The formalisation of grammatical meanings in Copenhagen structural linguistics. Some remarks.

Lorenzo Cigana
University of Copenhagen (NorS)

The aim of this outline contribution, which will receive a proper treatment elsewhere, is to describe a single piece within the broader mosaic of European Structuralism: an undercurrent of Danish structural linguistics focused on the analysis of the internal organisation of linguistic categories, in both their formal and semantic constitution. The principles of such analyses were discussed and developed within the Copenhagen Linguistic Circle. According to our hypothesis, they represent an important cohesive factor that may allow us to speak of a “Danish school” centred on this specific aspect.

This is mostly clear in the work of two main figures of the Copenhagen linguistic Circle, namely Viggo Brøndal (1887–1943) and Louis Hjelmslev (1899–1965), whose studies contributed to placing general morphology at the very heart of the Circle’s activities and interests (cf. Lejeune 1949: 126-135). Within this domain, two research directions were pursued in particular. Firstly, a semantic direction concerning the study of the so-called “fundamental meanings” (Hjelmslev: Grundbedeutungen, Jakobson: Gesamtbedeutungen)[1] of morphological categories, that is their semantic value. This direction can be related to proto-cognitivism as well as to some basic assumptions of phenomenology (namely Husserl’s theory of eidetic forms); furthermore, it reveals the presence of a Kantian undercurrent (Hjelmslev 1935, Burkard 2003, Fortis 2018: 172) possibly crossing not just German linguistics (see below) but structuralism as a whole. The second research direction concerned the formalisation of linguistic oppositions conceived as the underlying rationale of the former aspect. In this case, some elements can be highlighted that place this trend close to the general frameworks of logic and mereology, which were at the source of the Danish version of the so-called “theory of markedness” and possibly of the theory of prototypes.

We will examine these two threads more closely, connecting them to the wider panorama of European philosophical debate, before sketching a possible third thread.

Transcendental semantics towards an “empirical ontology”

As we have said, the first thread represents a semantic-oriented research direction: it aims to identify those general ideas that are said to be connected to morphological categories. This connection in itself was conceived rather differently by the two scholars mentioned above. According to Brøndal, such a connection should be regarded as generative, resembling a “deduction” in a Kantian sense: morphological categories arise from a meaningful substratum, that is, from a system of basic concepts ultimately belonging to those of traditional categorial philosophy (Jørgensen-Stjernfelt 1987) which justify their establishment on a theoretical level. As Brøndal himself stated, the aim of such a program was “to find in language those logical concepts that were elaborated by Aristotle’s philosophy up to modern logic” (cf. Brøndal 1943: Préface). This attempt intended not just to ensure a sound and rational foundation for grammar, but to reveal its underpinning and inherently logical organization, ultimately confirming the postulate of the identity between language and thought. On the other hand, according to Hjelmslev, the same connection shall not be regarded as a foundation, but as a result of a moulding of specific content-substances by linguistic forms. Under this perspective, grammatical categories receive a semantic interpretation on the basis of the so-called “hypothesis of meaningful content” (Hjelmslev 1928: 163 ff.), an operational postulate according to which the semantics of grammatical categories are to be described not as pure syntactical indexes or as a set of symbolic instructions ensuring correctness of connected speech, but have to be considered as “schematic images” (Cusimano 2012: 63 ff.), thus as meaningful wholes, conveying a specific sense and modelling our experience in a specific way.

We might summarize the two views by saying that Brøndal’s theory aimed to identify the noetic universal organization underpinning language, and could legitimately be labelled as universalistic, whereas Hjelmslev’s approach was more focused in reconstructing the linguistic, general structure of thought. Indeed, by comparing the table of grammatical categories designed by Brøndal[2] (see Fig. 1) to the one designed by Hjelmslev (see Fig. 2), and by temporarily disregarding their different orientation,[3] the proximity between the two models will stand out. Hjelmslev’s original and often misunderstood version of “localism” – stating that case-forms constitute the common ground of both spatial and logical representations (Anschauungen) and thus modulating Wüllner’s first formulation (Wüllner 1827, in Hjelmslev [1935] 1972: 42 ff.; cf. Fortis 2018: 172 ff.) into Wundt’s sense (Wundt 1904, in Hjelmslev [1935] 1972: 66) – is the result of such a research trend.

1) Symmetry direction, tendency, irreversibility Modus Imperative
double direction, balance, reversibility Subjunctive
2) Transitivity . point, moment, presupposition Aspect Perfective
.. line, duration, realisation Imperfective
3) Connexion separation, past, autonomy Tempus Preterit
× presence, now, connection Present
4) Plurality > unity, concentration, convergence Number Singular
< plurality, diffusion, divergence Plural
5) Generality θ particularity, arbitrarity Person I
o generality, universality II

Fig. 1 – Adaptation of Brøndal’s table of categories from Jørgensen-Stjernfelt (1987)


Intense (nominal) morphemes Extense (verbal) morphemes
exclusively homonexic government case persona, voice Relation

(direction, degrees of proximity, degrees of subjectivity)

exclusively heteronexic government comparison emphasis Intensity

(scalar degrees of qualities)

both homo- and heteronexic government number-gender aspect-time Consistency

(compactness, concentration, discreteness)

alternatively homo- and heteronexic government article mode Reality

(reality/unreality, desired realisation, non-realisation)

Fig. 2 – Adaptation of Hjelmslev’s table of categories (cf. Hjelmslev 1971c: 166)

However, even if such an effort in designing a “rational semantic model”[4] can be regarded as quite original given the systematic way it was carried out within a proper linguistic and comparative framework, it cannot possibly be considered specific to Hjelmslev and Brøndal: excluding the later reception of these two models,[5] and not mentioning its pure philosophical background (Aristotle and Kant), the sources of this approach can be traced back at least to Arnaud and Lancelot’s Grammaire générale et raisonnée (1660)  and to a line of scholars belonging to the German tradition of Allgemeine Sprachlehre, such as Karl Leonhard Reinhold (1757–1823), August Ferdinand Bernhardi (1769–1820), Johann Gottfried Jakob Hermann (1772–1848),[6] and including also Georg Michael Roth (1769–1817) and, later on, Jacob van Ginneken (1877–1945).

Indeed, both in Roth’s Grundriss der reinen allgemeinen Sprachlehre (1815) and in van Ginneken’s Principes de linguistique psychologique (1907), a central place is reserved for the method of justifying the categories of language on the basis of categories of thought (thus logical or psychological). In both cases, linguistic categories are said to arise from specific kinds of mental acts involving “external representation” (Roth: Darstellung) or specific forms of “adhering” to reality (van Ginneken: assent or adhésion)[7] through which the external world is organized in intentional, intersubjective experiences. Hjelmslev’s semantic analysis, given in 1934 and 1935–37, follows the same transcendental insights,[8] even if the premise is rather that linguistic forms (and not semantic ideas) are what provide the means through which noetic categorization is built up and can be analysed.

Far-reaching implications of this structural semantics trend, the elucidation of which lies beyond the aim of the present contribution, led to a change in the way the function of language is conceived: not as a mere tool for representing reality, but as the means for opening up possible scenarios and situating speakers in it, defining the very preconditions of enunciation.[9] Such a proto-pragmatist turn implies a progressive distancing from the “actantial model” that was so neatly summed up by Tesnière ([1966] 2015: § 97). Semantic analyses of linguistic categories, consistently comparable to Hjelmslev’s localistic approach, were also carried out by Paul Diderichsen (1905–1964), who worked on the general meaning of “reality” connected to the category of articles (Diderichsen [1939] 1966), and by Jens Holt (1904–1973) and Hans Christian Sørensen (1911–?), who specified the Grundbedeutung of limitation/illimitation connected to the category of grammatical aspect (cf. below).

The ultimate goal of this trend was the mapping of the “empirical ontology” linked to the general structure of linguistic forms (Hjelmslev [1939] 1971b: 141), ideally free from too blatant aprioristic biases thanks to the application of a watered-down principle of universality (cf. Roth 1815). This perspective can thus be seen as an application of Herder’s claim within the domain of empirical linguistic research: according to Herder, “the only acceptable critique of cognition was […] a Sprachkritik – a study of language that analysed the conceptual resources available in natural tongues” (Herder Metakritik, in Sämtliche Werke, XXI: 25, quoted in Benes 2008: 50).

The theory of correlative forms

The second trend will lead us to reconstruct a network of references and ideas that partially overlap with those belonging to the first, as it concerns some models of formalizing linguistic oppositions. More specifically, it is complementary to the former insofar as the semantic content of each category is said to be dependent on its internal structure. The core idea behind the models that flourished in the Thirties, and in particular Hjelmslev’s theory, is quite simple and can be summarised in the following way: (1) each linguistic unit is paradigmatically identified by its place within the system; (2) the system itself is defined as a network of oppositions; (3) the identity of each unit depends on the form of the opposition that connects (and differentiates) the unit from all the others. The effort to formalize such oppositions on the basis of a “broader-minded logic” (Jespersen 1924: 344) not only distinguishes Hjelmslev’s model from Jakobson’s and Trubetzkoy’s (Cantineau 1952), but allows for a “scholastic lineage” to become visible, connecting Hjelmslev’s (and to some extent also Brøndal’s) theory to what we could call the “second generation” Danish linguists such as Hans Jørgen Uldall, Knud Togeby, Jens Holt and Hans Christian Sørensen, whose need for a common method in general and comparative morphology led them to borrow their masters’ theories, and in some cases even to reshape them into partially different ones.

As the reader may know, Hjelmslev’s elaboration of a formalized system of opposition was tortuous to say the least and exacted a high toll on him, not just in terms of conceptual energy, but also in human relations: the later rift between him and Brøndal (Gregersen 1991, Rasmussen 1987) might have been caused by theoretical rivalry in establishing such a theory. On the one hand, Hjelmslev’s and Brøndal’s models are closely comparable (Rasmussen 1987, Cigana 2014), even if the specific geometry of correlates, that is the “extensional definition” of the two systems, does not overlap: Hjelmslev considers that each linguistic category can be established by a closed set of possible combinations of 6 terms (or 7, according to a later stage of the model), whereas in Brøndal’s version the number of terms is fixed at 6 and the possible combinations are less elastic. The details and the differences of the two models left aside, it is worth noticing that at some point of their work, the above-mentioned linguists began to draw concretely from the common set of assumptions on which both theories built, applying them in a critical way, and even adapting them according to their specific needs.

The issue of a possible scholastic tradition concerning this specific point was first addressed by van Ginneken, in a letter to Hjelmslev dated 25th September 1935.[10] Asking after certain details of a description proposed by Hjelmslev in La catégorie des cas (1935), he wondered if it could have been built upon Brøndal’s theory, which was discussed at the International Congress of Linguists (Rome, 1933). “The point is”, says van Ginneken, “that he [Brøndal] never quotes you [Hjelmslev], and since you don’t quote him either, I’ve started to think that this theory is the property of the Copenhagen’s school!”. Hjelmslev’s answer, dated 1st November 1935,[11] is just as interesting:

the system which you’re inquiring into derives indeed from Brøndal’s theory, yet its origins can be traced back to ancient grammars, since such a theory lies behind almost every grammatical model, whether implicitly or explicitly acknowledged. Fortunatov, Peškovskij, Karcevskij and Brøndal just gave a more exact formulation of it. Yet it doesn’t seem to me that the school of Copenhagen can pride itself on its property: at best, it may be said that it was the Copenhagen school that gave the finishing touches. At any rate, I guess it would be fairer to acknowledge my eminent colleague for having introduced the complete and definitive theory: it is Brøndal’s name, not mine, that you should cite in your work”.

In fact, the theories of linguistic oppositions were discussed at the meetings of the linguistic circle among a restricted number of members[12]: “During such meetings”, adds Hjelmslev, “Brøndal’s model had to reveal quickly its inadequacy in dealing with linguistic facts. I myself have tried to design a different theory which could satisfy my needs; I’m actually quite surprised to know that he still endorses that model. This answer is striking for more reasons: firstly, although quoting the Russian tradition, Hjelmslev doesn’t mention Jakobson and Trubetzkoj, who together developed the so-called “markedness-theory”,[13] a theory that competed – more or less to the same extent as Brøndal’s model – with Hjelmslev’s own, more complicated version, called “theory of participative oppositions”. At the same time, however, he gives complete credit to Brøndal for being the first in this respect. It seems as if Hjelmslev were rather intrigued by the possibility of acknowledging a “Copenhagen school” in the formalization of linguistic correlation, even if he explicitly rejects van Ginneken’s suggestion.

And indeed, something like that occurred, since Hjelmslev’s model was taken up by almost all the members of the “general grammar committee”: Jens Holt applied it in his Études d’aspect (1943: 103), by describing the internal articulation of the general category of aspect, suggesting that its distinction from the category of time; more or less the same operation was carried out by Hans Christian Sørensen in Aspect et temps en slave (1949: 101), who reformulated it, reworking the epistemological principles of glossematics; Knud Togeby, in his famous Structure immanente de la langue française (1965: 104-106, passim), assimilates the basic insights of Hjelmslev’s model with other theories, but gave a rather syncretic perspective on the morphological classifications he used. Finally, Hans Jørgen Uldall adapted it according to his own needs in the Outline of Glossematics (Uldall 1967), by overgeneralizing its reach beyond Hjelmslev’s original framework. Apart from the divergences that later made Uldall’s and Hjelmslev’s approaches incompatible, the former’s presentation allowed the epistemological underpinnings of the latter’s model to become evident. Among those, one in particular was of great importance: the principium individuationis of linguistic units (cf. Cigana & Jensen 2017: 91 ff.), which Uldall tried to harmonize with the basic assumptions of Hjelmslev’s theory of participation. The identity of linguistic units is said to be neither simply given nor fixed once for all, since it ultimately depends on the place the units come to occupy within the system. In its turn, each linguistic system exists in a state of general overlap, as the phenomena of syncretism, markedness and fusion show: due to this feature, the identity of linguistic invariants is conceived as fuzzy and permeable. In outlining the theoretical framework for this principle, Uldall draws from three sources: 1) from the notion of value given in Saussure’s Cours, 2) from a less expected analytical-aligned tradition, represented by Bertrand Russell, 3) from the philosophical debate concerning the principle of analogy, which, far from being a patent reference, lies rather in the background:

The question of identity is metaphysically thorny. Are two things ever quite the same? Is one thing ever quite the same at one moment as it was the moment before? I once had a Model T Ford which had most of its parts replaced and the rest considerably battered before I finally sold it for twelve dollars and fifty cents: was that the same car? And if not, what accounts for the continuity which there obviously was between the car I bought and the car I sold two years later? One way out is to declare firmly that all “events” are unique: the Model T at one moment is not the same as the Model T at any other moment, however short the moment elected as a unit of measurement. But if science is to be possible, it is clear that this will not do: one cannot make science out of an infinity of differences; science presupposes recognisable similarities, and similarity implies identity. Our somewhat robust definition of identity has been designed to fulfil this requirement (Uldall 1967: 52-53).

Two main ideas are brought together at this point: 1) Russell’s distinction between numerical (“absolute”) identity, which here is discarded as unattainable,[14] and qualitative (“relative”) identity or “equivalence” – which is retained, since both science and experience build upon it;[15] 2) the mechanism of analogy (“similarity”) that can explain how identifications are carried out both in science (by consciously taking into account only the relevant features or connections of a given entity) and in experience (by unconsciously selecting or excluding relevant features or qualia of a given entity). This reference is of no secondary significance, since it represents a necessary prerequisite of Hjelmslev’s theory of linguistic oppositions and consequently of all the above-mentioned versions that draw from it. This prerequisite states that each invariant (linguistically pertinent unit) has to be conceived as articulated into a set of variants or “qualities” (such as particular meanings for content-units, or phonetic occurrences, for expression-units)[16] which can be shared by the invariants themselves, generating overlapping forms.

Sketches for an open conclusion: beyond (or behind) the Copenhagen school

As we have seen, at the bottom of this theoretical nexus lies the idea according to which linguistic functioning is grounded on a web of qualitative identities conditioned by the same mechanism that governs analogical thinking. Yet, by following the line of the “school inheritance”, that is the theory of linguistic oppositions passed down from maîtres to pupils, another line becomes patent, which goes outwards and connects the mentioned “school” to a wider network of scholars in the domains of epistemology and social sciences. This network includes among others Harald Høffding (1843–1931), mediating by Svend Ranulf (in his turn a very interesting figure),[17] Émile Meyerson (1859–1933), Lévy-Bruhl (whose definition of “prelogism” was of course of paramount importance in this respect), but also more sociologically oriented scholars such as Alf Ross (1899–1979) and Ferdinand Tönnies (1855–1936). What allows all these names to be brought together is not just the fact that (scattered) references to their thought are attested across the works of the linguists mentioned above, but mostly the presence of a common factor in their reflexion: the functioning of analogical thinking (Høffding, Meyerson, Ranulf) as the subconscious rationale which governs not only cognitive operations but also the most elementary forms of social aggregation (Lévy-Bruhl, Ross, Tönnies).

The double line that we have sketched here, concerning the discussion on the semantic and formal constitution of linguistic categories, is just a thread of a broader tapestry we would gladly discuss further. Indeed, the reconstruction of the full network of possible influences, reception or simple references that ties together the Danish linguists and their European contemporaries still lies ahead of us; yet it’s a task that has to be carried out in order to evaluate structuralism in all its facets.


Ablali, D. (2017), “Louis Hjelmslev en toutes lettres : éléments de réponse au projet glossématique inachevé avec Uldall dans des lettres à Martinet, Jakobson, Benveniste et quelques autres”, in Chepiga, V. & Sofia, E. (eds.), La correspondance entre linguistes. Un espace de travail, Académia L’Harmattan, Louvain-La-Neuve: 65-85.

Benes, T. (2008), In Babel’s Shadow: Language, Philology and the Nation in Nineteenth-Century Germany, Detroit, Mich., Wayne State University Press.

Benveniste, É. (1970), “L’appareil formel de l’énonciation”, Langages, 87: 12-18.

Brøndal, V. (1943), Essais de linguistique générale, E. Munksgaard, Copenhagen.

Burkard, T. (2003), “Die lateinische Grammatik im 18. und frühen 19. Jahrhundert. Von einer Wortarten- zu einer Satzgliedgrammatik. Ellipsentheorie, Kasuslehre, Satzglieder, in Germania Latina – Latinitas Teutonica. Politik, Wissenschaft, humanistische Kultur vom späten Mittelalter bis in unsere Zeit, Eckhard Keßer & Heinrich C. Kuhn (eds), 781-830, Munich, Wilhelm Fink.

Cantineau, J. (1952), “Les oppositions significatives”, Cahiers Ferdinand de Saussure, 10: 11-40.

Cigana, L. (2014), La nozione di “partecipazione” nella Glossematica di Louis Hjelmslev / La notion de “participation” dans la glossématique de Louis Hjelmslev, thèse de doctorat en cotutelle (Università della Calabria, Université de Liège).

Cigana, L. (2016), “Analogia, paralogia e prelogismo. Svend Ranulf e il pensiero antico”, Janus. Quaderni del Circolo glossematico, 14: 43-70.

Cigana, L. (2017), “At the crossroad between psychology, phenomenology and linguistics: van Ginneken’s notion of « assent », Acta Structuralica. International Journal for Structuralist Research, Special Issue 1: 115-149.

Cigana, L. & Jensen, V. B. (2017), “Glossématique par correspondence. Hjelmslev et ses interlocuteurs (Martinet et Bazell)”, in Chepiga, V. & Sofia, E. (eds.), La correspondance entre linguistes. Un espace de travail, Académia L’Harmattan, Louvain-La-Neuve: 85-129.

Cusimano, C. (2012), La sémantique contemporaine. Du sème au theme, Paris, PUPS.

Fortis, J.-M. (2018), “Anderson’s case grammar and the history of localism”, in Böhm, R. & van der Hulst, H. (eds), Substance-based Grammar – The (Ongoing) Work of John Anderson, John Benjamins.

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Gregersen, F. (1991), Sociolingvistikkens (u)mulighed

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Hjelmslev, L.  (1971b), “La structure morphologique” [1939], in Hjelmslev 1971a: 122-147.

Hjelmslev, L. (1971c), “Essai d’une théorie des morphèmes” [1938], in Hjelmslev 1971a: 161-173.

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Hjelmslev, L (1985b), “Structure générale des corrélations linguistiques”, in Hjelmslev 1985a: 25-66.

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Diderichsen, P. [1939] (1966), “Realitet som grammatisk Kategori”, in 1966, Helhed og Struktur. Udvalgte Sprogvidenskabelige Afhandlinger, Copenhagen, GECGADS Forlag: 31-51.

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[1] Cf. Jakobson (1971 : 23): “Die Frage der Gesamtbedeutungen der grammatischen Formen bildet naturgemäß die Grundlage der Lehre von dem grammatischen System der Sprache”.

[2] Even if it was never fully and consistently fleshed out by Brøndal himself (cf. Jørgensen & Stjernfelt 1987).

[3] Going from logical concepts to linguistic meanings, in one case; going from linguistic forms to concepts, in the other.

[4] One of Brøndal’s most important works is the Theory of prepositions. Introduction to a rational semantics (Præpositionernes Theori. Indledning til en rationel Betydningslære, 1940, published in French in 1950).

[5] For example, Jens Holt (1904–1973) produced a Rationel Semantik (Pleremik), published in 1946.

[6] See Benes (2008: 49 ff.)

[7] See Cigana (2017).

[8] As is clearly denoted by the use of the term Anschauung, directly borrowed from a Kantian theoretical framework and denoting the “ideas” linked to morphological categories.

[9] Or its formal apparatus, as Benveniste has it (Benveniste 1970).

[10] The French original, quoted in Rasmussen 1987 and Ablali (2017), and is deposited in Hjelmslev’s archives at the Royal Library of Copenhagen.

[11] The original letter, in French, is deposited in Hjelmslev’s archives at the Royal Library of Copenhagen (cf. Rasmussen 1987 and Ablali 2017).

[12] A possible reference to the “comité de grammaire générale” instituted in 1931 within the Linguistic Circle (cf. Bulletin du Cercle linguistique de Copenhague, 2, 1935: 13-15).

[13] He gave a quite thorough account of it in the paper “Structure générale des corrélations linguistiques” (cf. Hjemslev 1985b), though.

[14] Cf. “The belief in absolute identity seems to me a piece of superfluous mysticism – harmless if it is not allowed to prey on the mind, but bearing the seeds of dark and hideous insanity” (Uldall 1967: 54 [53, n. 1]).

[15] Uldall’s inclusion of such distincion in the domain of semiotics and linguistics thus precedes the treatment by J. L. Prieto, cf. Cigana & Jensen 2017: 95.

[16] For instance, in Latin, the particular meanings “instrumental”, “locative”, “causal”, etc. are conceived as variants of the corresponding invariant, the “ablative” (cf. Hjelmslev 1935).

[17] Cf. Cigana 2016.

How to cite this post

Cigana, Lorenzo. The formalisation of grammatical meanings in Copenhagen structural linguistics. Some remarks. History and Philosophy of the Language Sciences.

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