Hjelmslev’s Univocity

by Beth Metcalf

 

Deleuze and Guattari describe the isomorphism, but never a correspondence, between content and expression.  By ‘isomorphism’ they mean there is the same kind of structural relation for both content and expression.  However, there is no ‘correspondence’, that is, there is no resemblance, conformity, or causal connection between these two independent and heterogeneous lines.  Only this univocity of isomorphism without correspondence can reach real difference, real distinction.  Double articulation is the heterogeneous distribution of content and expression that differentiates real distinction on a stratum.  It must not be confused with form and substance differentiated without real distinction (since substances are nothing other than homogeneously formed matter).

 

(A Thousand Plateaus 44)  “There is never correspondence or conformity between content and expression, only isomorphism with reciprocal presupposition.  The distinction between content and expression is always real, in various ways, but it cannot be said that the terms preexist their double articulation.  It is the double articulation that distributes them according to the line it draws in each stratum, it is what constitutes their real distinction.  (On the other hand, there is no real distinction between form and substance, only a mental or modal distinction: since substances are nothing other than formed matters…)”.   

   

Saussure presented his bond between ‘signified’ and ‘signifier’ as an attempt to break with the traditional notion of language as a correspondence between words and things.  He thought he had found an isomorphism without correspondence (since correspondence between signifier and signified was thought to be arbitrary).  However, Deleuze and Guattari see Saussure as still stuck in a conceptual isomorphism that reduces everything to a single closed stratum.  Deleuze and Guattari say (ATP 71-2), “….The system of the strata thus has nothing to do with signifier and signified, base and superstructure, mind and matter.  All of these are ways of reducing the strata to a single stratum, or of closing the system in on itself by cutting it off from the plane of consistency as destratification….”  Saussure’s sign is isomorphism between signified and signifier.  But Deleuze and Guattari see this isomorphism as not without correspondence.  They see Saussure’s isomorphism as merely another way of finding correspondences of already formed matters.

 

Saussure claims that the arbitrary correspondence of sound-image (signifier) with concept (signified) produces language as a form and not a substance.  However, Deleuze is saying that Saussure is unaware his ‘form’ already informs matter.  Saussure’s form of language, then, is a substance that reaches no real distinction between form and matter (since substance is nothing other than formed matter).  Although Saussure thought his sign was an “arbitrary” bond between signified and signifier, he still unconsciously correlated this sign with a referent (a structure of formed matter) that was not arbitrary.  An already formed substance may have the variability of a stratum.  However, it does not reach the intensive differential relation of the Idea which (D&R173) “….integrates variation, not as a variable determination of a supposedly constant relation (‘variability’) but, on the contrary, as a degree of variation of the relation itself (‘variety’).…If the Idea eliminates variability, this is in favour of what must be called variety or multiplicity.”  Saussure’s overcoding of form and matter never reaches this variety of real distinction.  Diagram 1 shows Saussure’s Semiology of isomorphism (conceptual variability) bringing form and matter, signified and signifier, into correspondence.  Saussure’s is isomorphism with correspondence, because he remains within formed matter differentiated only by opposition and negation.  (See Diagram 1.)

      

Deleuze and Guattari (ATP70) tell us that the abstract machine developed on the plane of consistency is not an undifferentiated aggregate of unformed matters (black night), nor is it a chaotic differentiation of formed matters (white night).  Deleuze says that real ‘difference’ has nothing to do with that Representational alternative.  Rather, in order to reach the univocity of difference, we must find that sub-representative field of unformed matter that is, nonetheless, differentiated.  But how do we reach this sub-representataive field?  Deleuze and Guattari tell us that Hjelmslev found a way.  Instead of the form-content duality (where ‘content’ is merely substance as already formed matter), Hjelmslev reaches a sub-representative plane of unformed matter (Purport).  This plane is every really distinct differentiation of unformed matter.  The isomorphism of content and expression remain in touch with this plane of unformed differentiation. Hjelmslev reaches heterogeneity of content and expression without correspondence.  He does this by cutting across the Representational divisions of form and substance with the heterogeneous differentiation that remains open to unformed Purport.  Hjelmslev escapes the white night/black night alternative by reaching the really distinct differentiation of absolutely deterritorialized (unformed) matter.  Hjelmslev reaches isomorphism (in touch with the real-formal distinction of ontological unity) without correspondence (without the homogeneity of form and matter, signifier and signified).  Hjelmsev reaches the heterogeneity of content and expression that differentiate all forms of real distinction.  All really distinct forms are isomorphic distribution.  Yet there is no prior correspondence between the really distinct heterogeneities of content and expression.

 

Hjelmslev (ATP 43-4) is called “The Danish Spinozist geologist” who analyzes the stratification of language.  Hjelmslev’s ‘net’ involves the notions of matter, content and expression, form and substance (See Diagram 2).  This breaks with the traditional form-content duality where content is nothing other than substance (i.e. already formed matter). 

 

Saussure cannot escape an isomorphic structure of conceptually formed matter with correspondences (form and substance, signifier and signified).  Deleuze and Guattari show us Hjelmslev’s univocity of isomorphism without correspondence.  Univocity reaches the differentiation of unformed matter.

 

Deleuze and Guattari write (ATP108),  “As Hjelmslev notes an expression is divided, for example, into phonic units in the same way a content is divided into social, zoological, or physical units (“calf” divides into young-bovine-male).  The network of binarities, or arborescences, is applicable to both sides.  There is, however, no analytic resemblance, correspondence, or conformity between the two planes.  But their independence does not preclude isomorphism, in other words, the existence of the same kind of constant relations on both sides.  It is by virtue of this type of relations that linguistic and nonlinguistic elements are inseparable from the start, despite their absence of correspondence.  The elements of content give the interminglings of bodies clear contours at the same time as the elements of expression give the noncorporeal expressed a power of sentencing or judgment.”  

 

Therefore, we see why Deleuze and Guattari call Hjelmslev “Spinozist”.  Hjelmslev's heterogeneity of 'content' and 'expression' is the parallelism of Spinoza’s ‘attributes’.  Hjelmslev's 'form of content' and 'form of expression' is the parallelism of Spinoza's 'powers' opening a transversality across the forms. (See my article 'Parrallelism and the Syntheses'.)  Hjelmslev reached the arbitrary relation between linguistic form (as sign function of the reciprocal presupposition between content and expression) and the unformed Purport.  He reached the isomorphic distribution of formal-real distinction each time.  But there is no correspondence of a form to a referent (an already formed purport). 

 

Spinoza’s Substance is Hjelmslev’s unformed matter or “amorphous Purport”.  Spinoza’s ‘attributes’ are Hjelmslev’s ‘content’ and ‘expression’.  Spinoza’s ‘powers’ are Hjelmslev’s ‘form of content’ and ‘form of expression’.  Spinoza’s univocity is real distinction in ontologically singular Substance.  Hjelmslev finds the real-formal distinction of double articulation and projects this onto the amorphous Purport (unformed Substance) to find a really different singularity actualized as a new formed substance each time.  Hjelmslev’s is the immanence of Spinozist univocity.  Just as Spinoza’s univocity is One Substance with real distinction of form, so also Hjelmslev’s univocity is identical and amorphous purport with the real distinction of formation.  This is in contrast to Saussure’s already formed substances without real distinction (one structure of constant variability of form-matter correspondences.)

 

Hjelmslev sees the Spinozist isomorphism, without correspondence, of univocity.  Isomorphism is a function that determines the reciprocal relation between ‘content’ and ‘expression’.  But there is no prior correspondence in this parallelism.  Deleuze says of Spinoza (Expressionism in Philosophy, p.109) “…the modes of different attributes have not only the same order and the same connection, but the same being; they are the same things…”  I take this to mean that there is isomorphism between Spinoza’s attributes.  They are really distinct but ontologically single. Deleuze says of Spinoza (EiP, p106), “Attributes are mutually irreducible and really distinct; none is cause of another, or of anything whatever in another.”  This means that there is “no correspondence” between the attributes of thought and extension.    

 

Helmslev’s ‘Purport’ is Spinoza’s ‘Substance’ of univocity.  Purport itself is unformed matter.  For Hjelmslev, language can form any singularity of purport.  Any really distinct form can be projected into unformed Purport to become any formed purport whatsoever.  For Hjelmslev, the sign is a function that fits together content and expression with real distinction each time.  Unformed Purport can take on any form whatsoever and is therefore arbitrary.  It is the Purport that is itself unformed and ontologically single, but it can take on any real distinction.  This means that there is no prior purport that can be the basis for the description of language.  On the contrary, any linguistic formation must depend on a prior double articulation.  In other words, Hjelmslev reaches a ‘transcendental empiricism’.    

 

Using the terminology of Deleuze and Guattari in describing Hjelmslev’s linguistics, the ‘abstract machine’ is the function that operates within the ‘concrete assemblages’ (content and expression).  Inside the ‘strata’ there are assemblages of content and assemblages of expression in reciprocal presupposition.  However, outside the strata, the ‘forms of expression’ are ‘incorporeal transformations’.  They inhere in the expressed of statements but are attributed to bodies.  But bodies are not the referent of a sign.  ‘Incorporeal transformations’ are events that express an incorporeal attribute and “intervene” to attribute it to a body.  (ATP86) “The form of expression is constituted by the warp of expressed, and the form of content by the woof of bodies.”  The abstract machine is the function that operates between the functives, content and expression, and effects their double articulation.

 

(ATP67)  “In short, we should never oppose words to things that supposedly correspond to them, nor signifiers to signifieds that are supposedly in conformity with them.  What should be opposed are distinct formalizations, in a state of unstable equilibrium or reciprocal presupposition.  “It is in vain that we say what we see; what we see never resides in what we say.”…..We are never signifier or signified.  We are stratified.”   

 

Deleuze and Guattari read Hjelmslev as finding the function between expression and content at the level of form.  The ‘form of expression’ and the ‘form of content’ are common and reversible.  Form is the transversal ‘abstract machine’ between the heterogeneous forms of expression and content.  The form of content is a nondiscursive multiplicity which is not a signified.  The form of expression is a discursive multiplicity which is not a signifier.  At this level of the opening of forms, there is a non-relation without ismorphism or correspondence. But the relation between content and expression derive from this non-relation. (ATP68)  “Form of content and form of expression involve two parallel formalizations in presupposition: it is obvious that their segments constantly intertwine, embed themselves in one another; but this is accomplished by the abstract machine from which the two forms derive, and by machinic assemblages that regulate their relations.”

 

Deleuze in reading Spinoza says, (EiP47) “Attributes are thus forms common to God [Substance], whose essence they constitute, and to modes or creatures which imply them essentially.”  And just as Spinoza’s heterogeneous parallelism of attributes and powers are univocal forms common to Substance and modes, so also Hjelmslev’s ‘form of content’ and ‘form of expression’ is a transversal formalization (of deterritorialized signs) common to unformed Purport and to the strata.  This common form, or abstract machine, is what allows the difference between the essence of Substance (on the plane of consistency) and the essences of modes (on the strata). The abstract machine is the common form of isomorphism.  But this isomorphism of Substance and modes is also the intensive non-correspondence that produces the difference in nature between the essence of Substance and the essences of the modes.

 

Whether the sign is thought to be an expression of an extra-linguistic content, or an entity that connects an expression (signifier) with a content (signified); the notion of language as a sign system of correspondences is untenable.  Deleuze and Guattari read Hjelmslev as saying something much different from that ‘classical’ notion.  For Hjelmslev, the sign is a function of real distinction (an isomorphism) between two heterogeneous functives (content and expression) that have no prior correspondence.  This allows him to reach that univocity of unformed purport that is, nonetheless, distributed into isomorphic non-correspondences.  Hjelmslev’s linguistics reaches any really distinct form of purport whatsoever.

 

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