EIGHT

Nothing and Everything

I. ON WHAT THERE IS NOT. Much of the preceding plus the premise of this chapter can be encapsulated thus:

Semiosis implies the capacity to produce, in the theoretical long run, infinitely many signs which presumably re-present items in what is traditionally conceived to be an a priori reality. But such re-presentation necessarily remains false to itself. Rather than re-presentation, there is mere pre-sentation (introduction of that which cannot be re-introduced in its identical form) of “semiotically real” items for an active subject (interpreter-interpretant; observer-observed). The entire system, especially given the self-falsifying character of the human animal’s signs, owes its very existence to a special agent: “nothingness,” charged with revving up the generator of signs which evolve from the realm of vagueness and inconsistency to increasing determination, and hence generality, though the task will always remain incomplete short of the infinite theoretical long run.

To begin, by addressing myself to this “theorem’s” taproot, in Gravitation (1973), the authors, Charles Misner, Kip Thorne, and John Wheeler, speculate on the nature of what they call “pre-geometry,” which is prior to both time and space. They suggest that it is the generator of logical relationships, a self-generating “calculus of propositions,” such as might immediately follow from a Spencer-Brownian logic of distinctions, with, at least in the beginning, the compelling simplicity of mere this/thatness. In the first place this calculus of propositions is suggestive of mindlike properties—as are, at a more primitive level, Spencer-Brown’s calculus and Peirce’s book of assertions. In the second place it presupposes the claim that “empty space” is not empty at all but is instead the scene of the most violent physics—the constant collapse and rebirth of the gravitational field, or in Bohm’s terms, the constant explication of the implicate. “Empty space” is described as having “foamlike” properties of alternating negative and positive fluctuations where the basic particles are incessantly created and annihilated, a sort of micro-counterpart of the moire effect (I must point out, however, that for Wheeler [1968, 1973], unlike Peirce, space is at this level radically discontinuous, the scene of a staggering multiplicity of mini-catastrophes).

Significantly, Wheeler and his associates who propagated this “geometrodynamic” concept envision a single entity, the gravitation-field geometry, which accounts for everything that is. It represents an attempt to undercut the set theoretical paradox of container/contained and part/whole, the equivalent of Schrödinger’s arithmetical paradox, and the discrepancy between space-time continuity and quantum discreteness of the material punctum. This conception of “empty space,” much like the “nothingness” of Sunyata and Bohm’s implicate (Wilber 1982), is not the product of negation, nor is it simply non-being.

To negate something is to make its intended force become absent. Frege (1919) argued that negation, regarding the exercise of judgment, does not depend upon incompatibility at the same level, but on assertion at one level and its negation at a metalevel. Freud’s (1925) negation is that of a denial (Verneinung) which suppresses, and at the same time conserves the repression (Verdrägung) of that which it negates—a sort of Hegelian negation of the negation. Both of these notions of negation are inadequate for the present purpose, which is more fundamental.

The notion of negation I am after is somewhat more comparable to Spinoza. He once revealed that every definition is a boundary which negates all other definitions and introduces language to what is up to this point a purely abstract calculus. Negation in this sense is not merely no. Neither is it not. Not is syntactic, while no can be communicated nonlinguistically (Wilden 1984). Like no, not refers to (indicates, points to) something whose existence or meaning is already at least partly specifiable. It requires a base capable of supporting some sign or thought-sign before it can point to anything, and what it cannot point to is the base supporting it—lest it negate its own foundation and self-destruct. The domain preceding this indexical pointing must be “iconic” in the most primitive sense. This ultimate ground of “nothingness” (pre-geometry) presupposes distinguishability (Wheeler), distinction (Spencer-Brown), and a cut providing iconicity (Peirce), which precedes indication (Spencer-Brown), indexing (Peirce), the actualization (Wheeler), or explication (Bohm), of something for someone in some respect or capacity (i.e., the semiosic process).

What, then, is this “nothingness” lying behind distinction, no, not, and indication? Like sunya,¹ it can be variously translated as empty, nothing, void, or open. The problem is that these words tend to convey the impression of some-thing blank—which is the fallacy also of Peirce’s “blank sheet of assertion” and goes against the grain of Wheeler’s “pre-geometry.” The “nothingness” I speak of, in contrast, precedes notions of thingness and of opposition or duality, all of which depends upon negation, distinction, and indication. Regarding mind, “nothingness,” simply put, is the emptiness of all intellection. Mental thought-signs have arisen out of distinctions which imply boundaries separating something from something else. In the total absence of thought-signs, it appears, we have “nothingness.” But this will not do the trick either. We must still contend with the full mind/empty mind dichotomy.

Let us, then, defer to a scholar versed in Oriental thought in search of a more adequate articulation:

Emptiness which is completely without form is freed from being and non-being because “non-being” is still a form as distinguished from “being.” . . . Emptiness is not a mere emptiness as opposed to fullness. Emptiness as Synyata transcends and embraces both emptiness and fullness. It is really formless in the sense that it is liberated from both “form” and “formlessness.” Thus Synyata, Emptiness as it is is Fullness and Fullness as it is is Emptiness; formlessness as it is is form and form as it is is formless. (Abe 1985:126-27)

In this light, a way of putting it is that every-thing as it is is no-thing, and no-thing as it is is every-thing. The holomovement is all and nothing; as nothing it is all and as all it is nothing. In the final analysis, emptiness is the simplest of simples made inordinately complicated when there is an attempt to articulate or conceptualize it. It is the most direct form of experience. If an alcoholic sees (distinguishes) snakes and points at (indicates) them while in an excruciating phase of delirium tremens, we may in turn point to the nonexisting snakes in our attempt to prove him wrong. But he is more right than we are: he is pointing at some-thing; we deludedly believe we are pointing at no-thing (Alice also marveled at the Queen who could see nobody on the road before her, and Odysseus used “nothingness” to fool the Cyclops by calling himself Nobody). Not an idea, a perspective, or a thing, “nothingness” is what it is, that’s it. Perhaps we can hardly go any further.

But the question must be asked: How does this “nothingness” jibe, if at all, with Peirce’s categories? Eugen Baer’s (1988:240-41) considering the state of “nothingness” to be a sort of Peircean pre-First, which consists of the “absolute nothingness” (CP:6.215), the field within which semiosis plays out its drama in “unbounded freedom,” like the random walk of a stick of chalk on a blackboard (CP:6.203), is revealing. Peirce was aware of the need for “nothingness” as that which makes possible the extraction of forms. As Peirce puts it, the “absolute nothing” (CP:6.215) of “nothingness” is not Hegelian being (CP:6.217). It is utter vagueness, dimensionless (CP:6.193), freedom, chance, spontaneity (CP:6.197-200). There are certain characteristics of the whole of consciousness in this field of “nothingness,” as a “chaos of unpersonalized feeling” (CP:6.33), which, nonetheless, possesses a definite intensity (CP:6.265). In this respect, Peirce’s cosmology entails a “hyperbolic” evolution which

proceeds from one state of things in the infinite past, to a different state of things in the infinite future. The state of things in the infinite past is chaos, tohu bohu, the nothingness of which consists in the complete absence of regularity. The state of things in the infinite future is death. The nothingness of which consists in the complete triumph of law and absence of all spontaneity. Between these, we have on our side a state of things in which there is some absolute spontaneity counter to all law, and some degree of conformity to law, which is constantly on the increase owing to the growth of habit. (CP:8.317)

Peirce must be partly exonerated for his hypercontradictory passage by virtue of the difficulty in articulating the slippery concepts he is attempting to confront head-on. “Nothingness,” as he seems to sense it, is the “other side,” a timeless orb framing his three categories whose very existence, meaningless outside temporality, perhaps creates the possibility for the evolution of time (CP:8.318).² Time, in impossibly traversing the frozen passage from finitude to infinity, gives rise to the categories, and these, in springing time from its condensed knot of primordiality, embody time, which is thus contained within itself. In addition to sunyata, this “nothingness” before time was is rather commensurate, I would submit, with the silent Tao, or Asat, the nonexistent sphere of the Rg-Veda: the silent, bottomless, unthinkable background of undifferentiated energy out of which everything emerges (T. de Nicolas 1976:89-107).

Peirce, to be sure, is clear on one important point: “nothingness,” the undifferentiated, is not merely “the nothing of negation”; it is “the nothing of not having been born” (CP:6.217). It is the unbounded freedom of tychism, which, ineffable and well-nigh unthinkable to the core, refuses worthy candidacy as a Peircean category. Yet Peirce recognized the need to distinguish the domain of “utter nothingness” (CP:6.490) from that of is-ness. As he puts it:

We start, . . . with nothing, pure zero. But this is not the nothing of negation. For not means other than, and other is merely a synonym of the ordinary numeral second. As such it implies a first; while the present pure zero is prior to every first. The nothing of negation is the nothing of death, which comes second to, or after, everything. . . . There is no individual thing, no compulsion, outward nor inward, no law. It is the germinal nothing, in which the whole universe is involved and foreshadowed. As such, it is absolutely undefined and unlimited possibility—boundless possibility. There is no compulsion and no law. It is boundless freedom. (CP:6.217)

If pure “nothingness” is the primitive category preceding Firstness (origin), Secondness (otherness), and Thirdness (meaning), we have, then, after Zero, One, as the first numeral, as unity, individuality and nonduality, or in Peirce’s terms, the Monad (see also Jung 1963). One is followed by Two, the distinguished-indicated split between this and that. Three, which brings the previously incompatible One and Two together, closes the circle, thus potentially reverting back to the continuity of the undifferentiated as a self-contained whole (following figure 5), though it contains the differentiated as the generation of a potentially infinite series of interpretants, each in some way the same as and yet different from all others. Parmenides’ summary of his position as “If One is not, then nothing is” is, in this manner, turned inside out as “Nothing is what One is not, and One, when it is, is what nothing (as a potentiality) was.”

In this sense the zero of “nothingness” becomes the continuous flux of Firstness: the ongoing processual stream before there is consciousness of what has been cut and marked out from “nothingness.” This is essentially Hanson’s (1958) distinction, following Wittgenstein, between seeing and seeing as, when sense data are put into their conventionally generated pigeonholes (see Merrell 1990). The flux can be grasped only by stopping it, not actually but conceptually, and the grasp can then be interpreted by resort and appeal to meanings even when they are not reflexively explicit but only implicit in action. Concepts or thought-signs ripped out of the continuous flux of experience are not by any stretch of the imagination determined by experience, for experience is part of the continuum which manifests no limits or boundaries. The establishment of limits is accompanied by the generation of thought-signs and consciousness of them, which serves to bring order to the world, creating its myriad pieces of furniture and giving rise to the possibility of generalities.

But the abstraction of thought-signs from the continuum is not entirely arbitrary, since, if we follow Peirce, the surprising “clash” of Seconds, of “real world” objects, persists in forcing itself into our attention in one form or another. Neither is the flux exactly characterless; the continuum, when cut and marked, manifests character at the location of the cut, which limits the range of possible interpretants for that particular cut. There is some free play, but the nature of the interpretants cannot be irrelevant to the nature of the original flux of Firstness as a potential for an indefinitely broad range of possible interpretants. The ultimate test of relevance is, most appropriately, Peirce’s pragmatic maxim (CP:5.402) which, if successful, yields dividends in both action (resulting from habit) and understanding (from meaning attached to the interpretant in question). And the degree of rigidity of the interpretants is a measure of Peirce’s principle of tenacity (CP:5.337), a sort of stubbornness factor which at times fetters more than it facilitates meaning. This success of interpretants by a stubbornness factor stringently limits alternatives, though it aids in the eternal push toward finality.

II. GETTING ALONG SWIMMINGLY. Thought has generally, though not always, brushed aside such intangibles as I outlined in the preceding section, while stepping up to a more comfortable level of abstraction in pursuit of negation. On the other hand, the West’s obsession with truth has placed it in deep and murky waters time and again. Simply put, in mathematics, syntax involves provability (yes/no, not, negation), while semantics involves truth. Both provability and truth have traditionally been the intellectual elixir motivating seekers of knowledge. In contrast, Eastern thought, as far as my meager understanding goes, involves pragmatics in the broadest possible stretch of the imagination, where the subject well-nigh disappears in the contextual soup of things. Leaving this point aside for the moment, I will probe a mite further into negation in an attempt to approximate the ground level of semiosis, and subsequently return to this most general sense of pragmatics.

Most notably, negation is germane to Whitehead and Russell’s Principia Mathematica (1910). The sole formation rule in their work regarding negation, the primitive proposition 1.7, states:

If p is an elementary proposition, NOT p is an elementary proposition.

While 1.7 could be an adequate formation rule for the arbitrary manipulation of marks on paper or noises uttered in sequence—the “formalist” philosophy of mathematics—things become messy once we start giving “NO” and “NOT” their interpretations we intuitively associate with negation in everyday communication. Admittedly, in the vast majority of sentences Whitehead and Russell’s formation rule as stated in the Principia would still serve us quite well. But its adequacy falters for those cases where the formula p is a simple construction that can be interpreted as referring to some existential characteristic of its own—such as its own truth in every truth-value model—i.e., Russell’s set theoretic paradox, a class which becomes a member of itself. And Whitehead and Russell (1910:13) seem ultimately to have had truth-value interpretation in mind, for they write that “the system must lead to no contradictions, namely, . . . both ‘p is a theorem’ and ‘NOT -p is a theorem’ cannot legitimately appear.”

But let’s get back to the more fundamental level of syntax. At the outset Whitehead and Russell appear to have achieved their goal by formalizing logic introducing (1) inference rules relating to negation, and (2) primitive definitions involving negation. These rules and definitions bring into play the laws of noncontradiction and the excluded middle (and eventually their intended truth-value interpretation). This attempt to avoid any and all contradictions led Russell to his Theory of Logical Types, devised especially to prevent paradox from raising its ugly head in set theory. Russell’s ploy, admittedly ad hoc, was to place restrictions not only on formal language use but, in addition, on the use of ordinary language, especially regarding its reference to formal language.

Eschewing Whitehead and Russell’s notation of falsity as o and truth as 1 which compose a metalanguage for assigning values to the formulas of their deductive calculus, I will opt for the more primitive Spencer-Brown and Peircean “nothingness” in place of o, and the mark-cut in place of 1. It might appear to those who cannot free themselves from the propensity to assign values to everything and anything that we now have two distinct levels, that is, a White-head-Russell “two-value logic,” with the negation sign connecting them. In this sense negation erases a mark-cut, thus reducing it to level o. However, one must be mindful that at this most primitive level the mark-cut is valueless, hence truth through falsity—the equivalent of 1 and o—does not yet enter the picture. The most that can be said is that, commensurate with Spencer-Brown and Peirce, an even number of negations applied to the same level will be the same as no negation, and an odd number of negation signs will reduce to a single negation. At this lowermost point there is as yet no -thing.

In other words, at the level of the mark-cut there is no value in the sense either of logic or of mathematics. When the most fundamental sort of “value”—which is not yet any “value” in the ordinary sense—is introduced, it is simply the equivalent of imaginary numbers, most adequately expressed in natural language as the statement ‘This statement is false,” which is neither true nor false but merely undecidable. Boolean algebra and the Theory of Logical Types disallow such undecidables: a statement must be either true or false, and if not, it is meaningless and hence worthless. In similar fashion, it is generally assumed that numbers must be either positive or negative or zero. The problem is that the imaginary number, √—I, is simply neither positive nor negative nor zero. Spencer-Brown extends this concept to Boolean algebra to compose, in addition to true, false, and meaningless, a fourth class, imaginary. Imaginary values, entailing oscillation between +I and -I, true and false, yes and no, either and or, this and that, are like a wave train produced by an “excited” computer caught in a double bind called a “synchronizer glitch” (Wilden 1984), or like the wave train model of an “excited” subnuclear particle (Kauffman and Varela 1980). Perhaps we have here a microcosm of Wheeler’s “self-excited” universe.

But we really must return to the comfort of solid earth beneath our feet. First and foremost, Spencer-Brown and Peirce’s “nothingness” and the mark-cut are not compatible with the empty set of set theory. A set is a collection of things each of which is a member of the set. The individual members are identifiable at one level, as is the whole collection supposedly at another level. The identity of, say, an orange (as token) is contained in the orange’s membership in the set of all oranges (as type). In addition, complementarity enters the scene. The set containing a particular orange here-now exists in complementary relationship with, and at the same time it constitutes, everything other than the/an orange, with a boundary dividing in essence this from that. And everything other than this orange constitutes the orange as orange within the set containing the orange. To consider everything other than the orange within the set of all oranges is like thinking of an orange without really thinking about it. The set is at that point not empty, though that which fills the container is implicit (implicate). Moreover, to consider the set of all real oranges with a radius of three feet or more is to be aware of an empty container, a sort of knothole, surrounded by that which is. This empty set is not mere nothing or “nothingness”; it is a contextualized container containing nothing. “Nothingness,” in and of itself, is unbounded.

According to orthodox set theory, from Cantor to Zermelo-Fraenkel to von Neumann-Bernays-Godel, there is only one empty set which is a member of all nonempty sets (Quine 1970). When properly and pragmatically contextualized, however, not all empty sets are identical. Donut holes, knotholes, and foxholes are different in terms of their complementary relations. The set of all nineteenth-century women presidents of the United States and the set of all twentieth-century kings of France are not the same, given the historical context of kings in France and the lack of women presidents in the United States. The set of all bald, hirsute men and of all barbers who shave all those who do not shave themselves are also both empty. In the latter case, the set of all bald, hirsute men is “empty” because of contradiction, and the set of all barbers who shave all those who do not shave themselves, if it is “empty,” is so as the result of a paradox, and if it is not considered to be “empty,” the paradox has not been acknowledged.

The empty set, then, can be construed as noticed absence in the sense of negation as ordinarily defined. It is an outlined absence, acknowledgment of a container without any contained. But a problem remains. The container generally is not, it cannot be, acknowledged without a pragmatically contextualized noticed absence as opposed to the presence of something “outside.” And the “outside” consists of things (that is, signs, the “semiotically real”) at the secondary level of something having already been distinguished and indicated. At the primary level, the “absence” can become an “absence” as such only with respect to that secondary level. In other words, noticed absence, that is, awareness of or consciousness of at least in the domain of a distinctively human semiotic, already presupposes some form of Thirdness, mediation, symbolicity. It appears that we can no longer return to the primitive taproot of the mark-cut; we cannot recall that original separating and calling up of a boundary distinguishing something from something else.

This presupposed Thirdness has to do with language. In our age of the “linguistic turn,” language is a much fought-over terrain. It is said to be a “prison-house,” sick, experiencing a crisis, corrupted by metaphysics, incapable of describing either the world or itself, undecidable, multiply ambiguous, and contentiously indeterminate. Many of those most responsible for articulating the problems with language, which includes the likes of Wittgenstein, Heidegger, Sartre, Gadamer, and Derrida, are among the most trenchant critics of Western reason and metaphysics. The problem with language, Derrida (1974:6) observes, “has never been simply one problem among others. But never as much as at present has it invaded, as such, the global horizon of the most diverse researches and the most heterogeneous discourses, diverse in their intention, method, and ideology.”

Derrida attacks the traditional account of the opposition speech/writing, which relegates writing to a secondary status while highlighting speech as the transcription of an epistemologically prior voice capable of speaking timeless truth in its immediacy. This prioritizing of speech, this logocentrism, also implies the generation of an entire set of binary offspring: presence/absence, inside/outside, thing/sign, identity/difference, reality/appearance. For each dichotomy there is presumably a cornerstone upon which one of the terms is privileged over the other as primary. One term supposedly remains pure, the other is blemished; one is superordinate, the other subordinate. Thus everything is already given a value. We are already caught up within the web of signs, wherever we are.

In line with Derrida’s critique, the 1-0 system derived from Whitehead-Russell, binary Boolean algebra, and by extension Saussurean semiology, especially as redefined to fit the pattern of binary-based information theory by Jakobson and Levi-Strauss, are simply outclassed when in the same ballpark with triadic semiotics. In any binary system, everything is already valued. There is no ultimate ground upon which to begin a signifying edifice. Peirce’s triadic system, in contrast, allows for no such delusions of presuppositionless premises. The triadic production of the interpretant is absolutely essential to a sign (CP:5.474). But triadic semiotics recognizes that the interpretant is an already advanced stage of signification at which point value has been interjected into the sign, with no turning back. In a radically fundamental sense the interpretant of a sign is its meaning. To reemphasize a most important point, if, as Peirce indefatigably argued, the only thought that “can possibly be cognized is thought in signs” and that “thought which cannot be cognized does not exist,” then all thought “is necessarily in signs” (CP:5.251). From this proposition, it follows that “every thought is a sign,” which “must address itself to some other, must determine some other, since that is the essence of a sign” (CP:5.253).

Moreover, since Peirce believed the interpretant of a sign is itself a sign of the same category, and that any sign must be interpreted or translated by a subsequent sign, then just as a sign is the interpretant or translatand of its predecessor, so the concept of the interpretant is that of infinite extension, a progressus as well as a regressus. There can be neither a first nor a last sign, nor is there any determinable center to the semiosic fabric. Hence there can be no ultimate presuppositions or foundations intuitively and intentionally generated ex nihilo. All signs, insofar as we can know them, be conscious of them, are mediated in the process of emerging and passing away. Consequently there can be no legitimate dichotomization or hierarchization.

Above all, the triadic semiosic fabric implies the sign user’s immanence: unlimited possibilities from within a bounded domain whose horizon remains perpetually beyond reach. This reveals the futility of any and all programs for constructing metalanguages with which to launch a universe of discourse into the stratosphere of Truth. Along these lines, Anthony Wilden (1980:122) points out that Russell’s theory, though a valiant effort to abolish paradox from his logical Garden of Eden, ultimately failed for two reasons: “(1) the transcendence of any paradox or double bind, in logic or in life, involves some form of meta-communication, and (2) the transcendence itself engenders paradox at the meta-communicative level—or at the level of the next logical type.”

In other words, Russell’s typing, and Tarski and Carnap’s metalanguages, are themselves paradoxical: they fuse and confuse distinct levels. First, they punctuate the continuum by erecting the initial 1-0 hierarchy, and second, they involve the use of negation, which is supposedly metacommunicative, since it is capable of reversing 1 to o and vice versa. The negation sign is thus necessary to the very idea of identity by its repetition an even or odd number of times.

The problem with Wilden’s critique, however, is that not only are metalanguages never without tangles, knots, and muddles, but contextualized meta-communication itself invariably merges levels. Lyotard (1984), effectively, and, indirectly but even more effectively, Rorty (1979) argue this point.³ Wilden is also well aware of this quandary, as his later work encyclopedically illustrates (Wilden 1987a, 1987b). Nonetheless, guided by a Western-style missionary zeal, he gallantly puts forth a sort of metaprogram for hewing out a path leading to a rectification of the entire mess—a Herculean, yet Faustian, task indeed.

Perhaps our only alternative is in good postmodern fashion to learn to live with/in the bind (this was the later Wittgenstein’s answer). To illustrate my point, I will begin once again with Russell, who, in reference to the violation of his logical types, tells us that

the imaginary sceptic, who asserts that he knows nothing, and is refuted by being asked if he knows that he knows nothing, has asserted nonsense, and has been fallaciously refuted by an argument which involves a vicious-circle fallacy. In order that the sceptic’s assertion may become significant, it is necessary to place some limitation upon the things of which he is asserting his ignorance, because the things of which it is possible to be ignorant form an illegitimate totality. (Russell 1910:38)

Suppose, for example, an honest and forthright scholar writes in the preface of her book: “At least one of all the sentences I write in this book is surely false.” The possibility of a paradox ensues, of course, since that very sentence runs the risk of being the false one. But if so, then it is true, and if true, then false. In order to ban all such threats, Russell decreed that a statement cannot logically refer to the totality of all statements, because as the member of the set within which it is included, it cannot be elevated to the same status as that set. Thus, the scholar’s phrase “all sentences” should be prohibited, for it belongs to an illegimate set.

However, the sentence I have just written must be prohibited as well, since the phrase “the phrase all ‘sentences’ is an illegitimate set” must also be a member of an illegitimate set. So now the question becomes this: “Is the phrase ‘the phrase’ “the phrase” ‘all sentences’ is an illegitimate set” is a member of an illegitimate set’ legitimate or illegitimate?” Logically speaking, it should be illegitimate, though practically speaking, and with due respect to Russell, it is conventionally quite legitimate. The occasion often arises in everyday language use to write such sentences as “All sentences are writeable,” “All sentences are written in a language,” “All written sentences are narratives of one form or another,” without their being considered pernicious. They are intelligibly perceived as true or false, and as meaningful or meaningless. Further, Russell’s very Theory of Logical Types essentially asserts that “all propositions must be generated and classified in such a way that the subject ‘All propositions’ never occurs.” This proposition itself must be forbidden by the nature of its injunction when applied self-referentially to itself (Davis 1972:149).

This conundrum—or so it must appear to those of an obstinate positivist bent—takes us back to Spencer-Brown’s imaginary values, which, he demonstrates, have been used for the construction of real answers in computer circuits, and, he suggests, imaginary values were employed by Fermat in generating his great proof. Spencer-Brown (1979:99) writes in this regard:

The fact that imaginary values can be used to reason towards a real and certain answer, coupled with the fact that they are not so used in mathematical reasoning today, and also coupled with the fact that certain equations plainly cannot be solved without the use of imaginary values, means that there must be mathematical statements (whose truth or untruth is in fact perfectly decidable) which cannot be decided by the methods of reasoning to which we have hitherto restricted ourselves.

In general, confining oneself to strictly defined binary Boolean equations eventually leads to undecidability of the Godelian type, which throws a monkey wrench in the works of logic and mathematics, traditionally conceived. On the other hand, Spencer-Brown demonstrates that with imaginary values, and from within a broader context, it is possible to generate answers to such undecidables by means of an equation’s turning back on itself, biting its own tail, and revealing information (by virtue of its in-forming itself, a formation within itself) regarding that which it expresses. Such an expression “is thus informed in the sense of having its own form within it” (Spencer-Brown 1979:100).

In a Peircean vein, the meaning of any given proposition can never be completely specified because the generalization of the conditional would be of the interpretant, or of Thirdness, incorporated in the “pragmatic maxim,” cannot precisely identify the object of which the proposition is a sign (CP:5.447n). This is the nature of the indeterminacy (Peirce’s counterpart to undecidability) of meaning. “All propositions” are hypothetical expressions about some aspect of the experienced world which must be, in some sense, indeterminate on account of the inevitable “clash” of this world (Secondness) on the author of the experiences (CP:3.93). Moreover, the object of a sign, like the sign itself, cannot be determinate, because every known property of both can never be fully specified:

The absolute individual can not only not be realized in sense or thought, but can not exist, properly speaking. For whatever lasts for any time, however short, is capable of logical division, because in that time it will undergo some change in its relations. But what does not exist for any time, however short, does not exist at all. All, therefore, that we perceive or think, or that exists, is general. So far there is truth in the doctrine of scholastic realism. But all that exists is infinitely determinate, and the infinitely determinate is the absolutely individual. This seems paradoxical, but the contradiction is easily resolved. That which exists is the object of a true conception. This conception may be made more determinate than any assignable conception; and therefore it is never so determinate that it is capable of no further determination. (CP:₃.93n)

This denial of absolute individuals because of their incessant fluctuation through time provides the grounds for Peirce’s doctrine of the indeterminacy of meaning. Since no object can be fully specified with respect to the totality of its properties, any proposition about it is vague insofar as it cannot hope fully to specify a determinate set of properties for that object. Hence the meaning of any proposition is always open to further specification. Given the incessantly fluctuating universe, however, in the domain of natural language use the equivalent of Spencer-Brownian imaginary values in a state of constant oscillation, like √-1, serves at least temporarily to halt the continuum with the generation of some element of discontinuity, bringing to a tenuous determination that which is indeterminate.

A car is thus that particular car at that moment; it is in a being of becoming state and at the same time in a process of becoming into being. It is and is not what it was, and it will have been and will not have been what it is. The car in one sense is a singularity at that spatio-temporal juncture, and in another, complementary, sense, it is what it was at all spatio-temporal junctures and what it will have been at all future ones. It is coterminous with all its instantiations, hence it violates Russell’s injunction against a set being a member of itself, and at the same time it simply is as it is during each and every instantiation. To put it another way, for the monist it is true that the car is the same car, yesterday, today, and tomorrow; for the pluralist it is false. The pluralist defends the truth of the car’s being different with each instantiation; the monist rejects his argument as false. Both the monist and the pluralist might brand the statement “the car is both the same and not the same at each moment” as nonsensical or meaningless. Spencer-Brown’s imaginary value, resting beyond negation, allows for this contradictory statement, however, as it does for statements barring excluded middles: hence it can be vague and/or general. In this sense, Peirce’s thought was far removed from that wooden variety, empirical positivist thought, that reigned for almost half a decade after his death.

Consequently, if our scholar in the preface of her book happens to write, “We can never write about ‘All sentences,’ ” she has committed a sin against Russell’s prohibition. But the fact is that she has written it. To do so she must have been able somehow to think about “all sentences” and potentially speculate about this supposedly unsayable set. So she merely did it, regardless of whether her action was self-contradictory or not. It must therefore be acceptable and even inevitable that she, as we all do, occasionally write sentences about “all sentences.”

Russell elsewhere tacitly acknowledges the practical validity of such everyday discourse. Wittgenstein’s Tractatus, which won his respect, claims that we can say things about the world as a whole only if we can get outside the world as a whole, but since we cannot do so, we cannot say anything about the world as a whole. This prompted Russell’s remark that “after all, Mr. Wittgenstein manages to say a good deal about what cannot be said, thus suggesting to the sceptical reader that possibly there may be some loophole through a hierarchy of languages, or by some other exit” (Wittgenstein, 1961:xxi). Wittgenstein obviously had this possible reservation in mind when, at the end of his treatise, he offered his reader the following notorious counsel: “6.54 My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them—as steps—to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.)” (Wittgenstein 1961:74).

Russell’s ideal logic is closed, but, speaking of the set of all possible logical systems, one must speak of openness, because of the inescapable self-contradictions and self-referential sentences in everyday language. The upshot seems to be that the mere fact of uttering a Russellian illegitimate sentence commits one to a form of relativism insofar as to comment about a totality renders that totality relative to one’s perspective, which in turn is relative to the indefinite range of other possible perspectives and descriptions of that totality.

In Hacking’s (1985) words, one’s style of reasoning commits one to a particular perspective, but, given other myriad styles of reasoning, commitment could equally have been made elsewhere. Peirce himself admits that ultimately any reason for trusting in reason must be undecidable (CP: 1.672). Nevertheless, like a sentence about “all sentences,” some form of trust in reason and the validity of argumentation is a matter of fact. If we deny this trust, our mouths and our pens will be paralyzed: we will not reasonably be able to reason about the impossibility of trusting reason. What we do when we reason—in whichever style—is simply do it. We do so, to use Peirce’s term, on instinct, by habit, and belief (CP.5.174). And doing it entails flatness: there are no permanent closed-system hierarchies here, only an infinite set of interconnected series, unlimited semiosis. This involves, in the broadest conceivable sense, a pragmatic, dialogic give-and-take, between the self, its other, and the Other—signs all.

III. INTO THE MAINSTREAM OF THINGS. In the final analysis, after all that has been written, warred over, and wrought regarding the “linguistic turn,” I can hope to offer no ultimate solutions. I will limit myself to reiterating what I believe to be a most important point: pure “nothingness,” that lowermost level from which all that is—i.e., all signs—emanates, is a far cry from the set theoretic form of noticed absence, which must presuppose the existence of some-thing. Such binary thinking demands truth and falsity, identity and contradiction, similarity and difference, presence and absence. The negative side of these dichotomies, however, is not mere “nothingness.” Noticed absence, I have suggested, is already valued, always mediated. It entails a giant step beyond the mark-cut, which itself arises out of “nothingness.” Pure “nothingness,” in contrast, exists at the more primitive level before the mark-cut, which itself is independent of 1-0, true-false, and all other such binaries. “Nothingness” is at most only sensed. It cannot be made explicit. It is no more existent than would be Plato’s shadows in the cave were the fire to be extinguished. There is nothing in contrast to which it can be conceived, perceived, and articulated.

This implies, regarding zero, an axiomatization of the natural numbers different from that of Peano. Zero represents not mere negation but the more primitive level I have referred to, that preceding the mark-cut. If what is (“being”) is attributed to the number 1, then what is not (“nonbeing”) is not o, as is ordinarily conceived to be the case for binary or Boolean logic. Rather, “nonbeing,” which maintains itself as a form of distinction and indication from “being,” is, more properly, the counterpart to -1. By the same token, even numbers can be distinguished from prime numbers, real numbers from imaginary numbers, and so on. Regarding the Boolean framework, interestingly enough, Leibniz alluded to the creation of the totality, of God, 1, from the cipher, o. And according to Frege, since nothing is usually attached to the concept “not identical with itself,” o should be the number which belongs to the same concept.

The term zero harks back to “cipher” by way of the Hindu Sunya (= void, nothing, open), which, to repeat, is essentially in line with my use of “nothingness.” As such zero implies—I do not say indicates or points to; though it is a sign, its “referent” precedes all signification—the absence of other mathematical signs. It does not “refer” to the nonpresence of “semiotically real” objects which are supposedly prior to, in a Platonic sense, the signs of which they are objects. Zero is simply a notation implying “nothingness.” If notation there must be, the o, topologically speaking, will fit the bill quite well. The term zero is a symbol (rheme in the Peircean sense), but “o,” also a symbol, is not exactly the equivalent of zero, “o” possesses the same status as other symbols nonetheless. As a sign among signs, it signifies, and unlike the vast majority of signs, it signifies no-thing (Rotman 1987). It is the void which Hermann Weyl (1949:75) envisioned when he qualified the Cartesian coordinates (0,0) with “0” as the midpoint between positive and negative integers as the “necessary residue of ego extinction.” At this “point” the ego is collapsed into the continuum such that distinctions that were there are simply no more. But it is not “nothingness,” as I use the term here, for there is a residue, a noticed absence, much like column II of figure 12, where the overlapping domains ABCDE . . . n remain dissolved in the soup of “o.” Thus, although zero, given its relation to sunya, is more adequate to the task of signifying “nothingness,” “o” can be used as a surrogate symbol.

Brian Rotman labels “o” a “metanumber.” I would, in contrast, disqualify it as a number entirely, though, with Rotman, I would define it as pure potentiality for the infinite generation of integers—comparable to Bohm’s implicate, Spencer-Brown’s unmarked space, or Peirce’s “nothingness.” And, following Rotman (1987:19), zero is equivalent to, for example, the (asymptotic) “vanishing point” in Renaissance painting. The “vanishing point” functions like a visual zero to facilitate the generation of an infinite number of perspectives supposedly offering to the spectator the possibility of objectifying herself, of looking in as if from the outside as an omniscient seeing subject.

This quest for omniscience, for the possibility of an “outside” perspective, is delusory, however. Its base is a flimsy raft caught in a tossing and turning sea. It is like Sheffer’s “stroke,” stipulating that the entire universe of logic arises out of inconsistency, that there is neither one thing nor another, and not both not-this and not-that.⁴ The edifice of dualisms previously standing straight and tall topple and disintegrate into myriad differences which move along with the ebbs of the tide and tend to fuse with the continuum. There is no some-thing that is prior to no-thing, the world prior to its representation, an identity prior to difference. That longed-for Oneness of all things, the union of opposites, is not of this world—i.e., the push toward absolute generality, regularity, law, will always remain incomplete. There are, in the “semiotically real” world, only differences, and differences of/in/among differences. Nothing necessarily precedes anything else, as if “o” preceded 1, 1 preceded-1, and-1 preceded “o.” Neither is there, in this respect, any retrievable origin or center.

The whole infernal system reminds one of that short-lived but excellent TV program “The Prisoner.” Patrick McGoohan, the main character, condemned to an amusement-park atmosphere with other ex-secret agents from all over the world, spends his time trying to escape and reveal the identity of No. 1, in whom total power presumably resides. He finally learns that he is No. 2, but he has no power: there is neither center nor focus of power; all is disseminated evenly throughout as differences. The system is, it appears, self-contained, self-regulatory, and self-organizing. The entire field of signs making up the system has created the very elaborate and labyrinthine set of objects they are believed to be denoting, naming, and representing. The vast illusion is now exposed: those objects are not anterior to the signs; the truths believed to be forthcoming through determinate lines of correspondence between signs and objects are chimerical; “nothingness” has revealed itself as the sole priority, whether regarding signs or things.

Yet we tend to carry on as if from some preordained point of origin, entering into conceptual space of ever-greater abstraction at each juncture. Perhaps this journey is inevitable. Everything that arises from “nothingness” is, Peirce repeatedly tells us, by way of inference, and, in the premises of this inquiry, of projection by dialogic self-consciousness. A cut or mark is made, and from that point an entire universe is generated. A cell comes into existence, which might form a minute part of the roots, the bark, the trunk, or the leaves of a tree consisting of countless cells. The tree’s leaves fall, its branches are broken off and decompose, new branches are grown, roots drill ever deeper; there is incessant exchange of material between the tree and the atmosphere, between the roots and the chemicals of the soil; birds build nests in it, squirrels make a home, insects attack it, the logger cuts it down, or it finally dies and returns to the earth. This concatenation of elements and events making up the existence and life cycle of the tree is for practical purposes almost infinitely complex. Yet we have a mere sign, one symbol, “tree” in English, to qualify it. What power of abstraction! And this is one of our more menial examples of the mind’s abstractive capacity. Ponder, for example, “democracy,” “love,” “E = MC²,” “deconstruction.”

This tree, what exactly do we see when we see it as a “tree”? Our experience of it suggests at first blush purely immediate and direct perceptual awareness, devoid of all hypothetical elements. Attending more carefully to this percept reveals that our sensation yields a complex shape, colored patches, gentle to-and-fro motion, and so on. Combining these sensations into a whole by no means produces a “tree.” We automatically, by embedded, habitual, inferential processes, endow the tree with a solid constituence beneath the bark, a root structure concealed underneath the surface of the ground, an obverse side which is not seen but is presupposed to be roughly comparable to the side of the “tree” open to view, and so on, even though there is no immediate empirical evidence for some of these inferences. We also assume the tree has self-identity, a certain permanence of existence. We ordinarily take it for granted that when we are not looking at the tree, it is there nonetheless. In short, we automatically go “beyond the information given” (Bruner 1957). This act of “construction” converts a complex of sensations into a “semiotically real” thing.

Of course there is no separate, completely autonomous entity tree, but myriad interconnecting cells making up a community, which is in turn interconnected with its environment. As nonduality, nonseparateness, emptiness of existence as a singular distinction, the so-called tree is really no “tree” at all. It has always been submerged in the vast undivided fabric, the holomovement, so to speak. The “tree’s” coming into “existence” depends on the conditions of its initial environment, and its continued “existence” is equally dependent upon its surroundings. This “existence” is a composite stream, a convergence, divergence, involution, convolution, harmony, and dissonance, of an overwhelmingly intricate conglomerate of “world-lines.” The tree is in this sense always already becoming in its interaction with its environment. It is, to avail myself of Deleuze and Guattari’s rhetoric, carbon-dioxide-becoming, H₂0-becoming, soil-becoming, bird-becoming, squirrel-becoming, insect-becoming, sun-becoming, wind-becoming, lumberjack-becoming, and so on. It is a series of events rather than essence, process rather than product, flow rather than fact.

A mind can also be qualified as such a composite stream, though its structure and functions, unlike those of the tree, are nonempirical. The mind as stream has been suggested by both Eastern and Western philosophers (the Buddha, Nagarjuna, Hume, Peirce, James, Bergson, Whitehead). By inference this mind bifurcates zero into integers, I into -I, and the undivided into things whose “existence” depends upon their relation to what they are not. You see the “tree,” “out there,” from your living-room window, as a complex of happenings not because of a multiple sequence of mechanical cause-and-effect events, because God thinks it, or because your consciousness has “collapsed” billions upon billions of waves into particles. You see it as you do because it belongs to your “semiotically real” world, and reciprocally, you are as you are to it because you belong to its “semiotically real” world.

You are the sign that relates to it; it is the related sign that in turn relates to you; both of you are interpreters and interpretants, connectors and connected, subjects and objects, along the semiosic flow of all happenings.