Interestingly enough, according to currently accepted limitations on knowledge, and especially following Gödel, if a sufficiently rich formal system presents itself as complete and self-sufficient, then it has an inconsistency hidden away somewhere in the closet; and if it is consistent, then it cannot but be incomplete. From the broadest possible view, the inconsistency of vaguenessor by implication, the quantum theoretical formulationprevents completeness, since some-thing cannot be, to use our above example, both a particle and a wave. In contrast, generality in the absolute sense demands completeness or nothing at all. But, as we have noted, there is no absolute generality in a finite world. Of course, from one reference frame an entity can appear as a particle and from another as a wave, but, since perspective is inevitably bound to particular reference frames, there can be no completeness for generality. On the other hand, though vagueness bans noncontradiction from its playground, it cannot entertain the actualization (into Secondness) of two inconsistent entities at the same instant: they are, so to speak, complementary, to be seen as one or the other alternately. Thus the inexorable incompleteness of generality and the inconsistency of vagueness are enforced. Generality and vagueness are in this manner themselves complementary at a more general level.
To take the analogy further, if I may be so permitted, the "quantum theoretical" or vague aspect of semiosis is indeterminate and linear, from First to Second. There must be a separate space-time property of each sign instantiation and its relation to and interaction with its "semiotically real" object. Such interaction implies, given Peirce's pragmatic maxim, contextualized action regarding the manipulation of signs. That is, before the truth of a given proposition can be established, we must determine its meaning, and to that end Peirce provided a criterion for meaning, his maxim, which states: "Consider what effects that might conceivably have practical bearings, we conceive the object of our conception to have. Then our conception of these effects is the whole of our conception of the object" (5.402).
What Peirce seems to be saying is that the meaning of a proposition is given in another proposition, and that in another, ad infinitum, all of them calling for some conceivable test, as a result of observable properties that one would expect under certain circumstances if the original proposition were true. Since the semiotic web is indefinite and, as far as the finite thinker is concerned, for practical purposes infinite in extension, the meaning of the original proposition, therefore, is destined to remain indeterminate.(1)
Moreover, such activity as called for by the proposition is subjective (i.e., mind-dependent). The "semiotically real" can itself be composed of contradictory, or complementary, alternatives, such as the switching of the two possible interpretants of a Necker cube as it flip-flops from face up to face down, and back again. In contrast, the "semiotically real object" and the "real object" will continue to be intransigently incompatible on certain points, for the finite community at least. There is saving grace, however, inasmuch as the sign and its "semiotically real object" can approximate (hopefully at least) the "real." Pragmatically speaking, then, each proposition can take on a particular contextdependent meaning, which is also dependent upon the context-dependent meanings of all related propositions, which, practically speaking, renders impossible any absolutely determinate meaning for some interpreter in a particular context.(2)
On the other hand, the "relativistic" or potentially general aspect of semiosis is, over the theoretical long haul of things, determinate and nonlinear: Thirdness. All sign entities in the semiotic field can theoretically be continuously mapped one onto another at certain points, hence the same space-time framework applies to them as a whole. Relations between signs are also theoretically "real"; they pertain to a given "semiotic reality." Generality, insofar as it applies to the "real," should be completely objective. This is, however, the ideal which can be no more than approximated. The "semiotically real" general sign is, and will always be for the finite mind, incomplete.
Thus the "clash" between First and Second, on the one hand, and Third, on the other, to yield "First-Second/Third," illustrates (1) complementarily relations between the two sides of the virgule, (2) the dual nature of the asymptote metaphor, and (3) inherent inconsistency and incompleteness of all "semiotically real" conceptions of the world. There appears to be a basic distinction, then, between law (Thirdnessand, by extension, the general laws of nature) and rules governing our Umwelt-generated perception and conception of the furniture of the world (items of Secondness as semiotic actualizations of the possibilities of Firstness). Law, that is, law as the final interpretant, the fullness of all things, requires reversibility (time symmetry), continuity, and determinacy regarding the flow of events. In contrast, our perceived and conceived world requires irreversibility, discrete events, and acausality (probability of happenings, natural selection, or, at the highest levels, selection by free will).
Law is the law of generation (of the Final Interpretant), which implies the end of the long trail having been reached, for every would be has been actualized as a this-hereness. The process is a fait accompli. The Minkowski "block" universe this concept evokes entails determinism, "objectivity" (subject/object), and limitlessness. On the other side of the ledger, semiosis is the ongoing flux of sign interaction. It is the locus of information to be processedthe "reading" of signsduring one's perceiving-conceiving the world, or, at the micro-level, during measurement in quantum theory. It is linear, irreversible, and timedependent for the finite, limited, immanent observer, the subject-object dichotomy having been dissolved. The whole picture, including process and product, the stream of signs and its congealment, is possible solely by way of this Heraclitean conflictive interplay of opposites: the possible-actual on one side and law on the other, or Firstness-Secondness on one side and Thirdness on the other. In a nutshell, then, the complementary incompatibilities I have alluded to in the immediately preceding discussion are, once again, quite comparably those between quantum theory and relativity (see Sachs 1988; Pattee 1982).(3)
It is significant to note that Peirce struggled with a related complementary theme with respect to his two types of "other": (1) the interaction between the self and the social and physical Other "out there," and (2) the dialogue between the self and its other inner self. For Peirce the self does not attain a state of self-awarenessawareness of its other selfuntil it has erred regarding its perception and conception of the Other "out there." When this occurs, the self artificially extricates itself from everything else in the universe which leads, residually, to what it is not as an objective realm set in the context of time and spaceand the Cartesian split suffers its first birth pains. Yet this move is necessary, though it need not necessarily be taken to its extreme manifestation. That is, there can be mindfulness of self and/in the Other rather than self pitted against the Other. Indeed, this relationship, which can be written self/other//Other, is a double binary which generates a triad, and what is most significant, a complementarily relationship.
The self is a curious and unique some- "thing." One assumes in general that it somehow represents an "object," "l-me," which functions in the external world as do all other objects. Yet it is nonempirical. As an "object" it is at most only partly available to any form of sensory experience. It is chiefly the product of imagination: it is inferred. One problem is that the self is not unary but binary in nature, and in addition, like all signs, it manifests a binary character. For Descartes self-consciousness is immediately intuited, and the self is autonomous: it is primary, existing independently of all external constraints. In contrast, Peirce's radically anti-Cartesian posture envisages a self which, like all signs, becomes external upon addressing itself to some other (CP:5.:253; also Michaels 1 977). In fact, it must determine some other, which is the task of all signs. In this sense, the self becomes aware of itself on becoming aware of what it is not, of the nonself, the Other (CP:1.324).
This becoming of awareness entails action/reaction, Secondness, the "real." During the rough and tumble of everyday life we are constantly "bumping up against hard fact." We develop habits and generate expectations, rather mindlessly taking things for granted as simply the way the world works. But the world inevitably sets up a resistance against our imposing ourselves upon it; it forces surprises on us, which constantly remind the self of what it is not. This notion of the "other, of not, becomes a very pivot of thought" (CP:1.324). Secondness is predominant in this scheme because it is essential to the very idea of "reality," for the "real" is that which "insists upon forcing its way to recognition as something Other than the mind's creation" (CP:1.325).
The "real" is actual, though of course it is Other. In conjunction with the self it makes up the other pole of a dyed. But the "real" is not immediately present to consciousness as such and such. Consciousness becomes aware of the "real" solely by binary mediationThirdnessbetween itself and that Other, and by inference, as it were. That is, there is no time in the "present instant" for an inference, least of all for an inference concerning that very instant. An inference is possible only mediately, after the occurrence of a new event. This new event in the form of a surprise shocks one to attention such that one can then generate an inference regarding (1) the break between that which was expected and the event that is perceived to have occurred, and (2) the reason for such a break in the first place. Consciousness of must be mediate, Peirce argues, since the presence of the "real" has no respect for one's will or wishes; consciousness of is not merely dependent upon an act of volition. This implies that the immediately present is conative rather than perceptive. Consequently, consciousness of the "real" present is a perpetual struggle over what was expected and what is perceived actually to take place, the break between them evoking an incessant call for revamped expectations (CP:5.462).
One is in some sense immediately conscious of one's feelings, of course, but they are not feelings of a self-conscious ego, for the ego-self is inferred rather than immediate (CP:5.462). Peirce suggests that we are in command of no power by which an intuition can directly and immediately be known. An intuition must exist at some primordial first instant, and for it to be an intuition in the full Cartesian sense, apprehension of it as a cognition must occur at the selfsame instant; that is, it must be an event occupying no time. But since for Peirce, (1) any and all cognitions are always in a process of becoming and passing away, (2) it is impossible to know intuitively if a given cognition is not determined by a previous one, and (3) a cognition, like a perception, is not available to consciousness except mediately, then (4) there can be no apprehension of an intuition in the blink of an instant (CP:5.264-3I7).
Given that any cognition for Peirce is consciousness of an object as represented to self-consciousness, he means to say the same of one's knowledge of or consciousness of one's self. Such self-consciousness is not "a mere feeling of subjective conditions of consciousness, but of our personal selves. Pure apperception is the self-assertion of the ego; the self-consciousness here meant is the recognition of my private self. I know that I (not merely the I) exist" (CP:5.225).
Kant once suggestedand Peirce agrees on this pointthat the retarded use of the "I" in children, since they manifest other powers of thought at an earlier age, was evidence of an undeveloped self-consciousness in them. When a child hears, say, a bell, she does not become aware of herself as hearing something which she herself is not; she is merely aware of some object which is making a sound. Or when she "wills" to move a table, she does not become aware of herself as desiring that the table be displaced, only that an object is fit to be moved (CP:5.230). The child soon discovers the relationship between objects "out there" and her own body as another object, which raises it to a level of importance and centrality. And later, after learning a language, the child is subject to sentences such as the warning "The stove is hot." And so long as she never comes into contact with the stove, she will not know whether it is actually hot or not. If she touches it, on the other hand, the sentence is verified in a striking way:
Thus [s]he becomes aware of ignorance, and it is necessary
to suppose a self in which this ignorance can inhere. So testimony gives the
first dawning of selfconsciousness.... In short, error appears, and it can be
explained only by supposing a self which is fallible. Ignorance and error are
all that distinguish our private selves from the absolute ego of pure apperception.
On so speaking of the ego, Peirce refers to the triad feeling-volition-cognition. Feeling is Firstness, quality. Volition is dual: force and resistance, agent and patient, self and Other. The shock of an unexpected event is volitional, the result of interaction between the self and the "real," which gives rise to dyadic consciousness of an ego and a nonego (CP:1.334-35). Cognition, or Thirdness, is the process of mediating between feelings and volitions. Metaphorically put: "Position is first, velocity or the relation of two successive positions is second, acceleration or the relation of three successive positions third" (CP:1.337). Peirce's analogy is apropos. Velocity is continuous, but there is merely change of position. In contrast, acceleration is continuous change of change; both position and velocity undergo successive alteration.
Quite obviously, feeling, volition, and cognition correspond to Peirce's tripartite sign. The representamen is immediate. That for which it stands, the object, is other than the self and subject to volition. And the idea to which the representamen gives rise is its interpretant, which entails cognitive activity. The object of representation is not the "actually real" but a "semiotically real object" represented by the sign, so the object of representation can be none other than another representation of which the first representation is the interpretant, and an endless train of representations can be conceived to have the "absolutely real" object behind it as a limit, which can no more than be approximated asymptotically (CP:1.339).(4) In brief, every interpretant becomes a sign-representation in the ongoing semiosic process. Like position, the sign stands for the "semiotically real object," which is moved along by the incessant transmutation of interpretants into sign-representations. And the interpretant, as mover, accelerates the sign, like the force of gravity at 32 ft./sec./sec. or the expanding universe which brings about the "red shift" phenomenon, toward the ideal limit.
This brings up the point, introduced above, that in addition to the external Other, there exists an internal one, the other self created by the passing of a sign into an interpretant, an interpretant into a sign, and the self of one moment into the self of another. The radical absence of the self from its other self, semiotically (i.e., symbolically) evidenced by shifters, creates not a stable but a restless semiosis incessantly sliding along the slope of signification. This renders the timeless identity of the self impossible: the self cannot be itself in the immediate present, but only what it was not during the moment past, and what it not yet is, what it will be, in the future moment.
However, the Other, above all, remains elusive. Regarding the sign triad, the interpretant is acknowledgment of the Other by way of mediation between representamen and object. But since it is itself another representamen whose interpretant is yet another one, ad infinitum, its self-identity incessantly conceals itself, and, as Derrida (1974:49) says of the signified, it is always on the move. The Other to which consciousness points via the interpretant is never fully present, though its presence is always felt, since the "real" represented by signs as the "semiotically real" remains as fugitive alterity and absence: "In the idea of reality, secondness is predominant; for the real is that which insists upon forcing its way to recognition as the mind's creation" (CP:1.326). The "real" conceived as Other is in this manner resistance, surprise, a subversion of exteriority against the self-conscious self.
But this sense of exteriority, of the presence of a nonego "which accompanies perception generally and helps to distinguish it from dreaming" (CP:1.332), is not merely a sense of the world "out there." It is the product, rather, of the dialogic self-other, "I-me," the "me" resting tenuously between the "1" and the "it," which constitutes the "real." Freud's (1925) concept of negation also bears on the "I-it" interaction. The prononoun it marks an irreversible loss of the self's self-presence, the self's "me" as absent from its "I." The child initially uses it to designate what will later correspond to its own displaced self. At this early stage there is no subject/object, no inner/outer. Gradually the "it" transmutes into "me" and becomes "outside" and "alien," in contrast to the "inside" and generally conceived "presentness" of the "I."
And thus Peirce's train of signs embodied in the "I-me" dialogue has lurched from the starting blocks. When one is thinking, the "I" uses signs by means of which to persuade the "me" that something or other is the case. In this activity,
a person is not absolutely an individual. His thoughts
are what he is "saying to himself," 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. The second thing to remember
is that the man's circle of society (however widely or narrowly this phrase
may be understood), is a sort of loosely compacted person, in some respects
of higher rank than the person of an individual organism. (CP:5.421)
In other words, the immediate "I" as First (icon) refers to the object (index) or that which is the object of persuasion, in addressing itself to the other, the interpretant (symbol) in the process of "coming into life in the flow of time," which in turn becomes itself a sign with its own object (CP:2.274).
This other-Other concept is illustrated by the two "Borgeses" of that remarkable little tale "Borges and I" (1962:246-47). The sentient Borges (Borges1) is the "subject" whose life "is a flight," for he loses more and more to the writer Borges (Borges2), the "predicate." Borges2, the fictional being who appears only in the mail, on lists of professors, or in biographical dictionaries, appropriates more and more of Borges1, who retreats into ever-smaller subframes. At the precise moment when Borges2 completely takes over, specific reference to either of the two disappears. THE BORGES (Borges, and Borges2) now exercises his dominance. There is no longer any line of demarcation between "subject" and "predicate" ("object"). THE BORGES is self-contained and self-sufficient: he is as he is. As such there can be no inconsistency or incompatibility between the two because there is no external reference point from which to make a cut between the one and the other. But as such neither can any fictionsi.e., the fictional Borges2be constructed from "within" the system, for fictions require (1) the existence of two partly inconsistent frames, and (2) incompleteness, such that a potentially infinite regress of metaframes can theoretically be constructed (see Merrell 1983). The status of THE BORGES, then, is at the meso-cosmic level equivalent to the cosmic experience of the ineffable totality within which the self is contained. In this state, nothing is marked or cut, there are no frames, and hence fictionality (i.e., what the "real" in part is not) is no longer possible, for all simply is. There is no longer any dialogue.
Thus the self-other relation emerging from the self-Other entails separation and union. Self and other are from one vantage logically distinct entities. The self enters into dialogue with its other and that other with the self, as separate selves in mutual relation. At the same time, from an alternate vantage, self and other are one, continuous and inseparable, a self-referential unity. In this respect the relation is closed rather than open, like the self-Other relation. But the question arises: How can the individual self come into existence if the self-other is an indivisible whole? An answer might be forthcoming, once again, in view of Peirce's asymptote. Self-other as an indivisible whole appears in the sense of a tenuous approximation to that ideal goal, when all dialogue ceases, when total Oneness prevails, and Truth in all its plenitude is made manifest: the self-other, that is, the interpreter, at this point becomes coterminous with the ultimate interpretant.
In addition, there is an approximation in the opposite direction toward the ideal self-Other relation wherein the self itself has reached finality: it is an absolute absolutely set apart from the absolute Other. Yet, as an approximation, there is no more than an illusion of the categorical split between the one and the other; there is always at least a modicum of oneness in the self-Other interaction (much like the Yin/Yang complementarily, which likely influenced Bohr in the development of his quantum principle). In other words, self-Other does not entail the same ontological status as self-other; rather, the apparent objectivity of the self in this case is over the long haul an idea, an inference, an artificial construct. It is the manifestation of a whole arrived at by reflection on what the that is and why it is other than this. Solely the self-other state is capable of erecting the self-Other construct, but the self-Other must be acknowledged in terms of something other than what it otherwise would have beeni.e., when there is awareness of error. Without the self-Other there can be no scientific discourse. In fact, there can be no dialogue whatsoever from which the self-Other can arise.(5)
The observing self, then, is only apparently an autonomous subject, and the Other only appears to be an object "out there" and ready to be manipulated by the subject. Once more, there is neither exclusively one nor many, continuity nor discontinuity, but perpetual interplay between them. In contrast, there is an ordinarily contradictory yet complementary relation between self-other and self-Other which in turn complements the complementarily between self and other and self and Other. If self-other and self-Other were a continuous, inseparable whole, it would undoubtedly evince qualities comparable to the Tao of Lao Tzu. It would be simply that which is, outside all sensation of time, space, and "stuff." It would be ontologically prior to all existent things: a closed, recursively autonomous, symmetrical, timeless systemtantamount to the Minkowski "block" or the originary Monad. In contrast, combining the two pairs to form self/other//Other creates a complementary relationship. In one of his earlier formulations of complementarily, Bohr (1934:91) concluded that the concept "bears a deep-going analogy to the general difficulty in the formulation of human ideas, inherent in the distinction between subject and object." Since that time, there have been few discussions of the problem of measurement or the meaning of quantum explanations without invoking the mind (self-other) of the observer as an irreducible element.
This schizophrenic collusion of many and one, of holism and atomism, that is, this contradictory complementarily, an important aspect of contemporary thought especially regarding both the quantum world and relativity, is, most significantly, patterned in Peirce's own metaphysical schizophrenia.
(1) In other words, the statement "Lemons are sour" can easily be put to the test by subjecting a lemon to the taste buds. But determinate meaning of the proposition is not to be found so easily. The range of all conceivable ramifications of this initial test must be exhausted, which include the chemical composition of citric acid, the pH factor of lemon juice, the ratio of H+ ions to OH- ions, the action of acidity on nerve endings on the tongue, impulses traveling from the taste buds to the brain, human cultural values regarding acidity in contrast to bitterness and sweetness, and so on. Each of these actual tests "out there" in the physical world implies, or directly involves, a subsequent proposition regarding what would be the case if certain conditions were to exist. The meaning of "Lemons are sour" cannot be exhausted short of an infinity of tests and generation of their respective propositions within pragmatic contexts.
Such proposition formulation and test procedures, however, are not always the product of intentional sign activity. For example, suppose a drug, x, reputed to help prevent cholesterol buildup, is released to across-the-counter pharmaceutical retailers. First, the "meaning" (i.e., use, which pragmatically endows the drug-as-sign with an interpretant, be it legitimate or not) of the drug is put to the test on the competitive market, and true to predictions, heart problems are lowered. Over time, consequently, habit is gradually developed on the part of the consumers. The drug's "meaning" becomes embedded; it is now purchased and used rather mindlessly (like a red traffic light, which, if disregarded, might subject one's car to a collision; therefore one stops the car by habit). For Peirce, what a sign "means" is ultimately determined by what habit is involved, which can be a bane and a boon. Without habit, community agreement and hence convention would be well-nigh impossible, but habit can also stultify, compelling one to mindless activity such that one is no longer conscious of one's motives and the consequences of one's actions (see Nesher 1983; Langer 1989).
In this sense, to speak of "semiotic reality" is to speak of relationships between a languageor other sign systemsand the "real." In the sentence "'Photon' refers to a discrete packet of energy," there is discrimination between the sign being discussed and the signs used to discuss it. "Photon" signifies something presumably in the "real" world called a "discrete packet of energy." But notice that reference consists of a relation between the sign "photon" and the signs "packets of energy," not directly between signs and things "out there" that are nonsigns. In other words, the sign "photon" refers to its "semiotic object" in the "semiotically real." I use this particular example to stress the point that the signs a physicist uses to qualify his observations and the signs of his theoretical language, in concert, are not some pristine mirror of the world. They are symbolic, and they take on meaning and value in the interconnected system of interpretation. No observation has any meaning at all until it is interpreted by theory, convention, or habit. "Photons" are "semiotically real" not because they establish some mystical linkage between signs and the "real" but because physicists can speak about them, and their expectations regarding them can be fulfilled by means of their shared assumptions, conventions, and understandings: "photons" are the joint opinion of the community in Peirce's conception.
(2) See Heelan (1970a, 1970b, 1971, 1983) for the context-dependency of "quantum logic"; also Merrell (1985a, 1990), where I develop this theme with respect to the semiotic perspective.
(3) I should point out at this juncture that I by no means wish to imply that Peirce is everything to everybody. He was a helpless child of his times in certain respects, as we all are. Besides, modern thought can be traced back to a plethora of "sources." Einstein can be found in Spinoza, in Parmenides, in the Kabbala; Bohr can be found in Oriental thought, as can Schopenhauer from one angle, Whitehead from another, and Peirce from yet another. The list is inexhaustible. Holton's (1973) "themata" and Jung's "archetypes"alluded to by physicist J. M. Jauch (1973) - are relevant here. If contemporary physics has picked up two contradictory "themata," one in quantum theory and another in relativity, I find it not at all surprising that Peirce's thought contains both, a contradiction he labored to resolve up to the end of his life.
(4) The term representation, as it is used in logical positivist jargon, is rapidly becoming outmoded. I prefer to use signification but have remained with Peirce's term when it becomes necessary within the context of his writing.
(5) Einstein's words are apropos in this respect:
A human being is part of the whole, called by us "Universe";
a point limited in time and space. He experiences himself, his thoughts and
feelings as something separated from the resta kind of optical delusion
of his consciousness. This delusion is a kind of prison for us, restricting
us to our personal desires and to affection for a few persons nearest us. Our
task must be to free ourselves from this prison by widening our circle of compassion
to embrace all living creatures and the whole of nature in its beauty. Nobody
is able to achieve this completely but the striving for such achievement is,
in itself, a part of the liberation and a foundation for inner secuity. (In