This was written when I was first getting into the semiotic of Charles Sanders Peirce. Re-reading it going on fifteen years later, I notice one glaring misreading of Peirce: Firstness is more or less indeterminate or determinate, not more or less vague or precise; only with Peirce's category of Thirdness can we speak of vagueness versus precision (and then there's also vagueness versus generality). I'm not going to revise and correct: if you're a logician, you can make the correction as you read, and it has no bearing on the validity of my argument; if you're not a logician, I leave the distinction between indeterminateness and vagueness as "an exercise for the reader."

Man makes the word, and the word means nothing which the man has not made it mean, and that only to some man. But since man can think only by means of words or other external symbols, these might turn around and say: "You mean nothing which we have not taught you, and then only so far as you address some word as the interpretant of your thought." In fact, therefore, men and words reciprocally educate each other; each increase of a man's information involves and is involved by, a corresponding increase of a word's information.

...Thus my language is the sum total of myself.

--C.S.Peirce, "Man, a Sign," 1868¹

How can each of these areas-- or any area-- of human activity be seen as an example of human communities and the signs they use "reciprocally educating each other"? What if everything experienced-- indeed, everything experienceable-- be viewed as constituted by the interplay of ordered networks of signs? It was in grappling with such questions that Peirce gradually developed his "semeiotic," and eventually became known as one of the founders of the present-day field of semiotics.

Yet to the first-time reader Peirce's thought may seem almost impenetrable. T.L. Short has put it well: "Let us journey into darkest semeiotica... immense, obscure, crabbed with dense tangles, and never before traversed."² One reason for the obscurity of Peirce's thought is that he spent most of his career in relative isolation in scientific and geodetic work, and so did not benefit from constant critical interaction with colleagues who might otherwise have pressed him to clarify his thought and terminology.³ Peirce's voluminous writings, few of which ever saw print during his own lifetime, have been reduced to something like a state of order in his posthumous Collected Papers; but the result is still rambling, repetitious, and filled with obscurities and inconsistencies as a result of the revision and growth of Peirce's thought over the years. Well might the reader be advised to bring pith helmet and machete to the study of Peirce's semiotic!

Nonetheless, one aspect of Peirce's semiotic stands out sharply even to the casual reader: the ubiquity of triadic structures. Three universal categories underlie Peircean semiotics; Peirce's sign involves three elements; Peircean subdivisions and classifications are often threefold. Why triadic? What does Peirce accomplish that could not equally well be carried out via the simpler dyadic sign? And why should as few as three categories suffice to embrace all of human experience? Peirce himself was acutely aware that he was open to charges of "triadomany," and defended himself on the pragmatic grounds that his method, flexibly applied, yielded fruitful insights into the world we dwell in.⁴

Criticism of Peircean semiotics on this fundamental point, and suggestions for either a tetradic or a dyadic revision of Peirce, have been not uncommon. In this paper I shall examine and respond to several of the arguments which have been put forth. In so doing, I hope to identify some of the key issues at stake. But to accomplish this requires that we first have some basic understanding of Peirce's semiotic. So I begin with a brief sketch thereof.

An Overview of Some Aspects of Peircean Semiotics

Semiotics, under a Peircean view, may be understood as an attempt to see all knowledge and experience as a structured system of signs in dynamic interaction with one another. The most familiar example of such a system of signs is human language. But Peircean semiotics is not restricted to this narrow model. Language, thought, emotion, sense perception, formal logic, mathematics, physical action, and human existence itself are only a few of the processes which can be seen as special cases of the Peircean sign.

And this sign can be generalized even further: Peirce saw a sort of low-grade semiosis in action not only in all living organisms but even in the regularity of nature itself. In line with his tendency to see continuity wherever he looked, Peirce saw distinctions, but no absolute separation, between the processes of human existence and the processes of nature. To posit any such separation would to Peirce violate what he often called his cardinal rule of thought: "Thou shalt not block the path of inquiry."⁵

Since Peirce's sign is completely general, his semiotic purports to yield an ontology, under which the universe as a whole, and each thing which lies or could lie within it, is a sign. In particular, the human being is a sign.⁶

Yet Peirce's semiotic can be trained on any phenomenon as a supple and subtle method of analysis to yield often surprisingly detailed and concrete insights. This "double-barrelled" combination of complete generality and concrete particularity arises out of the correspondingly "double-barrelled" nature of the three universal categories on which Peirce's semiotic is built-- categories which Peirce called Firstness, Secondness, and Thirdness.

A universal category is a factor which is found to be present in every phenomenon, "one [category] being perhaps more prominent in one aspect of that phenomenon than another but all of them belonging to every phenomenon." (5.43) Thus, Peirce's claim is that his categories of Firstness, Secondness, and Thirdness, in one way or another and to one degree or another, appear in every phenomenon which one could possibly encounter.

The "double-barrelled" nature of the categories derives from the fact that each category can be described both from a formal, combinatoric, logical viewpoint, and from a material, descriptive, phenomenological perspective. These logical and phenomenological aspects can be taken as, so to speak, two sides of the same coin (1.417-421).

Firstness, in its logical aspect, is monadic. It is whatever is what it is by itself, without comparison or relationship to anything else; independent of any "there," pure spontaneous, original, sui generis. Peirce correlates Firstness with the structure of abductive thought, and with the discernment of qualities in the logical structure of the act of perception. Phenomenologically, Firstness is any possible quality of feeling taken by itself, whether "the color of magenta, the odor of attar, the sound of a railway whistle, the taste of quinine, the quality of the emotion upon contemplating a fine mathematical demonstration, the quality of the feeling of love, etc." (1.304; cf. 1.302-321, 1.422-426, 2.619-644, 5.41-44)

Imagine that state which sometimes comes over a person on the brink of sleep, when on the edge of consciousness a quality springs unbidden into the fading awareness and fills it without division or distinction: "nothing at all but a violet color," or "an eternally sounding and unvarying" musical note. Such a quality-- or rather, the possibility of such a quality-- is a near approach to sheer Firstness (1.305). As embodied in experience, an instance of Firstness may be very broad and general-- for example, the entire Gestalt, sensory and mental, which an entire landscape or story or historical period evokes in one-- or it may be very particular-- for example, that quality pertaining to that fifth rung on the bannister of the staircase, with the funny little horsehead-shaped chip out of the paint on one side of it.⁷

Secondness, in its logical aspect, is dyadic. It is a First as it stands over against a Second, regardless of any Third; being in relationship to an Other; the action of cause-and-effect, stimulus-and-response, action-and-reaction. Peirce also relates Secondness to inductive thought and its extrapolation from individual cases, and to the imputation of individual existence to substances in the structure of the act of perception. In its phenomenological aspect, Secondness presents itself as brute fact, as struggle and opposition, shock, surprise, effort and resistance. It is the hard, uncontrolled givenness which we encounter in experience. (Cf. 1.317, 1.441-470, 2.669-693, 5.45-58)

Peirce's favorite example of Secondness is that of trying to open a door that is stuck:

Standing on the outside of a door that is slightly ajar, you put your hand upon the knob to open and enter it. You experience an unseen, silent resistance. You put your shoulder against the door and, gathering your forces, put forth a tremendous effort. (1.320)

Thirdness, in its logical aspect, is triadic. It is a First bound together in relationship with a Second by the mediation of a Third: "The beginning is first, the end second, the middle third." (1.357) It is combination, pattern, structure, mediation, continuity. A monad can form no combination with another; two dyads can join together only to form another dyad (think of two lengths of pipe screwed together); but triads can combine into arbitrarily complex structures (think of a tinkertoy set, or the colored plastic beads in a chemistry class which can snap together to form models of molecules).⁹ Thus, argues Peirce, there is from the logical side no need for a category of Fourthness.¹⁰ Peirce equates Thirdness with the structure of hypothetical or "abductive" thought, and with the conjunction into an organic unity in the act of perception of imputed individual entities and the qualities attributed to them. (Cf. 1.471-520, 1.551, 2.694-794, 5.171-174, 5.590-604)

In its phenomenological aspect, Thirdness is continuity, process, growth, and development; it manifests itself in law, regularity, generality. It is rationality, intelligibility, predictability; the formation, correction, and refinement of habit; most importantly, it is representation and signification: "A sign stands for something to the idea which it produces or modifies... That for which it stands is called its object; that which it conveys, its meaning (the sign itself); and the idea to which it gives rise, its interpretant." (1.339) Each sign is such a semiotic triad, composed of object, sign (or "representamen"), and interpretant. (Cf. 1.337-353, 1.471-520, 5.59-119).

Each sign has to it the hypothetical, "if-then" status of Thirdness; Firstness is potential, Secondness actual, Thirdness conditional; Firstness can be, Secondness is, Thirdness would be (given appropriate conditions).¹¹

A sign is a continuous, dynamic process, since the interpretant to which a sign interprets an object is ipso facto itself a further sign of the same object. Peirce spells this out precisely in a formal definition:

A Sign... is a First which stands in such a genuine triadic relation to a Second, called its Object, as to be capable of determining a Third, called its Interpretant, to assume the triadic relation to its Object in which it stands itself to the same Object. (2.242)

Peirce supplies his categories with several other twists important to an understanding of his semiotic. Among these is the approximativeness of the categories. Due both to the hypothetical nature of thought, and to the obstreperousness of reality, Peirce stresses that his three categories are to be seen as only an approximation to reality as experienced, a model subject to growth and revision, though, thought Peirce, a relatively good model as is (1.301).

Not unconnected with this approximativeness (cf. 1.528) are what Peirce calls the degenerate categories. In addition to genuine Firstness, Secondness, and Thirdness, Peircean semiotics works with a degenerate Secondness and two degrees of degenerate Thirdness. It must be confessed that Peirce is at his most obscure when discussing his degenerate categories: sometimes he describes them in terms of subcategories among his classes of signs, in places he defines them as the Firstness of Secondness and the Firstness and Secondness of Thirdness, at times he speaks of them in terms of combinatoric decomposition (Cf. 1.521-544, 2.265, 5.66-76). I believe we can give an interpretation, faithful to Peirce, which accommodates these diverse factors, as follows.

Degenerate Secondness is, logically speaking, a dyad more or less decomposed into a pair of monads, or instances of Firstness. From fully degenerate Secondness there runs an ordered sequence or "catena" of successively stronger levels of degenerate Secondness which in the limit converges to genuine Secondness. Phenomenologically speaking, one can think of the less than fully dynamic existence of one item relative to another-- for example, consider the quality of red and the quality of scarlet simply juxtaposed to one another (1.462). A slightly stronger example would be the actual existence of two actual pennies distinct from one another (1.465).¹³

The first degree of degenerate Thirdness ("first-degenerate Thirdness") is, logically speaking, a triad more or less fully decomposed into a congeries of dyads. This decomposition is in practice usually only approximate: most first-degenerate signs will fall somewhere on a graded continuum between the ideal endpoints of fully genuine Thirdness and fully first-degenerate Thirdness (Cf. 2.230-232, 8.376). Phenomenological examples, which can be made more precise under Peirce's division of signs, vary as widely as an object which one has selected by pointing it out (2.248), a remark uttered without further explanation (2.251), or an individual instance of a sign (2.245). In the limit, a pure world of first-degenerate signs would approximate to, for example, a stream of consciousness composed of sheer events and brute facts: think of the rapid-fire barrage of sound bites, remarks, and incidents on the evening network news!

The second degree of degenerate Thirdness ("second-degenerate Thirdness") is, logically speaking, a triad more or less fully decomposed into a congeries of monads. Again, this usually only approximate condition can be thought of as continuously variable between genuine Thirdness and full decomposition. Some phenomenological examples, again clarifiable under the division of signs, would be a photograph (2.247), the possibility of red as a warning of danger (2.244), or the general idea of geometric diagrams (2.250). In the extreme, a pure world of second-degenerate signs would approximate to, for example, a stream of consciousness made up of a montage of images, feelings, and sounds: imagine the experience of watching a rock video on MTV!

Note that first-degenerate Thirdness itself can undergo continuous partial decomposition into second-degeneracy; thus, a sign can embody a mixture of genuine Thirdness, first-degenerate Thirdness, and second-degenerate Thirdness in various proportions.¹⁴

We must also note the vagueness of Peirce's categories. Firstness and Thirdness can be more or less vague; Secondness alone is always precise. (5.446-450)

Firstness can be vague as one can "pin down" a quality only more or less approximately in terms of Firstness alone (cf. 6.224). Given two flowers seen a minute apart, how close is the redness of the first flower to the redness of the second? One may be able to form a fairly good offhand judgment-- but in terms of 1o alone it will not be altogether precise. Thus the redness of either flower has a penumbra of vagueness to it.

Likewise, Thirdness is more or less vague as meaning must be at least slightly indefinite in order to function at all (cf. 5.447, 6.326, 6.494-499). For example, the word "chair" is of the nature of a general law, instantiated in each object which is capable of being appropriately termed a "chair." The word must have some free play in it-- must be applicable to a more or less broad and fuzzy-boundaried class of entities-- if it is to be meaningful. And the same holds true of any more complex sign, be it a statement, an argument, a ritual, a belief system, a human being, or the wide world itself.

Indeed, the more common or important a sign, the more vague it will tend to be. Thus, as Peirce often remarks (cf. 6.494), one's deepest feelings, one's deepest beliefs, one's concept of God will all tend to be very vague indeed. This vagueness is not to be confused with the inchoate: for such signs to become more finely articulated by becoming richer in semiotic structure is one thing, but for them to become precise by the simple abolition of vagueness would be to empty them of meaning: language reduced to sheer Secondness!

The human being as a sign stripped of all vagueness would be, under a Peircean view, no longer a sign, but a mere algorithm: an object, a thing of mere Secondness, an "It." For Secondness alone is never vague, its precision the precision of a world of billiard ball atoms in mechanical collision.¹⁵

Important to the interplay of Peirce's categories is their varying intensity. The intensity of Firstness can vary since a quality of feeling may be experienced at varying levels of consciousness or attention-- though of course one can compare such instances of Firstness and judge them of different intensities only through Secondness and Thirdness (1.310, 6.222). Likewise degenerate Secondness, as a congeries of monads, may vary in intensity (2.283). And the intensity of Thirdness may vary as the representamen has only one "degree of freedom" in its relationship to object and interpretant, and so is relatively a First (cf. 2.242).

Important here also is the hierarchical nature of the categories. Secondness may be conceived apart from explicit attention to Thirdness, and Firstness apart from conscious supposition of either Secondness or Thirdness, but Secondness only manifests itself through Thirdness, and Firstness only through Secondness and Thirdness (1.549-554). Thus, "though it is easy to distinguish the three categories from one another, it is extremely difficult accurately and sharply to distinguish each from other conceptions so as to hold it in its purity and yet in its full meaning." (1.353)

Peirce applies his three categories to his sign to divide it into subcategories. His division of signs begins by considering which of the three categories predominates in the sign (representamen) itself; in the sign-object relationship; and in the sign-interpretant relationship.

According to the first trichotomy, if Firstness predominates in the representamen, we have a Qualisign, "a [potential] quality which is a Sign"; if Secondness, a Sinsign, "an actual existent thing or event which is a sign"; if Thirdness, a Legisign, "a law that is a sign," whether conventional or natural, and that acts through individual instantiations (hence Sinsigns) called Replicas (2.243-246).

According to the second trichotomy, if Firstness is most prominent in the sign-object relationship, the sign is an Icon, which denotes by qualitative resemblance (2.274-282); if Secondness, the sign is an Index, which refers to its object by dynamic (genuine) or existential (degenerate) relationship between sign and object (2.283-291, 305-306); if Thirdness, the sign is a Symbol, which signifies its object according to a general convention or habit (2.292-302, 307-308).

According to the third trichotomy, a sign-interpretant relationship characterized chiefly by Firstness is a Rheme or Term; by Secondness, a Dicisign or Proposition; by Thirdness, an Argument (2.250-253; cf. 2.92, 5.470ff.)

Under each trichotomy, a sign may be of not just a single type, but of two or all three types in varying degree (2.230, 265). And Peirce combines his three trichotomies to yield ten classes of signs according to the following diagram (2.264; "The lightly printed designations are superfluous"):

The boundaries are, again, approximations (cf. 8.376). Peirce's division yields ten instead of twenty-seven (=3x3x3) classes because a trichotomy involving Secondness makes the sign first-degenerate; one involving Firstness, second-degenerate; and a genuine triad can subdivide again in the same manner as before, while each dyad of a first-degenerate triad subdivides by catenation, and the monads of a second-degenerate triad can subdivide no further (1.543): subdivision can never make a partially degenerate sign less degenerate than it already is.¹⁶

In his later work, Peirce expanded his division of signs to ten trichotomies yielding sixty-six classes of signs; but seeds of this expansion were present in his earlier recognition of an asymmetry in his semiotic triad. Object, representamen, and interpretant are what they are only in the context of their sign relationship. But within this context (as the division of signs indicates) the representamen is what it is (of the three) most nearly independently of the other two-- that is, functions most nearly as a First-- while the interpretant is the most complex, most nearly determined as a Third by object and representamen; and the object is of intermediate complexity, occurring either itself as an instance of Secondness or determined dyadically by precisely one of the other two (2.235-242).¹⁷

This observation led Peirce to divide interpretant and object according to his categories. The interpretant subdivides into immediate, dynamical, and final interpretant; the object into immediate and dynamical object.

The immediate object is the qualitative object as immediately presented to interpretant by sign: the object "as it seems." The dynamical object is the object as it offers dynamic resistance or constraint to present representation and interpretation of it. together, immediate and dynamical object constitute a positive and negative "feedback loop" in semiosis which lies at the heart of Peirce's fallibilism (1.8-14; 5.238-243, 473).

The immediate interpretant is the potential interpretant as immediately presented by the sign; the dynamical interpretant, the interpretant as it actually "shakes down" in process to determine an effect or habit-change; the final interpretant, the interpretant as it would finally turn out in the community of interpretation in an infinite long-run. Peirce's teleology grows out of this division of the interpretant (4.536, 4.572, 5.475ff.)¹⁸

Peirce's Sign: Why Triadic?

It should now be very clear that triads and trichotomies form the warp and woof of Peirce's approach to semiotics. The debate over this triadicity has taken two divergent and incompatible avenues: proposals for a category of Fourthness which question the sufficiency of Peirce's semiotic, and proposals for a reduction to dyadicity which would render the semiotic triad unnecessary.

"One, Two, Three... But Where Is the Fourth?"

At least three proposals have been made for a Peircean category of Fourthness: those of Donald Mertz, of Herbert Schneider and Carl Hausman, and of Carl Vaught.

Mertz's proposal is the most easily disposed of. He examines Peirce's argument for the irreducibility of triads, as illustrated in "A Guess at the Riddle":

...the fact that A presents B with gift C, is a triple relation, and as such cannot possibly be resolved into any combination of dual relations. Indeed, the very idea of a combination involves that of thirdness, for a combination is something which is what it is owing to the parts which it brings into mutual relationship. (1.363)¹⁹

Mertz's argument may be convincing on its own terms, but Mertz is manipulating Peirce's polyads in ways which bear little resemblance to any way in which Peirce ever worked with them. In his first argument, Mertz is attempting to join a dyad with a triad without identifying which of the elements in the dyad is being joined to the triad. His second argument involves joining two triads by joining two elements in one with two elements in another. The former procedure has no precedent in Peirce, and the latter under Peirce's methods ought to yield a dyad, not a tetrad as Mertz thinks Peirce would have expected. Since Mertz gives us no clue as to how his procedures relate to those of Peirce, we have no way of judging whether Mertz is doing anything really entailed by Peirce's project, or whether Mertz is simply arriving at different conclusions because he is working out of different assumptions.²²

A more detailed proposal for Fourthness comes from Herbert Schneider. Schneider concedes three categories to be adequate for dealing with cognitive processes, but argues for "importance" as a category of Fourthness. He notes that, for Peirce, any purpose or good has meaning only in relation to a completely general summum bonum. "No Kantian idealist could have stated this conception of moral science more formally."²³

Schneider observes this scheme does not accommodate norms which might apply "even in the absence of a summum bonum," itches that call to be scratched for their own sake. Such norms he proposes as a phenomenological aspect of Fourthness: logical import is Thirdness, vital importance Fourthness. Satisfaction may comprise either the Thirdness of achievement or the Fourthness of satiety or contentment. The moral self-control of Thirdness in pursuit of an abstract summum bonum is only an abstract "intellectual framework" until it is taken up into the "concrete universal" of the moral self-criticism of Fourthness. Fourthness supplies what depth psychology, but not the Kantian "moral law within," acknowledges.²⁴

In logical terms, Fourthness would constitute a temporal sequence, though one which is an absolutely discontinuous string of points superimposed on the triadic continuum. Triadic semiosis is "prospective and cumulative"; tetradic semiosis adds a fourth factor which is non-cumulative, but "retrospective" along the hierarchy of categories, giving "meaningful individuality" to instances of Firstness. Since Firstness and Secondness "look 'forward'" to Thirdness while Fourthness "looks back" to Firstness, Thirdness in a sense "governs" Fourthness while Fourthness provides the steam to "drive" Thirdness.²⁵

Carl Hausman provisionally adopts Schneider's scheme, applied to both ethics and aesthetics with "importance" or "value" as a possible category of Fourthness. Hausman notes that Schneider's suggestion rejects "Peirce's own principle that a highest good makes specific goods intelligible," but that, quite regardless of this, Schneider puts a finger both on the problematic status of value in Peirce's semiotic and on an apparent "special connection" between value and Firstness.²⁶

Hausman turns to Peirce's categorial classification of the sciences to investigate the relations among value and the categories. Peirce categorially divided philosophy into phenomenology, normative science, and metaphysics, and normative science into aesthetics, ethics, and logic (1.186). Just as normative science rests on phenomenology and on the prior field of mathematics (within which two fields Peirce constructed his categories), so the categorial hierarchy is reflected in an order of dependence in which "ethics rest[s] on aesthetics, and logic on ethics," all three but especially aesthetics dependent on phenomenology.²⁷

All three sciences, according to Peirce, distinguish a kind of good and bad, "Logic in regard to representations of the truth, Ethics in regard to efforts of the will, and Esthetics in objects considered simply in their presentation," with both logical and ethical goods presupposing esthetic good. Remarks Hausman: "This is why Peirce says that ethics must appeal to aesthetics for aid in determining the summum bonum."²⁸ Considered thus, value itself is not a fourth category. Rather, it seems related but not identical to the teleological thrust built into Peirce Thirdness, and bound up with the categorial hierarchy.²⁹

Hausman notes that the categories can be related by what Peirce calls discrimination or distinction, prescission, and dissociation (1.353). We can prescind Firstness and Secondness from value, but neither value nor Thirdness from each other. Hausman speculates that value and Thirdness could be separated by "discrimination," "so interdependent that they are co-present as mutual grounds for one another," though this is difficult to determine since Peirce is none too clear as to what he meant by the term.³⁰

I think that Schneider and Hausman are correct to point out the problematic place of value in Peirce's thought. As Peirce himself was aware, as a natural scientist he devoted more attention to logic and less to ethics and aesthetics (2.120, 2.197).³¹ And I think the two are correct to note a connection between value and Firstness, though I consider Hausman's attempt to bring value in tandem with Thirdness more economical than Schneider's attempt at severing it altogether from Thirdness, and thus from a summum bonum. But I would concede Schneider's point that Peirce's account, as it stands, does justice better to the apollonian than to the dionysian side of human existence.

However Peirce, especially in his explorations of phenomenological Firstness (cf. 1.312-316) and his discussions of vagueness (cf. 6.494ff.), is far more sensitive to these issues than Schneider will grant. And a sequence of monads co-present with the semiotic "time line" which present themselves immediately and spontaneously in the interpretation of the sign ought to suggest a factor of the Peircean sign already familiar to us: the immediate interpretant.

Although Peirce is not explicit, the logical and phenomenological characteristics which Schneider attributes to Fourthness all fit well the spot the immediate interpretant occupies in Peirce's semiotic. By its relation to dynamical and final interpretant, the immediate interpretant is certainly "related but not identical" to the teleological thrust of Thirdness. And energetic immediate interpretants would "give a meaningful individuality" to Firstness. Finally, if Hausman's interpretation of "discrimination" is correct, then the immediate (unlike the dynamical or final) interpretant would indeed be related to the sign by discrimination.³²

The most detailed proposal for Fourthness comes from Carl Vaught. Vaught points out that, phenomenologically, there is a similarity between things such as a left hand and a right hand which does not seem reducible to a combination of identity and difference. According to Peirce, most spatial relationships can be dealt with predominantly in terms of the Secondness of objects in dynamic interaction or relative location. Yet as Vaught notes, Peirce vacillated over whether right and left can be distinguished in terms of Secondness-- for example, indexically (2.290)-- or whether Thirdness must be invoked, as for example in what physicists call the "right-hand rule":

Thus, your right hand is that hand which is toward the east, when you face north with your head toward the zenith. Three things, east, west, and up, are required to define the difference between right and left. (1.345)³³

In a parallel manner, on the logical level, Peirce insisted that analogy is reducible to a combination of univocity and equivocity, and is not a mediating third between them (3.421, 3.483-485, 1.34). Thus, a four-term analogical relation would be reducible to a combination of simpler terms. But Vaught argues that just such irreducible analogical tetrads occur in Peircean semiosis.

For semiosis gives rise to a sequence of signs and interpretants, each at a slightly different moment in time, and as Peirce's later distinction between immediate and dynamical object implies, the object itself is not static but constitutes a corresponding temporal sequence of objects in interaction with the sign/interpretant sequence. Within the vagueness inherent in Peircean semiosis then, says Vaught, lies precisely a similarity, irreducible to identity and difference, which embraces interpretant at t₁, interpretant at t₂, dynamical object at t₁, and dynamical object at t₂ in a tetradic analogical relationship which due to the vagueness is not precisely reducible to any combination of triads. As an example of this, consider a legisign which grows and develops over time: its form at any two instants can, under this proposed Fourthness, be seen as related by an irreducible analogical similarity. Likewise, the similarity between right and left can be seen only through a judgment of analogy.³⁵

Vaught's argument is both closely reasoned and richly textured, very much in the spirit of Peirce's own approach. If similarity is not to be understood (as Peirce saw it) as reducible to some combination of univocity and equivocity, then Vaught's argument is probably correct. But I think counter-arguments can be mounted on both logical and phenomenological fronts.

Logically, if the sequence of interpretants in Vaught's argument on analogy are considered, not as a sequence of discrete frames in a movie film (as Vaught takes them), but rather as a genuinely continuous flow of interpretants (and likewise the flow of dynamical objects continuous), then the need for the four-term relationship vanishes and Thirdness suffices. The situation becomes logically similar to, and no more problematic than, an account of a continuous function in differential calculus.

On the phenomenological front, I note that mathematicians define the "orientation" or handedness of a space by dyadic and triadic arguments alone. The proof is rather technical, but it enables one to speak of left- or right-handedness in space (of three dimensions, or even more) without resort to any tetradic combinations and without any prior invocation of right or left.³⁶

Greenlee's Dyadic Revision of Peirce

Much of the controversy over a suggested dyadic reinterpretation of the Peircean sign revolves around Douglas Greenlee's book, Peirce's Concept of Sign. In a symposium on this book in the Transactions of the Charles S. Peirce Society, Greenlee responds to criticisms by Joseph Ransdell, Jarrett Brock, and John Fitzgerald. In a later article Vincent Colapietro attempts an evaluation of an positive response to Greenlee's project.

"What is it for something to be a sign?"³⁷ This, says Greenlee, was one of the key questions with which Peirce was struggling in his semiotic. But Greenlee finds problematic an important aspect of Peirce's sign:

Peirce thinks of the sign as something which always points away from itself to an object. I go along with the idea that a sign always points away from itself. But I think it is a mistake to suppose that the pointing must always be to something referred to... What the sign always points to is that which interprets it-- what Peirce calls its 'interpretant.'³⁸

Greenlee finds the problem with Peirce coming to light in Peirce's use of such terms as "refers to," "represents," and "stands for." According to Peirce's own concept of abduction, semiotic is to be seen as a source of revisable hypotheses to be explored and tested in experience, and not an a priori construct.⁴⁰ And here it is that we encounter difficulties. For what does mathematics refer to? What is the object of logical connectives such as the conjunction "and"? The object of verbal commands? Of questions? Of music?⁴¹

Problems just as serious arise if we try to find a generalized meaning of the term "representation." If "'stands for' means stands in place of or as a substitute for something else," we exclude both self-referential signs (cf. 5.71) and habitual signs that mediate between expectation and response. The latter is a class that includes much of everyday human behavior. If we try to say that "the meaning of a word is what it stands for," this collides with the "pragmatic maxim," bound up with the teleology of Peirce's final interpretant, that meaning "lies in the future,"⁴² since it would imply that all propositions, even those "about the past, are really about the future." These considerations eliminate the possible solutions that signs are "representative because substitutive," or "because they possess meaning" (a function of the sign-interpretant relation under Peirce's semiotic).⁴³

What positive solutions can be suggested? Looking at Peirce's application of signs to human thought, Greenlee observes that Peirce's rejection of "mental-material dualism" suggests an equivalence between thought-signs and signs in general; that Peirce's distinction between actual and habitual notions (cf. replica and legisign) implies that "a sign may be an object actually cognized or the capacity to cognize"; and that Peirce's three categories extend such cognization not just to "intellectual ends" but to "'every sort of modification of consciousness-- Attention, Sensation, and Understanding.'" (5.298)⁴⁴

What Greenlee finds in all these characteristics of thought as sign, regardless of whether representation obtains, is a process of abstraction, "requiring a point of view in terms of which an object is relevant to the significance of the sign."⁴⁵ This point of view is the sieve (the interpretive grid, might we say?) through which it is selected by convention or agreement what is to be included in the process of signification.

"Now the chief semiotical question I want to raise for Peircean semiotic is whether abstraction is present in all signification." If so, we have found a general characterization of something very like a Peircean sign, but of which representation is not a necessary feature. For, argues Greenlee, Peirce's immediate object can carry all the freight that a sign characterized by abstraction requires its object to bear. When the sign is representative, the dynamical object may obtain; when not, then rather than construing as dynamical object the context in which the immediate object was expected (8.314; cf. 4.536), we can dispense with the dynamical object altogether. In either case, the immediate object can be interpreted in terms of direct or indirect "past experience as relevant to the interpretation of the present sign."⁴⁶

We can see that under Greenlee's proposal the immediate object becomes that content of signs temporally prior to the present sign, which is relevant to the present sign-interpretant relationship. The entire semiotic process is collapsed down into the temporal continuum of signs and interpretants. The sign process may be considered as polyadic if we include each previous sign relevant to the interpretation of the present sign, but fundamentally the sign is now dyadic:

Instead of insisting on triadicity, Peirce's semiotic should have insisted (a) simply on a differentiation of the sign from the dyadic causal relationship and (b) on the continuity of interpretation.⁴⁷

Greenlee also extends his reinterpretation to Peirce's division of signs by offering dyadic interpretations of the trichotomy Peirce defined in terms of sign-object relationship. The icon becomes a sign of "exhibitive import," displaying to its interpretant qualities and properties familiar from experience.⁴⁹ The index becomes a sign capable of "forcing" attention by modifying habit in the interpretant.⁵⁰ The symbol is more intractable: difficult to preserve distinct from the legisign under Greenlee's approach, the symbol ends up as the factor of conventionality co-present with every class of signs.⁵¹

The general consensus of the Greenlee symposium is that Greenlee's project is of value in its own right, but is not addressing the same set of issues which Peirce was trying to address.⁵² Ransdell and Brock remark that, in restricting semiotics to the subject matter of Peircean speculative grammar-- namely, the meaning of signs-- Greenlee so skews the scope of his inquiry as to make his conclusions almost inevitable.⁵³

"Greenlee contends that anything can have meaning (can be a sign), but he holds that not everything does have meaning." This, says Ransdell, is a crucial departure from Peirce, for it would mean that the world can be divided into signs and non-signs; that not everything incorporates Thirdness; and thus that "it ought to be at least possible to encounter a meaningless thing, something which does not, in fact, incorporate the relational structure in question." (Hence, I take it, Greenlee's distinction between dyadic signs and mere dyadic causation.) "But," continues Ransdell, "no such experience is possible, on Peirce's view... Peirce's semiotic is not about a class of objects. It is about what it is to be an object." Thus, objectification, signification, and interpretation are only different aspects of every phenomenon it is possible to encounter.⁵⁴

Since Greenlee rejects this, he gives the immediate object priority over the dynamical object. But, note Ransdell and Fitzgerald, for Peirce the dynamical object had priority as that over against which sign and interpretant stand; a closer logical analysis is necessary to bring out "something internal to the sign which relates it to the thing or circumstances"; and Peirce saw imaginative or fictive semiosis, in which the focus is upon the immediate object, "as logically more complex than (as 'parasitical' upon) semiosis involving a real object."⁵⁵

I would add that it is hard to see, from within Greenlee's system, what rationale there is for retaining the dynamical object at all, even in the case of representative signs, except perhaps as a code for a convention which distinguishes "real" signs from "fictive" signs. I take it this is what Ransdell is hinting at when he calls Greenlee's proposal "a semiotic of 'absolute' idealism."⁵⁶

We can better understand this priority of the dynamical object for Peirce if we see that what was central for Peirce in the sign was not merely meaning (as for Greenlee) but communication and inference. For Peirce, note Brock and Ransdell, all semiosis is dialogical, the original model for object-sign-interpretant being the utterer-utterance-interpreter structure of human communication. But since Peirce early rejected Cartesian intuition and Kantian synthetic a prioris, he abstracted (not generalized, as does Greenlee) features of this process to allow for the entry into the sign-interpretant continuum of quasi-dialogical factors neither derivable from nor reducible to sign-interpretant processes alone, hence irreducible Third. Thus in Peirce's view, says Ransdell, "The ultimate utterer of all signs-- all interpretive phenomena-- is reality itself." And thus the key Peircean questions, says Brock, are "How does it contribute to explaining the possibility of inference and communication? How do... signs function in the context of inference and communication? Learning and discovery? ...No such questions and no such answers can be found in Professor Greenlee's book."⁵⁷

Vincent Colapietro continues the response, conceding that it is an unfortunate choice of terminology to say that "a sign represents an object," since "represent" has connotations which are often but not always appropriate to the Peircean sign. To this degree, Greenlee has a point. But Peirce's definition of the sign/object relationship (like that of the triad itself) is purely formal. This relationship can be made more specific in terms of the (again purely formal) division of signs, division of object into immediate or dynamical object, etc.⁵⁸

What Colapietro stresses here is, I think, implicit in the logical/phenomenological "double-barrelledness" of Peirce's categories. As we have seen, Greenlee misses the logical or formal aspect since he does not deal with inference, and since his emphasis on meaning seems to lead him toward a sort of psychologism (witness his attempted distinction between significative and causative dyads).

Colapietro responds to specific objections by arguing that a word such as "and" can be seen as an index of relatively low intensity;⁵⁹ music, as a sign of the composer's "musical ideas," which are qualities of feeling (5.475); an imperative, as a sign whose dynamical object is the will of the speaker and whose energetic interpretant is the intended response (5.473).⁶⁰

More generally, we can see how Peircean fallibilism, formally considered, is a factor in all signs, hence how all signs in some sense require both immediate and dynamical object:

The fact that all signs have dynamic objects and, hence, external constraints makes semiosis a fallible process: any sign is open to the possibility of missing its mark... [but] it is only on the condition that there is a mark that there is a possibility of missing the mark... Commands and notes of music, no less than paradigmatic cases of representational semiosis, involve such a possibility, precisely because they could be constrained by something outside of themselves.⁶¹

Concluding Observations

We are now in a position to evaluate the proposals for a tetradic or dyadic revision of Peirce's triadic sign.

Two themes recur in the Fourthness arguments. One revolves around the understanding of continuity as it appears in Thirdness; the other involves areas in which one could wish Peirce had written more fully, or more clearly.

Schneider's Fourthness constitutes a discontinuous sequence riding "piggyback" on the continuity of Thirdness. Hausman manages to find a place for value as a factor in Thirdness, but this value remains an event-by-event, case-by-case affair. Vaught locates the analogical tetrad in the minute interstices of the flow of semiosis.

Although (as I have argued with Vaught) a proper understanding of continuity goes a long way toward clarifying matters Peircean, it seems that in each instance these writers are striving for a structure intermediate between pure continuity and total disconnection, a structure which exhibits features of both. But, as I have argued in my exposition of Peirce, we already have precisely such a structure in the interplay within the sign of genuine Thirdness and the two degrees of degenerate Thirdness.⁶²

Hausman is correct that Peirce devotes relatively less attention to aesthetics and ethics than to logic. Vaught detects genuine vacillations and inconsistencies in Peirce's thought on analogy and on the similarity of certain spatial structures. And Schneider points out correctly that Peirce skews his account somewhat away from the dark, mysterious, irrational forces of the psyche which twentieth-century psychologists have made us take into account.

I think all these are valid areas for further Peircean inquiry. And certainly there is no end to the tangled inconsistencies in Peirce! By the approximativeness of Peirce's own semiotic, a category of Fourthness may well emerge, but we could find this out only through such further inquiry. I think I have answered the proposals so far put forth, though I find it suggestive that they all hint at some sort of coincidentio oppositorum in which incommensurables can be reconciled, and the two potentially vague categories can precipitate out concretely without sacrificing spontaneity or becoming locked into the precision of Secondness. In such a direction, if any, I would suggest future Fourthness-hunters look.⁶³

At the same time, though, I would suggest a second look at Peirce's remarks on his semiotic meditative practice of "musement" (6.458-490), which resembles closely the sort of process just described. Peirce may seldom have spoken of anything like Schneider's "depth psychology," but one cannot read much of Peirce without being struck starkly by uncanny bass resonances in his tone of thought, like peals of distant thunder. It is this trait that so confounds some Peirce scholars who find him talking one moment like a hard-headed empiricist and the next like a New England transcendentalist mystic.⁶⁴ In his discussion of musement, Peirce essays (in terms of his three categories) an explanation of this process and a reconciliation of these coincident opposites.⁶⁵

Of Greenlee's dyadic project there is little to say that has not already been said. It is clear that between Greenlee and Peirce there lies the chasm of a fundamental philosophical option. It is the choice which Peirce summed up by contrasting his own stance of "realism" with the several shades of what he called "nominalism." (1.15-41, 5.77-107)

Which is prior-- the immediate object we construct, or the dynamical object which, like Peirce's jammed door, sticks without warning? What is the scope of our semiotic-- everything humanly understood and experienced (so that the world of real signs equals the sum total of the actual), or everything humanly understandable and experienceable (so that the world of actual signs instantiates a broader continuum of the real)? These are the kinds of fundamental options which may be fruitfully discussed, but which we more often bring to than derive from the conversation.

I think Colapietro puts it well when he says that what is at stake here is that, under the dyadic option,

it is we who initiate the process of semiosis by taking up some stance toward a complex. In contrast, an implication of [the triadic option] is that, at least in some cases, we are not the initiators of but the respondents to a world which is always already meaningful to some degree.⁶⁶

(Note: I have striven here more for lucid brevity than for anything like precision. For precision please consult the body of the paper! Caveat lector!)

Argument: A sign which (as its name suggests) embodies a logical argument. Also called delome. Example: a syllogism.

Category: A factor present in some way, shape, or form in every conceivable phenomenon; in some phenomena, one of the categories may be predominant. See Firstness, Secondness, Thirdness.

Catena: The "chain" of degrees by which relative existence approaches closer and closer to actual individual existence. Each "link" is one type of degenerate Secondness.

Degenerate Secondness: A dyad partially decomposed into a pair of monads: mere existence of a First relative to a Second. Example: two pennies lying in a row.

Degenerate Thirdness, First Degree of: A sign more or less decomposed into a mere collection of dyads or brute facts. Example: any course of events where "it's just one thing after another."

Degenerate Thirdness, Second Degree of: A sign more or less decomposed into a mere montage of monads or qualities. Example: a rock video; some surrealist paintings.

Dicisign: A sign which conveys a statement or piece of information. Also called proposition, pheme.

Dynamical Interpretant: The interpretant "as it actually is"; as it impacts on other signs and interpretants. See Teleology.

Dynamical Object: The object "as it really is"; as it constrains or corrects interpretations of itself. See Fallibilism.

Emotional Interpretant: The interpretant as it takes the form of a quality of feeling.

Energetic Interpretant: The interpretant as it takes the form of an action or event.

Fallibilism: The contention that all knowledge is provisional and fallible, though some knowledge is very highly probable, and a process of inquiry can help sort the wheat from the chaff. Fallibilism is grounded in the "feedback loop" between immediate and dynamical object.

Final Interpretant: The Interpretant "as it would be known really to be" at the end of an infinite process of inquiry, or in the light of an ideal future summum bonum. See teleology.

Firstness: One of Peirce's three categories. Firstness is monadic: whatever is what it is by itself without reference to any Second; any possible quality of feeling.

Icon: A sign which in some way resembles its object. Example: a portrait.

Immediate Interpretant: The interpretant "as it seems"; as presented by the sign as a possibility of interpretation. See Teleology.

Immediate Object: The object "as it seems," whether really so or not; the object as presented by the sign to the interpretant. See Fallibilism.

Index: A sign which is related to its object by actual cause-and-effect, or by existence relative to one another. Example: a weathervane as sign of wind direction; a finger pointing toward an object.

Interpretant: One of the three elements of the sign. The interpretant interprets the sign(representamen) as representing its object. Not to be confused with "interpreter"! A human being is an "interpreter," made up of a great many interpretants (thoughts, habits, actions, feelings, etc.).

Legisign: A sign which functions as a habit, custom, or law, whether conventional or natural.

Logical Interpretant: The interpretant as it takes the form of a general habit of law.

Object: One of the three elements of the sign. The object is represented by the sign(representamen) to its interpretant

Qualisign: A sign which can take the form of a quality of feeling. Example: red as a warning of danger.

Representamen: See Sign(b).

Rheme: A sign which conveys a single word, concept, or feeling. Also called. term, seme.

Secondness: One of Peirce's three categories. Secondness is dyadic; whatever is what it is by standing over against a Second, without reference to any Third; causation, brute fact, actual existence.

Sign: (a) The triad composed of object, sign(representamen), and interpretant. For Peirce, every conceivable experience is mediated through signs. (b) One of the three elements of the Sign(a). The Sign(b) is sometimes called the representamen. The Sign(b) (= representamen) represents the object to its interpretant. It is very important not to confuse sign in sense (a) with sign in sense (b): they are not at all the same thing! The former is a triad of three elements; the latter is one of those three elements.

Sinsign: A sign which takes the form of a single action, instance, or event.

Symbol: A sign which is related to its object by some habit or law, whether conventional or natural. Example: a written word as a sign of a sequence of spoken sounds.

Teleology: Peirce's contention that everything within the semiotic process has purpose by orientation toward an ideal future summum bonum, in light of which every sign would be knowable for all that it really signifies. Peirce's teleology is laid out in the structure of his immediate, dynamical, and final interpretant.

Thirdness: One of Peirce's three categories. Thirdness is triadic: whatever is what it is in relation to a Second by the mediation of a Third; structure, regularity, law, habit, continuity, holding under appropriate conditions. For Peirce, Thirdness is equivalent to the semiotic sign of object, sign(representamen), and interpretant.

Ultimate Interpretant: An interpretant which does not have to serve as a further sign of its object in order to be meaningful. Example: a jump, break, or transition in the flow of events or in one's attention.

Brock, Jarrett E. "Draft of a Critique of Greenlee's Peirce's Concept of Sign." Transactions of the Charles S. Peirce Society (TCSPS), 12:111-26.

Colapietro, Vincent. "Is Peirce's Theory of Signs Truly General?" TCSPS 23:205-35.

Fitzgerald, John J. "Ambiguity in Peirce's Theory of Signs." TCSPS 12:127-34.

Greenlee, Douglas. Peirce's Concept of Sign. The Hague: Mouton, 1973.

Hartshorne, Charles, and Weiss, Paul, Editors, Volumes 1-6; Burks, Arthur W., Editor, Volumes 7-8. Collected Papers of Charles Sanders Peirce. Cambridge: Harvard University Press, 1931-36, 1957-58.

Hausman, Carl R. "Value and the Peircean Categories." TCSPS 15:203-23.

Mertz, Donald W. "Peirce: Logic, Categories, and Triads." TCSPS 15:158-75.

Ransdell, Joseph. "Another Interpretation of Peirce's Semiotic." TCSPS 12:97-110.

Schneider, Herbert W. "Fourthness." Studies in the Philosophy of Charles Sanders Peirce, Wiener, Philip P., and Young, Frederic H., Editors. Cambridge: Harvard University Press, 1952.

Vaught, Carl G. "Semiotics and the Problem of Analogy: A Critique of Peirce's Theory of Categories." TCSPS 22:311-26.

¹In "Some Consequences of Four Incapacities," Collected Papers of Charles Sanders Peirce, 8 vols., ed. Charles Hartshorne and Paul Weiss (vol. 1-6), Arthur W. Burks (vols. 7-8) (Cambridge: Harvard University Press, 1931-36, 1957-58), 5.313-314. My citations from the Collected Papers will, as is customary, indicate volume and paragraph number: for example, 5.314 signifies volume 5, paragraph 314.

²T.L. Short, "Life Among the Legisigns," Transactions of the Charles S. Peirce Society (TCSPS), 18:285.

³Obviously, however, Peirce's influence was substantial on many of those who knew him, such as Josiah Royce, William James, and John Dewey-- as a result of which Peirce is known as one of the founders of American pragmatism, an honor to which Peirce responded by renaming his philosophy "pragmaticism," a term "which is ugly enough to be safe from kidnappers"! (5.414)

Peirce's connections with academia, after his 1859 graduation from Harvard, were limited to a few years spent teaching at Johns Hopkins (1880-84), and several lecture series delivered at Harvard around the turn of the century, arranged by William James in part to help Peirce out of financial straits. See also Max H. Fisch and Jackson I. Cope, "Peirce at the Johns Hopkins University," Studies in the Philosophy of Charles Sanders Peirce, ed. Philip P. Wiener and Frederic H. Young (Cambridge: Harvard University Press, 1952), pp. 277-311.

⁴1.568-572. Peirce confesses: "I fully admit that there is a not uncommon craze for trichotomies... I am not so afflicted; but I find myself obliged, for truth's sake, to make such a large number of trichotomies that I could not [but] wonder if my readers, especially those of them who are in the way of knowing how common the malady is, should suspect, or even opine, that I am a victim of it." (5.568)

⁵Cf. 1.135. This tendency in Peirce has been labelled panpsychism, as by Hartshorne, "The Relativity of Nonrelativity," Studies in the Philosophy of Charles Sanders Peirce, p. 218. But I think it would be equally correct to note here Peirce's insistence that "there is something in nature to which the human reason is analogous." (1.316, emphasis supplied) Note that for Peirce this double-edged stance both entails an affirmation of straightforwardly "anthropomorphic conceptions of the universe" (1.316), and is grounded in a Darwinian argument that any organism which is to survive for long must exhibit some reasonable degree of congruence with the processes of nature, or lose out to some other organism better able to do so (1.374-399).

I think the best explanation of this two-sidedness in Peirce is the observation that for Peirce both mind and natural process are special cases of semiosis rather than vice versa, and so, though neither nature nor mind is reducible one to the other, properties of either may be abstracted and by analogy extended to the other.

This semiotic embracing of two alternatives on a single continuum by distinguishing but not separating them is, under the heading of "synechism" or "continuity," one of the hallmarks of Peirce's thought. Cf. 6.169-173.

⁶This generality is for Peirce one of the differences between the "realism" of his semiotic, and the "tidal wave of nominalism." Cf. 1.1-27.

⁷Peirce's Firstness seems in many ways a counterpart to traditional qualia, though a more helpful image to get a "feel" for Peirce would be to think, not of qualities hierarchically classified, more general and more particular, but rather of more and less finely nuanced qualities set-theoretically arranged "within" one another or "overlapping," like the regions on a Venn diagram!

Peirce was less interested in the classification of qualities, and more in their subtle nuances: for example, the way the color scarlet resembles the blare of a trumpet, or an odor of frangipanni a personality (1.312-316). We are here in the realm of synaesthesia and creative metaphor-- a note to which Peirce returns in one remark on metaphor and the origin of language (2.290, fn.).

⁸As principle of individuation, Peirce's Secondness is indebted to the Scotistic notion of hiccaeity.

As regards Secondness as "Otherness," Peirce makes the etymological observation that the older English term for "second" was the word "other."

⁹Indeed-- see 1.288-1.292-- apparently the "snap-bead" model of molecules, which Peirce learned in his study of chemistry, was one crucial image in the formation of the logical aspect of his semiotic!

¹⁰As I have argued elsewhere in some detail (cf. fn. 62), Peirce's claim that Thirdness suffices is equivalent to the claim that semiosis can be built up according to a type of logical structure which mathematicians and computer scientists refer to as a "tree." "Trees" can involve structures of an order higher than three, but as every computer programmer knows, any tree can be transformed into a functionally equivalent "binary tree" involving only triadic relationships. Cf. Peter Grogono, Programming in PASCAL (Reading, Massachusetts: Addison-Wesley Publishing Co., 1978), pp. 249ff.

¹¹Note that the "must" of necessary being is absent from Peirce's semiotic scheme. Peirce considered the application of "must-be's" and "must-not-be's" to anything short of God as one more sign of "nominalism"-- cf. 2.18-77, esp. 2.28-30; "The Spirit of Cartesianism," 5.264. Cf. also Peirce's fallibilism, 5.587.

¹²The argument runs more or less as follows: (1) In any sequence of related signs and interpretants, each element serves as both sign to interpretants following and as interpretant of signs preceding, but there can be no first or last element of the sequence. (2) As applied to any finite span in a sequence, statement (1) and direct recursion iterated infinitely many times imply that elements of the sequence converge (as an infinite subsequence) to either endpoint of the finite span. (3) Applying statement (2) to every possible span traversed by the sequence implies that the semiotic sequence is in fact a linear continuum.

Note that this recursive structure supplies an explicit and rigorous connection between the triadic sign and the continuity which is such an important feature of Peirce's semiotic. An interesting sidelight is that Peirce's most formal definition of the dyadic structure of Secondness (1.445-447) involves indirect recursion, though not in such a manner as to yield continuity.

¹³This is my reading of Peirce's most extensive treatment of degenerate Secondness in 1.441-1.470. Peirce analyzes the first eight levels of degenerate Secondness, giving a diagram of the first eight "steps" of the catena.

"Poietical dyads," at the eighth step in the catena, are already within hailing distance of genuine Secondness, though in theory infinitely many steps along the catena still intervene. Another helpful "icon" might be to imagine the "steps" of this infinite catena converging to genuine Secondness as the sequence of points 0, 1/2, 3/4, 7/8, 15/16, 31/32,... converges to 1.

¹⁴My interpretation of the two degrees of degenerate Thirdness is based chiefly on Peirce's discussions in 1.471-481, 2.283, 5.66-76. Peirce's diagram of his division of signs, 8.376, may also, I think, serve usefully as an "icon" of the relationship among genuine, first-degenerate, and second-degenerate Thirdness.

¹⁵Cf. Arthur W. Burks, "Man: Sign or Algorithm? a Rhetorical Analysis of Peirce's Semiotics," TCSPS 16:279-92.

The perceptive reader will see here the potential connections between Peircean semiotics and existentialism! A Peircean semiotic treatment of alienation would also obviously involve the degenerate categories. For a suggestive but not fully developed treatment of these connections, see Walker Percy, The Message in the Bottle (New York: Farrar, Straus, & Giroux, 1975).

Percy has also written, from a Peircean semiotic viewpoint, a chilling and carefully thought out fictional treatment of "the human being as a sign stripped of all vagueness" in his most recent novel, The Thanatos Syndrome (New York: Ivy Books, 1988).

¹⁶My description of the matter here is much more clear and explicit than Peirce ever makes it. See also Gary Sanders, "Peirce's Sixty-Six Signs?", TCSPS 6:3-16.

¹⁷This can also be an alternative approach to the division of signs. Peirce's ten-class division was in place by some time in the 1890's; his sixty-six class division dates from about 1906. Cf. 8.342-379.

¹⁸Of course, any division of interpretant-- immediate, dynamical, or final-- can be an instance of any or all of the three categories. Peirce specifies the category which predominates in an interpretant by speaking of emotional, energetic, or logical interpretant. He also distinguishes an ultimate interpretant. Thus there are twelve kinds of interpretant altogether.

Peirce sometimes defines pragmatism as the pursuit of the (sic) ultimate final logical interpretant (5.475-476, 5.491). Any final interpretant is ultimate, but not all ultimate interpretants are final. A non-final ultimate interpretant (I believe) would be an at least partial discontinuity in the flow of semiosis-- a jump or break in attention, a contoured structuring of consciousness, such as apparently emerges out of our experience of time (cf. 6.325)

¹⁹Quoted in Donald W. Mertz, "Peirce: Logic, Categories, and Triads," TCSPS 15:169.

²⁰1.363, in Mertz, p. 170.

²¹Mertz, pp. 170-74. For Peirce's account of his "logic of relatives," see 3.456-552, esp. 3.483-487; and 4.307ff.

²²In this regard, I think Mertz could well consider more carefully why Peirce introduces his "existential graphs" into the argument. Peirce is not simply arguing in terms of propositional logic; his arguments overlap with what mathematicians today call "graph theory." See my remarks, fn. 10, on "trees" and "binary trees."

²³Herbert W. Schneider, "Fourthness," Studies in the Philosophy of Charles Sanders Peirce, pp. 209-10.

²⁴Schneider, pp. 210-13.

²⁵Schneider, pp. 211-214.

²⁶Carl R. Hausman, "Value and the Peircean Categories," TCSPS 15:207-09.

²⁷Hausman, pp. 209-10; cf. 2.198-199, 5.36, 5.122-132.

²⁸Hausman, pp. 21-13; cf. 5.36.

²⁹Hausman, pp. 214-16.

³⁰Hausman, pp. 216-21; cf. 1.353, 1.549.

³¹For a succinct account of Peirce's growing awareness on this point, see "Esthetics, Ethics, and the Summum Bonum," in Thomas A. Goudge, The Thought of C.S. Peirce (New York: Dover Publications, 1969; orig. ed., University of Toronto Press, 1950), pp. 301-06.

³²According to Peirce's later sixty-six-class division, final and even dynamical interpretant may be prescinded from immediate interpretant, much as Firstness may prescind from Secondness and Thirdness (cf. 8.337-340). That is, one can conceive of the interpretant without consciously positing final and dynamical interpretant, but not without supposing immediate interpretant.

³³Quoted in Carl G. Vaught, "Peirce's Theory of Categories," TCSPS 22:315-16. In physics classes, the "right-hand rule is usually taught to students as an indicator of the direction of rotation of the right thumb when right thumb, forefinger, and middle finger are held all at right angles to one another, and the hand is rotated with forefinger moving in the direction of middle finger. This is the "positive" direction of rotation, and an opposite rotation is designated "negative."

An illustration of the point Vaught is making is the fact that Soviet physicists use a left-hand rule, which interchanges positive and negative as compared to their Western counterparts!

Compare also such terms as "clockwise" and "counter-clockwise," or the older synonyms "with the sun" and "against the sun."

³⁴Vaught, pp. 317-18.

³⁵Vaught, pp. 313, 318-25.

³⁶The argument requires in rigorous form some knowledge of vector spaces, mathematical induction, and finite group theory. But the basic argument runs as follows. On a line, we can arbitrarily select one of the two possible directions and call it "positive"; the other, "negative." We can then extend this definition one dimension at a time by selecting one of the two directions along the nth coordinate axis as "positive" and joining it to the "positive" (n -1)-dimensional structure already established.

In Peircean terms, each act of selection is dyadic (more precisely, indexical); each act of joining is triadic. A final arbitrary indexical selection on the finished product gets us from "handedness" to "left-handedness" or "right-handedness."

³⁷Douglas Greenlee, Peirce's Concept of Sign (The Hague: Mouton, 1973), p. 7.

³⁸Greenlee, p. 9.

³⁹Greenlee, pp. 13, 23-24.

⁴⁰Greenlee, p. 52f.

⁴¹Greenlee, pp. 24, 51-52, 54, 56.

⁴²Greenlee, pp. 55-58. Cf. 5.6. Greenlee notes, p. 58, fn. 5, that some writers have proposed precisely such an interpretation of Peirce's pragmatist theory of meaning.

⁴³Greenlee, pp. 59-61.

⁴⁴Greenlee, pp. 61-63.

⁴⁵Greenlee, p. 64.

⁴⁶Greenlee, pp. 64-69.

⁴⁷Greenlee, p. 111.

⁴⁸Greenlee, pp. 106-17, 122-23.

⁴⁹Greenlee, pp. 81-84.

⁵⁰Greenlee, pp. 86-92.

⁵¹Greenlee, pp. 93-96.

⁵²Joseph Ransdell, "Another Interpretation of Peirce's Semiotic," TCSPS 12:97: "Greenlee's discussion is pertinent and valuable for anyone interested in the idea of semiotic. But I do not think his account succeeds, in general, in conveying an adequate understanding of what Peirce's semiotic is all about."

Jarrett E. Brock, "Draft of a Critique of Greenlee's Peirce's Concept of Sign," TCSPS 12:111: "Peirce's intentions are sacrificed (ignored, neglected, excluded, distorted, misunderstood, refuted) whenever they conflict with Greenlee's notion of a general theory of signs."

John J. Fitzgerald, "Ambiguity in Peirce's Theory of Signs," TCSPS 12:132: "...the aim of Greenlee's book seems to be to arrive at a definition of sign that will apply equally well in each instance. In so far as he takes that to be Peirce's aim too, I think that the evidence is to the contrary."

⁵³Ransdell, p. 98; Brock, pp. 111-12, 117.

⁵⁴Ransdell, pp. 98-99.

⁵⁵Ransdell, pp. 104-06; Fitzgerald, pp. 131-32. Ransdell, p. 105, states succinctly the connection between immediate and dynamical object which Greenlee rejects: The immediate object may truly represent the real object, but then it may not... But the real object is not to be thought of as an unknowable Ding an sich, screened from our view by its own manifestations, but rather as that which appears to us in the immediate object when our interpretation is correct."

⁵⁶Ransdell, p. 106: "It was precisely on [this] question of the eliminability of the object that Royce and Peirce disagreed." Ransdell quotes Peirce, 8.129: "The truth is, that Professor Royce is blind to a fact which all ordinary people will see plainly enough; that the essence of the realist's opinion is that it is one thing to be and another thing to be represented."

⁵⁷Ransdell, pp. 101-04; Brock, pp. 118-21.

⁵⁸Vincent Colapietro, "Is Peirce's Theory of Signs Truly General?", TCSPS 23:206-11.

⁵⁹Colapietro, p. 216. "Intensity" is my interpretation; Peirce's term, which Colapietro cites from a manuscript, is "not sufficiently complete sign."

⁶⁰Colapietro, pp. 217-218; cf. Fitzgerald, p. 132.

⁶¹Colapietro, pp. 219-21.

⁶²Cf. the diagram in f. 14. One concrete example of such a structure can be met with in a semiotic analysis of phenomenal time-- cf. Paul Burgess, "A Peircean Semiotic Analysis of Time, in Response to Richard Swinburne's Arguments on God and Time," paper for philosophical theology seminar.

Another good example would be the structure of immediate, dynamical, and final interpretant; cf. my response to Schneider and Hausman.

These structures bear a resemblance to certain constructions in point-set and geometric topology, a field of some interest to Peirce in its infancy around the turn of the century.

⁶³Paul Watzlawick, Janet Helmick Beavin, and Don Jackson, of the "Palo Alto" psychiatric research group, throw out further hints along these lines in their Pragmatics of Human Communication (New York: W.W. Norton & Co., Inc., 1967) when they discuss "aha!" insights, psychotherapeutic use of paradox, Zen koans, and the spontaneous transformation of interpretive viewpoint by which people can break out of emotional double binds and escalating disputes.

Watzlawick et al. seem indebted for their semiotics to Peirce and to Charles W. Morris.

⁶⁴Hence Goudge's guiding thesis of "naturalism" versus "transcendentalism" in The Thought of C.S. Peirce. Hence also Arthur Burks' attempt to strain out Peirce's "rhetoric" in "Man: Sign or Algorithm?"

⁶⁵See Peirce's "Neglected Argument for the Reality of God," 6.452-493.

⁶⁶Colapietro, p. 227.