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James Jakób Liszka
For a fuller account of the themes presented here see Meaning and the Three Essential Conditions for a Sign, to be published in The Peirce Seminar Papers.

Complexity is not only necessary in order to explain the evolution of living systems, but also meaning systems such as found in language. My argument here is that Peircean sign theory offers a unique solution to this rather complex problem by suggesting that complexity and sign formation are integral. Put as a thesis, the argument is that the very conditions required for complexity happen to be those conditions Peirce articulates as formative of a sign.

The essential conditions for a sign are spelled out very clearly by Peirce. For anything to count as a sign it must have the following three conditions (cf. Liszka 1996; 18ff): first, a sign must be about something (CP 2.230; W 1: 287); second, it must be capable of conveying something about the thing it is about (CP 2.228; 3.361; W 1: 287) and, third, it must be able to convey to something else, something about the thing it's about (CP 2.228; CP 2.308; CP 5.253). Peirce says "...a thoroughly genuine triad...exists in the universe of representations. Indeed representation necessarily involves a genuine triad. For it involves a sign, or representamen, of some kind, outward or inward, mediating between an object and an interpreting thought" (CP 1.480). We can state these three conditions a bit differently: for any process or complex of processes to generate meaning, it must be capable of mediation, directedness, and interpretation. As much as I would like to develop a detail account of all three processes and their interrelations, space limitations force me to focus primarily on the first process, mediation, with some reference to the other two (see the complete presentation in MEANING AND THE THREE ESSENTIAL CONDITIONS FOR A SIGN, forthcoming in The Peirce Seminar Papers)..

As a way of making the argument for my thesis here--that complexity and sign formation are integral--I will use a number of thought-experiments combined with some real-world example.s The argument that follows can be summarized in its barest essentials: first, complexity requires mediative processes. Second, mediative processes are not transmission algorithms, but must be transformative; the special type of transformation expressed by mediation is captured by Peirce's notion of inclusion or transitivity. Third, mediation, understood as inclusion, involves two processes: schematization and representation; schematization is the ability of the mediator to organize information from its source so as to make it interpretable for some other process; representation allows the mediator to serve as an efficient means of relation between source and interpretive algorithms. Fourth, schematization and representation involve an inherent bi-directedness to the process. Fifth, in order for a mediator to become a sign it must be realized in all three conditions for a sign.

Suppose a minimal arrangement: energy, matter, a process which is organized by means of them, something to process, something processed, and the environment in which these processes take place. This process will have a way of inputting something from its environment, and there will be only certain features of its environment to which it will respond. It will have an algorithm or rule which will express the design of its processing, and it will have a certain output.

Suppose the algorithm of this elementary process is purely transcriptive, in the sense that it substitutes one input feature for another, so that the output is a product on the same order as its input. However, suppose also that the algorithm maps the input onto itself, so that the output is the same as it input. Logically this is an identity function. The effect would be that the input would be simply transmitted thought its algorithm without alteration. This would be the formalization of a pure transmission. In that case, it is easy to see that no matter how many of these processes are reproduced, and no matter what complication of interconnections among them is established, the system will never exceed a level of meaning greater than any one of the processes. As Shannon (1950) showed,encoding the meaning correctly may help to avoid its entropy, but stringing together pure transmitting processes will not make the meaning transmitted grow. If the algorithm generates no meaning, then no matter how complex the system with just this algorithm, no meaning will be generated in it. consequently, if we suppose that meaning is generated from non-meaningful processes, then those non-meaningful processes which have this sort of algorithm could not generate meaning. If this algorithm expresses pure transmission, then no system composed entirely of pure transmitters, no matter how complex, will be sufficient to generate meaning.

In order to generate meaning from non-meaningful processes, then, the algorithm of its process must be capable of a transcription which transforms its input into an output that is in some sense different than its output. However, assuming that the algorithm transforms an input into an output different from its in put, no matter how many of the same processes are reproduced in the same environment, there will be no interconnections possible in principle. For this arrangement, too, the system is no more meaningful than any one of its parts;consequently, if any one process is non-meaningful, none are.

To avoid this situation there must be two distinct types of transcription algorithms, one that takes input from its environment and transforms it into some output different from its input, and one that can read the output of the other, for example, the manner in which mRNA reads the DNA as complementary nucleotides. The existence of two such algorithms (even if it occurs inside one process) is necessary in order to make a connection between two processes, and to complicate the system to a significant degree. Let's call processes of the second type readers and those of the first type, texts. As Peirce notes, "signs require at least two quasi-minds; a quasi-utterer and a quasi-interpreter...every logical evolution of thought should be dialogic" (CP 4.551). There are three possible scenarios in this regard: (1) the output of readers is the same as its input; (2) the output of readers is the same as the input of texts; (3) the output of readers is something different than either the text's input or output. A little reflection would show that of the three possible scenarios in this regard (3) is the one most likely to generate a level of complexity sufficient for the production of meaning in a system.

DNA processing illustrates this but with some additional insight. Biologists make a distinction between transcription processes that occur between the DNA and mRNA, and the translation of genetic information into a sequence of amino acids. Transcription occurs when the mRNA 'reads' the DNA, which is coded as ordered triplets of the four nucleotides. Just as each new DNA strand is a complementary copy of an existing strand, each new RNA molecule is copied from one of the two strands of DNA by the same base-pairing principle. The result is a transmission of the DNA by complementation . It is clear, however, that such transmission by complementation could only transmit the code without any complication to the genetic architecture of the system. Like equality, this complementation is a code and level preserving process. In order to accomplish some complication to the system, a transitive relation must be established. This is done by the tRNA. The tRNA carries a complementary transcription of the DNA which allows it to read the mRNA, but at the same time it has the capacity to read amino acids, "selecting" the one that it is coded for. Because the tRNA and the mRNA are complements of the DNA, the tRNA can also read it. Consequently the tRNA serves as the mediator between the mRNA and the amino acids, which will form the building blocks for proteins. Ribosomes provide the environment in which the mediation takes place.

In addition to the insights concerning genetic translation, Turing algorithms can serve as an indirect example of why mediation is necessary for a meaning-generating systems. The Turing algorithm works primarily on the basis of identity, substitution and position. It words with a set of complements, '1' and '0'. Substitution simply means, then, the replacement of one unit by the same type of unit. In effect, then, substitution in this case defines an equality relation. There is no transitive relation in Turing algorithms (position is purely a sequential process-although it is sometimes represented as if it were implication). Since systems of processes composed solely of identity and equality functions--no matter how complicated--can only be transmission of transcriptive processes, so are Turing processes. This would leave us with the intuition that any digital computer based on the Turing algorithm, no matter how complex, simply transmits transcriptions, and cannot be said to be a meaning-generating system i any reasonable sense of the term.

The same point is illustrated more intuitively by John Searle's "Chinese Room" thought experiment (1984: 28-42). Imagine an observer looking at a room which has an input slot and an output slot. Tape with Chinese symbols is inputted into the room, and Chinese symbols on a tape exit the output slot. The observer can read and understand Chinese. She can see that coherent statements in Chinese are entering, and correspondingly coherent statements relevant to the input are exiting. One might conclude that whatever is going on in that room, the "reader" understands Chinese.

However, when the room is opened and its inner workings revealed, we discover that the room is occupied by a professional transcriber who takes whatever symbol enters the room, refers it to a chart of substitutions, then replaces the symbol in the sequence prescribed by the algorithm. This employs only Turing algorithms--identity, substitution, position. The transcriber does not understand Chinese, nor does the room, and no amount of transcription will generate such an understanding. All meaning is external to the process (and we assume resides with the inventor of the room), and is merely transmitted by the process.

Reflection of the DNA process and difficulties with Turing algorithms shows that in order to have a system sufficient enough to generate meaning, there must be at least two basic types of processes, one which produces text, and the other which can read it, and, the reader-text relation must establish a transitive or implicative relation among input and output of the system. The transitive relation is a mediative relation, and if transitivity is necessary for mediation, then all systems sufficiently powerful enough to generate meaning must have mediators and be transitive in this sense. To illustrate how transitive relations are mediations, formally speaking, consider the formal character of that relation which Peirce calls illation. Thus, 'If A, then B', 'If B, then C', 'If A, then C' (cf. CP 3.165). Literally, this demonstrates that A is in ?B and B is in C. Transitivity also maps a primitive triadic relation: it shows that a third is connected to a first by means of a second. The existence of transitivity in a system makes it possible to expand by increasing levels of complexity which are tied to one another by inclusion. For example, consider what happens if equality, rather than transitivity is the only algorithmic operator in the system: A=B means that all A is included in B and all B is included in A (CP 3.173n2). The system does not expand beyond the level of either A or B, but either A or B define the same universe.

Transitive relations cannot be defined in terms of equality or substitution. B cannot be substituted for A, nor can C; nor is A identical to either B or C. The transitive relation is therefore a primitive triadic relation, necessary for any system complex enough to generate meaning. It is precisely for this reason, I believe, that Peirce thinks of illation as "the paramount semiotic relation" (CP 2.444n1).

Since the existence of mediators is crucial to meaning-generating processes, let's look a little more closely at the notion of mediator. The mediator forms a transitive relation with what it mediates. As we've seen, the transitive relation, according to Peirce, is best captured by the notion of inclusion, that A is somehow included in B and B included in C; in effect then A is also included in C. This suggests that in mediation A is carried through B to C, much as the way in which an intention is carried through a set of actions, so that the connection among A,B and C cannot be reduced to a set of dyadic relations. Transitivity is much like the act of giving in which something is transferred between two agents in a way that cannot be reduced to a causal sequence (CP 1.363). In transitivity A is included in B but also expanded by B to be also included in C which, in turn, expands B for further inclusion. What A provides for this transitivity, then, is the hook or anchor upon which successive inclusions are established. This can be spelled out more carefully.

If A can be considered as the source of transitivity--what Peirce would call a dynamoid object (CP 8.314; CP 8.343; CP 4.536)--then its role is to impart a certain determination to the processes which follow it. This determination is realized by a form which is captured by the process, and--should those processes become sign processes--this form will serve as what Peirce calls the ground for the process. The ground understood as form preserves some character of the source, yet allows it to be realized by a different process than the process at its source. In order for it to be engaged in a transitive relation, whatever other qualities a thing which includes it might have, there are some which will register this determination; otherwise transitivity could not take place.Put crudely, if A could not be fit into some slot in B, B cold not transfer A to be included in C. The mediator will then exhibit this form or ground by means of some qualities, properties or relations it has,independently of whether it serves as a mediator. When mediators become signs, the forms of these qualities, properties or relations are one aspect of its power as a sign. These are familiar enough to those familiar with Peirce. When the mediator shares qualities with what it mediates, it is a qualisign (CP 2.244); when its hic et nunc realizes the form of what it mediates, then it is a sinsign (CP 2.245); and finally when its pattern--however that may be realized--realizes the form of what it mediates, then it is a legisign ( CP 2.246).

The compression of air into sound waves of certain amplitude and frequency, which have a definite form, are transduced by eardrum and ossicles as vibration patterns and, eventually, as fluid waves in the cochlea. At this point such waves are further transcribed as patterns of neural firing, made possible by the effect of those fluid waves on the basilar membrane, to which are attached hair cells connected to neural receptors. Regardless of which of the three dominant theories of pitch we consider--Helmholtz's place theory (1866), Rutherford's frequency theory (cf.Békésy 1957), or Wever's volley theory (1937)--all agree that the neural firing patterns somehow retain the form expressed by the frequency of the sound wave which reaches the pinna of the ear; they simply disagree on how that neural pattern expresses it. What all three theories show is that what is transferred to other processes, beginning with the collection of sound waves by the pinna, is a transference of form, a certain transitivity, which ties the processes together, although each process includes this form, it also expands it by the very act of including it in something else.

When the mediator is part of a semiotic process, its ability to include something else within it own process allows it to serve as a representative of that which it includes; its ability to expand what it includes, allows it to be interpreted by some other process which cannot read A, but can read B. The purpose for such an arrangement is obvious. If a process were simply a sequence of processes, no transference of information about the source would be possible, since each process would only read the process that preceded it; the process would be purely dyadic, and so would treat its preceding process as if it were the source. The result would be a blind system, in which A follows B which Follows C which follows D.

What this also shows is that transitivity--understood as mediation--allows for directedness in the system of processes. The goal of opening the window is a source that is schematized in an imaginary plan, which involves a sequence of events (turn latch, pull up window), which are schematized in the motor cortex, which is then schematized in the interneurons, which is then schematized in the motor system.

To effect transitivity without mediation would be completely inefficient if not impossible for a system complicated enough to generate meaning. In order to read A, every process consequent to A would have to have a direct connection to it. Mediators are much more efficient since they can transfer information from processes below it without including everything below it. In this case the sign serves as its source's representative very much like the way in which a legislator may be said to represent her constituents: one voice in the place of many. The mediator reduces a number of more primitive processes, yet preserves something of its character in its expansion of them. In a certain sense, sound waves of a certain amplitude and frequency cannot affect certain parts of the brain in the way in which pitch can. The sign summarizes or reduces the output of lower-level processes and, consequently, can itself be worked upon by higher-level processes in a more profitable and efficient way. A sentence sums words which sums syllables which sums phonemes which sums distinctive features. Signs, according to Marvin Minsky, are very much like the way players of computer games use symbols to invoke processes inside their complicated game machines without the slightest understanding of how they work. "And when you come to think about it, it scarcely could be otherwise. Consider what would happen if we actually could confront the trillion-wire networks in our brains....Fortunately, for the purposes of everyday life, it is enough for our words or signals to evoke some useful happening within the mind" (1986: 57).

The transitivity in the relation among A,B and C, allows A to be included in both B and C, but A's inclusion in B makes that transfer possible. B, in effect, schematizes A for inclusion in C. B, like tRNA, performs a Janus-like operation since it is able to "receive" something from A, which it preserves yet transforms, into something which can be included in something else. We can think of schematization as Kant did, a way of articulating or formatting something so that it can be made intelligible for a higher-level process (cf. CP 1.35, 2.385). To use Kant's example, causality can be schematized temporally as an asymmetrical sequence of events, thus making it concept-ready. Similarly, auditory neural firing patterns are schematizations of the amplitude and frequency of the original sound waves and, by their means, retain the form or ground of that wave, yet transform it in a way that can address other higher processes in the brain. Schematizations are the way in which the mediator can address another process in the chain of processes. Schematizations permit C to read A by being able to read B. The schema formats C so that information about A can pass through B. Depending on the type of schematization, these are called by Peirce either semes (CP 4.538), phemes (CP 4.538), or delomes (CP 5.438).

Semes can be considered to be at the threshold of meaning, or the most primitive level of meaning, since they represent the point in the process at which the mediator can address an interpretant, or can cause the interpretant to interpret it, a process that is distinct from pure mediation. Peirce's two clearest example of semes--percepts and terms--illustrate this readily. anything below the threshold of a percept are generally meaningless for human agents, and similarly with words.

A mediator is a pheme on the other hand when it is schematized in such a way that it can become information-giving for interpretants or readers. Phemes are minimal units of information. Examples of phemes for Peirce include perceptual judgements (the affirmation of the content of what is seen), or propositions ('This car is read'). A mediator is a delome, finally, when it is schematized in such a way as to become inference provocative for interpretants or readers.


Békésy, Georg (1957). The Ear. Scientific American. 252(4): 66-78.

Helmholtz, H. (1962). Treatise on Physiological Optics. New York: Dover.

Liszka, James (1996). A General Introduction to the Semeiotic of Charles S. Peirce. Bloomington: Indiana University Press.

Minsky, Marvin (1985). The Society of Mind. New York: Touchstone.

Peirce, Charles (1931-1958). Collected Papers, vols. 1-8, C. Hartshorne, P. Weiss and A.W. Burks (eds). Cambridge, MA: Harvard University Press.

_____ (1982-1997). Writings of Charles S. Peirce: A Chronological Edition, vols. 1-5, M.H. Fisch et al. (eds). Bloomington: Indiana University Press.

Searle, John (1984) Minds, Brains and Science. Cambridge: Harvard University Press.

For an expanded version of this text, with illustrations and notes, please see,

Meaning and the Three Essential Conditions for a Sign, forthcoming in

The Peirce Seminar Papers

END OF: James Liszka, "Three Essential Conditions for a Sign: Mediation"

Posted to Arisbe website on May 20, 1998


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