peirce, the vague is generic to possibility; the general is generic to necessity (CP:5.448, 5.459, 5.505). Possibility is the condition for the generation of individuals, of Seconds, while necessity includes individuals. An individual “determines nothing but itself or always determines itself in determining anything else,” while something “which can of its nature determine something else without being itself determined” is a general (MS:899). Semiotically speaking, vagueness is distinguished from generality insofar as a vague sign, qua indeterminate, leaves its further interpretation to some other sign or experience. Denying such completion of its interpretant to the interpreter, the sign will always remain for the interpreter “semiotically real,” an incomplete manifestation of the “actually real” (CP:5.447, 5.505). Insofar as generality leaves further interpretation of the sign to the interpreter, the sign may approach near-universality, though it will never reach that point in a finite world. In this sense, a vague sign toward the “greatest lower bound” is a remote universal, while a general sign, toward the “least upper bound,” is a near universal (see McKeon 1952:243-45).

Apparently, then, Peirce’s vagueness and generality exist at opposite poles: Firstness and Thirdness, tychism and synechism—in other words, with regard to figure 4, toward o at one extreme and toward 3 at the other. Pure vagueness (the not-yet-selected) is that which is not clearly and precisely felt, sensed, understood, comprehended; it entails uncertainty (chance), leaving things open to the possibility of inconsistency—hence vagueness abrogates noncontradiction. On the other hand, pure generality (the having-been-selected) is that which is ideally applicable to everything, to the whole. Fusing individuals through some real or imagined commonality between them, generality must remain inexorably incomplete, since for Peirce a grasp of the totality, sub specie aeternitatis, will never be at hand—and hence it does away with the excluded-middle principle.⁸ We have, once again, the selected with respect to the nonselected, what is with respect to what is not, the “This, then that . . . n” juxtaposed with “Either . . . or . . . or . . . n”—and here, the problem posed in chapter 3 thus comes to the fore, which will be fleshed out further in chapters 6 and 7.

On the other hand, Secondness, lying between the two extremes, is the reactionary “clash” of the world “out there.” In its pure form, nothing more than a succession of particulars set apart by their differences, even though they may be well-nigh infinitesimal as they impinge upon the senses. They are haecceities—Duns Scotus’s term Pierce used often—in the most radical sense. Like Borges’s (1962:59-66) supernominalist in “Funes the Memorious” who was shocked to discover that others considered a dog seen from the front one moment and from the side at a later moment to be the same dog, such pure particulars play havoc with the idea of identity: there are only myriad similarities and differences.⁹ That is to say, identity and contradiction—i.e., classical binarism—are no more than a hopeful figment of the mind.

II. ON THE INCOMPATIBILITY PRINCIPLE. The distinctions having been outlined between Firstness (possibility, chance, spontaneity, vagueness), Secondness (particularity, haecceity), and Thirdness (necessity, habit, regularity, generality, law) are thus related to the previous discussion of Spencer-Brown’s calculus, Peirce’s existential graphs, and general topological forms. And, as we shall note, they can help to account for the lack of symmetry in figure 4. Consider an individual, say, a, in light of Henry Sheffer’s (1913) “stroke” function, which has been variously related to Peirce’s “ampheks,” his “logic of relatives” (Hartshorne 1970:206-10), and his logic of “statements” (Berry 1952; also see appendix 2).¹⁰ The stroke, “I,” written in an expression as “a׀a,” can be defined as “not both” or “neither,” which yields –a. From this point the other notations of classical logic, as well as the other calculi and logics in question here, can be generated according to the following roughly equivalent categories (see Roberts 1973):

Let it first be noted that in Peirce, Sheffer, and Spencer-Brown, a single notation is used to generate all the notations of classical logic. This is indeed significant. It ushers in an element of parsimony, of elegance predicated on negation and on the “not yet decided, needing-to-be-decided,” but “not yet merely indeterminate,” possibility of Firstness. Regarding sign relations as they have been described thus far, let us use this primitive form of calculus with only one symbol, a. Assume Firstness to be represented by an uncertainty between actualization into a Second of two different possible instances of a, a₁ and a₂, the first instantiation preceding the second one by a temporal increment. The expression of the two possible instantiations is bearing in mind that neither a₁ nor a₂ has yet been actualized, but, since both a₁ and a₂ are in a state of suspension or readiness to be actualized, the equation becomes . Conditions of symmetry exist between a₁ and a₂; there is no priority or privilege of one over the other. Secondness, which demands, in its purest form, distinguishability between each instantiation of a, is expressed by the equation , indicating that a₁ and then a₂ were actualized (recall that Secondness introduces a primitive form of asymmetry). Thirdness, signified by implication , finally introduces asymmetry, irreversibility, and “time’s arrow”—though the arrow in the expression has no bearing on experienced temporality, it is at this point merely a primitive logical constuct. Recalling Hartshorne’s (1983:88-89) words, Firstness ushers in independence, Secondness dependence (relationality), and Thirdness “the contrast between the already settled, decided past, and the not yet decided, needing-to-be-decided—not yet merely indeterminate—future.” That is, a₂ is not what it was but what it is, which necessarily includes a trace of that part of it which was but no longer is, and what is is subject to anticipation of what potentially will be in the future.

If we correlate the three categories as described here and their respective expressions with figure 4, we have figure 5. Category 1 is the feeling of what might be the case, 2 is the action, the effect, of that which is the case, and 3 is the representation (signification) of that which would be, or will have been, the case in the event that certain conditions are in effect. Category 1 implies “either this or that but not both,” 2 “this and then that,” and 3 “if this then that.” While 1 is mere atemporal oscillation between symmetrical entities, 2 is linear, hence asymmetrical and temporal, but solely in the sense of pure succession, and 3 attains, in contrast, the highest degree of asymmetry. In other words, disjoined terms are symmetrical, the binary operation of combining terms is temporal but purely linear, and, with the triadic relation, true asymmetry and hence irreversibility or temporality begin to exercise their force. Thus we have, potentially, the becoming of the “either . . . or . . . or . . . n” of consciousness of error, and subsequently the transitory switch—catastrophe—to a different level of signification. And thus it is that symbols begin to grow.

FIGURE 5

Hartshorne (1970:206) argues rather convincingly that asymmetry or one-wayness is attained at the most fundamental level with Thirdness. This comes about in its greatest defining power through Sheffer’s function, since not both and neither nor (conjoint negation) are (as Peirce knew well) the only functions each of which, taken singly, is capable of defining all the other logical symbols. In this fashion, roughly, the defining power of logical functions varies inversely with their symmetry. (Significantly, Howard DeLong [1970:31] notes that Peirce is an exception to most innovators of mathematical logic who knew little about stoic logic and its focus on the Liar Paradox and material implication, both of which were germane to Peirce’s work.)

This function becomes the domain of the either/or which Deleuze and Guattari’s schizophrenic subverts by affirming both disjoined terms, thus stretching the either/or out to “either . . . or . . . or . . . n.” It is also Beckett’s (1955:176) elaborate system of affirmations and negations, characteristic of which is: “It is midnight. The rain is beating on the windows. It was not midnight. It was not raining.” Differentiations become finer and finer: the staccato approaches legato, digitality approaches continuity, that is, generality, the undifferentiated. Exclusive disjunction makes a move toward inclusive and relatively unfettered disjunctions.

Now, following Deleuze and Guattari (1987), let 1 in figure 5 be called disjunctive synthesis, 2 connective synthesis, and 3 negatively conjunctive synthesis (Deleuze and Guattari call these three operations “productive recording,” “production of production,” and “productive consumption” respectively, as necessary concepts in their practice of “schizoanalysis”). As feeling (iconicity), disjunctive synthesis is immanence. It is not an inclusive or restrictive use of signs but their fully affirmative, nonrestrictive, exclusive use. It is a disjunction that must remain disjunctive, yet there is still the possibility of affirming both terms of the disjunction. Their affirmation is made possible by their very disjointness, their distance: one is not necessarily restricted by excluding it from the other—recall Peirce’s mark on the blackboard from chapter 1. This is in itself paradoxical, though a paradox whose two horns both differ and are deferred temporally: an oscillatory “either . . . or . . . or . . . n,” instead of the simple binary either/or (Deleuze and Guattari 1987:78). What we have here is a superposition of the one and the other. Such superposition is rather comparable to Heisenberg’s (1958a: 167-86) view of the wave function of quantum reality as a tendency for something, Aristotle’s potentia, the coexistence of a set of possible states. Or in Popper’s (1982) terms, remarkably similar to Peirce, it is the mathematical representation of a certain propensity (i.e., a habit).

The idea of superposition can be roughly modeled by the Necker cube in a state of readiness for oscillating between P (face up) and Q (face down), which is tantamount to indeterminable iteration, like a wave-train: (Comfort 1984; Kauffman and Varela 1980, Kauffman 1980). The superposition, or the mere possibility of sign disjunction, makes way for the construction of a “semiotically real” domain, P-Q, such that for any sign, S, S obtains in this domain if and only if it obtains as a semiotic equivalence with, or a subset of, either P or Q. Such sign domains represent, in Rescher and Brandom’s (1979:10) terms, superposition, sign disjunction (non-noncontradiction), inconsistency, and overdetermination (or in Peircean vocabulary, vagueness, which corresponds to Firstness).¹¹ The notion of superposition evokes, significantly enough, the quantum world or prototemporality, as described above. Overdetermination breeds the conditions for a sign interpreter’s becoming conscious of contradiction, inconsistency, paradox, and anomaly—i.e., that which was not expected, which causes surprise, and opens up the possibility of abductive leaps. Thus overdetermination entails interpreter-interpretant interaction. The interpreter is a participant rather than a passive recipient, and the interpretant becomes an actor in the semiosic drama rather than a mere object to be acted upon.

Category 2, connective synthesis, is a linear, binary coupling of “machines,” which reveals the other side of the coin: a pure succession of signs. For example, Deleuze and Guattari’s “desiring machines”

are binary machines, obeying a binary law or set of rules governing associations: one machine is always coupled with another. The productive synthesis, the production of production, is inherently connective in nature: “and . . .” “and then . . .” This is because there is always a flow-producing machine, and another machine connected to it that interrupts or draws off part of this flow. . . . And because the first machine is in turn connected to another whose flow it interrupts or partially drains off, the binary series is linear in every direction. Desire constantly couples continuous flows and partial objects that are by nature fragmentary and fragmented. (Deleuze and Guattari 1983:5)¹²

The “couplings” or connections are both biological (ontological, physiological) and social, both individual and collective, molecular and molar. The whole of technical machines is an organized system of production, whereas the human biological machine as a whole consists of a molar, aggregate level of organization, with its respective parts functioning at a molecular level (see also Merrell 1990).¹³ In whichever case, everything is coupled with everything else either physically or mentally (i.e., sign-things or thought-signs). That is, everything is a machine: something coupled with something else in the sense of this and then that, as succession, as eotemporality, in contrast to the prototemporal.

Moreover, this “coupling” is closely related to what might be dubbed “quantum chaos,” following Bohm, and “phase locking,” both of them nonlinear phenomena. In Bohm’s implicate order as a quantum potential, each electron-to-be-explicated is in a state of perpetual quivering, a sort of infinite sensitivity, since it is interconnected to all other potential entities in the holomovement. The entire quantum potential dictates an electron’s behavior in terms of an unimaginably intricate manifold, which, according to Bohm, is entirely determinate, though, given the complexity of the whole system, it must be for the mind short of anything but infinite capacity, completely unpredictable. Phase locking occurs when a set of oscillators gradually alter the frequency of their oscillations such that they begin resonating in harmony. A remarkable example of phase locking in nature is that of a group of fireflies which, at what appears to be some predetermined moment, begin coordinating their electrical impulses to bring about an illumination of their abdominal sections. “Jet lag” is a more familiar example. The biological clock is phase locked into a frequency dictated by the twenty-four-hour day. The disorientation experienced during jet lag is due to the body’s attempt to adjust itself to a different twenty-four-hour pattern (for an excellent study of phase locking regarding the cardiovascular system, see Win-free 1987).

At this juncture I must also emphasize that Deleuze and Guattari’s “machine,” though comparable to, as I pointed out in section II of chapter 3, is not to be confused with that of Maturana and Varela (1980), who highlight the “autonomous,” “autopoietic” character of the living organism as a “machine.” Maturana and Varela focus almost entirely, indeed in hedgehog fashion, on the autonomous aspect of the living organism as a homeostatic “machine.” In this sense, an autopoietic entity is viewed as that which is “distinguishable from a background, the sole condition necessary for existence in a given domain.” The nature of this entity and the domain in which it exists “are specified by the process of its distinction and determination; this is so regardless of whether this process is conceptual or physical” (Maturana and Varela 1980:138). In this fashion, the “machine” subordinates its environment to its own self-maintenance, retaining in the process its identity through an active compensation of the changes it undergoes. It is thus definable in a topological space consisting of a network of processes of production, transformation, and destruction of self-reproductive components that, through their interactions and transformations, constantly regenerate the network of processes that produce them.

On the other hand, according to my reading of Deleuze and Guattari’s “machine,” the closed domain of processes and relations specifying it by no means dictates total autonomy. Rather, it is also open to its environment. There is a constant exchange of material, energy, and information, which serves to alter “machine” as well as environment in the process, a conclusion that coincides roughly with the work of, among others, Ilya Prigogine regarding the nature of systems in interaction with their environment (see Jantsch 1980). Deleuze and Guattari (1983:1-2), with their characteristic rhetorical aplomb, write further of “machines” thus:

Everywhere it [the Id] is machines—real ones, not figurative ones: machines driving other machines, machines being driven by other machines, with all the necessary couplings and connections. An organ-machine is plugged into an energy-source-machine: the one produces a flow that the other interrupts. The breast is a machine that produces milk, and the mouth a machine coupled to it. The mouth of the anorexic wavers between several functions: its possessor is uncertain as to whether it is an eating-machine, an anal machine, a talking-machine, or a breathing-machine (asthma attacks). Hence we are all handy-men: each with his little machines. For every organ-machine, an energy-machine: all the time, flows and interruptions.

They allude to Molloy in Beckett’s novel, who continually transfers his sixteen sucking stones from one pocket to mouth to another pocket, a continuity of action corresponding remarkably to a mathematical group. This is an ideal example of process, the process of production. But the coupling is binary, between machines of distinction rather than successive differentiation. This “production of production” is inherently connective in nature. It is serial, and asymmetrical, yet atemporal in the sense of experienced time. Nevertheless the machines in their composite are flow machines, that is, process machines. The binary series is linear, and it produces continuous flows and objects that become over the long haul fragmentary and fragmented. This “sinistral” function, the production of I and you, we and they, good guys and bad guys, capitalism and communism, etc., corresponds to the cipher two, to indexicality, to the finger that points, to superordinate and subordinate, to the other and the Other. It marks the establishment of Deleuze and Guattari’s territoriality. And, whereas it is eotemporality, there is hierarchization but as yet no definite asymmetrical, temporal one-wayness. There is no more than Newtonian pushes and pulls the composite of which is devoid of real direction.

Category 3 in figure 5, negatively conjunctive synthesis, or “production of consumption,” is, so to speak, the via negativa giving rise to all that would be (Thirdness). As Deleuze and Guattari put it, this synthesis is the moment of awakening—an abductive leap as a result of thwarted expectations coupled with a conjecture, a hypothetico-deductive gamble—when one exclaims: “So that’s what it is!” But there is no finality here, no ultimate determinacy, for all is tentative and tenderly fallible. It is in this sense ultimately conjoint negation: “neither . . . nor . . . nor . . . n,” or “not both this . . . and that. . . and that. . .n”—and here, once again, we have Sheffer’s “stroke” in a new garment. It is a “vessel” or “matrix” (not a mere “hole” to be filled) through which a potentially infinite series of signs can pass. This is the prototypical schizophrenic—the Nietzschean subject who passes through a series of states and who identifies himself with each and every one of them: “every name in history is I” (Nietzsche 1969:347). The self becomes displaced and spreads itself out along the entire circumference of the circle, the center of which has now been abandoned. In Whitmanesque fashion it becomes everybody and everything, it becomes tantamount to the universe: its universe. “No one,” we are told, “has ever been as deeply involved in history as the schizo, or dealt with it in this way. He consumes all of univeral history in one fell swoop. We began by defining him as Homo natura, and lo and behold, he has turned out to be Homo historia” (Deleuze and Guattari 1987:21).

Given this perpetual displacement in time and space, the schizo is not in possession of his own self. He can be something or somebody solely by being something or somebody else. He is a nomad; his messages are indeterminately polyvocal; there is no stationary mooring, all is in a transient state. Consequently, he is racial (he belongs to all races), without exercising binary racism in the sense of the dyadic 2, for everything is relative to everything else. But this is not an “anything goes” enterprise, no logic of chaos, but a “nothing goes” game of successive cancellation; or better, it is “neither this . . . nor . . . nor . . . n,” which is not linear but expands in all directions simultaneously (and we have nonlinearity as opposed to the linearity of 2).

We are thus speaking of sign conjunction by negation which is characterized in terms of underdetermination (continuity), incompleteness, and schematization (Rescher and Brandom 1979:9-10), or what Peirce terms generality. Progressive underdetermination deals with familar circumstances so made familiar by (mindless) habit: commonplace or easily imaginable objects, acts, or events which are by their nature incomplete insofar as part or all of those objects, acts, or events have become so familiar that they are submerged (embedded, automatized) and no longer part of the experience of which one is conscious. Schematic or undetermined worlds contain blanks or blurs that remain unspecified or undefined, but which, by successive additions to a given world, can become increasingly more specifiable and defined. “This project,” Rescher and Brandom (1979:5) tell us,

seems especially plausible in a framework of emergent properties within a situation of temporal development which produces a succession of different “worlds” (or world-states) in such a way that the successive transitions move matters from the more to the less schematic. (That is, the earlier worlds are schematic with respect to properties, dispositions, or laws that only appear on the scene later on.) This perspective is posed by the sort of evolutionism from simple to more complex worlds or world-states envisaged by Herbert Spencer and C. S. Peirce in the latter part of the 19th century.

The move toward complexification with an accompanying proliferation of interpretants, of successive differentiation toward continuity or generality, is precisely the push into futurity of Thirdness. In this conception of generality, given the conjunction of a pair of sign domains, for a particular sign, S, S obtains in conjoint domains if and only if S obtains in both domains, though it can be the case that S obtains in neither of them. That S can obtain in both domains is important. As signs merge into signs and minds into minds within the field of semiosis, not only does the excluded-middle principle tend more often to make a hasty retreat, but also, since the features of individual signs have become foggy in the process, a set of signs or a given sign can come to embrace, in the minds of their users, wider and wider domains of signification.

That S might obtain in neither of the two domains is also crucial, since it is solely by a process of elimination that 3 in figure 5 can exist in the first place. Category 3, as symbolicity, as at least partial arbitrariness, re-presents what tentatively is by representing at least in part what is not. But since what is must be taken only provisionally, what is not is as ontologically fuzzy and indeterminate as what is. Everything must remain to a degree fuzzy, as if there were strange goings-on—though the overriding tendency, indeed a longing, is to put a stamp of finality on it. As such, 3, as the “least upper bound,” as nonlinear and continuous, bears on synechism. And it is necessarily the prototype of semiosis insofar as its lack of completion perpetually calls for, in fact demands, either a getting along swimmingly or a floundering about in the unruly sea of signification. As generality or continuity, therefore, the excluded-middle principle tends to languish, and even fall into impotence.

Conjoint negation (a₁׀a₂ or -[-a₁ ∧ -a₂]), therefore, marks the radical shift into Thirdness, which, mediating between I and 2 and at the same time stepping outside their zones of influence into its own light of day, provides unlimited possibilities. It is like Deleuze’s and Guattari’s wandering, deterritorialized schizophrenic. She is free to penetrate any plot of topological terrain, moving to and fro, resisting identification with anything in particular and representing nothing in general. She is unfettered by binds, knots, tangles, traps, and impasses. Significantly, the schizophrenic of conjoint negation owes nothing to society, to the “reality” into which society has interjected her: she is free of that awful web of inculcation, injunctions, and interdictions.

In short, if, in figures 4 and 5, 0 is atemporality, 1 is prototemporality, and 2 is linear eotemporality, then the nonlinear, apparently disordered, indeterminate, and fallible nature of 3 opens the doorway allowing for the initial glimpse of bio-nootemporality.

III. ORTHOGONAL LEAPS. At a higher level of abstraction, consider a more advanced specification of figure 5. Let 1 be defined as √-i—superposition implying the possibility for prototemporal oscillation or iteration in the manner of a continuous wave form by an operation on a pair of states: +1 and -1, or P and Q. Let 2 be defined as a purely linear, eotemporal succession of either positive or negative values (i.e., iterative affirmation or negation in the sense of “this, then this, . . . n” or “not this, then not this, . . . n”). And let 3 be defined by either [I|I = -1] or [-(-1 ∧ -1) = -1] (i.e., conjunctive negation such that +1 and -1 can be both affirmed and denied). These relationships can be diagrammed by what is called an “Argand circle,” which incorporates the function of the imaginary number, i ( = √-I), in the two-dimensional Cartesian plot (see figure 6). The y axis is represented by + √-I (i.e., i), and -√-I (i.e., i), and the x axis by -I and +1. This can be all clear to us in a flash, like the graphed acceleration problem in chapter 1, since we see it from a three-dimensional perspective and from an angle orthogonal to the two-dimensional plane.

FIGURE 6

Imagine, in contrast, our Flatlander dwelling on this two-dimensional plane. It would be for him well-nigh impossible to create a mental image of the entire circle, let alone draw it. An imaginary one-dimensional Linelander would not even be able to see any succession of iterants from his particular locale along the imaginary axis. Traveling along his lineworld, he might conceivably experience some sort of change in the primitive sense of a worm in a worm hole creeping forward and with tunnel vision experiencing something remotely the equivalent of “now this, now this . . .” For a three-dimensional being this aboriginal type of sequentiality has nothing to do with temporality: the Linelander’s trajectory is as far as he is concerned all there all at once, as if in bloc. That is, the x axis containing the whole integers is no more than artificially “temporal” as pure sequentiality, with -I representing the past, o the “now,” and +I the future.

What we need is a “time’s arrow,” which, precisely, is represented by the arrow orthogonal to the Argand plane. This arrow allows a three-dimensional grasp of the plane all at once, as if from a perspective sub specie aeternitatis, of what may be termed abstract or imaginary time. However, assuming the eye of an observer to travel along this “time line” would imply the production of “real” or concrete “sensed time,” as if the plane itself, along with the eye, were receding back into the horizon indefinitely. In other words, “time’s arrow” calls for a third axis—that of solid geometry—dynamizing the whole affair and providing for a transition with respect to the original axes. The two-dimensional Argand plane plus one dimension of time becomes roughly analogous to the Einsteinian four-dimensional space-time manifold of three spatial dimensions and one temporal dimension. And the eye moving into the horizon along “time’s arrow” in figure 6 becomes tantamount to an entity’s “world-line” within the Minkowski “block.”

FIGURE 7

Such pseudotemporal transitoriness coupled with switches from one axis to another to afford complementary grasps of things is illustrated in figure 7, to be viewed as a sphere, where the arrows represent the operations in the rectangle in figure 5 bringing about a transformation from one mode of signification to another. Each operation is a 90° orthogonal switch, and the sphere itself represents the “greatest lower bound,” o. From the o point, entry can be made into the interior of the sphere from the imaginary axis (+√-I, -√-I) from which there is accessibility to other axes. Operation a (+√-I → +I) is comparable to physicist John Wheeler’s (1980a, 1982, 1984) complementarity, choice, and selection, which allow for the exercise of distinguishability, bringing about a phase change and a “collapse” producing a thought-sign, sign-thing, or particulate entity, which, by way of operation b—mediary Thirdness (+1 → +t)—leads to irreversibility, temporality (that is, bio-nootemporality). Operation c (+t → + √-I) returns the process to Firstness, to the axis of possibility, of chance. Significantly enough, when considering the midpoint of the sphere to be moving along the infinity of its “point-worlds” on the “imaginary” time axis orthogonal to the Argand plane, it becomes evident that the “sphere” is in reality a “hypersphere” (see Kauffman and Varela 1980 and Kauffman 1986 for a discussion of the hypersphere with respect to the dynamics of Spencer-Brownian forms).

Moreover, the orthogonal moves are the metaphorical equivalent of a twist along the Mobius strip which changes “inside” to “outside,” right-hand to left-hand, end to beginning. Just as two trips around the Mobius strip return us to our original state, so operations a-b-c-c-b-a are a return to the same axis. This is fundamentally the set of operations depicted by Bryce S. DeWitt’s (1968) “popular” rendition of what is called “Smale’s Theorem”—the details are not relevant here—which illustrates that a two-dimensional sphere can be turned inside out via a differentiable homotopy of immersions in three-dimensional Euclidean space. DeWitt accomplishes his task through the set of topological transformations from a point to a point in figure 8, which in essence describes a torus and then turns it inside out, thus illustrating that the inward-turned two-dimensional manifold manifests no clear-cut “inside/outside” dichotomy. All is continuous, as Thirdness, generality, a temporal and mediary collusion of the values of the possible (as Firstness) and the singular (as Secondness). Given the similarity between the fourth and sixth stages of DeWitt’s transformations and either Peirce’s “scroll” or Lacan’s “interior 8,” it is reasonable to suppose that just as √-i, the Möbius strip, or the torus, is capable of an “inside-outside” self-returning cycle-oscillation, so also with thought-sign and thing-sign reiteration. The very important difference is, of course, that, regarding such reiterations as time-bound, asymmetrical, and irreversible, thus nothing is exactly as it was.

FIGURE 8

“So what’s the point?” someone asks. “Isn’t all this mere idle palaver? Can one arrive at a worthwhile conclusion with such apparent trivia?” Perhaps not. On the other hand, it may be well to point to what were once considered useless toys for the mathematicians’ playpens such as hypercomplex numbers, which later attained a certain application, namely, Hamilton’s quaternions. As the name implies, quaternions are four-term numbers constructed out of one real and three other units, which can be interpreted as directed quantities (vectors) in three-dimensional space. Quaternions have enjoyed a very useful role in the mathematical treatment of rotation of three-dimensional space about an origin, much like the figure 7 topology. Such rotary extensions have proved handy in certain formulae of relativity theory—the “Lorentz transformations” in the four-dimensional Minkowski “block,” as well as in quantum theory.¹⁴ Nothing, it would seem, is so far-fetched that it will be eternally barred from the “semiotically real.” I cannot be so presumptuous as to claim I have resolved any fundamental problems with my own very modest contribution. At most, perhaps I have been able to offer a brief glimpse into the vast realm of semiosis from a slightly different angle. What I also believe I may have illustrated is the important Peircean notion that semiosis, the field of signs perpetually transmuting themselves into other signs, is a self-referential, self-organizing whole. In this regard signs manifest the same function as all living organisms (Varela 1979; Maturana and Varela 1980, 1987; Jantsch 1980).

IV. BACK ON TERRA FIRMA, OR, OF WHAT IS “REAL.” Lévi-Strauss’s myths that speak themselves through “man,” Heidegger’s language bringing about its self-realization through us, Derrida’s “we are always already in the text,” Wittgenstein’s “the limits of my language mean the limits of my world,” and Peirce’s “I am the sum total of my thought-signs,” all testify in one form or another to the nonlinear, asymmetrical, irreversible, multiply in-formed “semiotics ≈ life” equation that has been vaguely suggested throughout this disquisition. However, there is a problem here. Pierce’s conclusion that the whole of “reality” is in a sense a universe of signs appears to contradict the distinction I have made between the “semiotically real” and the “real.” To repeat Peirce’s comments of 1906, there are two kinds of indeterminacy: (1) indefiniteness (vagueness) and (2) generality, in regard to which we are told that

the former consists in the sign’s not sufficiently expressing itself to allow of an indubitable determinate interpretation, while the [latter] turns over to the interpreter the right to complete the determination as he pleases. It seems a strange thing, when one comes to ponder over it, that a sign should leave its interpreter to supply a part of its meaning; but the explanation of the phenomenon lies in the fact that the entire universe, embracing the universe of existents as a part, the universe which we are all accustomed to refer to as “the truth”—that all this universe is perfused with signs, if it is not composed exclusively of signs. (CP:5-448n)

If the universe is “composed exclusively of signs,” if signs constitute all of “reality” that can be represented by other signs, whether as mere possibility or as law dictating what will be actualized, then need there be no boundary between the “semiotically real” and the “real”? A boundary of sorts does exist, however. In order to get a better handle on the distinction between the two uses of “real” here, I shall turn to Pierce on propositions as representation—i.e., representation not in its twentieth-century empirical positivist sense but with respect to the “semiotically real”—hence a more appropriate term might be signification (the “production of meaning”), also a synonym for semiosis (Greimas and Courtés 1982:299).

The general proposition “All solid bodies will fall in the absence of any upward force or pressure” is of the nature of Peirce’s “representation.” Nominalism, Pierce points out, would hold that that which is represented is not identical to that which is “real.” He concedes that what is “of the nature of a representation is not ipso facto real. In that respect there is a great contrast between an ideal of reaction and an object of representation. Whatever reacts is ipso facto real. But an object of representation is not ipso facto real” (CP: 5.96). On the other hand, Peirce diverges from the nominalist thesis in his belief that a general proposition stating what would happen under certain circumstances is of the nature of representation; it refers to experiences in futuro, which may or may not be experienced, and which may or may not serve to confirm the proposition, given Peirce’s fallibilism principle—I refer the reader once again to Peirce’s pragmatic maxim. Hence, when Peirce asserts that “really to be is different from being represented,” he means that

what really is, ultimately consists in what shall [in the long run of things] be forced upon us in experience, that there is an element of brute compulsion in fact and that fact is not a mere question of reasonableness. Thus, if I say, “I shall wind up my watch every day as long as I live,” I never can have a positive experience which certainly covers all that is here promised, because I never shall know for certain that my last day has come. But what the real fact will be does not depend upon what I represent, but upon what the experiential reactions shall be. (CP:5.97)

Ultimately, the matter comes down to Peirce’s asymptotic approximation to some perpetually undefinable truth on the part of the entire community, not the individual.

Another way of putting Peirce’s concept evinces a rough analogy with Popper’s (1972, 1974) thought, namely, his triad of Worlds.¹⁵ The orange-yellow flame produced by an NaCl solution subjected to a Bunsen burner flame, as a possibility, a feeling, a quality, as an impingement on the senses, though there is not yet conscious acknowledgment of it, is Firstness (Popper’s World 1). The mode of conditionality of the NaCl solution, its would be, is Thirdness, or law. The law is essentially the habit or real probability by virtue of which a particular future occurrence will (or will not) take place (Popper’s World 3). The orange-yellow flame produced by the solution thus enjoys a “reality,” though it would possess this “reality” even if Na never manifested itself for any observer as an orange flame.

In other words, it possesses Thirdness as law or habit more or less determining how a particular NaCl solution would behave under certain conditions. Comparably, the proposition “If this NaCl solution were subject to a Bunsen burner flame, it would produce an orange-yellow hue” is, we generally suppose, “real” (i.e., “true”) in terms of sodium’s general behavior. If put to the test, that “reality” can be confirmed by virtue of what actually appears to consciousness, or what consciousness, mediately as it were, and in interaction with the “real,” selects and distinguishes from among the entire set of possible percepts (the impact of Secondness) (Popper’s World 2).

However, the NaCl solution as a “semiotic object” of the proposition in terms of the hue produced on combustion is “real” only insofar as it is, in the theoretical long run, determined by other signs (i.e., the nature of ions in solution, the properties of Na and CI, their relation to other alkalis and halogens, chemical spectroscopy, etc.) (see note 17 of chapter 1). It is not the “actually real” dynamical object which serves to determine signs as such, but the “semiotically real” which is determined by other signs as such. This mediary rather than immediate nature of Secondness, as I have argued elsewhere (Merrell 1985a), is an absolutely essential component of Peirce’s doctrine of signs. The universe as we can possibly know it, then, is a “perfusion of signs,” and as far as we can know, it may be “composed exclusively of signs.” In sum, whatever is “real” has no intelligible status except insofar as it is determined by the process of signification (i.e., Peirce’s “representation”).

Against the nominalist postulate that what is signified cannot be a mirror image of the “real,” Peirce argued indefatigably that all is in theory knowable, though it can be known absolutely solely in the theoretical long run. Peirce points out that if what lies behind that which is signified is never itself given in the signified, then any attempt to characterize it would entail the contradiction of attempting to signify the unsignifiable, to know the unknowable (CP:5.257, 5.312). Peirce admits that though knowledge of things in themselves is entirely relative to human experience and to the nature of the mind, “all experience and all knowledge is knowledge of that which is, independently of being represented” (CP:6.95). Even lies “invariably contain this much truth, that they represent themselves to be referring to something whose mode of being is independent of its being represented” (CP:6.95). Yet, he also admits, “no proposition can relate, or even thoroughly pretend to relate, to any object otherwise than as that object is represented” (CP:6.95). All knowledge, then, is knowledge of the “semiotically real,” of particulars generated by finite individuals or human communities—they are invariably tinged with vagueness, while the proper “real” objects of knowledge are generals to which knowledge aspires but will never reach absolutely. To repeat, knowledge is always and invariably a process of representation, or in terminology more proper to this inquiry, a process of signification. Peirce promises that the “real” will surely someday be ours if we persist with sufficient tenacity, but we will never live to see that day. Hence a boundary will always exist between the “real” and a given “semiotically real” world.

Peirce’s “realism,” guaranteeing that sufficient efforts expended to know the “real” will achieve success in the theoretical long run, is based on mathematical principles justifying probable inference: that the character of an aggregate may be determined by a large enough sampling of the parts (CP:2.102, 2.785, 5.110). This probable end as the result of a collective enterprise is a sharp contrast to the necessary goal of the solitary Cartesian mind introspecting absolute truths. In the former the effort to know is limited by the intensity and duration of the inquiry; the latter is a purely nonhistorical, rational process, whose limits are defined by the ability to avoid contradictions, for a contradiction inevitably leads to a failed attempt to achieve a necessary conclusion (Thompson 1952). However, Peirce’s dilemma is that of a paradox not entirely unlike the tu quoque arising out of the Cartesian leap of faith in reason. If, as Peirce asserts, nothing is absolutely incognizable, then how can he know it? Peirce was aware of this problem, and he even insisted that his principle of the ultimate cognizability of all things rested on grounds for which no reason could be given. He openly conceded that

the assumption, that man or the community . . . shall ever arrive at a state of information greater than some definite finite information, is entirely unsupported by reasons. There cannot be a scintilla of evidence to show that at some time all living beings shall not be annihilated at once, and that forever after there shall be throughout the universe any intelligence whatever. (CP:5.357)

To put it pithily, the belief that nothing is incognizable is itself based on an incognizable premise. In essence we have the paradox: “‘nothing is incognizable’ is incognizable.” By extension, regarding self-consciousness, it can be stated from the Peircean perspective that “‘the self is not incognizable’ is incognizable,” which places the self, the cognizing mind, in the same grab bag with all signs. The self can know its own introspecting self no better than it can know the “real,” which is to say that it can know itself in theory but not in practice.

And we are once again reminded of Peirce’s enigmatic “man ≈ sign” equation—a topic to be taken up more thoroughly in chapters 6 and 7 in the guise of “mind ≈ sign.” If the universe “is profused with signs,” then we, ourselves, are signs. We naturally tend to read this equation with incredulous eyes. It appears demeaning, even in a sense humiliating. Signs surely must exist to suit our purposes?

However, if we return for a moment to Peirce’s remarks on vagueness and generality, we begin to comprehend the interaction between signs and ourselves on an equal basis. Further determination of the vague sign is left up to the sign’s interpretant; further determination of the general sign is chiefly the responsibility of the interpreter. Since a corpus of signs invariably contains signs which are either vague or general or both, and since all ideas (thoughts) are signs, a given corpus of ideas must evince vagueness and generality (CP:5.448). Determination of the signifying corpus must depend on a collaboration, and mutual interdependence, between interpreter and interpretants; hence, like the observer-observed pair of quantum theory, they are inseparable. Indeed, they are in a sense coterminous. They are, themselves, composed exclusively of signs.

As Peirce puts it, “the fact that every thought is a sign, taken in conjunction with the fact that life is a train of thought, proves that man is a sign” (CP:5.314). We inhabit, we are, a world of vague and general, inconsistent and incomplete, signs. Hence according to Peirce’s objective idealism, the “semiotically real” domain is, ipso facto, methodologically and epistemologically real, yet ontologically ideal insofar as the “semiotically real” will never become identical with the “real” in our finite world. Therefore we collaborate with signs “out there” and with thought-signs “in here” toward completion of their (our) determination.

In this manner, Peirce attributed a certain organicity to signs. Whereas earlier he declared that “the word or sign which the man uses is the man himself’ (CP:5.314), by 1892 he had backtracked somewhat with the suggestion that “every general idea [thought-sign] has the unified living feeling of a person” (CP:6.270). Yet in spite of Peirce’s apparent realism, he never could escape the objective idealist imperative of maintaining a distinction between the subject-mind as architect of signs and the subject-mind as object of knowing. One still tends to retort from the gut, however, that even though a sign, a thought-sign, or a general idea possesses the same qualities of feeling we attribute to a human being, there must be some very fundamental difference between a person and a sign. Since an interpretant is determined by its respective sign (representamen), it must exist apart from its interpreter. But were it possible for an interpretant to be absolutely determined by its sign, its object would be a self-contained univocal singularity: there would be no latitude on the part of the interpreter, who would at this point necessarily become indistinguishable from the interpretant; she would become, herself, the ultimate interpretant. Fortunately we do not run this risk, for, that ultimate interpretant being inaccessible to us, we will always remain to a greater or lesser degree apart from the sign we are in the act of interpreting. Nonetheless, we are inexorably partly interjected into it:

Whenever we think, we have present to the consciousness some feeling, image, conception, or other representation, which serves as a sign. But it follows for our own existence (which is proved by the occurrence of ignorance and error) that everything which is present to us is a phenomenal manifestation of ourselves. This does not prevent its being a phenomenon of something without us, just as a rainbow is at once a manifestation both of the sun and of the rain. When we think, then, we ourselves, as we are at that moment, appear as sign. (CP:5.283)

Peirce seems to imply that every interpretant popping into consciousness is subject to further determination by the interpreter who is, herself, a further representation of that selfsame interpretant.¹⁶ A distinction can be made solely as a result of ignorance and error, which raises the interpreter’s consciousness to an awareness of something other than herself. It follows, Peirce argues, that in the same manner the laws of nature influence matter. A law is a general, a Third, in contrast to an existing object, which is simply a blindly reacting entity to which all generality, representation, and signification is utterly foreign: the general law is oneness, which sets the parameters for the behavior of individual material entities, the many. Its oneness is indivisible, and the manyness of the individuals remains incompatible with it, yet they are determined by it. This, Peirce remarks, is the “great problem of the principle of individuation which the scholastic doctors after a century of the closest possible analysis were obliged to confess was quite incomprehensible to them” (CP:5.107). Peirce’s concession to a tinge of mysticism in his response to this problem is perhaps inevitable: the universe must possess, he suggests, the characteristics of an utterer who, in dialogic fashion, interprets her own utterances. Peirce continues:

Analogy suggests that the laws of nature are ideas or resolutions in the mind of some vast consciousness, who, whether supreme or subordinate, is a Deity relative to us. I do not approve of mixing up Religion and Philosophy; but as a purely philosophical hypothesis, that has the advantage of being supported by analogy. Yet I cannot clearly see that beyond that support to the imagination it is of any particular scientific service. (CP:5.107)

Elsewhere, Peirce might appear to be a candidate for the Intellectual Club of Unbridled Speculation on suggesting that the universe is a Supreme Symbol. Like an idea, the universe is a representamen “working out its conclusions in living realities.” And since every symbol must have, “organically attached to it, its Indices of Reactions and its Icons of Qualities,” which exercise the fundamental role as subject and predicate of the symbol (proposition), they comprise a Text, the “Universe being precisely an argument,” which, though at present incomplete, if given indefinite unfoldment, can potentially be played out in the long run (CP:5.119). The universe as argument is both utterer-representamen and interpreter-interpretant, which is to imply that, viewed as a timeless whole, somehow it contains both its argument and its own counterargument.¹⁷ It is tantamount to √-i, the Mobius strip, or the torus, which, when turned inside out, becomes its mirror image—recall Eco on the mirror image.

This notion also implies Peirce’s description of the process of thought as dialogism (CP:6.338). While I have briefly discussed the dialogical nature of semiosis elsewhere (Merrell 1990), it takes on special importance in the present consideration of the one and the many, the whole and its parts, continuity and discontinuity. Peirce makes a gallant effort to articulate the distinction between absolute truth (the one) and that which an individual might take to be the truth (one among the many). First, nobody is absolutely an individual. Rather, her thoughts are what she is always engaged dialogically in “saying to herself,” that is, “saying to that other self that is just coming into life in the flow of time. When one reasons, it is that critical self that one is trying to persuade; and all thought whatsoever is a sign, and is mostly of the nature of language” (CP:5.421).

Second, one’s circle of society as a collectivity “is a sort of loosely compacted person, in some respects of higher rank, than the person of an individual organism” (CP:5.421). Combining these two points, one is led to the conclusion that the self is constantly displaced by its other, which perpetually presents, so to speak, a counterargument to the self which the self in turn must counter, an ongoing process tending toward habit. On the other hand, the self dialogues with that collective Other, the community, which, if the dialogue were interminable, would culminate in the final community opinion regarding the “real.” These two processes “render it possible for you—but only in the abstract, and in a Pickwickian sense—to distinguish between absolute truth and what you do not doubt” (CP:5.421).

In other words, one self is the utterer-representamen, the other is the interpreter-interpretant (or critical self) which is constantly emerging into the flow of time. In this manner, the self-other interaction is incompatible with “real” (experienced) time, though not abstract (imaginary) time. But since at the very moment the self enters “real” time it leaves its role as interpreter behind and becomes the utterer, the first self, the self of, so to speak, différance in the sense of Derrida (1973), that other self, as interpreter-interpretant, must ultimately sink into the abstract along with Absolute Truth. That is to say, if the critical self (as individual and as community) is destined ultimately to embrace Absolute Truth, though this cannot be realized in “real” time, that Absolute Truth must be distinguished from all particular signs, habits, and beliefs entertained by any given individual in its dialogue with its individual and collective other.

In this sense the ideal critical and collective self is an abstraction from the “semiotically real” world as such and “real” time as such. This characterization of the other self, however, can be articulated only insofar as it is related to the known or phenomenal self, the first self, especially in light of the fact that it partakes of the nature of sign. The phenomenal self at the center of the sphere in figure 7 can shrink to a point, or it can project itself outward into indefinitely expansive space and indefinitely future time. It does so in dialoguing with its own other, which constantly engages in generating countersigns (propositions, arguments) in response to the signs the first self puts forth. In this fashion the self plus its other, upon expansion, encompasses more and more of the community dialogue. But since the individual can never be identical with the whole, the community Other is always “out there,” generating its own countersigns (propositions, arguments), which serve to reveal the individual self’s errors of its ways. The Other constitutes a repository of community knowledge, a particular “semiotic reality.” As this “semiotic reality” becomes increasingly general, the outer sphere undergoes expansion, though over finite time and given anything less than a community of infinite capacities, the sphere’s boundaries are destined to remain indeterminate.

There is apparently an inconsistency in Peirce’s thought here: the otherworldly critical and collective Other appears to be somehow partly, though in the theoretical long run wholly, outside time and space in contrast to the concrete thisworldly time-and space-bound phenomenal self. This attests to a host of conflicts (scholastic realism and pragmatism, objectivity and idealism, commonsensism and mathematically abstract theoretical formulations), all of which are rather contradictorily embraced by Peirce’s umbrella label objective idealism. It also bears witness to the inevitable vagueness and generality of all signs with which the universe is apparently perfused. Yet there is so intimate a connection between the Other and the individual observer (self plus other) that they cannot be divorced. The community Other’s “semiotically real” world and the world of the individual (subjective) observer are, in a manner of speaking, incomplete or foggy mirror images of one another. That is to say, the effect of the “real” along the x axis in figure 6 makes up the Other’s “semiotically real,” while the imaginary (y axis), which is individual and subjective, serves to generate, as it slides along the time axis by recursion and oscillation between this and that, potentially an infinite variety of “semiotically real” worlds, each of them affording a tenuous grasp of the “actually real.”

A given “semiotic reality” is thus perpetually displaced as a result of the interaction at their meeting point of the individual, subjective, and imaginary generation of signs by the self-other, on the one hand, and on the other, the Other’s world of forms “out there.” The traditional opposition between episteme and doxa must now be viewed as a struggle between complementarities, as an interaction which creates “reality” as such. The imaginary is no longer to be understood as a mere fiction that contrasts with the “real.” Rather, it is an integral part of the “real” itself, essential not only to its representation as signification but to its very composition. And the “real” cannot exist as such without being able to see itself at once as neither this nor that, this or that, this and then that, and both this and that. Self, other, and community Other are the instruments by means of which the “real” engages in this self-reflective dialogue.

Such intrigues and enigmas are most likely inevitable in any and all holistic configurations.