Louis Hjelmslev in the context of "Neurobiology"

The idea of language as a linguistic system appears in the linguistic theory of Ferdinand de Saussure, J.R. Firth, Benjamin Lee Whorf, Louis Hjelmslev, and Michael Halliday.

The paradigmatic principle - the idea that the process of using language involves choosing from a specifiable set of options - was established in semiotics by Saussure, whose concept of value (viz. “valeur”), and of signs as terms in a system, “showed up paradigmatic organization as the most abstract dimension of meaning”

Structural linguistics, or structuralism, in linguistics, denotes schools or theories in which language is conceived as a self-contained, self-regulating semiotic system whose elements are defined by their relationship to other elements within the system. It is derived from the work of Swiss linguist Ferdinand de Saussure and is part of the overall approach of structuralism. Saussure's Course in General Linguistics, published posthumously in 1916, stressed examining language as a dynamic system of interconnected units. Saussure is also known for introducing several basic dimensions of semiotic analysis that are still important today. Two of these are his key methods of syntagmatic and paradigmatic analysis, which define units syntactically and lexically, respectively, according to their contrast with the other units in the system. Other key features of structuralism are the focus on systematic phenomena, the primacy of an idealized form over actual speech data, the priority of linguistic form over meaning, the marginalization of written language, and the connection of linguistic structure to broader social, behavioral, or cognitive phenomena.

Structuralism as a term, however, was not used by Saussure, who called the approach semiology. The term structuralism is derived from sociologist Émile Durkheim's anti-Darwinian modification of Herbert Spencer's organic analogy which draws a parallel between social structures and the organs of an organism which have different functions or purposes. Similar analogies and metaphors were used in the historical-comparative linguistics that Saussure was part of. Saussure himself made a modification of August Schleicher's language–species analogy, based on William Dwight Whitney's critical writings, to turn focus to the internal elements of the language organism, or system. Nonetheless, structural linguistics became mainly associated with Saussure's notion of language as a dual interactive system of symbols and concepts. The term structuralism was adopted to linguistics after Saussure's death by the Prague school linguists Roman Jakobson and Nikolai Trubetzkoy; while the term structural linguistics was coined by Louis Hjelmslev.

Syntactic Structures is a seminal work in linguistics by American linguist Noam Chomsky, originally published in 1957. A short monograph of about a hundred pages, it is recognized as one of the most significant and influential linguistic studies of the 20th century. It contains the now-famous sentence "Colorless green ideas sleep furiously", which Chomsky offered as an example of a grammatically correct sentence that has no discernible meaning, thus arguing for the independence of syntax (the study of sentence structures) from semantics (the study of meaning).

Based on lecture notes he had prepared for his students at the Massachusetts Institute of Technology in the mid-1950s, Syntactic Structures was Chomsky's first book on linguistics and reflected the contemporary developments in early generative grammar. In it, Chomsky introduced his idea of a transformational generative grammar, succinctly synthesizing and integrating the concepts of transformation (pioneered by his mentor Zellig Harris, but used in a precise and integrative way by Chomsky), morphophonemic rules (introduced by Leonard Bloomfield) and an item-and-process style of grammar description (developed by Charles Hockett). Here, Chomsky's approach to syntax is fully formal (based on symbols and rules). At its base, Chomsky uses phrase structure rules, which break down sentences into smaller parts. These are combined with a new kind of rules which Chomsky called "transformations". This procedure gives rise to different sentence structures. Chomsky stated that this limited set of rules "generates" all and only the grammatical sentences of a given language, which are infinite in number (not too dissimilar to a notion introduced earlier by Danish linguist Louis Hjelmslev). Although not explicitly stated in the book itself, this way of study was later interpreted to have valued language's innate place in the mind over language as learned behavior,

The Copenhagen School is a group of scholars dedicated to the study of linguistics, centered around Louis Hjelmslev (1899–1965) and the Linguistic Circle of Copenhagen (French: Cercle Linguistique de Copenhague, Danish: Lingvistkredsen), founded by him and Viggo Brøndal (1887–1942). In the mid-twentieth century, the Copenhagen school was one of the most important centres of linguistic structuralism, together with the Geneva School and the Prague School. In the late 20th and early 21st centuries, the Copenhagen school's approach to linguistics has evolved from purely structural to functionalist, culminating in Danish functional linguistics—which, despite the "functional" moniker, nonetheless incorporates many insights from the founders of the Linguistic Circle.

Johannes Trolle Hjelmslev (Danish: [ˈjelˀmsle̝w]; 7 April 1873 – 16 February 1950) was a mathematician from Hørning, Denmark. Hjelmslev worked in geometry and history of geometry. He was the discoverer and eponym of the Hjelmslev transformation, a method for mapping an entire hyperbolic plane into a circle with a finite radius.He was the father of Louis Hjelmslev.

Originally named Johannes Trolle Petersen, he changed his patronymic to the surname Hjelmslev to avoid confusion with Julius Petersen. Some of his results are known under his original name, including the Petersen–Morley theorem.

Hans Jørgen Uldall (Danish: [hænˈɕɶɐ̯ˀn̩ ˈulˌtɛˀl]; 25 May 1907 Silkeborg, Denmark – 29 October 1957 Ibadan, Nigeria) was a Danish linguist known for developing the linguistic theory of glossematics with Louis Hjelmslev.

In linguistics, glossematics is a structuralist theory proposed by Louis Hjelmslev and Hans Jørgen Uldall. It defines the glosseme as the most basic unit of language.

Hjelmslev and Uldall eventually went separate ways with their respective approaches. Hjelmslev's theory, most notably, is an early mathematical methodology for the analysis of language which was subsequently incorporated into the analytical foundation of current models of functional–structural grammar such as Danish Functional Grammar, Functional Discourse Grammar and Systemic Functional Linguistics. Hjelmslev's theory likewise remains fundamental for modern semiotics.