Hjelmslev’s Net

“God is a lobster, or a double pincer, a double bind.”

— From A Thousand Plateaus by Deleuze and Guattari


Linguist Louis Hjelmslev developed a semiotic model which elaborated Saussure’s two part signifier and signified into the double dual of the substance of content, the form of content, the substance of expression, and the form of expression. Contents are “formed matters”, and expressions are “functional structures”. Both are further separated into a substance and a form. The original signifier can be considered the form of expression, while the original signified can be considered the form of content. The two types of forms are like a net of warp and woof (why else a net?), dividing an undifferentiated unformed matter (Earth, purport) into two types of substances.

Deleuze and Guattari cast this net from Hjelmslev’s use in language into universal application by way of examples in geology and biology: sedimentation/folding and molecular genetics. The two planes of content and expression are the First Articulation and Second Articulation, respectively, the first of which “chooses or deducts”, and the second of which establishes “functional, compact, stable structures”. In their geology example, the First Articulation is the process of sedimentation, and the Second, folding. Generally, the two substances deal with territorialization, deterrritorialization, and reterritorialization, and the two forms are concerned with coding and decoding (and recoding?).

Additionally, there is talk of the molar versus the molecular (as continuous/discrete or unity/multiplicity?) but the molar is not form, nor is the molecular substance, nor vice versa. The First Articulation moves from molecular substances to molar forms; the Second Articulation moves from molecular forms to molar substances. How confusing! What does it all mean? One could spend a lifetime lost in these fun-house reflections!

I propose that the four basic logical operators of Linear Logic are in correspondence to the double articulation of Hjelmslev’s Net.  Content is Conjunction, Expression is Disjunction, Substance is Additive, and Form is Multiplicative. Content and Expression is Substance or Form; Conjunction and Disjunction is Additive or Multiplicative.


Gilles Deleuze and Felix Guattari / A Thousand Plateaus: capitalism and schizophrenia

Manuel De Landa / The Geology of Morals: a neo-materialist interpretation http://www.t0.or.at/delanda/geology.htm

Luke Feast / The Science of Multiplicities: post-structuralism and ecological complexities in design http://researcharchive.vuw.ac.nz/handle/10063/142


[*3.170, *4.46, *4.88, *4.112, *4.146, *5.70, *5.174, *6.10]



9 Responses to “Hjelmslev’s Net”

  1. Plato’s Divided Line « Equivalent Exchange Says:

    […] double duals. I believe Eikasia should come before Pistis, as the substance and form of content in Hjelmslev’s Net. Considering the vertical axis, Episteme as Dianoia and Noesis should surely be there for Plato, […]

  2. Monism = Pluralism « Equivalent Exchange Says:

    […] Bell’s blog entry about William James’ radical empiricism reveals relations between Hjelmslev’s Net and Linear Logic. To begin with, Hume was concerned with disjunctive relations (of expression) to […]

  3. J.-Y. Girard’s Linear Logic « Equivalent Exchange Says:

    […] Linear logic is a substructural logic invented (or discovered, if you’re a Platonist) by logician Jean-Yves Girard. Many other logics can be embedded into it, including classical and intuitionistic logic, so in a sense it is a “logic behind logic”. Linear logic can be partially derived from the rejection of the structural rules of weakening and contraction, the first of which adds arbitrary propositions and the second reduces duplicated propositions to single occurrences. Due to these changes in the logical rules, logic is transformed from being transcendental (truth transcends its use) to pragmatic or materialistic (truth is restricted by use). Therefore linear logic can be given a “resource interpretation” that makes it a logic not of truth but of things: producing and consuming, giving and taking, pushing and pulling, like the desiring machines of Deleuze and Guattari (see Hjelmslev’s Net). […]

  4. The Here and the Now « Equivalent Exchange Says:

    […] situated in space and time (see SpaceTime). Every perspective is due to expression and content (see Hjelmslev’s Net). Here is space, now is […]

  5. E. F. Schumacher’s Four Fields of Knowledge | Equivalent eXchange Says:

    […] fourfold is very similar to Hjelmslev’s Net, where Content is Inner Experience, Expression is Outer Appearance, Substance is unitary […]

  6. The Quadralectics of Marten Kuilman | Equivalent eXchange Says:

    […] association of  his four-fold of visibility with communication, it is also reminiscent of Hjelmslev’s Net. Then, invisibility could be understood as content, and visibility as […]

  7. J.-Y. Girard’s Transcendental Syntax, V2 | Equivalent eXchange Says:

    […] believe a closer analogy for the fourfold of Transcendental Syntax is to Hjelmslev’s Net than to Kant’s Analytic-Synthetic Distinction. If so, then Performance and L’usage are […]

  8. A Game of Fourfolds, Part 4 | Equivalent eXchange Says:

    […] example, the Four Elements are more than the opposite pairs of Air and Earth, Fire and Water. In Hjelmslev’s Net, Substance and Form combines with a superficially similar Content and Expression. However, above is […]

  9. Memetics – Strange Rider Says:

    […] Hjelmslev’s Net | Equivalent eXchange […]

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