Isomorphism, the one and many

Lecture by Hendrik De Smet (KU Leuven).


The isomorphic principle maintains that languages maximally preserve one-to-one correspondences between meaning and form. In historical linguistics, explanations of language change in terms of homonymy avoidance, synonymy avoidance or ambiguity avoidance all more or less explicitly hark back to the isomorphic ideal. However, though soundly rooted in Structuralist and Functionalist theory, isomorphic thinking has received major criticism in recent decades. Variation is now generally considered pervasive and often stable in language, rather than a fleeting anomaly. This makes the workings of isomorphism seem inconsistent and its use as an explanation of change gratuitous. Moreover, some changes are strikingly un-isomorphic (De Smet et al. 2018). It has even been argued that many-to-many correspondences between meaning and form offer functional advantages (Van de Velde 2014).

In this talk, I want to reassess the value of the isomorphic principle. Although it needs to be recognized that violations of isomorphism exist and may indeed make good functional sense in their own right, there also remains strong and independent evidence in support of the isomorphic principle, not only from historical linguistics but also from language acquisition and animal communication. This evidence suggests that the isomorphic principle is not so much ill-conceived, as at times misunderstood. What is needed, therefore, is a better understanding of the nature of isomorphism and the conditions under which it operates. The following three principles are proposed.

First, isomorphism interacts with how the meaning side of the linguistic sign is organized. It is generally accepted that meanings are organized around a prototypical core sense, from which peripheral senses are derived (e.g. Geeraerts 1997; Evans 2005). It is proposed here that isomorphic pressure is stronger for core senses than for peripheral senses. This predicts that signs will mostly enter into variation over their peripheral senses. For example, in he was upset with the verdict the preposition with is used in one of its peripheral senses and competes with at, about and over; but in its core comitative and instrumental senses, as in she opened the envelope with a knife, competition with other prepositions is almost non-existent.

Second, meanings are often coded redundantly in the syntagm. For example, in this man walks into a bar the number of the subject is coded three times, first by this, then in man (as opposed to men), and finally by the -s ending on walks. This type of redundancy is a design feature of nearly all communicative codes because it safeguards communication against the inevitable ‘noise’ of the environment. For example, Shannon (1948) famously estimates English prose as being 50% redundant. Although redundancy is an apparent violation of isomorphism, syntagmatic redundancy can also be regarded as an extension of the formal side of the sign and, thereby, as a way of sustaining polysemy. This principle can be expected to play out in semantic change: polysemy in a sign can be diachronically stable as long as the context of the sign offers sufficient clues for disambiguation.

Third, signs also maintain paradigmatic relations, which are generally believed to keep meanings in check through contrast. However, while paradigmatic relations can in principle enforce isomorphism, they vary in strength. It is proposed that contrast depends crucially on the salience of a ‘choice point’. Choice points are salient if they are structurally embedded and if they can be anticipated. This, among other things, predicts that systemic redundancy (where a language develops competing forms to express the same meaning) typically arises from semantic change outside choice points, in non-competitive structural niches. For example, English deontics have to develop primarily in contexts in which deontic must or shall not occur.

In sum, it is the structural organization of language that largely dictates where and how isomorphism can exert its influence.


De Smet, H., F. D’hoedt, L. Fonteyn, & K. Van Goethem. 2018. The changing functions of competing forms: Attraction and differentiation. Cognitive Linguistics 29(2): 197-234.

Evans, V. 2005. The meaning of time: Polysemy, the lexicon and conceptual structure. Journal of Linguistics 41: 33-75.

Geeraerts, D. 1997. Diachronic prototype semantics: A contribution to historical lexicology. Oxford: Oxford University Press.

Shannon, C.E. 1948. A mathematical theory of communication. The Bell System Technical Journal 27: 379-423.

Van de Velde, F. 2014. Degeneracy: The maintenance of constructional networks. In R. Boogaart, T. Colleman & G. Rutten (eds), Extending the scope of construction grammar, 141-179. Berlin: De Gruyter.


Hendrik De Smet er lektor i engelsk sprogvidenskab ved universitetet i Leuven. En af hans primære forskningsinteresser er historisk lingvistik på et funktionelt og kognitivt grundlag, og han forsker særligt i mekanismerne i sprogforandring (bl.a. inferens, analogi og priming) og grammatikalisering. Hendrik De Smet har skrevet om bl.a. reanalyse og aktualisering, produktivitet, konkurrence og den individuelle sprogbrugers rolle i sprogforandring. Blandt hans øvrige forskningsengagementer er korpusopbygning og -udvikling og formidling af sprogvidenskabelig viden.