The idea of continuity, or unbrokenness, which is the leading idea of the differential calculus and of all the useful branches of mathematics, plays a very great––if covert––part in all scientific thought, not least in linguistic theorizing. Mathematics, despite its fundamental allegiance to purity and the ideal, is also an observational, experimental science of diagrammatic thought. When language is viewed as a patterned system of cognized relations, the method of investigating the pattern comes close in spirit to mathematical reasoning. This is particularly true when the relations are understood to be points on a continuum, similar to the “cuts” a topological analysis would identify in the mathematics of spatial relations. Linguistic oppositions are analogous to such “cuts” because they are simultaneously discrete and mutually contingent points along the form/content continuum that informs all language structure. Such points, when cumulated, are equivalent to the inventory of linguistic categories in any natural language. While oppositions are based on the idea of mutual exclusivity, in language (as distinct from logic) they are to be understood fundamentally as reintegrated in language use and language history by their inherence in a continuum where gradience or contrast subsists alongside polarity.
Markedness is a formal universal, a property of all oppositions in language, which superimposes a value system on the network of oppositions in language. Markedness theory investigates the interaction between the form and the substance of linguistic oppositions, and it is this dual focus that binds the theory to the idea of continuity in the mathematical sense.
A “topological” approach to language structure inspired by Jakobson’s articulation of the affinities between mathematical reasoning and the conceptualization of grammatical relations––by the language user as well as the language analyst––is embedded in the framework of a linguistic theory that takes the form of meaning, i.e., markedness, to be the key to the understanding of language structure.
All contemporary linguistic theorizing is structural in the sense of this conception of language as a system of patterned relations. This means that whether they acknowledge their debt to Jakobson explicitly––as Chomsky and Halle did by dedicating their Sound Pattern of English to their teacher––or work unwittingly in the paradigm established for all subsequent investigations of language structure by Jakobson’s seminal “Russian Conjugation” essay (1948), all contemporary practitioners of mainstream linguistics are essentially working in the Jakobsonian mode.