Apropos of the preceding post, a theoretical aperçu is in order by way of explication for those readers who have an appetite for such things.

A diagram is AN ICON OF RELATION. Diagrammatic correspondences between form (expression) and meaning (content) are instantiations of the principle of ISOMORPHISM. There is a fundamental sense in which isomorphism can be said to pervade the structure of language, namely, the sense in which rules at the core of grammar are not merely statements of regularities but are coherent. The notions associated with the terms ‘rule’ and ‘coherence’ need to be discussed separately.

Although the concept of rule was not prominent among the theoretical advances of the early European structuralists, it is nonetheless clear that its ubiquitousness today owes much to an understanding of grammatical relations as patterning and regularity that goes back to pre-war discussions (principally in Prague and Copenhagen) of the foundations of linguistic theory. What is missing from both pre- and post-war theorizing, however, is the notion of the coherence of linguistic relations, and as a corollary, the precise means whereby coherence is to be expressed in the practice of linguistic description.

All along, the potential for making coherence an explicit principle in the understanding of language structure existed unexploited among the many overt achievements of early structuralism, specifically in the idea of MARKEDNESS. Coherence obtains when rule relations signify the mirroring of markedness values across content and expression levels, or between different aspects of expression (as in the case of some morphophonemic congruences). The latter case––an automorphism––is the focus here. Since patterning is present at all levels of grammar, to the extent that the rules of language structure expressing this patterning reflect congruences of markedness values, we can attribute their coherence (their raison d’être) to such cohesions. What is more, we can do this uniformly in virtue of the isomorphism of grammar as a whole. Nothing proves the validity of this universal notion of coherence better than the evidence of linguistic  change. The drift  of a language involves the actualization of patterns that are coherent in just this sense, and the rejection of those that are not.

Rules are more than mere generalized formulas of patterns when they embody specifications of coherence between linguistic elements, namely, cohesions between units and contexts. This criterion of rule coherence remains true and valid but practically vague without the necessary involvement of markedness, because it is markedness that provides the explicit means of expressing coherence. While there may be several goals of language change, the overarching telos of linguistic change is the establishment of a pattern––not just any pattern but specifically the semeiotic kind Peirce called a diagram. Since diagrams are panchronic signs, it is not surprising that they subtend both linguistic synchrony and linguistic  diachrony. Diagrammatization can be seen as one species of the process by which unconformities in language are reduced or eliminated over time. These dynamic tendencies can be couched in structuralist terms: system is brought into conformity with type, while norms are brought into conformity with system.

Diagrams and diagrammatization in language are states, resp. processes, whereby relations mirror relations, as between form and content (isomorphism) or between form and form (automorphism). They are states in synchrony and real tendencies in diachrony. As a corollary, all language states are the cumulative results of preceding states (ontogeny recapitulating phylogeny). Moreover, there is no telos in language “beyond” diagrammatization: (1) conformity to a pattern is diagrammatic in itself; and (2) language conforms to nature by diagrammatizing content in form. (These two positions effectively put an end-­stop to the Cratylistic debate.)