The Origins of Arbitrariness in Language

Human language exhibits mainly arbitrary relationships between the forms and meanings of words. Why would this be so? In this paper I argue that arbitrariness becomes necessary as the number of words increases. I also discuss the effectiveness of competitive learning for acquiring lexicons that are arbitrary in this sense. Finally, I consider some implications of this perspective for arbitrariness and iconicity in language acquisition. A Language Design Task Imagine you are inventing a language. It should associate signals (“forms”) that can be produced and perceived by the users of the language with perceptual or motor categories (“meanings”). Assume that both forms and meanings are patterns of values across sets of dimensions and that you have been given the form and meaning dimensions. Assume further that the specific design task includes a set of meaning categories that need to get reliably conveyed. That is, given a particular pattern across the meaning dimensions, if it belongs to one of the given set of categories, a user who knows the language should be able to assign a form to it, that is, an appropriate pattern across the set of form dimensions. Similarly, given a pattern across the form dimensions, if it belongs to one of the set of form categories that you have built into your language, a user who knows the language should be able to assign a meaning to it. Furthermore, the form assigned to an input meaning should be the “right” form; that is, the form that gets output should pass the comprehension test in the reverse direction. Providing this form to a user who knows the language should result in an output meaning that is at least closer to the original meaning than to any of the other meaning categories. In the same fashion, the meaning assigned to an input form should pass the production test in the reverse direction. Your language is not hard-wired into a user; it must be learned through a series of presentations. A presentation consists of a pairing of a form and a meaning selected randomly from the set of possible form-meaning pairs that are built into the language, with a small amount Note that in this sense, these simple languages deviate from human languages, which permit multiple forms for the same meaning and multiple meanings for the same form. But the constraint has to roughly hold for communication to get off the ground, and young children learning language seem to behave as though it does (Markman, 1989). of noise added to both the form and the meaning. Two constraints that you need to consider in your design are ease of learning and ease of storage. Each user has finite resources for learning and storage, and there is an advantage to languages that are learned with fewer presentations. The main issue of concern in this paper is how the solution to a language design task of this type is constrained by the number of distinct meanings that are to be conveyed by the language. I will argue that there are advantages to languages with systematic relationships between forms and meanings and advantages to languages without such systematicity. I will then discuss how competitive learning fares at learning both types of languages. Finally I will discuss the implications for acquisition and evolution of human language. Iconicity and Arbitrariness How Iconicity Can Help Learning the association between forms and meanings can be facilitated if there is a systematic relationship between the patterns. A simple example of such a relationship is a correlation between the values on a form dimension and a meaning dimension. There are two possibilities for where such a correlation might come from. One is for it to be based on a natural relationship between the two dimensions, for example, if they are the same dimension at a more abstract level. Such relationships are familiar in human language from onomatopoeia, in which form imitates meaning on one or more acoustic/auditory dimensions, for example, pitch. Examples of this type are more common in sign languages, where a movement of the hand in signing space may represent a physical movement of some object in meaning space. A further possibility is for the relationship between the correlating dimensions to be completely arbitrary, or at least opaque to the users. In some sign languages, for example, American Sign Language and Japanese Sign Language, movement towards or away from the head represents the gain or loss of knowledge: learning, remembering, forgetting. But the motivation for the association between the form and meaning dimensions in this case would require that the user know that knowledge is in some sense in the head. Thus the relationship between the form and meaning dimensions in this case could be viewed as arbitrary by a particular learner, though the learner might still notice the systematicity of the relationship, that is, that within this set of signs the head represents the location of knowledge. These kinds of systematic relationships between form and meaning are referred to as iconicity. I’ll return to the topic of iconicity and arbitrariness, the absence of iconicity, in human language later in the paper. In an iconic language, there is less to learn than in a purely arbitrary language, so learning should be faster and require less storage. This is easily seen by imagining a language with five meanings to be conveyed and a single dimension each for form and meaning. An arbitrary language would require storing separately each of the five form-meaning pairs of values on this dimension, but a completely iconic language with a perfect correlation between the dimensions would only require a single value, a correlation of 1.0. This is illustrated in Figure 1. Figure 1: Arbitrariness and iconicity. Two simple languages, each with one form and one meaning dimension and five meanings to be conveyed. Noisy form-meaning pairs are indicated by circles in form-meaning space. In an arbitrary language, there is no correlation between form and meaning. In a perfectly iconic language, form and meaning correlate. Iconicity can play a further role in the comprehension of the language. If an unknown or poorly learned form is presented in the presence of constraints on the possible meanings for the form, for example, if several candidate meanings are present, then iconicity can add further constraints. For example, if a user of a language knows that loudness in forms that refer to emotions tends to correlate with the strength of the emotion referred to, then for a particularly loud novel form, the user can eliminate candidate emotions that are mild. How Iconicity Can Interfere However, this advantage of iconicity should decline as the number of meanings to be associated with forms increases. Increasing the number of form-meaning pairs causes the average distance between these pairs in formmeaning space to decrease. Because of the noise that is part of form and meaning patterns, each form-meaning association occupies a region of the space. In other words, as the number of form-meaning pairs increases, the likelihood that the form regions for two different pairs share the same meaning (synonymy) or that the meaning regions for two different pairs share the same form (ambiguity) increases. Obviously both sorts of overlap can interfere with communication; a noisy form pattern might get assigned to more than one meaning category, for example. They also interfere with learning; it will be more difficult to make the proper associations if forms or meanings are sometimes ambiguous. Now consider how iconicity affects the likelihood of these sorts of overlap. Because iconicity constrains the possible form-meaning associations, it results in a narrowing of the space. This is illustrated in Figure 2. If we imagine the fixed set of meanings that are to be conveyed in the language as non-overlapping channels in the form-meaning space, then the possible forms for each can be viewed as circles (or hyperspheres in spaces of more dimensions) that can be slid back and forth in the channels, resulting in different languages. If we arrange two of these circles so that a portion of one is above a portion of another, we have the sort of overlap that represents ambiguity. There are obviously more ways to arrange the circles and avoid ambiguity in an arbitrary language like the one on the left than there are in a highly iconic language like the one on the right.