Diagrammatic Icons and their Motivations: Central Concepts and Examples

Note: What follows is a linguistic essay I wrote during my time as a student pursuing a master’s degree in computational linguistics. I stumbled over it a few days ago while going through some old data. Given the general scarcity of information about the topic of iconicity, I’ve decided to publish it here. Despite its shortcomings, I believe that it can serve as an entry point to this fascinating area of linguistic research.

The relationship between the form of language and its meaning has fascinated thinkers since at least the times of Ancient Greece. Plato’s famous Cratylus dialogue discusses in what way names might relate to their intended meanings (Jowett [1892]). In the course of the dialogue, Cratylus and Hermogenes ask Socrates whether names are created “arbitrarily” or “naturally”. Socrates responds that

the best possible way to speak consists in using names all (or most) of which are like the things they name (that is, are appropriate to them), while the worst is to use the opposite kind of names.”

In the course of the dialogue, Hermogenes emerges as the representative of a view adverse to Socrate’s conviction, namely that names gain their meaning by customary use and convention. Hermogenes argues that the essence or, to put it less enigmatically, the meaning of a name cannot possibly be known through its form. Therefore, an indefinite number of other names exist, each of them equally well suited to represent the same meaning.

Two and a half millennia later, modern thinkers are still discussing answers to the age-old question of whether there is an a priori connection between form and meaning. Nowadays, although people have long ceased to defend the notion of a naturally predetermined name for each thing, proponents of a more nuanced but related view to that of Socrates have produced many arguments in favour of the existence of some kind of predictive relationship between form and meaning.

Could it be that, although there is no inherently “right” way to assign a name to an object, there might still exist other linguistic signs, possibly more complex than mere names, whose external forms suggest their meanings in at least some respects? While Saussure has echoed Hermogenes’ view and elaborated on it during the late 19th and early 20th century, extending the question of arbitrariness beyond isolated words & names, linguists of the “post-Saussurean” epoch continued to take the analysis of linguistic structures even further. Some of these researchers, among them Halliday, have thereby arrived at conclusions not anticipated by Saussure. Halliday argues that

“Saussure took the sign as the organizing concept for linguistic structure, using it to express the conventional nature of language in the phrase “l’arbitraire du signe”. This has the effect of highlighting what is, in fact, the one point of arbitrariness in the system, namely the phonological shape of words, and hence allows the non-arbitrariness of the rest to emerge with greater clarity. An example of something that is distinctly non-arbitrary is the way different kinds of meaning in language are expressed by different kinds of grammatical structure, as appears when linguistic structure is interpreted in functional terms.” (Halliday [1977:113])

In the above quote, Halliday is alluding to the notion that language as a social communication system is both “arbitrary” and “natural” (or “non-arbitrary”). His main point is that these two seemingly paradoxical characteristics occur on different levels of a language. In this context, what used to be called “naturalness” by the philosophers of Ancient Greece has its modern analogue in the notion of iconicity.

The concept of iconicity derives itself from Peirce’s well-known typology of signs which sought to distinguish between three elementary types of signs:

“(…) It follows that there are three kinds of representations:

First. Those whose relation to their objects is a mere community in some quality, and these representations may be termed Likenesses.

Second. Those whose relation to their objects consists in a correspondence in fact, and these may be termed Indices or Signs.

Third. Those the ground of whose relation to their objects is an imputed character, which are the same as general signs, and these may be termed Symbols.” (Peirce [1867])

Nowadays, a representation is simply called a sign and likenesses are known as icons. The terms index and symbol are still used in the same way as in the original paper.

At a later point in time, Peirce further subdivided icons into images, metaphors, and diagrams the latter of which he defined as complex signs. This definition implies the existence of various parts that the complex sign consists of. Presumably, these various parts are not separate from each other but stand in definite relationships. Therefore, a diagram consists of two fundamental building blocks: its parts and their relationships among each other.

Just like other types of complex signs (such as graphical diagrams), complex linguistic constructs are composed of parts and their relationships among each other. In his monograph Natural Syntax, John Haiman set out investigate the correspondence between the parts & relationships of diagrams and the parts & relationships of their corresponding concepts. Based on his inquiries, Haiman proposes that “languages are like diagrams”:

“There is therefore some correspondence between the parts of a diagram and the parts of the concept which it represents. The parts of a diagram do not necessarily resemble the parts of the corresponding concept. In Peirce’s terminology, each of these parts may therefore be a symbol rather than an icon of its referent. But the essence of a diagram is that the relationship among the parts of the diagram does resemble the relationship among the parts of the concept which it represents. This (attenuated) resemblance justifies our calling a diagram a kind of icon: a diagrammatic icon.” (Haiman [1985:9ff])

In the above quotation, Haiman argues along the same line as Halliday: Although the individual “sub-signs” representing the parts of a diagram might be symbolic in the Peircean sense, the diagram’s overall appearance could be iconic. That is to say, the relationships established by the diagram between its parts resemble the relationships within the parts of the conceptual object depicted. Thus, neither Halliday nor Haiman deny the existence of conventionally or arbitrarily created signs but point out that there is more to the structure of language than just convention or arbitrariness. Haiman writes:

“The general validity of the doctrine of arbitrariness is so obviously correct that it scarcely requires the authority of a Whitney or of a Saussure to establish it. We could even go further and inquire what similarity could possibly exist between a sound on the one hand, and any non-auditory phenomenon on the other.” (Haiman [1985:3])

Haiman’s statement goes hand in hand with Halliday’s point of view quoted above. Language requires a certain degree of arbitrariness in order to allow for the expression of non-auditory phenomena. Otherwise, one could never express non-auditory concepts such as colours simply because they cannot be represented by sounds. The same goes for abstract concepts, impressions of other modalities (e.g. smells) and so and so forth. An association between a symbol and its referent is established through convention and ostensive definition.

In the further course of his discussion, Haiman proposed that an ideal diagram has the property of being homologous. In a homologous diagram, “not only will every point in the diagram correspond to some point in the reality depicted, but the relationships among these points will correspond to the relationships among the points in reality” (Haiman [1985:11]). He continues to break down the concept of homology into two independent concepts, namely isomorphism and motivation. He defined isomorphism as an unambiguous one-to-one correspondence between a part of a diagram, and a part in the conceptual space. By motivation he meant “the property whereby diagrams exhibit the same relationship among their parts as their referents do among their parts” (Haiman [1985:11]).

By using these definitions, Haiman unfortunately introduces a new and quite idiosyncratic terminology. Givón argues that this is neither necessary nor supported by traditional usage:

My first assumption in this paper is that a reasonable sense of “iconicity” must presuppose the notion of “isomorphism”, so that an iconic code is “an isomorphically constructed code”. In this regard, I depart slightly from Haiman’s position. Haiman posits a distinction between isomorphism and diagrammatic representation, whereby the former represents the parts within the whole but not necessarily their relationships, while the latter represents both. To me, this distinction is arbitrary and not supported by traditional usage, neither in the ‘hard’ sciences nor in philosophy (Givón [1983:188]).

In order to back his point up, Givón cites Aristotle as having said that “things are alike when, though they are not absolutely the same and though they are different individuals, they, nevertheless, have the same form” (Givón [1983:188]). In this regard, Aristotle’s characterization very much conforms with what modern dictionaries have to say:

Isomorphism: The quality or state of being isomorphic
isomorphic: Being of identical or similar form, shape, or structure


Isomorphism: See isomorphic
isomorphic: Corresponding or similar in form and relations


That is to say, the notion of isomorphism already entails a correspondence in structure, not just an agreement in the number of matching parts between signifying diagram and signified meaning. Therefore, Haiman’s newly introduced term homology is redundant and idiosyncratic, two good reasons not to use this term.

Haiman’s definition of motivation has similar problems. Historically speaking, as Haiman himself informs us, the term was coined by Saussure:

Motivation as a linguistic term was introduced by Saussure to describe compound or complex signs like the French word dix-neuf ‘nineteen’. Although the components of this word are themselves arbitrary, the compound is in contrast ‘relatively motivated’. It is necessary to emphasize Saussure’s recognition of the contrast between arbitrariness and motivation, since he gives no definition of ‘motivation’ in the Cours.” (Haiman [1985:14])

Thus, Saussure’s notion of motivation doesn’t seem to have a lot to do with Haiman’s definition of motivation quoted above which describes motivation as a property of a diagram and a “sub-property” of homology. This confusing situation begs the question of how to define the fundamental terms necessary to discuss the phenomenon with more clarity in mind. Without claim for the superiority of the following definitions, I would define the central concepts addressed so far as shown in the following table:

iconicityresemblance between form and meaning
iconsign with the property of iconicity
isomorphismresemblance in structure (parts and relationships)
diagrammatic icon, diagramicon realizing the property of iconicity through isomorphism
motivationtendency influencing the language generation process

The above definition of iconicity is meant to position this concept as the constituting property of Peirce’s icons. On the other hand, we have the property of arbitrarinesswhich I define through negating its dichotomous counterpart.

In fact, I think that the term arbitrariness is not a good choice to represent the counterpart to the notion of iconicity. I hold this view because the meaning of the term does not conform with what is usually referred to as arbitrary outside of the linguistic context:

existing or coming about seemingly at random or by chance or as a capricious and unreasonable act of will
b) based on or determined by individual preference or convenience rather than by necessity or the intrinsic nature of something


arbitrary: Based on random choice or personal whim, rather than any reason or system


While one could argue that the first of these three definitions partly fits the term’s actual use in linguistics, the other two definitions highlight the term’s relatedness to the concept of “unreasonability” or irrationality. Although it is of course possible to create arbitrary, non-iconic linguistic objects such as nonsensical words through a wilfully irrational act, this is only one way (and arguably the least frequent) of how new linguistic forms are created. Non-iconic forms could also be created through other processes such as sound change where an initially iconic form gets phonologically distorted to such a degree that the resulting form’s iconic origins can’t be identified without etymological investigations. Such a form would not be iconic (anymore) but also couldn’t be rightfully called arbitrary as there was no wilful, conscious act to influence such a development.

Following Peirce’s fundamental typology of the sign, the term symbolicity could be a more neutral way to designate the defining property of symbols, namely that the signifier does not resemble the signified due to actual arbitrariness, distortion or convention. In order not to add to the terminological confusion, I will however not insist on using this proposed alternative.

In the above table, I have defined motivation as a tendency influencing the language generation process. In other words, a specific kind of motivation influences how meanings are serialized into concrete linguistic utterances. Depending on the kind of motivation and what other motivations were involved in the language generation process, the end result will be more or less iconic and transparent or—on the other hand—symbolic, arbitrary, or opaque.

As a consequence of the above definition, in order to identify which motivations have had their share in the creation of a linguistic utterance, one has to ask for the “Why?” behind its form. What tendencies motivated the creation of an utterance? To put it differently, how can a linguistic form be explained? Investigations of this kind presume, of course, that language actually is the result of such a motivated creation process.

Since the motivational processes underlying language generation are not (and may never be) accessible to direct, causal observation, it seems evident to model them as stochastic processes. Haiman quotes a (near) universal discovered by Joseph Greenberg and then emphasizes that it is to be understood as a statistical tendency rather than an absolute law:

“In (…) Greenberg’s examples (…) we are dealing with statistical tendencies rather than ironclad immutable laws: a number of fortuitous tendencies, notably sound change, may obscure these patterns and result in paradigms in which the formal contrasts do not reflect the semantic or conceptual contrasts.” (Haiman [1985:5])

Formulating linguistic motivations as mathematical objects opens them up to quantitative analysis. Reinhard Köhler, in his introduction to a textbook about the field of quantitative linguistics, argues that because linguistic patterns hardly ever apply in all cases, they should be viewed as statistical correlations rather than deterministic laws:

“It can be shown that these properties of linguistic elements and of the relations among them abide by universal laws which can be formulated strictly mathematically in the same way as common in the natural sciences. One has to bear in mind in this context that these laws are of stochastic nature; they are not observed in every single case (this would be neither necessary nor possible); they rather determine the probabilities of the events or proportions under study. It is easy to find counterexamples to each of the above-mentioned examples; nevertheless, these cases do not violate the corresponding laws as variations around the statistical mean are not only admissible but even essential; they are themselves quantitatively exactly determined by the corresponding laws. This situation does not differ from that in the natural sciences, which have since long abandoned the old deterministic and causal views of the world and replaced them by statistical/probabilistic models.” (Köhler [2005:1])

Indeed, there have been practical attempts to utilize quantitative methods in the field of iconicity research. Holger Diessel, using logistic regression analysis, was able to demonstrate a significant correlation between clause order and the sequence of conceptual events denoted by the clauses: “Temporal clauses denoting a prior event precede the main clause more often than temporal clauses of posteriority” (Diessel [2008]). This tendency is a special case of the more general tendency of temporal motivation whose influence steers a language generation process towards producing forms with the property of temporal iconicity.

Quantitative & formalized methods of language analysis have both enemies and proponents. Haiman quotes Lewis Thomas as regretting that “people in other fields of endeavour, hankering to turn their disciplines into exact sciences, beset by what has since been called ‘physics envy’, set about converting whatever they knew into numbers and thence into equations with predictive pretensions” (Haiman [1985:257]). On the other hand, proponents such as Reinhard Köhler (quoted above) argue that by formalizing linguistic analysis, we can arrive at more precise and objective conclusions. My personal take on this issue is that although quantitative, automated methods cannot replace qualitative and causal reasoning, their results can surely help to validate the generality of tendencies one has detected through qualitative, manual analysis.

After having assimilated and tried to clarify the central concepts in the context of iconicity, it is time to discuss some more concrete examples of phenomena that are open to be interpreted as iconic. The distinction between iconicity and arbitrariness (or symbolicity) is not a binary one. Rather, there exists a whole spectrum of varying intensities of iconicity between the two extreme poles “fully iconic” and “fully symbolic”. In other words, some linguistic forms are more iconic than others.

Consequently, there exist a few cases of iconically motivated tendencies that are much less controversial than others because their motivation is so easily explained and understood. One of them, temporal iconicity, has already been introduced above. It postulates that the sequential order of language elements in a text tends to correspond with the temporal sequence of events in the conceptual domain. The most famous example of this type of iconicity was proposed by Roman Jakobson when he cited Julius Caesar’s “Veni, vidi, vici”:

“The chain of verbs-Veni, vidi, vici-informs us about the order of Caesar’s deeds first and foremost because the sequence of co-ordinate preterits is used to reproduce the succession of reported occurrences. The temporal order of speech events tends to mirror the order of narrated events in time or in rank. Such a sequence as ‘the President and the Secretary of State attended the meeting’ is far more usual than the reverse, because the initial position in the clause reflects the priority in official standing.” (Jakobson [1965])

As another more extensive example of temporally motivated iconicity, consider the following biographical text about Napoleon Bonaparte’s early life:

a) He was born Napoleone di Buonaparte in Corsica to a relatively modest family of Italian ancestry from the minor nobility. He was serving as an artillery officer in the French army when the French Revolution erupted in 1789. He rapidly rose through the ranks of the military, seizing the new opportunities presented by the Revolution and becoming a general at age 24. The French Directory eventually gave him command of the Army of Italy after he suppressed a revolt against the government from royalist insurgents.

b) He was serving as an artillery officer in the French army when the French Revolution erupted in 1789. He was born Napoleone di Buonaparte in Corsica to a relatively modest family of Italian ancestry from the minor nobility. The French Directory eventually gave him command of the Army of Italy after he suppressed a revolt against the government from royalist insurgents. He rapidly rose through the ranks of the military, seizing the new opportunities presented by the Revolution and becoming a general at age 24.

The first of these two texts is an original excerpt from the Wikipedia article about Napoleon Bonaparte while the second is the same text with a different sentence order. Notice how the original variant naturally displays temporal iconicity. Upon reading the second text, one of the first things that most readers would notice is that the event that came at the very beginning of Napoleon’s life (his birth) is not the very first thing mentioned in the linear order of the text. Another peculiarity that catches the reader’s eye is the word “eventually” in the third sentence which one would expect at the end of the narrative.

In order to preserve the temporal order of events when switching the order of the sentences around, the introduction of temporal adverbs is necessary:

c) He was serving as an artillery officer in the French army when the French Revolution erupted in 1789. Before that, he was born Napoleone di Buonaparte in Corsica to a relatively modest family of Italian ancestry from the minor nobility. The French Directory eventually gave him command of the Army of Italy after he suppressed a revolt against the government from royalist insurgents. Prior to that, he rapidly rose through the ranks of the military, seizing the new opportunities presented by the Revolution and becoming a general at age 24.

Even after having added the temporal links at the start of the second and fourth sentences, the original temporal order is not entirely reestablished. This is due to the limited scope of the temporal links which only connect the sentences in a pair-wise, consecutive manner and not across multiple sentences. In other words, we might now be able to deduce that the events described in the second sentence occurred before the events in the first sentence and those in the fourth occurred before those in the third but we can’t tell for sure whether, for example, the fourth sentence should precede the first sentence in terms of mirroring the conceptual order of events.

Of course it would be possible to further modify the text in order to reestablish the original temporal sequence of events. For example, one could start the last sentence in example c) thus: “Prior to that and after his time as an artillery officer, he rapidly (…)”. Obviously, this approach adds a lot of redundancy to the text, making the text less economic. It follows that for this example, the tendency of temporal motivation goes hand in hand with the tendency of economic motivation. The latter kind of motivation strives to steer the language generation process towards an end result that has as high an informational content as possible, among other things by eliminating redundancy.

The phenomenon of agreement between two or more motivations doesn’t seem to have been studied extensively in the literature. In the past, it seems that researchers have preferred to focus on the counterpart to agreement, namely competing motivations.

Besides being used to encode temporal relationships, the linearity of language can also be used to express other types of sequential orders such as social hierarchy, for example: “The President and the Secretary of State attended the meeting”. Temporal iconicity as well hierarchical iconicity are subtypes of the more general form of sequential or linear iconicity all of whom have in common that they rely on language’s property of linearity.

Another subtype of linear iconicity could be called conditional iconicity. Its motivational tendency states that in conditional constructs, the the condition very strongly tends to precede the conclusion: “If the children behave well, they can have some ice cream later.” One could argue whether this type of motivation is actually the same as temporal motivation because the condition usually, if not always, temporally precedes the conclusion.

Another very uncontroversial form of syntactic motivation could be expressed in the following way: More form implies more meaning. It is widely accepted that there exists an iconic relationship between the quantity of form and the quantity of meaning. Consider the following sentences:

  1. Bill’s problem grew ever bigger.
  2. Bill’s problems grew bigger and bigger.

The sentences are equivalent. The reduplication of the comparative construction in the second sentence iconically implies that some quality, in this case big, is growing in intensity over time. Additional examples are easy to find, especially in very idiomatic and fixed expressions: “the very, very big dog”, “over and over again”, “more and more”, and so and so forth.

The fact that linearity and asymmetry are fundamental properties of the linguistic form raises the question of how to represent symmetrical relationships between concepts. However, as Haiman has pointed out in an article specifically on this topic, many languages offer ways to express symmetry or at least suggest it (Haiman [1983]). Haiman identifies coordination as a means to parallelize two clauses:

  1. The further you go, the hungrier you get.
  2. If you go further, you get hungrier.

The sentences are very close to synonymity but the differ in their structures: While the first uses coordination to put the the clauses in parallel, the second uses subordination. The iconicity of the structure of the first sentence lies in the symmetry of how the two clauses are expressed. In other words, their structural symmetry is a diagrammatic icon of two parallel processes occurring simultaneously: “going further” and “getting hungrier”.

Besides the types of iconic motivation discussed above, many other kinds have been identified in the literature. Generally speaking, the classification of the different types of motivation and iconicity is still an open question. A well-structured typology of motivations would be a great help in understanding iconicity and therefore the creation of such a typology presents a very promising area of research.

To the right, a (very preliminary and incomplete) typology of motivation referred to in this text is presented. On a fundamental level, one could make a distinction between external and internal motivation.

“Though Saussure emphasized the arbitrariness of the linguistic sign, he did nevertheless recognize that ‘the sign my be relatively motivated’. Thus French dix-neuf is more motivated (is relatively less arbitrary) than vingt. If we make a distinction between two kinds of motivation, we can consider dix-neuf an example of internal motivation, as it depends on arbitrary facts internal to the language system, i.e. the signifier-signified correlations dix=‘ten’, neuf=’nine’. (…) On the other hand, we may characterize perfect onomatopoetic motivation, should it be found to exist other than as an idealized type, as ‘external motivation’.” (Du Bois [1983:344])

On the next level, the distinction between iconic and economic motivation is made. The latter refers to the theory that the length of a linguistic utterance might positively correlate with the extent to which it conveys unfamiliar information. Consequently, reduced linguistic forms might indicate economic motivation. Arguments have been made that a great deal of arbitrariness in syntactical constructs results from the interaction of multiple plausible motivations. The competition between these two motivations is one of the classic examples of competition throughout the literature.

Another type of motivation (not mentioned in the typology because I am currently struggling with the question where to put it) could be called dramaturgic motivation. Although temporal motivation is very strong and dominant, it is still a tendency and therefore subject to being overridden by others motivations in certain contexts. As an example for such a situation, consider works of fiction. From the point of view of dramaturgic effectiveness, it would often be detrimental to simply enumerate the events occurring as part of the plot in a strictly sequential fashion. In fact, an entire genre, crime fiction, relies on the suspense generated from nonlinear storytelling.

The next two levels in the typology represent the already quite concrete types of iconic motivation discussed above. As already stated above, the typology is very incomplete. This is at least partly due to the focus of this text on iconic motivation.

Summing up, iconicity designates a relationship of resemblance between the two Saussurean aspects of a sign: its form and its meaning. An icon is a special kind of sign whose appearance resembles its meaning in some way. Iconic diagrams, in turn, are a special case of iconic signs whose resemblance to its meaning is structural rather than pictorial or metaphorical (that is, in contrast to the other subtypes of iconic signs according to Peirce). Iconicity is the result of iconic motivation which is in competition or agreement with other types of motivation. The typological classification of motivational types and the investigation of their interactions during the language generation process present very interesting and useful but also challenging fields of research.


  • Diessel, Holger [2008]. Iconicity of sequence: A corpus-based analysis of the positioning of temporal adverbial clauses in English. In: J. Newman (ed.), Cognitive linguistics. de Gruyter: Berlin.
  • Haiman, John [1985]. Natural Syntax. Dordrecht: Reidel.
  • Haiman, John [1983]. Symmetry. In: J. Haiman (ed.), Iconicity in Syntax, 73-95. Amsterdam: John Benjamins Publishing Company.
  • Halliday, Michael [1977]. Ideas about Language. In: J.J. Webster (ed.), Collected Works of M.A.K. Halliday. London: Continuum.
  • Jakobson, Roman [1965]. Quest for the essence of language. Diogenes: Zurich.
  • Jowett, Benjamin [1982]: The Dialogues of Plato. New York and London: Macmillan Publishers. Available online: https://archive.org/details/dialoguesofplat01plat
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  • Peirce, Charles Sanders [1867]: On a New List of Categories. In: Proceedings of the American Academy of Arts and Sciences, Cambridge. Available online: http://www.peirce.org/writings/p32.html