N-articulations

I was recently asked to do a remote lecture on Louis Hjelmslev’s work. I accepted. It was mainly on the ‘Prolegomena to a Theory of Language’, mixed with ‘Structural Analysis of Language’ and ‘La stratification du langage’. I won’t comment on that lecture, considering it’s already in the past. Instead, what I want to do is to expand on that lecture, to further elaborate what is known as Hjelmslev’s net and what he, later on, came to refer to as the stratification of language or, should I say, just stratification, of just about everything.

The problem with Hjelmslev’s work is that it’s fragmented, bits of it being published in this and/or that language. It is also super dense. Now, don’t get me wrong, I like complexity and complex conceptual frameworks. The problem is rather that his key works are rather short, so he doesn’t really end up fleshing out his concepts. For example, he introduces concept after concept, some of which he later on abandons in favor of other concepts. I can see why he does that, but I don’t think it’s the best way to go about it. To be fair, I can’t blame him for doing what he set out to do. I don’t think he introduces too many concepts, but rather that he doesn’t spend much time elaborating them.

As this is going to be a quite a slog (believe me!) and there’s going to be a lot of concepts that will be discussed (but’s that’s logical rigor!), I’ll provide you with a cheat sheet. I won’t italicize the concepts here, unlike in the text, because otherwise I’d be italicizing the whole cheat sheet. I’ve abbreviated Gilles Deleuze as D, Félix Guattari as G, and Deleuze and Guattari as D&G. I’ve simplified some things in it, so if something is off, it’s because I didn’t want to go on and on about each concept. That would have been counterproductive.

Cheat sheet

Signs and non-signs

Anyway, what is interesting about Hjelmslev’s work is his relational and functional approach. The gist of that is that parts functions as parts of a whole, which, in turn, functions as a part of another whole alongside other parts. This is not a unique to him, even though it might be unique to him in linguistics. You’ll find a much better explanation of how parts and wholes function in Baruch Spinoza’s ‘Ethics’. That said, I realize that comparing Hjelmslev to Spinoza is unfair, considering that comparing anyone to Spinoza is unfair.

Hjelmslev also has this “insane meaning theory” that everything else is based on, as pointed out by Félix Guattari (208) in ‘Hjelmslev and Immanence’. The insanity of it is that meaning does not reside in language, as such. Meaning is tied to the sign, yes, but it is not the sign itself. Instead, when we take a closer look at language, how it works, it appears to us that the meaning that we through signs, and only through signs, is based on non-signs, what Hjelmslev (29) refers to as figuræ (figurae, figures) in ‘Prolegomena’. In his (29) words:

“A language is by its aim first and foremost a sign system; in order to be fully adequate it must always be ready to form new signs, new words or new roots.”

This is evident from how languages keep changing, how what people used to say back in the day, whenever that was, is no longer the same as it is now. Of course, the further back you go, the more likely it is that things have changed, so that what people said yesterday isn’t that different from what they say today. Anyway, his point simply is that a sign system must be adaptive. He (29) continues:

“But, with all its limitless abundance, in order to be fully adequate, a language must likewise be easy to manage, practice in acquisition and use.”

This explains why things don’t change that much and how, oddly enough, we keep repeating the same stuff, over and over again, instead of coming up with something new all the time, despite the limitless potential. He (29) continues:

“Under the requirement of an unrestricted number of signs, this can be achieved by all the signs’ being constructed of non-signs whose number is restricted, and, preferably, severely restricted.”

Here we move from signs to non-signs, to the figuræ (figures). He (29) elaborates the role of these non-signs in sign systems:

“Thus, a language is so ordered that with the help of a handful of figuræ and through ever new arrangements of them a legion of signs can be constructed.”

Simply put, you get signs from non-signs, meaning from non-meaning, sense from nonsense, which is pretty insane, well, for a linguist, as explained by Guattari (207-209). Hjelmslev (29) summarizes how sign systems, such as a language functions:

“We thus have every reason to suppose that in this feature – the construction of the sign from a restricted number of figuræ – we have found an essential basic feature in the structure of any language.”

Guattari (207) paraphrases this:

“What defines language is not signification, but its capacity for reproducing an infinity (a flow) of signs, given a finite (axiomatic) figure machine.”

So, oddly enough, what is remarkable about an actual sign system, such as a language, is that it is never a mere sign system, a pure sign system. It is rather a system of non-signs, a system of figuræ, that operates to create signs, as Hjelmslev (29) goes on to explain:

“Languages, then, cannot be described as pure sign systems. By the aim usually attributed to them they are first and foremost sign systems; but by their internal structure they are first and foremost something different, namely systems of figuræ that can be used to construct signs.”

This is why he (29) insists that defining a language as a sign system is unsatisfactory. For him (29), signs are therefore external functions, whereas the figuræ are internal functions. What I like about his (27) definitions is that he never slips to saying that sign is the meaning, but rather argues that sign is meaningful, a bearer of meaning, when it is defined by a function, in contradistinction to a non-sign. What is important here is how we get something, something meaningful, something sensical, from what amounts to, well, nothing, nothing meaningful, nothing sensical. I would say that this is why Guattari (208) thinks that Hjelmslev’s meaning theory is enough to make linguists go insane. Then again, there is more to this, why it’s such an insane theory for the linguists, but we’ll get to that shortly. Part of that is the emphasis on function, which we’ll return to in just a minute.

Functives: content and expression

What I find particularly interesting about Hjelmslev’s relational and functional approach is what later on became known as his net. Hjemslev (35-36) explains this in the ‘Prolegomena’:

“By virtue of the sign function and only by virtue of it, exists its two functives, which can now be precisely designated as the content-form and the expression-form. And by virtue of the content-form and the expression-form, and only by virtue of them, exists respectively the content-substance and the expression-substance, which appear by the form’s being projected on to the purport, just as an open net casts its shadow down on an undivided surface.”

To make more sense of this, we must lock on to a number of key concepts: content and expression, substance and form, and purport. For him (29-30), content and expression are functives. They are entities connected to one another as terminals through sign function or, in short, function. They are virtually the same, but not actually same. What I mean by this is that they are the same, but they are not the same, inasmuch as they enter into relationship with one another as terminals, i.e., when they function in relation to one another. In his (30) words:

“[A] function is inconceivable without its terminals, and the terminals are only end points for the function and are thus inconceivable without it.”

He (37-38) goes as far as to say that there is no reason to refer to functives as content and expression, as you could just say that there are these functions, that exist between terminals, between entities. He (37) indicates that he uses content and expression out of habit, having chosen them “in conformity with established notions”, and thus using them is “quite arbitrary.” I can see why he would do that, why he opts to refer to functives as content and expression. It’s just easier to comprehend at a glance.

To be clear, he (20) defines function as something is in between a whole and its parts, what he refers to as a class and its segments. He (20) adds to this that the terminals of the function are the functives. If terminal seem odd to you, think of the word as a point of connection, like in electric circuits or at transportation nodes, such as bus stations, railway stations, seaports, or airports. A functive is a fancy way of saying “an object that has function to other objects”, as he (20) points out. To complicate this a bit, a function can also be a functive, if there is a function between functions. He (20) mentions this to distinguish between two types of functives, those that are functions of functions, and those that are not functions of functions, what he refers to as entities, which, in turn, is just another word for a terminal, “an object that has function to other objects.”

I don’t know about you, but I’d say that he opted to make use of the established notions, content and expression, not because he needed to do so, out of respect for others in his field or fields, but because the functive as function of a function or as a terminal or entity is pretty confusing at a glance. I had to take a moment to get through that bit, to make sense of it, so, yeah, it must have made sense to him to opt for the established notions. I guess you could make it work, as you’ll see soon enough, but it’s just unwieldy.

Deleuze and Guattari (511) comment on this in ‘A Thousand Plateaus: Capitalism and Schizophrenia’, noting that content and expression are simply two functives of a function. That is also why Guattari (204) states in ‘Hjelmslev and Immanence’ that you might as well call them A and B. Content and expression are just a “pseudo-dualism”, as he (204) points out. For him (204), the problem is Hjelmslev’s loyalty to linguistics, paying homage to “Papa Saussure”, while clearly seeking to go beyond linguistics. You can see this already in the ‘Prolegomena’. He starts with linguistics, only to go beyond it, ending up with semiotics.

Hjemslev (30) goes on to specify that content and expression are tied to the sign function or, in short, function, appearing only in solidarity, only if the function is there. To be more specific, as he (30) points out, the sign function or, in short, function “is in itself a solidarity”, whereas these two entities, these two terminals, are solidary, always presupposing one another, which is why they never appear in isolation, why they make no sense on their own. In his (30) words:

“An expression is expression only by virtue of being an expression of a content, and a content is content only by virtue of being a content of an expression.”

And, to be clear, as he (30) goes on to emphasize:

“[T]here can be no content without an expression, or expressionless content; neither can there be an expression without a content, or content[]less expression.”

He (30) exemplifies this with how a thought can be thought but it is not a linguistic content without that thought being expressed, one way or another. Conversely, if we just make random sounds without giving any of it any thought, there is something being expressed, but the expression is not a linguistic expression, considering that it lacks the linguistic content for it to be linguistic expression.

Hylomorphism

Before I move on, I think it is worth clarifying a couple of terms used by Ferdinand de Saussure. Why? Well, while they are not used by Hjelmslev, they help us to understand why they are not used. Saussure (111-113) relies on a distinction between matter/substance and form in his ‘Course in General Linguistics’. For him (112), there is, on one hand, “the indefinite plane of jumbled ideas” and, on the other hand, “the equally vague plane of sounds”. That’s what he means by matter or substance. If you ask me, the problem with Saussure is that he isn’t too specific about this, considering that he appears to be using matter or substance synonymously. It is then segmented according to a form that is produced at the borderland between the two planes, as clarified by him (112-113). He (112) visualizes this with a diagram depicting the surface of a body of water, providing a top-down view of it, with ripples forming on its surface caused changes in atmospheric pressure (better known as wind), dividing it into a number of waves. In summary, we get something like this once we add the signifier and signified to the mix as well (I):

	Substance	Form
Signified (content)	indefinite plane of jumbled ideas shapeless thought mass	definite plane of ideas conceptual order
Signifier (expression)	indefinite plane of sounds shapeless sound mass	definite plane of sounds sound order

The problem with this type of duality is that it is hylomorphic. What is hylomorphism? To give you the short answer, it is how matter takes form. The long answer goes back to Aristotle. He (133) explains this in his ‘Physics’, noting that matter is “that out of which” something is made. He (133) uses the example of how syllables are made out of letters. Conversely, form is therefore that which organizes the matter, or, rather the organization of the matter.

Deleuze and Guattari (369, 408) address hylomorphism in ‘A Thousand Plateaus’. For them (363), it is a model that implies “both a form that organizes matter and a matter prepared for the form”. In its simplest form (no pun intended), hylomorphism results in what I’d call naïve realism, in reducing matter into content (things) and form into expression (words), as Deleuze and Guattari (369) point out. That’s, however, not a real concern here as both Saussure and Hjelmslev are opposed to such views. For Deleuze and Guattari (408), there are two problems with hylomorphism. Firstly, matter is deemed to be homogeneous. Secondly, form is considered to be fixed.

I can’t be entirely sure whether Saussure’s matter or substance is homogeneous, considering that he (112-113) doesn’t comment on it. Then again, he (112-113) does mention that he is dealing “two shapeless masses” and the examples he provides, a sheet of water and a sheet of paper, do make you think of something that is considered to be homogeneous. Moreover, he (15) does consider language (langue) to be homogeneous, which does suggest that. Then again, he (15) notes that speech is heterogeneous, which goes against that. Therefore, I’d say this has more to do with the second problem, how form is considered to be fixed.

While I’m a bit uncertain about the homogeneity, the issue of fixity is certainly something that undermines Saussure as he couldn’t care less about language as an everyday thing. He (13-14) is certainly aware of it, that it is a “social product”, considering that he acknowledges how it is, on one hand, something that individuals do, or, as he puts it, execute, and, on the other hand, shared by individuals, so that language is never simply individual but collective. That said, his definition of language as social or collective is not exactly what I’d call social or collective as, for him (14), speech (parole) is merely individual, consisting of willful and intellectual acts that the person expressing something chooses to express. In his (14) words, “[t]he speaker uses the language code for expressing his own thought”, while “the psychophysical mechanism … allows him to exteriorize these combinations.” In other words, for him (14) language is something that all humans have, at least potentially, assuming that one is part of a social group. He (14-15) bases his definition of language and the study of language, what we’d call linguistics, what he calls semiology, on “the heterogeneous mass of speech facts”, but quickly dispenses with it and its heterogeneity in favor viewing language of a storehouse of homogenous linguistics facts. He ends up treating form as “[a]n invariable form” and matter “a variable matter of the invariant”, “extracting constants from variables”, as explained by Deleuze and Guattari (369). This is an odd move, considering that his starting point is speech, heterogeneous and variable.

That’s odd because he moves to assert that language is homogeneous and invariable, which then, somehow, allows him to treat all that everyday heterogeneity and variation as mere deviation from a standard. The problem here is that the supposed homogeneity, invariance and universality of language is based on the heterogeneity, variation and particularity or singularity. In other words, the problem with this is that it is taken for granted that there is a constant or an invariant, instead of constant or continuous variation. I’d say that it’s not that there aren’t generalities, regularities or tendencies, as there are, but they are just that, something that is now common, for whatever reason that may be, but might not have been common in the past nor be common in the future.

This is issue also undermines Hjelmslev, albeit, I’d say it has less to do with his formulations than it has to do with his unwillingness to address the issue. He (100-101) is explicit about this, noting in ‘Structural Analysis of Language’, that as far as he is concerned, he sides with Saussure, focusing solely on the form, so as to take what Saussure started to its logical conclusion. He (188) also comments on this in ‘La stratification du langage’, noting that speech is just that which is arbitrary in language, how certain strata meet one another in this and/or that relationship with one another. In other words, he isn’t or doesn’t appear to be too keen on speech because it is arbitrary. So, he’d rather focus on language as a system of stabilized connections between variants in usage on certain strata or, more simply put, between linguistic or semiotic acts, and the standards that act as the sets of these possible stabilized connections, as he (188) points out.

I think he could have addressed it as his formulations give way more room to do so than Saussure’s formulations, but he just didn’t. I think he was reluctant to do so because it just wasn’t something that people did as pragmatics was hardly a thing back then. Of course, that’s still on him, just as it is on Saussure. Anyway, when it comes to hylomorphism, Hjelmslev fares better than Saussure in this regard. This is because even though his formulation is also plagued by its fixity, he doesn’t rely on the Aristotelian opposition between matter and form.

A moment of candor

While it may seem like I’m just against Saussure, looking give him a bad rap, there are some things that I like about his work. For example, while I might not agree with his views, as I am for sure against structuralism (in the form that it is generally understood), I can appreciate the fact that he went against the tide, basically saying ‘fuck it’, ‘fuck y’all’, I know you guys like to keep doing more of the same, but ‘fuck your semantics’, ‘fuck your phonetics’ and ‘fuck your philology’, ‘yolo’, I’m after something with this and I’ll do it no matter what you, the old guard, think of it, because it’s not like you are going to support something that will, in all likelihood, relegate you and your work as subordinate to my (his) work, as noted by Hjelmslev (97-98, 100) in ‘Structural Analysis of Language’, albeit in a less colloquial manner. This is also Hjelmslev’s view, albeit, again, he explains that in less colloquial manner than I just did (for the sake of emphasis, and to make this less of slog for you to read, believe me!), and, well, he isn’t afraid to express it, which probably didn’t make him any friends. He (2) starts kicking doors down right in the beginning of his ‘Prolegomena’ by going after semantics, phonetics, and philology for their lack of structure, for being content of being merely descriptive and for their “zealous haste” to accumulate knowledge, you know, for just doing more of the same in a disconnected manner, bearing relevance to ‘fuck all’ as I might express it to grab your attention.

To be candid, to speak freely, as a parrhesiastes, I can’t stand linguistics as it is, stuffy, boring, irrelevant and disconnected from everyday life, while also pretentious, acting, as if it wasn’t all that. If you think that structuralism, what Saussure or Hjelmslev discuss, is boring, which it is, and disconnected from everyday life, which it is, do not engage in morphology, phonetics, phonology, semantics, or syntax, you know, the cornerstones of linguistics, unless you are really into institutional sclerosis. Then there’s the disingenuity of all that, the underhandedness of it, just doing more of the same, despite the presuppositions that just don’t hold or, rather, could hold, assuming that you could make them hold, which I doubt.

For example, when you have something like second language acquisition (SLA or L2), I can see what the point is, there being a logic to it, practical value and applicability, fair enough, but all of that builds on the presuppositions that languages exist, that this and/or that language exists as a given, a priori, and that the first language you acquire from other people becomes your native language, which, in turn becomes the invariant that functions as the standard against which the supposed non-native speakers are to be judged in terms of their competence as they try to learn that language. Now, to be clear, I believe that languages do exist, don’t get me wrong, but what I don’t believe is that they exist, on their own, as given, a priori. Instead, they exist as political entities. So, the issue I take with most of linguistics, including structuralism, as well as SLA or L2, is that there is this reliance on presuppositions that just don’t hold once you hold them up to close scrutiny. I just don’t get it how people can keep on doing more of the same if they are made aware of the issue, that what is supposed to keep it all together just doesn’t hold. I don’t know about you, but I sure rethink things if I realize that whatever I’m dealing with just doesn’t make any sense. I don’t mind having been wrong or inconsistent about something. It happens. No one is perfect. I acknowledge that and move on. It’s okay to change your mind. I do that all the time.

Deleuze and Guattari (75) do an excellent job explaining this in  ‘A Thousand Plateaus’, how linguistics, as a field or a discipline, fails to keep itself in check as it has these presuppositions. They (75-76) explain this through an example, which bears direct relevance to language learning:

“When the [teacher] instructs [the] students on a rule of grammar …, [the teacher] is not informing them, any more than [he or] she is informing [him- or] herself when she questions a student. [He or s]he does not so much instruct as ‘insign,’ give orders or commands. A teacher’s commands are not external or additional to what he or she teaches us. They do not flow from primary significations or result from information: an order always and already concerns prior orders, which is why ordering is redundancy. The compulsory education machine does not communicate information; it imposes upon the child semiotic coordinates possessing all of the dual foundations of grammar (masculine-feminine, singular-plural, noun-verb, subject of the statement-subject of enunciation, etc.)”

Exactly! To paraphrase this, to get to the gist of this, language is not about communicating information between people, but about making sure that people know their place. Okay, it is also about communicating information, but only in the sense that there has to be information that is successfully emitted or transmitted for it be observed, as they (76) point out. That said, that’s not all there is to it, which is why they (76) state that:

“Language is made not to be believed but to be obeyed, and to compel obedience.”

And that (76):

“Words are not tools, but we give children language, pens, and notebooks as we give workers shovels and pickaxes.”

As well as (76):

“A rule of grammar is a power marker before it is a syntactical marker.”

So, for example, when one studies how students learn language, how they fare, how supposedly competent they are in a certain language at a certain age or level of education, one presupposes that there is such a thing as linguistic competence, which, in turn, presupposes that there is this language, that it is like this, and that one must adhere to it. In other words, one presupposes that there is a given standard and that the students are to adhere to this standard.

While the intention might be good, to promote language learning, the problem with this is that it reinforces this conception of language and native speaker competence. I’d be fine with this kind of research if the researchers were honest enough to mention that what they are studying and how they are studying it is based on certain presuppositions. The point I’m making here is that there are these presuppositions and, to be frank, they don’t look too good. There’s no hiding behind them. Well, okay, you can hide behind them, you can keep ignoring the issue, but that’s just that, you are now deciding to do that. Also, by willfully ignoring the issue you are making it apparent that you are doing it because it suits you, because you’ve managed to convince the funding agencies, both private and public, that your research is needed. Needed for what? To indicate that students achieve a certain linguistic competence, which is, conveniently, defined by the researchers themselves (and their predecessors, like in an apostolic succession to maintain orthodoxy), so that you can keep your job. It also serves both private and public interests, reinforcing state language policies and private education business, so it’s no like there’s going to be a shortage of money for that.

Now, I’m not fond of criticizing others without giving them any credit and/or explaining what it is that they could do to fix the issues that I’m trying to make them aware of. So, what could the researchers do? Well, instead of drinking the kool-aid, they could point out that they are, in fact, interested in looking at how teachers impose upon the students in this way, as expected of them by their superiors, and how the students come to acquire not only a language, as judged according to a certain standard, a certain constant extracted from a number of variants, but also this view that treats that constant extracted from the variants as a given.

The problem isn’t that researchers study languages, but rather that they take them for granted. Instead of looking at what this or that standard language consists of and how it is defined, for example, in terms of grammar, we should be asking who gets to define that, whose interests it serves and, conversely, who do not get to have a say and whose interests it does not serve or even goes against.

Now, of course, when we shift from what to who, we are not trying to find this and/or that person responsible for that. We are not interested in blaming this and/or that researcher or this and/or that teacher for doing and/or saying this and/or that, but rather investigating what makes them do and/or say what they do and/or say, what makes them express what they express. I don’t know about you, but I couldn’t care less about the people involved, nor their views on why they do and/or say what do and/or say. What interests me is what makes those people do and/or say what do and/or say. It might be interesting to assess people’s views, what they think motivates them do and/or say whatever it is that they do and/or say, not because I’d take their word for it, but because it’d be interesting to assess what it is or might be that makes them explain their own actions in this and/or that way.

Anyway, be that, all that, as it may, I agree with Michel Foucault on this issue, how the researcher, what he refers to as the intellectual, should never seek to speak for others, to tell how tell how things are, followed by telling how they ought to be, as if it was their responsibility to do so, as they “are themselves agents of this system of power” that “blocks, prohibits, and invalidates” people’s access to knowledge, not by the means of censorship but by “subtly penetrat[ing] an entire societal network”, as expressed by him (207) in conversation with Deleuze in ‘Intellectuals and Power’. In other words, when we have some as applicable as SLA or L2, the problem with it is exactly that applicability, how the researcher is a pawn in this system of power, in this case the education system, complicit, if not complacent, functioning to provide legitimation for the system of power. The researchers should be aware of that, always keeping that in mind, and “struggle against the forms of power that transform him into its object and instrument in the sphere of ‘knowledge,’ ‘truth,’ ‘consciousness,’ and ‘discourse’”, as aptly put by Foucault (208).

Unformed matter, formed matter and form

Having explained content and expression, Hjelmslev (31) moves on to explain his definitions of substance, form and purport. However, before I elaborate on his definitions, it is worth noting that mening (Danish for meaning) is translated as purport by the English translator, Whitfield, whereas the French translators, Una Canger and Annick Wewer, opt for sens (sense). While all of these, mening, purport and sens, work, conveying the same meaning, purport, or sense, none of them is very intuitive. Hjelmslev (31) refers to it as “an amorphous mass”, as “an unanalyzed entity”, which is defined only in relation to sign function or, in short, function. When we think of it in terms of function, yes, meaning, purport or sense, are all apt terms, as it has to do with that which is conveyed by whatever it is that is expressed. However, they are not that great when contrasted with substance and form. He (32) explains substance as that what is formed from purport by the form or, conversely, form as that which forms substance out of purport. In other words, purport is, in fact, the matter out of which substance is formed by the form. Therefore, we could also call purport matter and substance formed matter, as done by Guattari in his commentaries on Hjelmslev work.

For example, in ‘Hjelmslev and Immance’, Guattari (208) refers to purport as matter-meaning continuum, divided into content and expression continuums by Hjelmslev. In ‘The Role of the Signifier in the Institution’, he (73) refers to matter, substance, and form, although he (73) also opts to call matter meaning. He (95-96) does the same thing in ‘Towards a Micro-Politics of Desire’, noting that what Whitfield has opted to translate as purport is, on one hand, about matter, but, on the other hand, about meaning or sense. In ‘A Thousand Plateaus’ Deleuze and Guattari (3, 40-41, 43-45, 49, 53, 56, 61, 72, 141, 146, 165, 225, 258, 267, 338, 340, 503, 505, 511, 531) refer to formed matter, i.e., substance or materials, and unformed matter, i.e., matter or meaning (purport or sense).

In summary, we have matter-meaning, either as the unformed matter or as the meaning, purport or sense when it is considered in relation to a sign function or, in short, a function. In other words, we have meaning, purport or sense, which we know to exist, to be there, or so to speak, but we cannot explain it in its own terms. We get to meaning, purport or sense, yes, we reach it, but it appears only in the function, once we link content and expression. This leads us to form.

Hjelmslev (32) notes that matter is unformed, existing solely for the purpose of acting as a substance for a form, whatever that may be, which means that substance is formed matter. Therefore, to be precise, substance is not substance for form. Instead, matter is the substance for a form, which means that, in a sense, it would be more appropriate to refer to matter, or, rather unformed matter as substance, as opposed to using it the way he does. Then again, I think it would be preferable to refer to matter, which is to be understood as unformed matter when contrasted with formed matter that is relevant only when we also take form into consideration.

The problem here is that not only has Hjelmslev added one more concept to Ferdinand de Saussure’s system, purport (matter-meaning), and renamed signifier and signified as expression and content. Instead, he has reworked the whole system, as explained by Oswald Ducrot and Tzvetan Todorov (21-22) in ‘Encyclopedic Dictionary of the Sciences of Language’. In summary, Saussure’s substance, “semantic or phonic reality considered independently of any linguistic utilization”, is Hjelmslev’s purport (matter-meaning) and Saussure’s form, “segmentation” or “configuration” is Hjelmslev’s substance (formed matter), so that the added concept is not purport (matter-meaning), but form, to be understood as “the relational network” which defines substance (formed matter).

Isomorphism

To link Hjelmslev’s substance (formed matter) and form to content and expression, it would appear that there is no reason to consider content any different from expression, considering that both have substance (formed matter) and form, as noted by Ducrot and Todorov (22). Their form is identical, is it not? Ducrot and Todorov (22) acknowledge that this is indeed the case, that their forms are identical, that there is isomorphism, i.e., that they share the same logic of “combinatorial relations among units”, but that does not mean that there is correspondence or conformity between the two, that they are realized the same way.  There is unity but also variety, as explained by Deleuze and Guattari (46) in ‘A Thousand Plateaus’:

“The same formal relations or connections are then effectuated in entirely different forms and arrangements.”

They (85-86) further elaborate this:

“[W]e are presented, despite the variety in each of the sets, with two formalizations, one of content, the other of expression. … Precisely because content, like expression, has a form of its own, one can never assign the form of expression the function of simply representing, describing, or averring a corresponding content; there is neither correspondence or conformity. The two formalizations are not of the same nature; they are independent, heterogeneous.”

In other words, what’s in common between the two, content and expression, is that they both appear as forms, hence the isomorphism, and that’s that, which is why they are still distinct from one another, why they do not collapse into one another.

Guattari (337) further comments on this in ‘The Machinic Unconscious: Essays in Schizoanalysis’, noting that this isomorphy is, in his view, never perfect. Why? Well, because the two forms, form of content and form of expression, never represent, describe or aver to one another. Taking his comment into account, it seems that referring to it as isomorphy is slightly off. The basic principle is there, they are both forms, yes, both sets of relations, one for content, one for expression, yes, that makes them isomorphic, but that’s about it.

I guess this is why Deleuze (61) states in his book on Foucault, titled ‘Foucault’ that “there is no isomorphism or conformity” between the two, only mutual presupposition and, more elaborately, that (31):

“But the fact remains that the two formations are heterogeneous, even though they may overlap: there is no correspondence or isomorphism, no direct causality or symbolization.”

This is still, well within what’s been covered so far. He (61) exemplifies this:

“[T]here is neither causality from the one to the other nor symbolization between the two, and that if the statement has an object, it is a discursive object which is unique to the statement and is not isomorphic with the visible object.”

So, as already pointed out, the only isomorphy you’ll find pertains to the forms, that the form of content and form of expression are both forms. To be honest, I don’t know what caused this change of heart. This has puzzled me for a long time. I mean Deleuze and Guattari, together and on their own, seem to be talking about the same thing, but in one instance it is deemed to be about isomorphy but in another instance it isn’t. Maybe this is one of those things where people ended up thinking that isomorphy meant correspondence between the forms, which it isn’t, so Deleuze ended up dropping it in his book on Foucault. Maybe it’s about Foucault’s views, instead of Deleuze’s views. Then again, I doubt that. He is clearly explaining Foucault’s views through his own views, at times comparing them, so it’d be odd that he’d be merely explaining Foucault’s views while defining the relation between the forms the same way as he does with Guattari in his own works. I think Guattari’s (337) comment about the lack of “a perfect isomorphism” or the incongruity of the forms is helpful here. It’s like there is a certain isomophism, a certain degree of isomorphism, yes, in a sense, but, strictly speaking, there isn’t isomorphism.

This leads Deleuze and Guattari (86) to comment that Stoics were the first to grasp how bodies (the corporeal content), in the broadest sense of the word, like a lake as a body of water, and statements (the incorporeal expressions) were independent from one another, so that one incapable of altering the other, which is also what Spinoza argues (131-132) in his ‘Ethics’, how thoughts can only affect other thoughts and how bodies can only affect other bodies.

This is not to say that the statements (expression) do not intervene with bodies (content), as they do, as they are only attributable to bodies, but the bodies themselves are not altered, as Deleuze and Guattari (86) go on to add. This is also not to say that bodies (content) do not matter, as they do, as they (86-87) point out. But instead of thinking of one or the other, content or expression, in isolation, we should think of them in combination, “[s]o that the same x, the same particle, may function either as a body that acts and undergoes actions”, as an A, “or as a sign constituting an act”, a speech act, to be more specific,  as a B, “depending on which form it is taken up by”, the form of content or the form of expression, as they (87) point out.

Spinoza would agree with this , considering that, in his ‘Ethics’ (45, 55, 132), the human mind and the human body are one and the same thing, a mode, a modification of substance, conceived under one of the two attributes that constitute the essence of substance that we humans are aware of, thought or extension. In his (131-132) words:

“Thus it follows that the order or concatenation of things is identical, whether [substance] be conceived under the one attribute or the other; consequently the order of states of activity and passivity in our body is simultaneous in [substance] with the order of state of activity and passivity in the mind.”

Which, for him (86) amounts to saying that:

“The order and connection of ideas is the same as the order and connection of things.”

It is worth noting here, before I continue to comment on content and expression, that Spinoza’s view of attributes sharing the same order and connections between the modes is often referred to as parallelism, but he never actually uses that term in his works. Instead, as noted by Deleuze (107, 365) in ‘Expressionism in Philosophy: Spinoza’, parallelism is attributable to Gottfried Wilhelm Leibniz (556) who uses it to in ‘Reflections on the Doctrine of a Single Universal Spirit’, to distinguish his own monist views from (Cartesian) dualist views:

“Those who favor a universal spirit will readily assent to this, for they distinguish this spirit from matter. I find, however, that there is never any abstract thought which is not accompanied by some images or material traces, and I have established a perfect parallelism between what happens in the [mind] and what takes place in matter.”

Note how he states that his views are not only marked by a parallelism but a perfect parallelism. Anyway, he (556) continues:

“I have shown that the [mind] with its functions is something distinct from matter but that it nevertheless is always accompanied by material organs and also that the [mind’s] functions are always accompanied by organic functions which must correspond to them and that this relation is reciprocal and always will be.”

Conversely, while advocating for “the doctrine of parallelism”, he (556) argues against a perfect separation of body and mind. In addition, while explaining this, he (556) argues, or at least seems to argue, that mind always retains something of the body, which, I’d say, is something that Spinoza would not be willing to state. It is also worth mentioning that while Spinoza is acknowledged in this text, being given thumbs up for his monism, “his demonstrations are” considered to be “pitiful and unintelligible” by Leibniz (555). Therefore, I’d say that parallelism is attributable to Leibniz rather than to Spinoza, as pointed out by Deleuze (106, 365).

Deleuze (107) further elaborates this:

“When Spinoza asserts that modes of different attributes have not only the same order, but also the [s]ame connection or concatenation, he means that the principles on which they depend are themselves equal.”

Exactly! If you look at how Spinoza (86) explains that, the order and connection of ideas (thoughts, thinking things) are the same as the order and connection of things (bodies, extended things), not that the ideas and the things are the same, that they parallel one another. In other words, there is only isomorphism, a shared logic of “combinatorial relations among units” but no correspondence, nor conformity between the two, which matches Hjelmslev’s take on content and expression, as explained by Ducrot and Todorov (22).

You could, of course, still call isomorphism a kind of parallelism, in the sense that there is indeed a shared logic, “the equality of the principles from which independent and corresponding series follow”, as noted by Deleuze (108-109). I agree with this. That seems to be the case.

You could also insist that, for Spinoza, a mode considered under one attribute is paralleled with a mode considered under the other attribute, as noted by Deleuze (108-10). I am, however, a bit doubtful of whether this holds or not for Spinoza, whether he thinks that the idea of a thing (a thought of it) is matched by the thing (the body in question). For example, he (83) reckons that we humans think and that we can think of not only something that exists but also something that does not exist, in the sense that we can think of a person who no longer exist, who no longer lives. This is what he means when he (82) says that an idea is a matter of conception rather than perception, something involves thinking rather than passively receiving information of what’s out there, beyond us. He (82) also states that an idea is only adequate, i.e., not confused, when it is considered intrinsically, in itself, on its own terms, as opposed being considered extrinsically, in relation to an object.

He (113) clarifies this by differentiating between three types of knowledge. The first kind of knowledge he labels as opinion or imagination, what we get from perception or having read or heard something which offers us fragments or confused knowledge. The second kind of knowledge he labels as reason, what we get from common notions, i.e., what is shared between this and/or that, whatever it may be. The third kind of knowledge he labels as intuition, which is what we get when we understand not the things but their essences, what it is that makes this this and not that and vice versa, for example what makes me me and not you and you you and not me or what makes hurricane Gordon hurricane Gordon and not hurricane Mitch and vice versa. Deleuze and Guattari (263-264) make note of this in ‘A Thousand Plateaus’:

“[T]he proper name is no way the indicator of a subject[.] … [It] does not indicate a subject; nor does a noun take on the value of a proper name as a function of a form or species. [It] fundamentally designates something that is of the order of the event, of becoming or of the haecceity.”

This is followed by a couple of examples which help us to understand why proper names are not just about me or you, as markers of subjects or as functions of objects, i.e., how we are, for example, humans, mammals, and animals, but about something else, as they (264) point out here:

“It is the military men and meteorologists who hold the secret of proper names, when they give them to a strategic operation or a hurricane.”

That’s why, for them (264), “the proper name is not the subject of a tense”, something that we could replace with a noun or a pronoun, “but the agent of an infinitive.” This hints to Spinoza’s definition of all things having a modal essence, i.e., degrees of expressive power or intensity pertaining to their capacity to act and be acted upon, and modal existence or non-existence, how things are always composite things, how they always consist of other things, to use the terms introduced by Deleuze in chapters 12 and 13 of ‘Expressionism in Philosophy: Spinoza’. A thing, everything and everybody, be it a thinking thing (an idea or a thought) or an extended thing (a body), always has latitude, i.e., “intensive parts falling under a capacity”, and longitude, i.e., “extensive parts falling under a relation”, as summarized by Deleuze and Guattari (256-257) in ‘A Thousand Plateaus’. In short, a thing, me and you included, is no longer to be understood nor recognized for what it is but for what it can do and what others (that can also do) do to it, as explained by Deleuze and Guattari (256-257).

Anyway, to go back a bit, just a bit, it is worth adding here that, for Spinoza (109-114), we get from the first to the second kind of knowledge and from the second to the third kind of knowledge, and that the first kind of knowledge is inadequate knowledge, whereas the second and the third kinds of knowledge are adequate knowledge. The first kind of knowledge stems from the limitations of being a human, a mere human, a limited body that is capable of distinguishing only so many things at the same time, continuously exceeding this limit, which results in confusion.

The second kind of knowledge is adequate because it is about reason, about rationality, about ratiocination, about the ratios of parts and wholes and how they agree with one another, as clarified by him (109-111). I’d say that Hjelmslev is dealing with this kind of knowledge as he is concerned with the relations between parts and wholes.

Spinoza doesn’t spell it out for you, but the third kind of knowledge, intuition, is adequate because it pertains to essences, what makes substance what it is, substance. What makes the third kind of knowledge superior to the second kind of knowledge is that while both are adequate kinds of knowledge, the second kind of knowledge is limited to dealing with what is common between this and/or that and therefore does not pertain to essences, as essences are always particular or singular, whereas the third kind of knowledge does pertain to the essences of things, what is particular or singular about something or somebody.

Deleuze (104-105) further comments on this, noting that, for Spinoza, each statement (expression) carries a distinct sense while also designating an object (content), which then becomes a designated object (content) for another statement (expression) that comes to function as a distinct sense, which, in turn comes to function the same way, ad infititum. To my understanding, this is what Deleuze (19-21, 39-40) also states in ‘The Logic of Sense’, how sense appears in the expression as that which is expressed, subsisting or inhering to it, but without being it, as the event that takes place between what Deleuze and Guattari refer to as the expression (words) and the content of the expression (things), and how, once expressed, it can always double as the content for another expression. Importantly, this doubling is very flexible, allowing us to address the relations between the semiotic and the non-semiotic, as in between words and material things, as well the relations within the semiotic, as he Deleuze (37) points out. This can also be extended to cover the relations between the non-semiotic, as done by Deleuze and Guattari in ‘A Thousand Plateaus’, albeit that is, of course, done through the semiotic as we cannot explain it, put it in words, without doing that through the semiotic.

In summary, Hjelmslev’s content and expression are, in a sense, the same, yet they are, in a sense, different. This is the same for Deleuze and Guattari who takes these from Hjelmslev. To clarify this, how they can be the same, yet different, we must pay close attention to Spinoza’s train of thought. As already pointed out, all modes are modifications of substance, conceived under one of the two attributes, thought or extension, which, in turn, constitute the essence of substance, among other attributes of which there are infinite (we just know the two). In other words, there is always this link between the modes and the substance as modes can only be conceived through attributes that constitute the essence of substance. To be clear, this does not mean that expression functions by having a content that it points to, like words pointing to corresponding things or things that conform to them.

Plane-matter

To make more sense of this, all of this, what has been covered so far, I’m going to explain how Hjelmslev’s net functions, step by step. Let’s start with matter, also known as meaning, purport or sense (II).

I could have labelled matter as meaning, purport, sense or matter-meaning, but, for the sake of clarity, I think it is apt to just call it matter here. I have included plane here, to indicate that there is only one plane, what Deleuze and Guattari (72) briefly refer to as “the Matter of the Plane” in ‘A Thousand Plateaus’.

The plane of consistency

Deleuze and Guattari tend to refer to this plane also as a plane of consistency. It is mentioned so many times in ‘A Thousand Plateaus’ that it is pointless to provide you the page numbers for all of those instances. Relevant to Hjelmslev, it is discussed in the chapter, or, rather plateau known as ‘The Geology of Morals’. They (43) point out that:

“[Hjelmslev] used the term matter [matière] for the plane of consistency or Body without Organs, in other words, the unformed, unorganized, nonstratified, or destratified body and all its flows, subatomic and submolecular particles, pure intensities, prevital and prephysical free singularities.”

In other words, Hjelmslev’s matter is Deleuze and Guattari’s plane of consistency. But what is plane of consistency or, rather, what is consistency? Well, the thing is that they keep mentioning it, but it takes some 300 pages or so for them (323) to provide a definition beyond their (144) earlier remark about it being “neither totalizing nor structuring”:

“[C]onsistency: the ‘holding together’ of heterogeneous elements.”

To be honest, that is how I would think of consistency, how something, whatever that may be, holds together. Massumi (xiv), their translator, notes in his foreword to the book that it is exactly that, but further specifies it, warning not to think of it as about homogeneity but about “holding together disparate elements”, what Deleuze calls style in ‘Proust and Signs: The Complete Text’, “a dynamic holding together or mode of composition”, so that when we say that something has style, that style is not a given, but that what appears to us as that style, composed of a bit of this and a bit of that, whatever it is that gives it that style.

To me, style is like that, how it comes together. I don’t know how I ended up watching a short video, but the gist of that video was covering a photoshoot done at a movie set. You could say it was just a basic model shoot, a model posing for a camera in some location, which happened to be a movie set, but that’s not all there was to it. The photos were shown on the video, matching the moments when they were taken, to see what the photographer was able to render visible to us. Then again, it is not just about the photographer. The style of those photos are much more than just the photographer and much more than a camera, a model and a background. The thing is that they had this 1970s vibe to the set, as did the model’s attire, hair and makeup, and the photographer shot it with a medium format SLR, on film, which results in this … style, this consistency of all of those elements, including the lighting, that come together in those photos.

The Spinozist take: the plane of immanence

Elsewhere in ‘A Thousand Plateaus’, Deleuze and Guattari (254-255, 266, 268-269, 281-282) also refer to the plane as a plane of immanence. The first time this appears in the book, they (253-254) are discussing Spinoza. That’s why they call it that, the plane of immanence.

They (254) note how Spinoza’s substance (Hjelmslev’s matter, not Hjelmlev’s substance) is like a plane “upon which everything is laid out.” To use Spinoza’s (45, 59, 82) own definition, it is that which is self-caused and from which everything else necessarily follows, so that there are “an infinite number of things in infinite ways”. In addition, substance is, by his (46) definition, that which exists by itself, which makes it eternal, so that everything else owes its existence to it. In short, (Spinoza’s) substance is, in itself and for itself, expressive, as explained by Deleuze (99) in ‘Expressionism in Philosophy: Spinoza’.

What else is there then for Spinoza? Well, as already explained, for Spinoza (45), there are also attributes and modifications of substance or, in short, modes. For him (45), attributes are what constitute the essence of substance. For substance to be both essential and infinite, i.e., infinitely essential, its constitution must involve infinite attributes, as he (45) points out. As already noted, we, as humans, are aware of two attributes, extension and thought. In terms of modes, what he (82) also refers to collectively as things, we have bodies (extended things) and thoughts (thinking things), which express the essence of substance. Highly importantly, the existence of modes depends on their essence, as indicated by him (46, 82). Simply put, you do not exist, nor does anyone, nor anything else, if they are not essentially extended. It is essential that they are. It is the same with thoughts. They are understood as such only by virtue of that essentiality. It’s a simple yes or no thing. It’s as simple as that. That said, an essence will do just fine without a mode, i.e., an existing body or thought, as he (83) goes on to add. For example, the existence of this table that I write on is not necessary to its essence as it is possible to conceive its essence even in its absence, nor is my idea of a table necessary for others to conceive it as a table. This leads us to the distinction between attributes and modes, how attributes pertain to modal essence, to “a particular or singular essence”, for example what makes this table this table and not some other table (otherwise this table would be some other table), whereas modes pertain to modal existence, whether this or that mode, i.e., thing, exists or not, as summarized by Deleuze (192-193, 201) in ‘Expressionism in Philosophy: Spinoza’.

As an additional note on translation, which may be of interest to those interest in affect, it’s worth commenting that in the Latin original the modifications of substance are “substantiæ affectiones”, which could then also be translated as affections of substance. The problem with translating that as affections is that, according to a dictionary, such as the Oxford English Dictionary, these days one typically understands it (OED, s.v. “affection”, n.¹) as about feelings:

“The action or result of affecting the mind in some way; a mental state brought about by any influence; an emotion, feeling.”

I might be wrong about this, but I reckon Spinoza isn’t going for this definition. Instead, he builds on an older, more general sense of the word (OED, s.v. “affection”, n.¹), which is rarely used in such a way these days:

“The action of affecting, acting upon, or influencing something; (also) the fact of being affected.”

The origin of the English word is in Latin, which a dictionary (OED, s.v. “affection”, n.¹) will tell you as being about “mental or bodily condition”. I think this is worth emphasizing, how, for Spinoza, affect is therefore not only about the body or about the mind, but about the body and the mind. This makes sense, considering that Spinoza’s affections of substance pertain to how both bodies and thoughts are indeed modifications of substance, having this or that bodily or mental condition, existing in this or that state, as the substance undergoes affections or modifications.

I believe Spinoza’s choice to call them affections of substance is particularly apt if we take a closer look at the core of his ethics in which everything, whatever we are referring to, let’s say you or me, to keep things interesting for us, you and me, is defined as having the capacity to act and be acted upon, as he (215) explains this:

“Whatsoever disposes the human body, so as to render it capable of being affected in an increased number of ways, or of affecting external bodies in an increased number of ways, is useful[.]”

What’s worth noting here is that affect or, rather, affecting, is always tied to the affections (or modes), to those affections (or modifications) of substance that are defined according to their capacity to act and be acted upon, which is another way of saying capacity to affect and be affected. This applies to everything, to every affection or mode, which makes this relational.

Deleuze explains this particularly well during his lectures on Spinoza in January 24, 1978:

“The only question is the power of being affected.”

Now, there is an emphasis on the bodies, yes, as opposed to thoughts, yes, which would make affect only about bodies, but if you read Spinoza’s ‘Ethics’, his own handy definition of affections or modes also takes thoughts into account. He (174) states that we experience pleasure and pain, the former involving “the transition … from a less to a greater perfection” and the latter involging “the transtition … from a greater to a less perfection”. So, for example, if I were to blind you, you’d then be less perfect in the sense that you’d be less able to act (e.g. can’t see where you are going) and be acted upon (e.g. can’t see what others are showing you). But if I were to provide an eye surgery, assuming you have poor sight, it would then result in a greater state of perfection, because you capacity to act and be acted upon would be increased. This is clearly very bodily. There’s no doubt about that. There’d be pleasure in better eyesight and pain in having no sight. Now, we can do the same with thoughts. If I were to threaten you, or come across as threatening, having, for example, blinded people in the past or there being stories of such, just the thought of it, pondering what are the odds that I might blind you, is enough to limit your capacity to act and be acted upon, because now you do your best to avoid me, regardless of whether I have or have not blinded anyone in the past. Note how I’m not doing anything to you physically, body on body, yet, it appears that I have had a certain effect on you. Such fear may also have the effect that, perhaps, you end up having physical symptoms, vomiting or the like, just by thinking that, that I might be a physical threat to you, even in the case that I am not (and I am not, to be clear), when it’s just hearsay.

In his letter to Lodewijk (referred to also as Louis and Lewis) Meyer, Spinoza (282-283) explains to Meyer that it is crucial not to confuse the infinity and eternity of (Spinoza’s) substance with the spatial and temporal finitude of the modes. In other words, (Spinoza’s) substance is indivisible, whereas modes are divisible (albeit infinitely). Deleuze (201) explains this in ‘Expressionism in Philosophy: Spinoza’:

“I do not think that there are, for Spinoza, any existing modes that are not actually composed of a very great number of extensive parts.”

To make more sense of this, what he (287) means by “a very great number” has to do with something that cannot be determined by, nor assimilated with any number, as explained by Spinoza (282, 287).

This means that we cannot argue that (Spinoza’s) substance consists of modes, because what is indivisible cannot, as a whole, consist of divisible parts, as he (283) points out. He (283) exemplifies with how we are tempted to think that a line is consists of points, even though it isn’t (or it is, but then conceived as consisting of infinite points). Also, keep in mind that substance is not made up of modes as modes are modifications of substance, as already pointed out. In other words, modes depend on substance, not the other way around.

You might be wondering why even mention that substance is indivisible, whereas modes are divisible. Well, this is because Spinoza (283-284) goes on to make a crucial point quantities or quantification, something that people often fail to grasp. In his (283-284):

“[W]e conceive quantity in two ways, abstractly … and superficially; … superficially in so far as we imagine quantity through the senses; abstractly when the conception is in the understanding only.”

In other words, there are two ways to think of this, abstractly, what he considers to be correct, and superficially, what he considers to be incorrect. He (284) further elaborates this:

“Now, if we consider quantity as it is in the sense and the imagination – and this indeed very readily and most commonly happens – we then find it divisible, made up of parts and multiple; but when we consider it abstractly, as it is in the intellect and a thing per se, which it is extremely difficult to do, then do we perceive it to be … Infinite, Indivisible and One.”

The point he makes here is that when we think of quantity, we are tempted to think of it as about numbers, but that’s, strictly speaking, incorrect. He (284) acknowledges the utility of the superficial conception of quantity, helping us to make sense of time and space, but that’s that for him, just about utility. In other words, quantities should not be confused with numbers, even though that’s exactly what people do, even most academics (hence poorly or inadequately conceived distinction between qualitative and quantitative studies, but that’s another story), as numbers offer just a way of conceiving quantities. To be clear, numbers and quantities are not the same thing, nor do numbers determine quantities, as he (285) points out. We can, of course, determine quantities numerically, but numbers do not determine quantities as quantities are not, in themselves, numbers. To use his (285) terminology, number is an image of quantity, a way to imagine quantity, but not quantity itself, which is why he summarizes this as:

“From this it is clear that measure, time, and number, are nothing but modes of thinking, or rather of imagining.”

If you fail to grasp the distinction, what he explains here, keep in mind that a meter (or a foot), a square meter (foot) or a cubic meter (foot) are measures of space, not space itself, just as a second, a minute and an hour are measures of time, not time itself (what Spinoza refers to as duration, as does Henri Bergson, time being treated as the measure). So, when we ask how much time we have left or how much space is there, we are treating time (duration) and space as something that they are not, reducing them into something that is measured out of convenience and, I’d say, habit.

But what’s the problem with equating quantities with numbers? Isn’t this just an exercise in pedantry? Does it even matter in practice? What difference does it make? Well, while we may go about our lives, happily ignoring this, the problem with equating quantities with numbers is that creates a whole host of problems that we have to deal with, as he (284) goes on to point out.

He (285) exemplifies these problems and the absurdities it results by noting that the way we are tempted to think time works, divisible into certain measures of time, pushes us to make sense of each of these units by dividing it again and again, ad infinitum. He (285) asks us to consider what is an hour anyway? If you divide it, you get half an hour, then a quarter of an hour and then something that becomes harder to think, seven and half minutes, followed by 3 minutes and 45 seconds and so on and so forth, the point being that this way an hour never passes by, as he (285) points out, hence the absurdity of it. We could, of course, divide an hour by minutes and then by seconds, followed by fractions of seconds, but we’d run into the same nonsense.

For those who are interested in this issue, Aristotle mentions similar absurdities, commonly known as Zeno’s Paradoxes, in his ‘Physics’ (book VI, part 9), such as how the slowest runner can never be overtaken by the fastest runner because, while gaining on the slowest runner, halving the distance amounts to just that, halving the distance, and how an arrow can only be motionless as it can only occupy a certain place in space at any given moment. Aristotle rightly points out that you are an idiot if you think like this because time is not composed of moments.

Something tells me that you are now thinking that no one is that stupid, like come on, and I agree with you that no one thinks that a slower runner cannot be overtaken by a faster runner, nor that an arrow is motionless. That’s not, however, the problem here. The problem here is that people do regularly conflate time (duration) with the measure of time and space with the measure of space (not to mention that the measure of time is, in fact, a measure of space, based on the movements of astronomical objects), as they do with numbers and things (bodies and thoughts), as explained by Spinoza (285). In summary, the problem is that people “do in fact deny the Infinite”, as he (285) points out.

He (286) exemplifies the inadequacy of numbers, how numbers are not the same thing as quantities by presenting two non-concentric circles (III):

His (286) rendition looks slightly different, the size of the smaller circle being a bit larger and having named the larger circle A B and the smaller circle C D, but the differences in rendition don’t change anything. The point he (286) makes is that there are infinite positions for that smaller circle within the larger circle or, conversely, that there are infinite positions for that larger circle around the smaller circle. Numerical computation is of no use here, as he (286) points out.

The funny thing is that while we can conceive infinity as something that is unlimited or unbounded, we can also conceive infinity as limited or bounded, what he (287) also refers to as indefinite. To clarify this, in his ‘Ethics’ he (45) refers to the former as absolute infinity and to the latter as infinity after its kind. He explains this well in his letter to Meyer, but I believe the point he wants to make in his ‘Ethics’ with this distinction is to make sure that you do not lapse into thinking that there is something that is separate from substance from which everything else necessarily follows.

He (227) explains this better in one of his letters to Henry Oldenburg, noting that if we think of space as space, on its own terms, as pertaining to the attribute of extension, as one of the essences of (Spinoza’s) substance, it must be unlimited, i.e., absolute. If, however, we define it as limited by thought, then it is limited or bounded, it can only be infinite after its kind, in terms of space. We can also explain this by flipping this on its head. What I mean is that if the example he uses in his letter to Meyer wasn’t about infinity after its kind, that is to say infinite only in terms of space (extension), then he’d be contradicting himself, considering that, for him, only substance is absolutely infinite.

Anyway, as you can see, there is a maximum, as defined by the limits of the larger circle, and a minimum, as defined by the limits of the smaller circle, as indicated by Spinoza (286) in his letter to Meyer, so that we could even argue that it is possible to conceive a larger or smaller infinity if we alter the size of the circles, while maintaining that, be that as it may, we are still faced with infinite positions for those circles, as he (287) goes on to specify. Deleuze (204) comments on this, noting that it is indeed possible then to state that a mode has an infinity of parts, as does any mode, while also stating the infinity of its parts is, for example, double that of another mode without there being any absurdity to that.

Spinoza (286) acknowledges that you can, of course, use numbers, indicate the numerical size of one of the circles from which you can then calculate the size of the other circle or the numerical sizes of both circles, but that is beside the point, as that’s not what he is after here. In his (286) words:

“[The person] who would attempt to express all the inequalities of such a space by numbers must begin making the circle something else than it is.”

Again, this is not to say that we no longer have any use for numbers, nor that we can’t think of things as finite and divisible, as acknowledged by him (287), but rather that when we take a moment to think about this, it’s clear that’s not how things really are. We cannot rely on numbers to explain Spinoza’s substance or Hjelmslev’s matter. It would indeed be like “making the circle into something else than it is”, as Spinoza (286) points out.

I think Spinoza’s definitions of substance and its modes are quite useful as they help us to understand how, for Hjelmslev (32, 34), matter is a continuum, an amorphous mass or zone. What I mean is that when we have, for example, a continuum of sounds, there are infinite alternatives for laying down boundaries in this amorphous mass or zone, for gridding it, which results in a different number of figuræ (for sounds: phonemes), as pointed out by Hjelmslev (34-35). In his words (35):

“[T]he possibility that language can make use of are quite indefinitely great; but the characteristic thing is that each language lays down its boundaries within this infinity of possibilities.”

Make note of how he (35) uses the words ‘indefinitely’ and ‘infinity’ to explain this, matching Spinoza’s (287) definitions of unbounded infinity, pertaining to (Spinoza’s) substance, in itself, in its own terms, and bounded infinity or the indefinite, pertaining to the modes, to the modifications of (Spinoza’s) substance. In other words, explain this how Spinoza (45) explains this in his ‘Ethics’, (Hjelmslev’s) matter is, in itself, absolutely infinite, whereas, once specified, as this or that kind of matter, as formed matter, matter is merely infinite after its kind.

To be clear, the continuum of sounds discussed by Hjelmslev (34) is, of course, a bounded infinity, that is to say indefinite, as the production of sounds is bounded by the relevant parts of the human body, as also evident from his (35) examples. There are infinite ways to produce sounds within those bounds. In addition, those bounds also differ from person to person, so that one person’s infinity can therefore be larger or smaller than someone’s else. It is worth noting that the indefiniteness of this, the bounded infinity, has to with how the continuum is limited, pertaining only to sounds or, rather, the production of sounds. In other words, this continuum is not the continuum, matter itself, but rather a modification of it, which is why it is a particular continuum. If it were the continuum, about continuity itself, it would have no boundaries and we’d be dealing with matter.

It is the same with a thought continuum, what Hjelmslev (32) also refers to as an amorphous thought mass, as each language segments it in different ways. In his (32) words:

“Each language lays down its own boundaries within the amorphous ‘though-mass’ and stresses different factors in it in different arrangements, puts the center of gravity in different places and gives them different emphases.”

This simply means that there are infinite ways to segment a continuum into a number of minimal units, what Hjelmslev (34) calls figuræ (figures). In this case a continuum of sounds is segmented into a number of minimal sound units known as phonemes and a continuum of thoughts is segmented into a number of minimal thought units known as morphemes (or monemes). Guattari (207) comments on this:

“What defines a language is not signification, but its capacity for reproducing an infinity (a flow) of signs, given a finite (axiomatic) figure machine.”

Hjelmslev (32) elaborates on this:

“It is like one and the same handful of sand that is formed in quite different patterns, or like the cloud in the [sky] that changes shape. … Just as the same sand can be put into different molds, and the same cloud can take on ever new shapes, so also the same [matter] is formed or structured differently in different languages.”

Which means that, as noted by Guattari (207), for Hjelmslev (32):

“What determines its form is solely the functions of the language, the sign function and the functions deducible therefrom.”

To be clear, to make sure that you don’t think that matter disappears once it is formed into formed matter in relation to form, Hjelmslev (32) adds that:

“[Matter] remains, each time, [matter] for a new form, and has no possible existence except through being [matter] for one form or another.”

In other words, while matter is formed into formed matter, it is not irreversibly reduced into formed matter.

Right, it is time to return to the discussion of plane of immance. Deleuze and Guattari (254) warn their readers not to confuse these elements with atoms, as atoms are “finite elements … endowed with form”, whereas these elements do not have form, as already established. They (254) warn their readers not to think that these elements can be “defined by their number” as “[t]hey are infinitely small, ultimate parts of an actual infinity”, i.e., infinitesimals and infinities, “laid out on the same plane of consistency or composition.”

As you may have noticed, they (254) have opted to refer to the plane of immanence not only as the plane of consistency, but also as the plane of composition. This is particularly important for Spinoza (83, 95) as the movement of these elements pushes them to compound with one another, depending on how fast or slow they move in relation to one another, so that these elements come to compose other elements and, conversely, these composite elements come to decompose if the elements they are composed of come to move at different speeds. Composition is also a neat way to explain this as, for Spinoza (45, 54, 93), we can only understand the elements in reference to other elements, as each element is defined by other elements, as caused by them and conceivable only through them, whereas substance is defined by itself, as self-caused and self-conceived, as there can only be one substance. To be clear, the elements are distinct from substance, but substance is, nonetheless, their cause, not their transient, nor ultimate cause, but their immanent cause as nothing can be exist outside substance as only substance is self-caused, as he (62) points out.

As elements move, at this or that speed, they can be conceived as parts and/or wholes, so that what appears to be a part of a whole can itself be a whole that consists of parts. This is what Spinoza means with composition and decomposition when he (96) states that:

“We may easily proceed thus to infinity, and conceive the whole of [substance] as one individual, whose parts, that is, all [elements], vary in infinite ways, without any change in the individual as a whole.”

In other words, A and B can compose a composite C, which, together with D, can compose a composite E, so on and so forth, ad infinitum. Conversely, A can be understood as a composite, being composed of B and C, which in turn, are themselves composite, composed of D and E, F and G, respectively, and so on, and so forth, ad infinitum. This may trouble you as infinite composition and decomposition has no end. Surely it has to end somewhere? Well, yes and no. Yes, in the sense that we can reach a logical conclusion, where can no longer decompose something into something smaller, to a more basic unit, or compose something into something larger. No, in the sense that as substance is infinite, infinite composition and decomposition are not a problem. This has, however, more to do with our finiteness, how we think of this and/or that as also finite, whereas the infinitesimal elements are infinite, distinguished from substance, which is also infinite, by their movement. Anyway, Deleuze and Guattari (254) further elaborate this:

“There are thus smaller and larger infinities, not by virtue of their number, but by virtue of the composition of the relation into which their parts enter. Thus each individual is an infinite multiplicity, and the whole of [Spinoza’s substance] is a multiplicity of perfectly individuated multiplicities.”

Only to add that (254):

“The plane of consistency … is … abstract yet real and individual; its pieces are the various [composites] and individuals, each of which groups together an infinity of particles entering into an infinity of more or less interconnected relations.”

And (254):

“There is therefore a unity to the plane of [immanence], which applies equally to the inanimate and the animate, the artificial and the natural. This plane has nothing to do with a form or a figure, nor with a design or a function.”

They (254) warn us not to think of there being an origin or a goal to this, because, according to Spinoza (46, 77), substance has no beginning nor end, nor can it act or have a goal, as such, because it is self-caused, always perfect, and thus cannot lack anything. In their (254) words:

“Its unity has nothing to do with a ground buried deep within things, nor with an end or a project[.]”

Following that warning, they (254) define the plane of immanence once more:

“Instead, it is a plane upon which everything is laid out, and which is like the intersection of all forms, the machine of all functions[.]”

And once more (254):

“It is a fixed plane, upon which things are distinguished from one another only by speed and slowness. A plane of immanence or univocality[.]”

In addition, following Spinoza, here one is always many, as they (254) go on to emphasize:

“The One is said with a single meaning of all the multiple. Being expresses in a single meaning all that differs.”

This is also why they call it a plane of immanence, composition or univocality, instead of a plane of analogy. The problem with analogy is that it relegates difference as that which is between this and that, between A and B, which are taken for granted as meaning or identity, as the starting point.

What is interesting about this is not, however, the plane itself, what Spinoza calls substance. What is interesting about this is the infinite composition and decomposition, as they (254) point out. This is not to say that the plane is not important, nor interesting, but what follows from it, what flows from it, is even more important and more interesting. They (255) elaborate this:

“[T]here is a pure plane of immanence, univocality, composition, upon which everything is given, upon which unformed elements and materials dance that are distinguished from one another only by their speed and that enter into this or that individuated [composition] depending on their connections, their relations of movement.”

The consolidated take: consistency is consolidation

To use another word to explain this, in addition to the aforementioned consistency and composition, Deleuze and Guattari (329) state that “[c]onsistency is the same as consolidation”, “the act that produces consolidated aggregates, of succession as well as coexistence[.]” They (330) further elaborate this:

“Consistency necessarily occurs between heterogeneities, not because it is the birth of a differentiation, but because heterogeneities that were formerly content to coexist or succeed one another become bound up with one another through the ‘consolidation’ of their coexistence and succession.”

To link consistency and consolidation to composition and immanence, to mix this with the Spinozist terminology, they (507) summarize that:

“In effect, consistency, proceeding by consolidation, acts necessarily in the middle, by the middle, and stands opposed to all planes of principle or finality.”

They (549) mention in the notes that they borrow these terms, consistency and consolidation (and a couple of others, such as intercalation, i.e., insertion of something in between two things or parts, and interval, the relation between those two things, whatever they may be), from Eugène Dupréel’s work. I don’t have access to all of these texts, so I won’t comment on them in detail. I do, however, have access to ‘La Cause et l’Intervalle: ou Ordre et Probabilité’, which translates to something like ‘Cause and Interval: or Order and Probability’.

Dupréel (36-37) exemplifies this with two blocks of two of stone, A and B, lodged in moraine, situated at a certain distance from one another. The weight of the stones exert force that keeps them there, where they are in this imaged example. But there are also other forces at play, what he calls intercalary phenomena, such as wind, rain, gravel moved by a current and the like. These forces may be irrelevant to this scenario. They may also alter the existing state of affairs, so that the relation, in this case distance, between the two rocks changes. They may also reinforce the existing state of affairs, making sure that the stones remain where they are. For example, the deposition of gravel can cement the two rocks in place, without changing their position, so that the weight of the rocks is no longer relevant, so that the force of gravity is, no longer, the force that maintains the relation between A and B. This is what he, and Deleuze and Guattari, mean by consolidation. To be clear, it is not that gravity is not, no longer, relevant, at all, but that the relation between rocks A and B remain the same, even if the agglomeration that they are now stuck in changes place. Here intercalation involves a substitution of forces, so that the outcome remains the same despite the change in the forces. The interval of A and B is thus maintained by an intercalary term C, which is inserted in between them.

He (37-38) states that this is how everything is, for as long as it is, coexisting, arranged in this and/or that way, parts being held together and ripped apart by various forces. He (38) adds to this that consolidation can not only be spatial, i.e., about coexistence, but also temporal, i.e., about succession. He (38) exemplifies this with the rhythms of life, how people’s sleeping patterns are synched with the existing lighting conditions, i.e., consolidated in a certain way, so that if they move from one place to another with different lighting conditions, the change in conditions makes this apparent as people retain their sleeping pattern despite the changes.

Consolidation can, of course, also be social, regardless of whether it is spatial or temporal, as he (38) goes on to add. He (38) exemplifies this by noting that certain holidays occur at certain intervals, once a year at a certain date. For example, Christmas was originally a celebration of winter solstice, something for the people in the northern hemisphere (Europe). However, it is also celebrated in the south, even though the days don’t get longer, but shorter. This is because this holiday does not, no longer, have anything to do with the position of the sun. Instead, it has to do with beliefs and traditions. The point is that in this example religion, with its legends, dogmas and structures, appears to operate as a consolidator of succession (a temporal consolidator). One order of succession, the winter solstice of the northern hemisphere is consolidated by religion in the southern hemisphere.

But what is the value of consolidation? Why Deleuze and Guattari use it alongside consistency and immanence? Wouldn’t one of them be enough? Well, in my opinion, and this is, indeed, just my opinion, just my take, consistency emphasizes what things consist of, as a bit of this and/or a bit of that, whereas immanence emphasizes how it happens simultaneously, whereas consolidation emphasizes how all that what is drawn together in simultaneity, to this and/or that extent, in this and/or that arrangement or configuration, for as long as they hold together, tends to remain the way it is, so that the existing order of things is reproduced, as Dupréel (39) goes on to point out. It is not that things do not change, as they do, as this or this force can be substituted by that or by that force, but that they can and do change only so much. He (39) adds that this is especially the case where and when humans are part of the mix as humans can take various things into consideration so that this and/or that change do not have enough impact to change something else. He (39) exemplifies this with agriculture, how you can grow this and/or that crop, maximizing its potential, by knowing the soil and getting rid of the weeds.

To give you an everyday example, think of someone in some position. There are forces that maintain the person in that position. Those forces can be anything, weak, strong or something in between. If that person consolidates his or her position or is said to have consolidated his or her position, it means that the person is harder remove from that position. This can, of course, be good or bad, for that person, as well as good or bad for others. If someone is in a weak position, the good thing and the bad thing is that it is fairly easy to remove that person from that position. If you’d like that person to remain in that position, it’s bad. If you’d like that person to be removed from that position, it’s good. Conversely, if you like that person, the good thing is that it is hard to remove that person from that position. If you don’t like that person, the bad thing is that it is hard to remove that person from that position. In short, consolidation has to do with the arrangement, what makes that position weak or strong in the first place and what may weaken or strengthen it.

Dupréel’s (40) views are also in line with their views and Spinoza’s views, which is why it makes sense for them to refer to his work. He (40) emphasizes the organic (life) is not superimposed on the inorganic, nor an extension of it, nor its effect. That wouldn’t be immanent. Instead, he (40) argues that life is an intercalary phenomenon (taking place in the middle) that occurs at certain (spatiotemporal) intervals, maintaining and advancing a certain order of things, within or in relation to an existing order of things. Consolidation is also in line with Spinoza’s (136-137) view of how everything “endeavours to persist in its own being”, while also being subject to change. Related to this, I think it’s only apt that Guattari (152) states in ‘The Machinic Unconscious’ that the forms are homeostatic, i.e., self-regulating, maintaining themselves in equilibrium, not by resisting change but by adapting to it. So, in a way they change, in relation to what else is there, but only to maintain themselves, if that makes any sense.

As a sidenote, I couldn’t help but to notice how Dupréel’s intercalation is about what takes place in the middle. Deleuze and Guattari (21, 23, 25, 263, 286, 293, 296-298, 426, 432-433) like to tell us that we are always in the middle, in milieu, intermezzo, on a plateau, like grass that grows in between things, for example between paving slabs. This could take me on a tangent on grass grazing nomads, but this essay is going to be long enough even without it.

The psychoanalytic take: the BwO

If you are familiar with Spinoza, you should have little trouble understanding their Spinozist definitions. They also provide a different take on matter based on psychoanalysis (or, to be more accurate, schizoanalysis). If you are familiar with that instead of Spinoza’s work, you should find that easier to comprehend. This is something that they developed in ‘Anti-Oedipus: Capitalism and Schizophrenia’ and then reworked in ‘A Thousand Plateaus’. Anyway, they (43) call Hjelmslev’s matter also the Body without Organs (BwO). But what is the BwO?

I’d say that the easiest way to grasp this is to think of bodies in the broadest sense of the word again. For example, they (40) note that earth itself is a body without organs, which is why they also refer to it as planomenon in that context. If that doesn’t seem to make sense, think of earth as a planet, as a celestial body. That said, it could be what we generally think of as a body, a human body, like my body or your body, as in somebody, anybody. It’s just that simple, as they (8) point out in ‘Anti-Oedipus’:

[I]t is produced … as the identity of producing and the product.”

To make more sense of that, they (8) add that:

“Above all, it is not a projection; it has nothing whatsoever to do with the body itself, or with an image of the body. It is the body without an image. This imageless, organless body, the nonproductive, exists right there where it is produced[.]”

In other words, it is what it is, as they (9) go on to point out. It lacks nothing. It is perfect in its own right. It has no origin nor destination. That is all very Spinozist to me, albeit it might also be just me seeing things that way, having just covered the Spinozist parts.

The initial problem with the BwO is that it is easy to think of it as having to do with a dismembered and/or a gutted body, as a body that lacks body parts, but that’s not what they are after with that. If you think that a body has organs, for example limbs, that it needs to have them, you are already on the wrong track. It is rather about bodies that are not organized. This is why they (30) state in ‘A Thousand Plateaus’ that:

“A body without organs is not an empty body stripped of organs, but a body upon which that which serves as organs … is distributed[.]”

And (30):

“[T]he body without organs is opposed less to organs as such than to the organization of the organs insofar as it composes an organism.”

As well as (30):

“The body without organs is not a dead body but a living body all the more alive and teeming once it has blown apart the organism and its organization.”

As you can see, it is the same as Hjelmslev’s matter or their plane of consistency, pertaining to consistency, composition, style or consolidation that brings together heterogeneous elements, whatever they may be. They (40) state that:

“This body without organs is permeated by unformed, unstable matters, by flows in all directions, by free intensities or nomadic singularities, by mad or transitory particles.”

Only to add that (40):

“In effect, the body without organs is itself the plane of consistency.”

The problem with BwO or, rather, the way it is discussed by the two in ‘A Thousand Plateaus’ is that it sometimes appears to be the same as the plane of consistency and sometimes distinct from it. They (507) acknowledge this in the conclusion:

“Does the plane of consistency constitute the body without organs, or does the body without organs compose the plane? Are the Body without Organs and the Plane the same thing?

If I understand their answer correctly, they (507) answer this by noting that this is a matter of perspective, as “composer and composed have the same power.” From the perspective of Hjelmslev’s matter, of Spinoza’s substance, we are dealing with the plane. From the perspective of Hjelmslev’s formed matter, understood in relation to form, of Spinoza’s modes of substance, that is to say from our perspective, we are dealing with the BwO. At least in ‘Anti-Oedipus’ they (19) venture to explain it from our perspective:

“The body without organs is an egg: it is crisscrossed with axes and thresholds, with latitudes and longitudes and geodesic lines, traversed by gradients marking the transitions and the becomings, the destinations of the subject developing along these particular vectors.”

The point with the egg is that it is an undifferentiated body, whereas the body of a hatched creature is already differentiated, meaning that its body can only do whatever it is capable of based on its constitution. Okay, it is the same with the egg, no doubt, but without knowing what that egg is, what it contains, it is capable of virtually anything once it hatches. To be clear, it is not actually capable of anything, because it will have its limitations. The point is rather that inasmuch as we don’t know what it is, a bird or a dinosaur, or something that we have never even encountered, it might become capable of just about anything.

Guattari (284) explains this in other words in ‘Planes of Consistency’:

“The body without organs is essentially a principle of corporeization and individuation [strata]: it is the production of subjectivity … by the way of the promotion of localized enunciation.”

They discuss this in more detail in ‘A Thousand Plateaus’, dedicating an entire chapter or plateau to it, ‘How Do You Make Yourself a Body without Organs’. The point of that chapter or plateau is that the BwO is something that you make, which means that it is a matter of practice, exercise or experimenting, as they (149) point out immediately, following an image of a Dogon Egg (a mythical egg of the world for the Dogon people). In their (149-150) words:

“It is not at all a notion or a concept but a practice, a set of practices.”

They (150) add to this that it is not only something that can be done, but also something that is done. Every time you experiment something, you are making yourself a BwO. In other words, here the BwO is discussed as an everyday thing. What they (161-162) want to emphasize here is that it’s about experimentation, trying out a bit of this and/or a bit of that, letting go of yourself as a subject. It has these notions of pliability and malleability, capacity to be transformed, that make them (411) think of metal as a BwO par excellence, being “neither a thing nor an organism”.

To my understanding, the way I understand it, the problem with the plane is that it seems so all encompassing, which is the point, considering how it is Spinoza’s substance, which is all there is, at least before we address the modes. In contrast, BwO allows them to situate it, to localize it, so that any body can be understood as a body without organs, me, you, this chair that I’m sitting on, this keyboard that I’m writing on, even the whole planet, while also making it so it is, nonetheless, the plane. Then again, from an another point of view, it’s not as apt as that plane when you try to get the point across. There is a risk of getting stuck on the subject, which is exactly what they do not want.

The thing is that BwO is carried over from ‘Anti-Oedipus’, where it is used quite frequently, to ‘A Thousand Plateaus’, where it is used less frequently, at least when compared to the number of times plane of consistency is mentioned. It makes more sense in ‘Anti-Oedipus’ as some of the terminology, such as desire and desiring machines, just makes it easier to comprehend what they are after with it. I’d say that it this specificity to desire that they (154) mention in ‘A Thousand Plateaus’ that makes it hard to grasp unless you already know what they mean by desire.

Hjelmslev’s net

Now that it should be clear what Hjelmslev’s matter (aka matter-meaning, meaning, purport and sense) is all about, how it is a plane (and a body without organs) for Deleuze and Guattari, it is time to move on, to explain how content and expression, formed matter (substance) and form come together (IV):

This is Hjelmlev’s (36) net, using his terms, as translated by Whitfield, appearing “just as an open net casts its shadow down on an undivided surface.” I modified it, using other terms that I find more apt for the purposes of presenting it like this (V):

Here plane and matter, together as the matter of the plane, have a white background, the content and expression planes have a black background, and formed matter and form have a grey background. To purpose of using these different backgrounds is to visualize how we have matter, on one plane, content and expression that presuppose one another, and formed matter and form that make little sense without one another. The important thing here is to realize that formed matter appears only as form is projected on matter, as explained by Hjelmslev (35-36). This is exactly why I think it is more apt to refer to it as formed matter, requiring both matter and form, instead of referring to it as substance. It is not, however, wrong to refer to it as substance. I think it is just more intuitive this way. What I wanted to do here is to just clarify how formed matter and form only make sense once they cast a shadow on “an undivided surface”, on matter or plane (matter of plane), as indicated by Hjelmslev (36).

Stratification

Hjelmslev changes the terms a bit in ‘La stratification du langage’. Guattari (204) comments on the changes in ‘Hjelmslev and Immanence’, noting that prior to this Hjelmslev was still fairly conservative, upholding Saussure’s legacy, only to do “everything he could to mess this all up” in ‘La stratification du langage’ by opting to think of everything in terms of strata. To make sense of strata, they are the compartments or panels formed on the plane by Hjelmslev’s net, as mentioned by Guattari (205) in ‘Hjelmslev and Immanence’ and as further explained by Guattari (284) in ‘Planes of Consistency’, so that formed matter of content, form of content and formed matter of expression and form of expression are all strata.

To be clear, Hjelmslev does not really focus on the stratification of language, but rather on the stratification of semiotic systems, as he (165) is quick to point out in his own text. The thing here is that he wants to focus more closely on the strata, rather than on the two planes, which distances him from Saussure, as he (165) himself points out. He (165) retains the planes from Saussure, but the strata are his conceptions.

The relationship between the formed matter and the form is referred to by him (166) as manifestation. He (166-167, 170) calls the relation between these two manifestation because the form has to be manifested or demonstrated in something to be apparent to us. To be more specific, this also means that the form is to be understood as the manifestee, and the formed matter the manifestant, as indicated by him (186), while a manifestation, the relation between the two, is composed of figuræ (figures), as he (186) goes on to point out. To be clear, the figuræ (figures) are what make that relation that manifestion and not some other manifestation. In addition, the relation between the two planes, or more specifically, the two forms of the two planes, is what he (170) calls solidarity. In the case of ordinary language, what he also refers to as a denotative semiotic, this solidarity is known as denotation, as he (170) goes on to add.

The emphasis on form (on form of content and form of expression) still remains, as indicated by him (169). Form is now understood as an exclusive set to which something is chosen from the formed matter, whereas, conversely, the formed matter is an inclusive set or, rather a more inclusive set than the form, as explained by him (172). We always focus on the form and if we wish to be more inclusive, that is to say turn our attention to the formed matter, we still focus on the form, perhaps a form that is more inclusive than a previous form, but a form nonetheless, as he (172) goes on to add. In other words, there is always more to investigate, always some residue, as we can only investigate matter through form and, at best, comprehend it as formed matter. This is why he (172) he states here that form and formed matter are not absolute terms, only relative terms. What he means by this is that the distinction between form and formed matter is an auxiliary distinction that we make in order to comprehend how we make sense of matter through form.

Guattari (42) also comments on this in ‘The Machinic Unconscious’, noting that while we have matter and we can only make sense of that matter through form, we do need the formed matter (Hjelmslev’s substance) to be there for us to make any sense of this. In his (42):

“This should quite naturally lead us to only consider the existence of forms insofar as they are expressed or enacted by particular substances.”

So, yes, I’d say that Hjelmslev is correct when he (169) gives emphasis on form, as that is how we make sense of matter, but Guattari (42) is also correct in the sense that we cannot make sense of forms without there being that formed matter, without there being actual expressions. If the act or the expression is not there, if there is no articulation or, rather, double articulation, there is nothing for us to consider.

Guattari also comments on this in ‘Lines of Flight: For Another World of Possibilities’. He (117) noes that the substances or formed matters of content and expression are their meanings. What he (117) means by this is that matter always appears to us as substances, as formed matter, and that we can only make sense of form inasmuch as “it is manifest, functionalised in substances.” In other words, we make sense of matter through form, which is why he (117) states meaning appears in substance or formed matter. He (118) summarizes this by stating that:

“No form can exist for itself outside of processes of formation.”

He (118) wants to emphasize this in order to prevent people from thinking that forms are like Platonic ideas that exist for themselves, as pre-existing, and then just somehow manifest themselves in reality as representations of those forms.

While this distinction between form and formed matter is only relative, not absolute, it is, nonetheless, helpful once you get over the initial confusion. Hjelmslev (173-174) notes that formed matter serve form and that there are, in fact, multiple formed matters may share a form, which means that forms may exhibit multiple formed matters. He (173-174) exemplifies this with how we can express something in different ways. We can, for example, say it, write it or draw it. This is why he (174) stresses that the relationship between formed matter and form is manifestation. To be more specific, he (174) notes that we typically think that, for example, speaking and writing are separate from one another, having distinct forms. He (174) thinks that this is incorrect as there is a single form, in this case the form of expression, that has multiple formed matters that compete for their manifestation. This does not, however, mean that a certain formed matter cannot serve another form on another plane, i.e., as a form of content, as he (174) goes on to point out. The limitation applies only to each plane considered in isolation, as indicated by him (174-175).

To paraphrase this, any number of formed matters can be manifested by the same form, but any number of forms cannot manifest the same formed matter. In other words, a form may impose itself on any number of formed matters, which is why I have opted to refer to it as formed matter rather than substance. This only makes sense, considering that matter only appears to us as formed matter, having this or that form. In short, matter appears to us as having a form, whatever that may be, but it cannot exhibit itself as having multiple forms at the same time. This also applies to content, so that the same form of content, for example an animal, is conceived in different ways, selecting only of its features, for whatever reason. He (176) exemplifies this with the word ‘dog’, how it has the same form of content, but not the same formed matter for different peoples, so that to some it is marked by its utility, used for as a draft animal or as a hunting animal, while for others it is a holy animal or an unholy animal. In other words, the same animal is manifested to us in a certain form, as arranged in this and/or that way, because different peoples collectively appreciate different things in them, as he (176) goes on to add.

To be clear, the net should not be presented like this (VI):

Nor like this (VII):

Why? Well, because there is no sequence, no linear progression from one to another, no move from a plane to two planes, nor a move from purport to substance followed by a move from substance to form. Instead, it should be presented like this (VIII):

The point here with the ⇌ is to indicate how formed matter and form appear at the same time. I also tried to make it clear that we can think of this, all of this, in two ways, so that, on one hand (on the left-hand side), we have the plane which is then presented as two planes, and, on the other hand (on the right-hand side), we have the net that is projected on matter.

I think the presentation could still be improved upon as it might still make you think that we move away from matter, having only formed matter and form in its stead. Perhaps this is more intuitive (IX):

I think this is better or, rather, more intuitive presentation of what is going on because formed matter and form now appear on matter, like a net thrown on a surface, rather than appearing next to it, outside of it. I am well aware that is not how this is usually presented, so feel free to object to this. What I wanted to do here with this presentation is to make it clear that the net is cast upon matter. This simply means that content and expression, and formed matter and form, all appear simultaneously, projected on matter. There is no separate matter that exists outside formed matter and form. Instead, we know matter only through formed matter and form. To be clear, matter does not magically cease to exist nor end up having no role in this once the net is there.

The problem with presenting everything on one plane, in 2D, is that it might make you think that formed matter and form are still separate from matter, nested in it, or so to speak. It might not make you think of this as a grid, like an overlay (X):

What is at the bottom is matter, what is in the middle is formed matter, and what on top is form. The point here is to illustrate how formed matter only makes sense as matter overlaid by form. I kept the white and grey here just because I wanted to keep the presentation consistent. The problem with this is, however, that it makes it appear that matter, in its infinity, appears to us as formed matter, like we knew it all at the same time through this and/or that form. To use Spinoza’s circular presentation in his letter to Meyer, this could also be presented like this (XI):

The point here is to indicate how there are infinite ways of forming the matter, albeit always to this or that extent, within these or those limits, something which isn’t (that) apparent in the tabulated presentations. I think this also illustrates what Hjelmslev (32) refers to as the arbitrary relation between matter and form. Here form, the outline of the smaller circle, is in an arbitrary relation to matter, the larger circle, meaning that it could be in any position within the larger circle, there being infinite alternatives to it, while forming the matter into formed matter, indicated here by the grid overlaying the grey within the smaller circle. I don’t think the grey is needed here, as the grid would do just fine, but I’ve kept it here for the sake of consistency.

Moving on, Hjelmslev (36) states that to go from one formed matter, from the formed matter of content, to another formed matter, to the formed matter of expression, it can only be done through forms. This is why the previous formulations need to be altered yet again. Let’s go back a bit, to the more traditional presentation (XII):

The point here is that, according to Hjelmslev, the formed matter of content is isolated from the formed matter of expression, as explained by Guattari (205) in ‘Hjelmslev and Immanence’. The thing to keep in mind here is that content is always the content for an expression, which is why we commute from the content plane to the expression plane through the forms.

If we approach this from the point of view of functions and functives, the sign function is between the two functives, between the form of content and the form of expression. Therefore the sign is the unit that consists of the two functives, form of content and form of expression, operating as the sign for both the formed matter of content and the formed matter of expression, as explained by Hjelmslev (36). It is in that sense that we can indicate that there are two movements, one going to the inward direction, toward the formed matter of content, and another going to the outward direction, toward the formed matter of expression, as specified by Hjelmslev (36), as presented like this (XIII):

To go back a bit, we can also present this in a more intuitive manner (XIV):

It is also worth noting that while the content plane and the expression plane are distinct from one another, there is no reason to call one content and the other expression, as noted by Hjelmslev (37). Point here is that there are two functives, content and expression, that function in relation to one another and the only reason for him (38) to call them content and expression, instead of functive A and functive B, is conformity, using terms that people are already familiar with. Therefore, we could also present it all like this (XV):

As an expression can double as content for another expression, we might as well make this apparent in the presentation (XVI):

Note here how I switched back to ↓ from ⥮. I did that only because it makes sense, as a first expression is, of course, something that takes place before a second expression.

We can also explain this as pertaining to double segmentarity, aka double articulation, as done by Deleuze and Guattari (40-45, 57-58, 64, 72, 142-143, 352, 502, 504) in ‘A Thousand Plateaus’. The point here is that an articulation is always a double articulation, involving both a content and an expression, as they (502) point out. But before I explain what double articulation is, it’s worth clarifying what articulation is. The short answer is that it’s about division or segmentation. Saussure (10) explains this in ‘Course in General Linguistics’:

“In Latin, articulus means a member, part, or subdivision of a sequence[.]”

To which he (10) then adds that:

“[A]pplied to speech, articulation designates either the subdivision of a spoken chain into syllables or the subdivision of the chain of meanings into significant units[.]”

Which then leads him (10) state that:

“[W]hat is natural to mankind is not oral speech but the faculty of constructing a language, i.e. a system of distinct signs corresponding to distinct ideas.”

In my view, what’s worth noting here is not the last point, as Hjelmslev wouldn’t agree with that, there being correspondence, nor would Deleuze and Guattari, but that you have two divisions or segmentations. That’s what’s worth noting here. It leads us to double articulation, which is a term borrowed from André Martinet. He (34) explains it concise manner in ‘Double Articulation as A Criterion of Linguisticity’:

“Double articulation posits the existence of a process whereby a person who wants to communicate an experience unconsciously lets that experience be analyzed into a succession of elements, each one corresponding to one of the monemes of the language he will be using for his communication, and ordered according to the syntactic patterns of that language.”

As a sidenote, if you are unfamiliar with monemes, it’s an umbrella term for morphemes, like when you have different plural morphemes in English but only one plural moneme, as explained by Martinet (34). Anyway, that is the first articulation, which is then followed by the second articulation:

“The second articulation, that of the vocal, perceptible face of the monemes into phonemes[.]”

He (34-35) elaborates this, further emphasizing that this is not a conscious process:

“[It] does not result from a process performed by the man who is about to speak: as soon as the suitable moneme has been chosen, its vocal form, ready made, will be at his disposal; the choice of the moneme horse will automatically determine that of /hɔrs/ with its four phonemes in that order; the speaker’s only problem will be to prevent various forms of interference due to situation or context from tampering with the normal production of /hɔrs/.”

What he means by double articulation is that each articulation is, in itself, double, not that we articulate something once and then a second time, as Martinet (37-38) and Deleuze and Guattari (44) point out. There is always more articulation, followed by more articulation, as acknowledge by Martinet (37-38). He (228) further explains double articulation in a section dedicated to him in Herman Parret’s ‘Discussing Language’:

“[L]anguage, organized as language, with its double articulation, supposes from the start a limitation of what can be communicated[.]”

He (228) reckons that “only what can be said is said” as “[a] language segments the world in a certain way”, so that “[o]ur need for communication is limited by language” while, at the same time, “we would be lost in the mist” were it not for language. This is also why Deleuze and Guattari refer to double articulation also as double segmentarity, as already noted. Anyway, we could present it like this (XVII):

Martinet (237) also further comments on this in the section dedicated to him, noting that contrary to many others who start from phonology and then move to syntax, the movement is from content to expression, not the other way around, so that the first articulation deals with content and the second with expression. Deleuze and Guattari (40-41, 44) go with Martinet on this one.

The thing with double articulation is that it involves an initial move from formed matter to form, followed by another move from form to formed matter, as explained by Deleuze and Guattari (40-41). This means that it appears to be incorrect to present manifestation, the relation between the two strata, as ⇌ rather than as → and ← respectively (XVIII):

Hjelmslev seems to have changed his view on the relationship between formed matter and form, considering that he (179) acknowledges in ‘La stratification du langage’ how different formed matters can serve the different form, rather than presenting them as appearing simultaneously, as explained by him (35-36) in the ‘Prolegomena’. I don’t know if this change is attributable to Martinet or not, but, be that as it may, there seems to be a change here. Then again, I don’t know whether it changes anything, really, considering the problem with this presentation is that it ignores how “[e]ach stratum exhibits phenomena constitutive of double articulation”, how they are already doubled, as noted by Deleuze and Guattari (40). In other words, this is correct, but only insofar as we consider double articulation in isolation.

To be honest, I don’t think it matters what we call these, functives, content and expression, the first and the second expression, or the first and the second articulation, as the point is that they can double up, as one can act as the other. That’s why Deleuze and Guattari (44) point out that “[e]ven though there is a real distinction between them, content and expression are relative terms” and that they “are two variables of a function”, so that “‘first’ and ‘second’ articulation should also be understood in an entirely relative fashion”. This is also why Guattari (204) notes in ‘Hjelmslev and Immanence’ that as this is the case, we might as well call one A and the other B.

Guattari (60) vizualizes the relation between content and expression and double articulation slightly differently in ‘Schizoanalytic Cartographies’. I have edited it a bit to illustrate this point better, as he (60) is addressing something else as well, which I am not doing here (XIX):

So, this is how content is linked to the given, from which we appear to start, that being the first articulation, and cross over to expression, which is linked to the giving, that being the second articulation. Now, obviously you can’t have something that is simply given, as it is the giving that gives us the given, yet, you need the given to get more giving, and so on, and so forth, ad infinitum.

To make more sense of this, I edited his (60) original a bit more, to include the vertical arrows that are in the original and a horizontal arrow that is not in the original (XX):

The vertical arrows, pointing up and down, have to do with deterritorialization (which I will explain in the next essay), whether something is infinite (up) or finite (down). Think this is terms of various parts, as already discussed, that form finite (down) complexions and territorial cutouts, and infinite (up) rhizomes and constellations, as he (58-59) points out. The infinite ones are far from equilibrium, i.e., far from stable or balanced, and the finite ones are close to equilibrium, i.e., close to stability or balance, as he (61) goes on to add. In terms of their deterritorialization, the infinite ones are drifting irreversibly, whereas the fines ones are drifting reversibly, as he (61) also points out.

The horizontal arrow has to do with discursivity, whether what we have is the given (left), which he (59) indicates as being plural, or giving (right, which he indicates as being unary. On the plural or given side (left) you have the rhizomes (up) and complexions (down), and on the unary or giving side (right), you have the constellations (up) and the cutouts (down), as listed by him (58-59).

This may seem a bit bizarre, but, what I get out of this is how the given is always highly complex, i.e., plural, hence our difficulty of coming terms with it, whereas, oddly enough, the giving is fairly simple, i.e., unary. How so? Well, as he (58, 61, 69-70) points out, in terms of discursivity / non-discursivity (that horizontal left-right arrow), all that is unary (right, giving, non-discursive) is marked by discontinuity, appropriation and mixing, whereas all that is plural (left, given, discursive) are marked by (intercalary) continuity, multiplicity and fusion. In other words, in the process of giving, something is always taken (or extracted, appropriated) from the given (continuity, multiplicity) and rendered much more simplistic (discontinuous). Now, of course it’s not simply about giving, as something separate from the given, as giving is always about giving the given, on the basis of the given, in n-number of articulations.

To give you an example, something that is just thought, when you express something, you take it from a great pool of what else is there. You have a lot of options. It could something very simple. It can also be very complex, but it will never be as complex as from where it is extracted, subtracted or appropriated. This is why, for him (58) the unary is reducible to being about expressing something in terms a “minimal discursive alternative ‘there is/there is not’.”

This is great in two ways. Firstly, it appeas that the given is always something really complex. You take something from it, which will then be less complex than from which it was taken. Secondly, oddly enough, it appears that the given, in all its complexity, is based on the giving, which is something that can be very simple.

He doesn’t call it double articulation in this context, but he (67) refer to it as the “double movement of the affectation and the effectuation of consistencies”. To clarify this is a bit, he (66) indicates that the movement from the given or content to the expression or giving is the affect part or its virtualization (the potential of whatever it is that we are dealing with, could be this and/or that). Conversely, he (66) states that the movement from the giving or expression to the given or content is the effect part or its actualization (when that something was once was virtual, a mere potential, but there nonetheless, comes into effect). This only makes sense if you consider the two at the same time, not one after another (as if there was such a thing as some given that has not been given, one way or another and as if there was some giving that didn’t involve some given, something that you work with). In other words, there needs to be that reciprocity, what Hjelmslev (30) calls solidarity in in the ‘Prolegomena’.

In short, given is always, in a sense, an effect, what’s already there, in effect, if you will. It’s what has to be there for anything to happen. As Hjelmslev (30) points out, there is no expression without content. Similarly, giving is always an affect or, rather the affectation, what must take place for there to that effectation, which, once in effect, we consider to be an effect. So, again, as Hjelmslev (30) points out, there is no content without expression.

It doesn’t matter what terms we use here as there’s still a problem that needs to be addressed. Well, it’s not a problem that has anything to do with the way Hjelmslev explains all this, but rather how I present it. The problem with my presentation is that no matter what terms I use, I risk presenting this as if there were something that just is the content for some expression. This is why the presentation needs further modification (XXI):

The point here is to illustrate how we have a functive that functions as the content for an expression, which, in turn, is also a functive that functions as the content for another expression. This is how they double up. This should also make it clear to you how it is somewhat misleading to call one articulation the first articulation and another the second articulation. There is no first, nor second expression. We might as well present it like this (XXII):

The point is to illustrate how just have functives link up in functions. It does, however, make more sense to use content and expression to explain how the two functives function in relation to one another. Now, I expanded this only by adding one extra functive to the mix, but we could go on and on with it, ad infinitum. The problem here is that no matter what you do, it’ll look like there is a first and a last functive or articulation. If we isolate this as having three articulations or two sets of double articulations, it does make sense to replace the initial ⇌ with → and the final ⇌ with ←, but that’s the problem right there, thinking of the process as consisting of isolated instances. There is always something before and something after, which is why in ‘A Thousand Plateaus’ Deleuze and Guattari insist that we always in the middle, in between whatever it is that we are dealing with, both spatially and temporally.

Guattari (205) comments on this in ‘Hjelmslev and Immanence’, noting that it would be more apt to abandon the formulation in which there are two planes, one for content and another for expression, in favor of one plane, the plane of consistency, because there is no beginning nor an end, only n-number of articulation and n-number of strata.

The problem with all the formulations is that they focus solely on one semiotic mode, in Hjelmslev’s case language. To be more specific, he explains all of this in terms of ordinary language, what we might also call a denotative semiotic, as opposed to a connotative semiotic or a metasemiotic, as indicated by him (168) in ‘La stratification du langage’. This is done for the sake of simplicity of presentation, as pointed out by him (168-169).

Levels: Layer upon layer

Hjelmslev (177-178) further complicates things by noting the strata are, in themselves, stratified. In other words, even the layers have layers. What I’ve covered so far, the ordinary language, i.e., the denotative semiotic, is the most immediate and apparent level as it pertains to collective appreciation, but it is not the only level, as he (177) points out. He (178) lists two additional layers: the socio-biological level and the physical level. The three levels exist in a hierarchy. The physical level is at the bottom, forming the physical basis of everything else. It is overlaid by the socio-biological level, which, in turn, is overlaid by the immediate semiotic level. This is how we get three levels that operate on both planes, as he (177-178) points out. This is also why his formulations are also applicable to something that is non-semiotic, as acknowledged by him (168). We could present the three levels as something like this (XXIII):

The problem here, however, is that the semiotically formed matter, appears to be isolated from the physically formed matter, when, in fact, it is, not that simple. This is easy to grasp as we are, in fact, constantly dealing with the socio-biologically formed matter, as well as the physically formed matter, at the same time. Our access to the physically formed matter is therefore not simply negotiated by the socio-biologically formed matter, except in the sense that we are, of course, socio-biologically constituted.

Anyway, the point he (177-178) wants to make is that just as formed matter serves form, involving a choice or deduction of matter, in order to appear as formed matter, as Deleuze and Guattari (40) point out, the socio-biologically formed matter and physically formed matter also serve the semiotically formed matter, so that the formed matter involved is each time chosen or deducted from the non-semiotic levels to serve the semiotic level. That said, this also works the other way around so that the semiotically formed matter specifies the socio-biologically formed matter and the physically formed matter and that the socio-biologically formed matter specifies the physically formed matter, as he (178) points out.

To explain this in plainer terms, the readily apparent semiotic level feeds on the non-semiotic levels. For example, the socio-biological level and/or physical level are always there when we speak (speech organs, vibrations of air), when we write (hands, paper), draw (hands, paper), paint (hands, paper/canvas), shake hands (hands) or just smile (facial muscles). We can also further narrow down these, to point out the obvious, how, for example, writing typically relies on a black or otherwise dark ink, a liquid substance (formed matter!), or solid pigment (formed matter!) that is applied on a sheet of paper (formed matter), to do the job and, to be honest, it does the job really well. We can contrast it with, for example, with drawing and painting, which use different solid or liquid substances (formed matter) that make it possible to use color to convey a sense (matter-meaning!).

The inorganic and organic strata

Despite introducing them, Hjelmslev (179-181) barely comments on the two non-semiotic levels. Deleuze and Guattari, however, do. They (502) call the physical level a physicochemical stratum, which is why I have opted to call the levels layers (in case you wonder about that choice).

Hjelmslev (179-182) would not agree with that, considering how he insists that levels are levels, pertaining to different formed matters that, in turn, pertain to matter, not different layers or strata, but I’m going to with Deleuze and Guattari on this one, considering that he does not further elaborate on these, whereas they do. Hjelmslev (182) considers the levels superimposable, having some correspondence of structure between the levels, which is nowhere to be found between the strata (between formed matter and form, nor between content and expression). I’d say that the thing with Hjelmslev is that he is so focused on the semiotic level that he ends up relegating the non-semiotic levels to a secondary status, whereas Deleuze and Guattari are willing to go shed this prejudice toward them and explore them on their own terms as strata.

 It’s also worth noting that I prefer calling the physicochemical stratum the inorganic stratum because they contrast it with the organic stratum. I have used this example before, probably more than once already in my previous essays, but I’ll go with anyway because it’s also the one they (41):

“In a geological stratum, for example, the first articulation is the process of ‘sedimentation’, which deposits units of cyclic sediment according to a statistical order: flysch, with its succession of sandstone and schist. The second articulation is the ‘folding’ that sets up a stable functional structure and effects the passage from sediment to sedimentary rock.”

To be clear, they (41) exemplify this process or double process with sedimentation, which I think is an apt choice, but I’m not so sure about what they call folding. I think it would be more apt to call it cementation. I’d say folding is what follows or, rather, may follow cementation. To my understanding, in geology folding has to do with the bending or curving of the cemented sediment, in this case the sandstone strata. It is a deformation that occurs under certain conditions. In the French original, in ‘Capitalisme et schizophrénie: Mille plateaux’, they (54) refer it to as plissement, which to my understanding translates to what is known as active folding or buckling in geology. It occurs when the strata buckle under lateral pressure, so that they shorten horizontally but thicken vertically, which results in folds. I don’t think it matters that they skipped the process of cementation, because that only means that their example of physical level double articulation is a bit off. When you make that correction, it still holds. No problem.

The reason why Massumi may have opted to translate that as having to do with folding might have to do not only with how bucking is, in itself, a type of folding, but also with how the word ‘fold’ works better on its own than the word ‘buckle’. Fold (OED, s.v. “fold”, n.¹) was once used as pertaining to a surface:

“The surface of the earth; the ground.”

And (OED, s.v. “fold”, n.¹):

“Dry land; the earth, as the dwelling-place of man. in, on, upon fold: on the earth; often as a mere expletive.”

While the word is not, strictly speaking, used this way anymore, that seems to be its etymology, probably being related to what we these days call a ‘field’. The word can also pertain to an enclosure of some kind (OED, s.v. “fold”, n.²):

“An enclosure of any kind[.]”

Most cases have to do with shepherding, but that is beside the point. What I find interesting here is how fold has something to do with enclosed space. That’s actually the general sense of the word: (OED, s.v. “fold”, n.³):

“A layer or ‘thickness’ (of cloth, etc.); a coat (of an onion).”

This is actually relevant to the lecture I gave, but I won’t get tangled up on that. Anyway, there seems to be an added emphasis on what changes it brings about (OED, s.v. “fold”, n.³)

“A bend or ply, such as is produced when any more or less flexible object is folded; one of the parts, or both of them together, which are brought together in folding[.]”

Or, in plainer terms (OED, s.v. “fold”, n.³):

“Something that is or may be folded; a leaf of a book, a sheet of paper, one of the leaves of a folding-door.”

And relevant to geomorphology (OED, s.v. “fold”, n.³):

“A winding or sinuosity; spec. an undulation or gentle curve of the ground; a slight hill or hollow; the general grouping of heights and hollows.”

And relevant to geology (OED, s.v. “fold”, n.³):

“A bend in rock strata, esp. one having a wave-like form.”

As you can see, folding is not only relevant to geomorphology and geology, albeit I’d say Deleuze and Guattari are still getting ahead of themselves by skipping the process of cementation. That said, I think fold is, in fact, otherwise a very apt word to use here, considering it has that sense of being a surface, you know like a stratum or a layer, and an enclosure, like how layer is always on top of something else, in addition to being bendy or pliable.

Other good alternatives would be ‘ply’ (OED, s.v. “ply”, n.) as it pertains to “to layers and flexion”:

“Originally: a layer or thickness of cloth or fabric, a fold; (later also) a strand or twist of rope, yarn, or thread (also figurative).”

And (OED, s.v. “ply”, n.):

“Now also: any of the layers composing a multilayer material such as plywood or laminated plastic.”

And, understood as an attribute (OED, s.v. “ply”, n.):

“Designating a material or product composed of the specified number of layers or strands.”

Plywood is, of course, a very good example of this, as mentioned among the dictionary definitions.

Ply also shares the notion of bendiness or pliability with fold (OED, s.v. “ply”, n.):

“A bend, a part of something which bends; esp. a hinged joint part way along a limb.”

And (OED, s.v. “ply”, n.):

“The condition of being bent or turned to one side (literal and figurative); a twist, turn, direction; a bias, inclination, or tendency of mind or character.”

It’s also possible that Massumi was aware that Deleuze was working on a book on Leibniz, which came to be known as ‘Le Pli: Leibniz et le Baroque’, subsequently translated to English as ‘The Fold: Leibniz and the Baroque’. It is in this book that Deleuze takes a closer look at plissement or folding. These terms invite us to examine how the world works in Leibnizian terms, if that’s what you are into, instead of psychoanalytic or Spinozist terms.

As I’ve explained in the past, if you are familiar with the process of sedimentation and cementation, perhaps because you’ve studied geology, geomorphology and/or hydrogeography, this should be easy for you to comprehend. I can’t say I’m an expert in any of those fields, but I’ve done the relevant introductory courses, so their example was super clear to me. The point here is that streams and rivers pick up all kinds of formed matter in the flow, selecting or deducting certain types of matter, typically sand, and deposit it downstream, where that matter is reformed as matter, cemented into layers of sandstone. If you’ve ever seen a cross section of sandstone, you can see these layers. Now, of course, streams and rivers don’t come ready made, nor does the matter exists without form, amorphously, which is why this process or dual process (sedimentation/cementation) should not be considered in isolation, although, I know, I just did that, as do they (41). Instead, we need some formed matter, for example sand, to exist in order for it to eroded and then subsequently be carried away. It’s the same with the sandstone. They undergo further changes as more and more layers are deposited on top of each other, and may undergo a metamorphosis under certain temperatures and pressures, so that we can longer identify the deposited layers as sandstone but as, for example, quartzite. The point here is that matter is constantly (re)formed.

Another example they (49) provide is the process of crystallization that occurs on a crystalline stratum, which, I think, is the best example of manifestation, how matter becomes formed matter through form:

“[O]n a crystalline stratum, the amorphous milieu, or medium, is exterior to the seed before the crystal has formed; the crystal forms by interiorizing and incorporating masses of amorphous material. Conversely, the interiority of the seed of the crystal must move out to the system’s exterior, where the amorphous medium can crystallize[.]”

To make sense of this process of crystallization, it has two articulations. First one is nucleation, the seeding of a crystalline structure, which is a random or at least seemingly random process. The second articulation involves the crystal growth, the expansion of the crystal, increasing its size.

The point they want to make with these examples is that a stratum always has a substratum and, ultimately, that substratum consists of matter, which we understand as formed matter. Assuming that I understand this correctly, this has to do with how content is always content for an expression. I also think this has to do with how formed matter serves form and how the lower levels serve the higher levels. In simpler terms, there are layers upon layers. Just think of it, how a layer is like sheet of paper, but in actuality you can only find layers on top of something. They are never isolated like a sheet of paper. That’s pretty much the dictionary definition of a layer (OED, s.v. “layer”, n.):

“A thickness of matter spread over a surface; esp. one of a series of such thicknesses; a stratum, course, or bed.”

And stratum (OED, s.v. “stratum”, n.):

“A quantity of a substance or material spread or laid over a surface, esp. horizontally, to a more or less uniform thickness; a thin layer or coating; esp. each of two or more parallel layers placed successively one upon another.”

And (OED, s.v. “stratum”, n.):

“A natural layer or bed of sediment or rock having a consistent composition and representing a more or less continuous period of deposition, typically consisting of a series of narrower homogeneous layers and itself forming one of a series of successive distinct layers[.]”

As well as (OED, s.v. “stratum”, n.):

“A distinct layer of animal or plant tissue; esp. one of a number of such layers.”

Plus (OED, s.v. “stratum”, n.):

“A region of the atmosphere, of the sea, or of a quantity of gas or liquid, defined for purposes of analysis or calculation as bounded by horizontal planes; a more or less horizontal region within a fluid substance, without a clear physical boundary but distinguished from adjacent regions by internally consistent properties.”

And by extension, used figuratively (OED, s.v. “stratum”, n.):

“Something conceived of as constituting or belonging to one of a series of layers, as a particular period or process within a chronological sequence, a level or grade within a hierarchy, etc.”

As you can see for yourself, what’s common with these definitions is that there is no such thing as a layer or a stratum that exists on its own, by itself. That’s why there are layers upon layers, why a stratum always necessitates some surface underneath it, a substratum. We could say that metastratum is the ultimate substratum, but that’s only sort of accurate. We can think of it as such, but it is rather that there needs to be matter for there to be layers in the first place. There can be no formed matter without matter. So, strictly speaking, matter is the metastratum, yes, but it cannot be a substratum as isn’t formed matter. If we seek to assess matter, i.e., the metastratum, we are, in fact, assessing the strata, a stratum and a substratum, or, rather, the process of stratification, how matter is given form, not the (unformed) matter itself.

To be more accurate, Hjelmslev’s matter is what Deleuze and Guattari (40) call metastratum. To further clarify the terms here, when they discuss stratification, what they call the plane of consistency, the plane of immanence or the body without or organs (BwO) is referred to as the metastratum. In other words, a stratum always relies on another stratum, a substratum. That substratum is, in itself, matter that has been formed, organized and stratified in this and/or that way. This is why illustrating Hjelmslev’s net three dimensionally is much more helpful than the traditional presentation as panels.

Deleuze and Guattari (52) also use the terms epistratum and parastratum. The former pertains to how the stratum on top of its substratum is the epistratum of that substratum, how strata are piled up on top of one another, whereas the latter pertains to how the strata expand horizontally. They (52) use them to explain how strata are divided or fragmented vertically and horizontally. If there was no division or fragmentation of the strata, the strata would extend infinitely, in perfect continuity, one stratum simply on top of another stratum and so on, and so forth, ad infinitum. That is, however, not the case. This means that while there is continuity and diffusion, there is also discontinuity and breaks, as they (61) point out.

They (41-42) also provide an example of the socio-biological level, what they call an organic stratum. Here the connection to the body without organs (BwO) is reversed, so that the process of organic stratification has to do with “how to ‘make’ the body an organism”, that is to say how to organize the body as a living entity. They (41) state that:

“The entire organism must be considered in relation to a double articulation, and on different levels.”

Note how they (41-42) are extending Hjelmslev’s levels here, stating that there are, in fact, levels within levels, or layers within layers, strata within strata. The first level they mention taking place within the socio-biological level, within this organic stratum, is the level of morphogenesis, i.e., the generation of form. The first articulation (content) deals with sequencing and segmentation of protein fibers, whereas the second articulation deals with their compounding, folding of the fibers to create compact structures. In contrast to the physical level or the inorganic stratum, here the process does not involve simple folding, but rather infolding, folding up or curling up on itself. The second level they mention is the level of “cellular chemistry presiding over the constitution of proteins”. Its first articulation involves segmentation that is caused by “successive modifications and polymerization” involving “hundreds of chemical reactions”, producing a limited number of temporary chemical compounds. Its second articulation assembles these temporary compounds and (re)constructs them as stable products. The third level they mention is the level of the genetic code. It involves the sequencing of protein units and nucleic units, consisting of binary relations within each type and biunivocal relations between these two types.

To further comment on folding and infolding, the difference between the inorganic and the organic strata, there is an insightful comment made by Jonathan Strauss, the translator of ‘The Fold’ by Deleuze (not to be confused with the book). You’ll find what’s contained in this short article also in his book on Leibniz, where it appears to be taken from, at least to a certain extent. Anyway, Strauss (227) comments on how Deleuze (227) differentiates between folding and infolding, between what Deleuze and Guattari (55-56, 62-63, 71, 77) refer to as plissement and repliement in ‘Mille plateaux’, and between folds and infolds (I just made that up), what Deleuze (227) calls plis and replis. Both pli and repli pertain to fold or folding, but repli includes a notion of repetition, a continuous folding, as pointed out by Strauss (227). Continuous folding results in infolding, turning inward, coiling into oneself, as he (227) goes on to add. Invagination is another word that Deleuze and Guattari use for infolding (54) in ‘A Thousand Plateaus’ or repliement (71) in ‘Mille plateaux’.

The aforementioned sheet of paper is a good example of infolding. It is not stratified like rock formations, like layers of sandstone, for example, but it is, nonetheless, stratified. A sheet of paper may seem like a homogeneous sheet of material, but, in fact, it consists of countless microscopic fibers, typically cellulose fibers, that are pressed together, kind of like felt, so that the paper is held together by the fibers that lock on to one another by curling or coiling, i.e., by infolding. This is what Deleuze and Guattari (41-21) mean when they differentiate the inorganic stratum from the organic stratum.

What is common to all the levels, including the physical level and the socio-biological level, is that they are all stratified to this and/or that extent. They (45) note that there are two processes that define how stratified or destratified something is: electrification and combustion. The former has to do with the construction of strata, how “similar particles group together to form atoms and molecules, similar molecules to form bigger molecules, and the biggest molecules to form molar aggregates”, involving “‘the attraction of like by like’”, as explained by them (45). The latter has to do with the deconstruction of strata, which is the opposite process, as they (45) point out. What defines something as a stratum then is what they (49) call a unity of composition.

The anthropomorphic stratum

The most important level is, of course, the semiotic level. This is not because the other two levels aren’t important, because it is clear that they are, but because we make sense of them, everything really, through the semiotic level. In other words, we do not assess the other levels without going through the semiotic level. Anyway, what Hjelmslev calls the semiotic level, Deleuze and Guattari (60) call the anthropomorphic stratum.

Contrasting it with the organic stratum, to explain what differentiates humans from other lifeforms (note how life also appears in forms, as formed matter!), there are two key features to what Deleuze and Guattari (60) call the anthropomorphic stratum. Firstly, the form of content becomes alloplastic, as opposed to homoplastic, which, to my understanding, simply means that instead of knowing its place, staying put, keeping to itself, the anthropomorphic stratum spills over to the organic and inorganic strata, bringing changes to them. While I can’t be sure, I believe this is what Hjelmslev means when he (178) points out in ‘La stratification du langage’ that the semiotic level specifies the non-semiotic levels. Anyway, the point is that “it brings about modifications in the external world”, as they (60) point out. That is also why they (502, 504, 513) also refer to it as the alloplastic stratum. Secondly, the form of expression shifts from genetic to linguistic, to operate “with symbols that are comprehensible, transmittable, and modifiable from outside.” This also means that “[w]hat some call the properties of human beings – technology and language, tool and symbol, free hand and supple larynx, ‘gesture and speech’ – are in fact properties of this new distribution” of content and expression, as they (60) point out.

They (60-61) flesh out what differentiates the humans from the non-humans, i.e., what makes the anthropomorphic stratum different from the organic stratum. Instead of taking it for granted that humans have this linguistic capacity as something built in, as something that people are born with, as something that simply marks their forms of expression, they (61) point importance of the interplay of content and expression. They (61) exemplify this with the importance of not only using your vocal organs but also your hands to express yourself.

To give you a bit of more context, Deleuze and Guattari (60-61) refer to André Leroi-Gourhan’s book ‘Gesture and Speech’ in which he (112) points out that “[w]e possess no direct means of studying language before writing.” He (195) further emphasizes this point:

“Through an increasing precise process of analysis, human thought is capable of abstracting symbols from reality. These symbols constitute the world of language which parallels the real world and provides us with our means of coming to grips with reality.”

Hjelmslev (26) makes the same observation in ‘Prolegomena’, acknowledging the importance of invention of alphabet to the study of language. To be clear, neither is saying that writing is essential for language, that you need to have writing for there to be language. No, No. What they are saying is that language appears to us as something that we can study, as a metasemiotic if you will, as this or that language because of writing. We do just fine without writing. Again, this is not to say that writing isn’t useful, because it is, because it certainly is, but that people did just fine without it. But if language isn’t about writing, then it must be about speech, about using your vocal organs. Well, yes and no. Yes, in the sense that’s how speech is produced. No, in the sense that that presupposes that those organs are vocal organs to begin with. As Leroi-Gourhan (112) points out, the tongue, for example, is as nimble as it is not because it has an intrinsic phonetic function, but because it is crucial in processing food. The point here is not to argue that hands aren’t great when it comes to writing, nor that vocal organs aren’t great when it comes to speech. It is rather that while they are great for writing and for speech, they’ve come to take up those functions. In other words, the matter is there, yes, formed in a certain way, yes, hands first acting as forelegs, only to be reformed as hands, which frees them for the task of writing, among other things, of course, becoming what Deleuze and Guattari (61, 303) refer to as the hand-tool couple. Similarly, the vocal organs are there but they no longer there for screeching, like it is with many other primates that live in dense forests, as matter formed in that way, but for speaking, having been reformed once the prior function no longer served a purpose, as they (62) point out. The vocal organs establish a new relation with the facial muscles to establish what they (60) call the face-language couple.

It is worth noting that what Leroi-Gourhan and Hjelmslev mean by writing is, in fact, linear writing. Leroi-Gourhan (195) distinguishes between two types of visual expression: graphic expression and phonetic expression:

“[G]raphic symbolism enjoys some independence from phonetic language because its content adds further dimensions to what phonetic language can only express in the dimension of time. The invention of writing, through the device of linearity, completely subordinated graphic to phonetic expression[.]”

This is not to say that graphic expression was subsumed by phonetic expression as “[a]n image possesses a dimensional freedom which writing must always lack”, as he (195) goes on to add. It therefore manages to resist being linearized by phonetization. That is what art is. That said, we are so, so accustomed to writing as a defining feature of language that it is hard for us to even consider what we consider to be art to be about language. In his (196) words:

“Our life is molded by the practice of a language whose sounds are recorded in an associated system of writing: A mode of expression in which the graphic representation of thought is radial is today practically inconceivable.”

To make more sense of this, what he (196) means by radial is to be contrasted with linear. Writing is linear, grapheme after grapheme, morpheme after morpheme, word after word, clause after clause, sentence after sentence, paragraph after paragraph, chapter after chapter, and what not. Art is not linear. He (196) explains how something can be radial by noting that certain cave paintings have figures that form circles, some animal figures being in the center, while other surround them in a certain order. He (196) acknowledges that we could just ignore this as art, but the thing is that they involve a pattern, which means that it isn’t just some random depiction of “animals hunted, nor ‘writing’, nor ‘imagery.’” They are clearly about something, but it is impossible to say what because the context is missing. In contrast to writing which functions by explaining, they are what needs to be explained.

He (195-196) notes that while we are tempted to think of this as no longer relevant, applicable only to art, we find such multidimensionality or non-linearity in some sciences that utilize equations or formulations, such as in organic chemistry, because in these contexts the linearity of writing is considered an impediment. It is, as if, the equations or formulations speak for themselves, as he (196) points out. So, oddly enough, sciences are in certain ways like art. He (196, 199) reckons you find this also in the context of advertising as well as religion.

Why did I just explain something that appears to be beside the point? Well, I wanted to explain that so that it would it clear that writing is not the only way to make sense visually. I think Deleuze and Guattari (64) put this into words better than I do:

“[T]he hand creates a whole world of symbols, a whole pluridimensional language, not to be confused with unilinear verbal language, which constitutes a radiating expression specific to content[.]”

It is also worth noting that writing can be understood as pertaining to the content plane, whereas speech can be understood as pertaining to expression plane, yet, oddly enough, it is writing that makes speech something that we can study, as agreed by both Leroi-Gourhan and Hjelmslev. In other words, there is this interplay of content and expression.

Deleuze and Guattari (61) further elaborate how these hand-tool and face-language couplings function. The point here is that tools are extensions of hands which once served a different function, grabbing tree branches or projected us forward as forelegs. This is the alloplasticity of the anthropomorphic stratum. Hands are formed matter, matter that is formed according to a certain form that extends their functionality beyond themselves, to other formed matters that come to serve as tools that can be used to manipulate matter into this and/or that formed matter. This is the same with speech. As they (62) point out, one no longer fills one’s mouth with food and noises but with words. One’s larynx, mouth, tongue, lips and facial muscles are formed matter, matter that is formed according to a certain form, which, in turn enable the production languages as certain forms which, in turn, define matter in a certain way as formed matter, as they (61-62) point out.

This does not, however, mean that the organic stratum that serves the anthropomorphic stratum is subsumed by the anthropomorphic stratum, despite being its substratum, as they (64) out. On the contrary, “it constitutes the prehuman soup immersing”, so that “[o]ur hands and faces are immersed in it”, as they (64) go on to add. In other words, “[i]t’s all in the head”, yet it is all very real”, as noted by (64) them.

The anthropomorphic double articulation consists of “the manual articulation of content” and “the facial articulation of expression”, as stated by them (64). There is a very real and, to use Spinozist terms, essential distinction between things (content) and words (expressions), yet this distinction also applies within these “attributes, genres of being, or irreducible categories”, so that each articulation is also double in its own right, so that content can double as an expression, just as an expression can double as a content, as they (64) go on to add. You’ll find this both in “pluridimensional language” and in “unilinear verbal language” that comes to serve as a basis for linear writing, as they (64) point out. If you want to a better explanation of double articulation as a feature of language, go back a bit to the point where this is explained through Martinet’s work.

Unlike the genetic code that serves as the form of expression of the organic stratum that is spatially linear, the language code that serves as the form of expression of the anthropomorphic stratum is temporally linear, as indicated by them (62). The underlying code of the organic stratum appears to be fixed in time, having only a spatial dimension, appearing as such, at any given moment, and thus has no “emitter, receiver, comprehension, nor translation, only redundancies and surplus values”, as specified by them (62). In plain terms, as the genetic code is limited to coding on its own, in relation to itself as genetic code. The genetic code is therefore merely linear.

In contrast, the underlying code of the anthropomorphic stratum is not fixed in time, which allows it to overcode itself as a stratum, i.e., translate one code to another code, for example one language to another language, and the two other strata, the inorganic and the organic strata, as they (62) go on to add. This is how the semiotic level is able to specify the other levels, to use Hjelmslev’s terms, to provide a scientific conception of the world, translating all “the flows, particles, codes, and territorialities of the other strata into a … system of signs … into and overcoding specific to language”, as they (62) point out. The language code is therefore superlinear. This superlinearity, this capacity to overcode or translate anything is highly important for them (62) as it allows language to act as a form of expression wholly independent of formed matter. Simply put, it can operate independently because, as a form, it can impose itself on any matter, to translate it in its own terms. In contrast, the genetic code is unable to do that, as they (62) point out. It cannot impose itself on just about anything as a form.

There is, however, a certain similarity between the organic stratum and anthropomorphic stratum that I have yet to mention. It is the autonomy of expression, which, for them (59-60), means that anything organic has the capacity to alter its own states of affair, in order to, for example, adjust to environmental pressures. This is what they (60) mean by homoplastic. To give you an actual definition of homoplasy, it is analogous convergent evolution, “the development of organs or other bodily structures within different species, which resemble each other and have the same function” but do “not have a common ancestral origin”, as explained by Vladimir Makarenkov, Dmytro Kevorkov and Pierre Legendre (73) in ‘Phylogenetic Network Construction Approaches’. For example, bat, bird, and insect wings are homoplastic features as they have developed independently from one another, as they (73) point out.

Simply put, on the inorganic stratum the articulations, like in those examples, one simply following the other, so that the distinction between the content and the expression is merely formal. That means that we can distinguish them as such, but that is us making that distinction. Everything is connected to everything in one way or another, directly or indirectly. In contrast, on the organic stratum, the distinction between the two is real, which simply means that the expressions now live lives of their own, hence the autonomy. I’d say that the autonomy is, of course, relative, as it is not like the living matter of the organic stratum is somehow suddenly cut off from the rest of the world. No, No.

To simplify things, the anthropomorphic stratum can cross over to the other two strata. This is what makes it alloplastic, rather than merely homoplastic. This is also the point Hjelmslev (177-178) makes in ‘La stratification du langage’ about how the readily apparent semiotic level feeds on the non-semiotic levels., while also specifying them. The problem with this conception is that while it is accurate, while it is correct to state that language is what permits us to speak of anything, be it linguistic or non-linguistic, there’s a risk of this being understood as saying that words simply correspond to things.

Denotative semiotic, connotative semiotic and metasemiotic

As a final thing pertaining to stratification, I’m going to explain what Hjelmslev means by denotative semiotic, connotative semiotic and metasemiotic. So far, I’ve explained things on the semiotic level (anthropomorphic stratum) in terms of ordinary language, what Hjelmslev also calls the denotative semiotic. To give you a more precise definition, he (73) defines the denotative semiotic in the ‘Prolegomena’ as “a semiotic none of whose planes is a semiotic.” I believe this warrants a bit more attention as this is particularly poorly worded. So, to be clear, the denotative semiotic is in itself a semiotic. It wouldn’t be a semiotic without being a semiotic. Otherwise it would be non-semiotic. In other words, it is a semiotic system, or a structure, if you will. It can therefore be illustrated quite plainly (XIV):

In contrast, the expression plane of the connotative semiotic is, in itself, a semiotic, as defined by him (73). This means that there is a content plane and an expression plane within the expression plane (XXIV):

The content plane of the metasemiotic is, in turn, itself a semiotic, as defined by him (73). This simply means that we can reverse this configuration, so that the content plane has a content plane and an expression plane (XXV):

As you can see, there is a clear difference between these three semiotics. The denotative semiotic should be the easiest to wrap your head around, but it does simplify things too much. The problem with it is that it makes it seem like there are only two articulations, one pertaining to content and another pertaining to expression, when there are, in fact, articulations within articulations. The connotative semiotic helps us to understand that. Simply put, in that configuration we have not only have denotation, so that we say that a word means this thing, this material thing, but also connotation, that it also means these other things and to make sense of how we get to say that it means that thing, that material thing, we need to take all those other things into account as well.

To be more accurate, the denotative semiotic has two terminals of a function, i.e., two functives. They are tied to that function, which means that they are in reciprocal presupposition, appearing in solidarity. This is, however, “a deliberate simplification” of language, as pointed out by him (73). The connotative semiotic makes this apparent as there are functions that can themselves double as functives, as explained by him (20). In this case there are two functions and four functives, as one of the two functives of one of the two functions is, in itself a function, for which there two additional functives.

It should look something like that (XXVI). Anyway, as the expression plane of the connotative semiotic is doubled, having its own content and expression planes, we need to take those planes into account at same time we take the content plane of the connotative semiotic into account. As explained by Hjelmslev (74), “any functive of the denotative language must be defined in respect to” the connotative language that consists of connotators, including but not limited to stylistic forms, styles, value-styles, media, tones, idioms, vernaculars, national languages, regional languages and physiognomies. The gist of this is that there is a system within a system. The denotative system is nested within the connotative system as its expression plane.

We can also flip that configuration on its head, so that the now there is a denotative system within a metasemiotic system, functioning as its content plane. In that case one is assessing a semiotic system through another semiotic system, hence the moniker metasemiotic. To be clear, it is even possible to treat the semiotic system that assesses another semiotic system as what is assessed by yet another semiotic system, ad infinitum, as explained by him (77).

To simplify things, the denotative semiotic is like the everyday understanding of language, in which word (expressions) corresponds to things (contents), while the connotative semiotic complicates this by adding that words (expressions) do not simply correspond with things, but with other words (expressions), which, in turn, refer to other words (expressions) and things (contents). The metasemiotic is a more specialized case here as it deals with the analysis of a semiotic through a semiotic (self-referentially, hence being meta), which is a fancy way of saying that it’s, for example, about the study of language through language, as mentioned by him (77).

Unless I’m mistaken, which, to be honest, might be the case, considering that I’m crossing over to Guattari again, this is what he means when he (58-59) argues in ‘Schizoanalytic Cartographies’ that there are three levels of the unconscious. The first level has to do with the referent or denotatum, what, I guess, we could also call, somewhat naïvely, the level of denotation, which pertains to whatever is there or what we reckon to be there anyway (because, you know, we make sense of them semiotically, which takes us to the next level). The second level is the semiotic level. It presupposes the level of the referent or denotatum, but adds to it as otherwise it would be its own level. This would be the connotion. It pushes us from referent or denotatum to designatum, so that, oddly enough, we may talk of something like a unicorn, even though there is no such thing as a unicorn, as no such animal exists, as, strictly speaking, it’s a figment of our imagination. Of course, we can argue that such a thing does exist, because, well, in a sense it does, as otherwise it would be impossible to speak of such a creature. Notice how we have the non-discursive and the discursive here (more of this to follow). The third level is what we deal with, albeit, also unconsciously. It presupposes the first level, the denotation, and the second level, the connotation. This third level is the pragmatic and subjective level, which involve the two levels coming together, the referent, the denotation, that material content, and the semiotic, the connotation, that semiotic expression, which, of course, doubles up on itself, having its own relative thought content.

It is worth keeping in mind that, for Deleuze and Guattari, this is all unconscious. So when Guattari says that it is that way, that it’s happening under the hood, as we speak, he really means it. We don’t have to tell our hand to move, put conscious effort to it, nor to our tongue to make certain movements so that we can articulate clearly, so that we can form sound sequences that others can then understand. Even if we correct others, like do it like this, move your hand like this, no, not like that, but like this, see, or your tongue needs to be like this, touching the gum ridge, ah, yes, better, we aren’t telling our hands or tongues to do all that, separately, in order to help them to do what they should should be doing, according to me. This does not mean that we do not have awareness, that we aren’t conscious, no, no, but rather that much of what we say or do, or just do if you want to lump it together, as performing, is unconscious.

Moments of confusion

The great difficulty of all these formulations is that the terms are interchangeable, hence Guattari’s comment about why not just call them A and B. It gets really confusing when, on one hand, we focus on language in isolation, so that content is about thoughts, which makes it discursive rather than non-discursive, and expression is about the act of expressing those thoughts, using your body to do that, materially, which makes it non-discursive rather than discursive, and, on the other hand, when we focus on language in the world, so that content is about the material world, which makes it non-discursive, and expression is about the thoughts about that material world, which makes it discursive. If you end up confusing the terms because of this, you are not alone. I’ve found myself mixing them up, my bad, and so has Deleuze, who is generally very consistent with these terms, only to mix them up when he (34) states in his book on Foucault that:

“[A diagram or an abstract machine] is defined by its informal functions and matter and in terms of form makes no distinction between content and expression, a discursive formation and a non-discursive formation.”

This can also be found in the French original and therefore it is not just an issue that cropped up in translation. It could be that he wants to confuse the reader, to emphasize the point that from the viewpoint of the diagram or the abstract machine it makes no difference. He (38) mixes them up again a few pages later:

“But, more than this, it is here that two forms of realization diverge or become differentiated: a form of expression and a form of content, a discursive and a non-discursive form, the form of the visible and the form of the articulable.”

Here content and expression are correctly paired with non-discursive and discursive, only to then incorrectly pair content/non-discursive with the articulable and the expression/discursive with the visible. Again, this blunder is also in the original, so the translator is not to blame for this. I don’t know how to explain that, really. It might be that he simply wasn’t careful enough or that Guattari was the one responsible for the stuff that had to do with language and semiotics, so when Deleuze did that book on his own, he ended up with a couple of errors. My guess is that it was a bit of both.

Some years ago I wrote an essay ‘Seeing Things Unreel – From Appearance to Apparition’. It was as all good, as intended, the form of content and the form of expression paired the way they were supposed to be, in my manuscript and in the proofs that were sent to me. I happened to be reading this part of Deleuze’s book on Foucault at the time, which is how I ended up noting in correspondence that I’d like to swap the terms around, like they are in that book, incorrectly. So, if you ever come across that essay and think, hey, what the fuck, these are the wrong way around, it’s because they are, because I fucked up, because Deleuze fucked up. I can’t fix that, nor can he, as what’s done is done (that’s the pro/con of a print logic), but the good thing is that we can learn from our mistakes. I certainly have. Plus, now that you know of this, that there is this danger of confusion, at least you can avoid getting confused by that.

The difficulty with all this is to keep track of what it is that we are dealing with. Is it like with Hjelmslev, where the emphasis on language or, more broadly speaking, semiosis, focusing on denotation and connotation, in order to make sense of the material world, to create a certain conceptual order of things?

Or is it like with Deleuze and Guattari who expand on that to take the material world more seriously, so that the focus is not so much on language or semiosis, in their inner workings, what they are, but rather on what they do, not as something self-contained, remaining merely conceptual, stuck in language or semiosis (focusing solely on that connotative semiotic), but how they acts upon that material world (in relation to that denotative semiotic)?

You could, of course, argue that I didn’t fuck up in my essay, considering that I (22) focused on the regimes of signs, i.e., the forms of expression on the anthropomorphic stratum. In linguistics and semiotics the form of content is generally understood to be the thought content, as studied in morphology (morphemes), which makes it discursive, and the form of expression is generally understood to be the material production of sounds, the expression itself, as generally studied in phonology (phonemes) and phonetics (phones), which makes it non-discursive. So, did I fuck up after all? Well, inasmuch as we go beyond the semiotic systems, yes, but, inasmuch we limit the discussion to how a semiotic system is constituted, no. So, as I (22) explain the regimes of signs and how they are constituted, how they double up as connotative semiotics, as illustrated in figure XXIV, it is, oddly enough, accurate to refer to the content as discursive and to the expression as non-discursive. So, in the end, I’d say that I didn’t fuck up. Deleuze and Guattari (111) point out how that works:

“[O]one can proceed as though the formalization of expression were autonomous and self-sufficient.”

To be clear, a regime of signs is a form of expression, as stated by them (22). It’s constituted through double articulation, the first articulation being the content (morphemes) and the second articulation being the expression (phonemes), as explained by Martinet (34) in ‘Double Articulation as A Criterion of Linguisticity’. He further comments on this, how the morphemes come first and how the phonemes come second in his (237) interview:

“Some do not approve of my applying ‘second articulation’ to the phonematic articulation and ‘first articulation’ to what comes in the second place in linguistic analyses.”

Before he explains why this is the case, he (237) explains why people are tempted to reverse the order:

“Historically the structural approach started with phonology and, from there, we came to syntax. Therefore people want phonology to be the first articulation.”

He (237) then explains why that should reversed, going from the thought to the expression:

“If, on the other hand, we view language as a means of conveying experience, experience is thought of as an unanalyzed whole and the first segmentation will be established on the level of this unanalyzed whole. We could loosely say that, prior to being communicated linguistically, a headache is articulated into [morphemes].”

This is basically the same point that Hjelmslev makes when he (30) states in the ‘Prolegomena’ that there can be no contentless expression, nor expressionless content. Martinet is, however, willing to entertain such an idea, as he (237) reckons that traffics lights require only the second articulation (expression). Something like a language cannot be that simple, as he (237) goes on to add:

“It is because languages must be able to convey everything that one cannot be content with a tool where each communicative act would be an unanalyzable grunt.”

In other words, there must be some content for that expression, otherwise it’s just that, a meaningless sound, a grunt. So, content can be understood as the discursive and expression can be understood as the non-discursive, if we focus solely on a semiotic system. If this is confusing, it’s because it is. There’s just so many things on so many levels to keep tabs on. So, in the end, while I may have not been mistaken, after all, the lesson to be learned here is still the same: this can be pretty confusing.

Now, of course, that’s not all there is to this, which is why Deleuze and Guattari (111-112) argue against such views that limit it all to operating within a semiotic system. So, yeah, you can do that,and there’s merit to it, as done in linguistics and semiotics, but going beyond that is recommended as otherwise one is dealing with just the connotative semiotic, in abstract terms, ignoring all that’s concrete, that denotative semiotic.

It is exactly because of this confusing terminology that I’ve called things material things here, in this essay, to emphasize that there is more to this than just language or semiosis, which, I believe, Hjelmslev (36) does, however, acknowledge in the ‘Prolegomena’. I’d say that with Deleuze and Guattari, when they are dealing with content, they are dealing with the material world, and when they are dealing expression, they are dealing with language or other semiotic modes. With Hjelmslev, I get the feeling that there is still this import from Saussure, where the material world gets relegated to thoughts about the material world, even though, he does seem vacillate on that, as noted by Deleuze and Guattari (523, 526) in the notes section of ‘A Thousand Plateaus’ and by Guattari (41) in the ‘The Machinic Unconscious’. This is not to say that Deleuze and Guattari are claiming that language isn’t important, that it is not through language that we make sense of the world, but that we should not focus solely on language or, more broadly speaking, semiotics. Guattari’s ‘Schizoanalytic Cartographies’ is pretty difficult, but he (268-269) does expand on this, which should help their readers to better the connection between their work and Hjelmslev’s work.

More to come

I thought I’d also write about how stratification meshes with assemblages and abstract machines, but I opted to avoid even mentioning them in this context. To be clear, they are worth discussing in this context, but I opted not to do that, cutting a portion of this essay that I had written, in order to maintain focus. I will dedicate another essay on that because the thing is that you need that part to fully appreciate what Deleuze and Guattari have done with Hjelmslev’s work.

I didn’t venture into explaining how meaning or, rather, sense appears. I think I could have done that and not just mention that in passing as having to do with matter-meaning and sign function, but I thought it would be better to just explain stratification first. I think there is enough complexity in all this without venturing further, for now.

To give you a summary, to explain the gist of this, Hjelmslev’s stratification and Martinet’s double articulation are not only confined to linguistics and, more broadly speaking, semiotics. Deleuze and Guattari manage to explain how everything is stratified and how everything is articulated twice, even the articulations themselves, except the plane of matter, i.e., plane of consistency or plane of immanence. This is why they (67) state in ‘A Thousand Plateaus’ that “[w]e are never signifier or signified”, that “[w]e are stratified.”

To be fair, I think Hjelmslev flirts with this idea in ‘Prolegomena’. There is a passage in which he (36) points out that a ring is a formed matter of expression, i.e., a sound sequence, which makes sense to us only when it is ordered among other formed matters of expression, among other sound sequences, defined as such in relation to the form of expression. In this context he (36) also points out that a ring is a formed matter of content, i.e., a material thing, that only makes sense to us when it is ordered among other formed matters of content, i.e., among other material things, defined as such in relation to the form of content. Unless I am mistaken, this is what Deleuze and Guattari state in ‘A Thousand Plateaus’, albeit in their own terms, while also expanding on this.

This does not mean that Deleuze and Guattari ignore what Hjelmslev refers to as the semiotic level and what they refer to as the anthropomorphic stratum. No, no. It is rather that they explain what else is there, the inorganic and organic strata, and how the anthropomorphic stratum ends up seeming like it is the only stratum even though it is not. I particularly appreciate how they insist that we must treat them not just as merely given, as formed matter, what Hjelmslev calls substance, because in order to be formed matter, they must also involve matter and form. Hjelmslev thinks otherwise, but I think that has to do with his unwillingness to go beyond linguistics and semiotics.

I also want to point out that I recommend reading the originals and forming your own thought, instead just relying on what I’ve explained in this essay. I may have erred here and there, that’s only likely, but that’s part of the process. It happens. I’m sure my previous formulation of Hjelmslev’s net could use some brushing up, but we’ll see if I ever bother to fix it in that previous essay. I think the toughest part of this essay was coming up with ways to visualize such complex process, to avoid making them appear in isolation or in linear fashion. There’s also a lot of concepts and a lot of terms, some of which are just another way of saying the same thing, but that’s what you get when you engage with the work of Deleuze and Guattari. You just have to live with it and make sense of it. Anyway, I’m happy if I got something right and, more importantly, it is of use to someone. I’m happy if it just provokes you think.

References

• Aristotle (1929). The Physics (P. H. Wicksteed and F. M. Cornford, Trans.). Cambridge, MA: Harvard University Press.
• Deleuze, G. ([1986] 1988). Foucault (S. Hand, Trans.). Minneapolis, MN: University of Minnesota Press.
• Deleuze, G. ([1968] 1990). Expressionism in Philosophy: Spinoza (M. Joughin, Trans.). New York, NY: Zone Books.
• Deleuze, G. ([1969] 1990). The Logic of Sense (C. V. Boundas, Ed., M. Lester and C. J. Stivale, Trans.). London, United Kingdom: Athlone Press.
• Deleuze, G. ([1988] 1991). The Fold (J. Strauss, Trans.). Yale French Studies, 80, 227–247.
• Deleuze, G. ([1988] 1993). The Fold: Leibniz and the Baroque (T. Conley, Trans.) London, United Kingdom: The Athlone Press.
• Deleuze, G. (2000). Proust and Signs: The Complete Text (R. Howard, Trans.). Minneapolis, MN: University of Minnesota Press.
• Deleuze, G. ([1978] 2019). Seminar on Spinoza, Continuous Variation (T. S. Murphy and C. J. Stivale, Trans.). https://deleuze.cla.purdue.edu/seminars/spinoza-velocities-thought/lecture-00
• Deleuze, G., and F. Guattari (1980). Capitalisme et schizophrénie: Mille plateaux. Paris, France: Les Éditions de Minuit.
• Deleuze, G., and F. Guattari ([1972] 1983). Anti-Oedipus: Capitalism and Schizophrenia (R. Hurley, M. Seem and H. R. Lane, Trans.). Minneapolis, MN: University of Minnesota Press.
• Deleuze, G., and F. Guattari ([1980] 1987). A Thousand Plateaus: Capitalism and Schizophrenia (B. Massumi, Trans.). Minneapolis, MN: University of Minnesota Press.
• Ducrot, O., and T. Todorov ([1972] 1979). Encyclopedic Dictionary of the Sciences of Language (C. Porter, Trans.). Baltimore, MD: Johns Hopkins University Press.
• Dupréel, E. (1933). La Cause et l’Intervalle: ou Ordre et Probabilité. Archives de la Société Belge de Philosophie, 5 (2): 1–51.
• Foucault, M., and G. Deleuze ([1972] 1977). Intellectuals and Power. In M. Foucault, Language, Counter-Memory, Practice: Selected Essays and Interviews (D. Bouchard, Ed., D. Bouchard and S. Simon, Trans.) (pp. 205–217). Ithaca, NY: Cornell University Press.
• Guattari, F. ([1973] 1984). The Role of the Signifier in the Institution. In F. Guattari, Molecular Revolution: Psychiatry and Politics (R. Sheed, Trans.) (pp. 73–81). Harmondsworth, United Kingdom: Penguin.
• Guattari, F. ([1975] 1984). Towards a Micro-Politics of Desire. In F. Guattari, Molecular Revolution: Psychiatry and Politics (R. Sheed, Trans.) (pp. 82–107). Harmondsworth, United Kingdom: Penguin.
• Guattari, F. (2006). Hjelmslev and Immanence. In F. Guattari, The Anti-Œdipus Papers (S. Nadaud, Ed., K. Gotman, Trans.) (pp. 201–223). New York, NY: Semiotext(e).
• Guattari, F. ([1971] 2006). Planes of Consistency. In In F. Guattari, The Anti-Œdipus Papers (S. Nadaud, Ed., K. Gotman, Trans.) (pp. 283–298). New York, NY: Semiotext(e).
• Guattari, F. ([1979] 2011). The Machinic Unconscious: Essays in Schizoanalysis (T. Adkins, Trans.). Los Angeles, CA: Semiotext(e).
• Guattari, F. ([1989] 2013). Schizoanalytic Cartographies (A. Goffey, Trans.). London, United Kingdom: Bloomsbury.
• Guattari, F. ([2011] 2016). Lines of Flight: For Another World of Possibilities (A. Goffey, Trans.). London, United Kingdom: Bloomsbury.
• Hjelmslev, L. ([1943] 1953). Prolegomena to a Theory of Language (F. J. Whitfield). Baltimore, MD: Waverly Press.
• Hjelmslev, L. (1954). La stratification du langage. WORD, 10 (2–3), 163–188.
• Hjelmslev, L. (1972). Structural Analysis of Language. In B. Malmberg (Ed.), Readings in Modern Linguistics (pp. 97–105). Stockholm, Sweden: Läromedelsförlagen.
• Leibniz, G. W. ([1702] 1989). Reflections on the Doctrine of a Single Universal Spirit. In G. W. Leibniz, Philosophical Papers and Letters (2nd ed) (L. E. Loemker, Trans., Ed.) (pp. 554–560). Dordrecht, the Netherlands: Kluwer Academic Publishers.
• Leroi-Gourhan, A. ([1964] 1993). Gesture and Speech (A. Bostock Berger, Trans.). Cambridge, MA: The MIT Press.
• Makarenkov, V., D. Kevorkov, and P. Legendre (2006). Phylogenetic Network Construction Approaches. Applied Mycology and Biotechnology, 6, 61–97.
• Martinet, A. (1974). Andre Martinet. In. H. Parret (Ed.), Discussing Language (pp. 221–247). The Hague, the Netherlands: Mouton.
• Martinet, A. (1984). Double Articulation as A Criterion of Linguisticity. Language Sciences, 6 (1), 31–38.
• Oxford English Dictionary Online (n. d.). Oxford, United Kingdom: Oxford University Press.
• de Saussure, F. ([1916] 1959). Course in General Linguistics (C. Bally and A. Sechehaye, Eds., W. Baskin, Trans.). New York, NY: Philosophical Library.
• Savela, T. (2019). Seeing Things Unreel – From Appearance to Apparition. In I. Hansen and S. Ruokkeinen (Eds.), Working on it: PhD Research at the Department of English, University of Turku (pp. 11–28). Turku, Finland: University of Turku.
• Spinoza, B. ([1661] 1870). Letter IV. In B. Spinoza, Life, Correspondence, and Ethics (R. Willis, Trans., Ed.) (pp. 226–229). London, United Kingdom: Trübner & Co.
• Spinoza, B. ([1663] 1870). Letter XXIX. In B. Spinoza, Life, Correspondence, and Ethics (R. Willis, Trans., Ed.) (pp. 281–288). London, United Kingdom: Trübner & Co.
• Spinoza, B. ([1667] 1884). The Ethics. In B. Spinoza, The Chief Works of Benedict de Spinoza, Vol. II (R. H. M. Elwes, Trans.) (pp. 43–271). London, United Kingdom: George Bell and Sons.