Deleuze on Sense, Series, Structures, Signifiers and Snarks (Part A)

By John Brady

“For the Snark was a Boojum, you see.”
(Lewis Carroll, The Hunting of the Snark)

How do words mean?

This problem is so fundamental it has birthed entire incommensurable projects. In one way, the entire distinction between anglophone analytical philosophy and so called “continental” philosophy can be seen as hinging on two differing approaches to this question and the attendant consequences that reside with each approach.

In The Logic of Sense Deleuze tackles this problem by incorporating threads of analytical philosophy of language, the Lacanian interpretation of Saussurean linguistics, the paradoxes of the ancient Stoics, Game Theory, and the fantastical writings of Lewis Carroll, and it’s every bit as awesome as that sounds.

At the nexus of all of these threads is developed a novel theory of Sense as a paradoxical object that is essential to all and any structure. We will, here, explore the role that Deleuze argues sense plays in the meaningfulness of propositions, as well as its paradoxical character. Part B will investigate sense’s role in any and all Structure.

The Dimensions of the Proposition


Analytical philosophy, beginning with Frege (perhaps the progenitor of the project), has seen the question of language to be the question of Denotation, or Reference. Words refer to things. A proposition refers to a complex of things forming a state of affairs, which can be analysed into its constituent parts. This has been financed by the focus on the determination of Truth. What is needful is an account of why and how true propositions are true. True propositions are true in virtue of their elements denoting objects within a state of affairs that holds. This is nowhere near as simple as it sounds, paradoxes soon conflate this simple picture, necessitating a number of novel and interesting approaches to just how this denotation is to function. Be that as it may, Deleuze points out that the meaning within a proposition is not exhausted by denotation alone; denotation being merely one of three initial fundamental dimensions. Propositions denote, however that is the case, and point towards the states of affairs for their truthfulness. Denotation concerns truth and falsity, and speaks to the power of words to relate, piece by piece, to objects.


However, the meaning of a proposition is not exhausted by an inquiry into what its constituent terms denote. Another dimension is that each and every position is anchored to a point of enunciation. The proposition turns us to a speaker, or a writer, who asserts, believes or posits it. In a way this anchoring to a subject precedes denotation: imagine wandering in the desert and coming across a forgotten stone tablet, on which is inscribed a host of complex yet incomprehensible symbols. Prior to the question of whether what is inscribed on the tablet is true or false, is the knowledge that someone created the tablet to some ends. The archaeological question that precedes the laborious task of translating or interpreting the symbols is a question of motives: is it reasonable to assume that the creator of the tablet intended these marks to denote anything at all?

A negative example also demonstrates the primacy of manifestation to denotation: should a cat sit on a keyboard and accidentally cause a proposition to appear on the screen, the question of the truth or falsity of the proposition only makes sense if we then take up this proposition to evaluate it. The cat hasn’t “sat” a true or false proposition, we “discover” and re-state it.


However, we still don’t have enough to account for the meaningfulness of the proposition. Imagine that after study into the mysterious stone tablet it was ascertained that the script belongs to no language, past or present, but to the scrawlings of a mad man who, nonetheless, intended to denote things with this private language. It’s not enough that we intend to denote, for a proposition to have meaning it needs to occur within a language that always goes beyond the original “manifester” — an entire network of signs relating to one another. It could be argued that could the mad man be interviewed, he could provide the explanation of the symbols such that the symbols could denote and his intention would be vindicated— however, how would he provide such an explanation to us if not by using language or across some other sign system that is only as effective insofar as it is shared and complete?

The “I” that manifests is born into, already, a system of signification that makes it possible to intend their denotations. The dimension of signification refers to all that needs to be in place for the proposition to be able to reliably denote in the first place (logical structure, lexicon, syntax, grammar). So, it would seem that signification is the ground, or the most fundamental dimension, of the three dimensions of the proposition. Or is it?

The Circle of the Proposition

Denotation turned us towards manifestation, which turned us towards signification. Does the buck stop there? Unfortunately not. Signification is not so suited to ground things because it partakes in a number of paradoxes that are only dissolved by virtue of the other two dimensions.

The first of these is dramatized in Lewis Carroll’s What the Tortoise Said to Achilles. There we see that a simple deductive syllogism, of the kind “all men are mortal, Socrates is a man, so Socrates is mortal”, can only force its conclusion if another premise is granted, a premise that affirms the validity of the form of the argument itself: i.e. “the conclusion of a valid deductive syllogism is true if its premises are all true”. However, once this premise is added to the original syllogism, a further premise is required for the exact same reason, onto infinity (If A & B & C are true, then Z is true=“D”). The significations that a system of logic is require infinite support that the mere appending of additional or definitional premises cannot fully provide, because of their necessary endless proliferation.

Should we meet such a Tortoise, we would no doubt throw our hands up in exacerbation and say “You know what I mean”, thus providing the dimension of manifestation as ground. As in, beyond what all the propositions and their elements signify, allowing them to denote more or less precisely, you grasp what it is that I, as your interlocutor, am trying to accomplish with all of this speaking. Stepping away from the notion of language (which is based on the network of signification) to the order of speech we refer ourselves back to manifestation as ground.

Putting aside the fact that any speech requires a field of language (even simple pointing requires a previous understanding of precisely how an outstretched index finger signifies), pure speech is still insufficient to ground the proposition. If I were to misspeak, and accidentally ask for a bear when I intended to ask for a beer, and you buy for me a plush toy bear, I can point to the dimension of manifestation in reprimanding you: Why would I have asked for a bear? However, in this case it is a question of substituted denotations. Without denotation there would be no question of “you know what I meant”, because “you know what I meant” here always means “you know what I intended to denote”.

Take the bark of a dog — this is perhaps the most rudimentary proposition, and if we wanted to ground the proposition on manifestation we would do well to take it as our model: the dog’s bark bears no signification beyond its opposite — its silence (which, incidentally, was signification enough for Sherlock Holmes to solve the case in Silver Blaze). Furthermore, in their lack of articulation, dogs mostly fail at expressing true and false propositions. One is here reminded of a Gary Larson Farside cartoon in which a scientist creates a “dog translator” only to discover that dogs are merely always saying “Hey! Hey! Hey!”.

We could imagine a rudimentary human language composed entirely of these barks of the affirmation of self-existence, and nothing more. However, even our dog does not escape the developing circle of the proposition: their efficacy as sentinels and guards is precisely in that dogs bark at things. Without denotation the barking of the dog would foreclose the possibility of it being a guard, or even a pet (who would keep an animal that barks as loud as a dog if it didn’t bark at something, but merely barked to affirm its existence, whenever its existence was found by it to be?)

To come back to people, for me to say “you know what I meant” is to rest upon the dimension of the proposition whereby my intending denotes states of affairs in the world. If I misspeak, this is the dimension of manifestation (my speaking and your hearing) failing in reference to a power in speaking to denote that proves itself to be fundamental.

So, we’ve returned to denotation, only to then begin again being referred down the chain. However, there is a second paradox of signification that will take us directly back to denotation in a single step (thus a pure circle going in both directions).

We’ve said that signification is that dimension of the proposition in which all that is needed for the proposition to denote in the first place is contained. When I use a noun to denote a thing, my denotation rests on an entire dictionary of nouns having already been given such that my denotation can pick out one and only one object within the state of affairs. In China, for example, one is often provided with ceramic or plastic or paper cups with which to drink, unless one specifically qualifies “cup” with the adding of an adjective “glass”. In English, asking for “a glass” negates everything else within the semantic domain of “cuphood”, and in fact takes its efficacy precisely through this act of negation relative to similar objects in a class. Learning words, therefore, is not a process of addition, but of negation and subtraction, that cuts up the field of the “signified” into smaller and smaller regions with ever more precise signifiers that demarcate themselves by merely being not there neighbors. This perhaps provides a solution to Lewis Carroll’s “unanswerable” riddle “What’s the difference between a raven and a writing desk?”: A raven is not a writing desk whereas a writing desk is not a raven.

The paradox, therefore, is that all of the signified is given up front in order that the first word should be learnt. When the child says of its mother “mama” it also says of all things in the universe “not-mama”. The signified is all given at once, but only one signifier has been learnt. The introduction of this single signifier onto the uniform field of the signified introduces an imbalance that can begin the process of signification proper (later, the remaining signified of not-mama is divided further and further through the learning of new signs which merely are the names for incisions and negations). And what is it that begins this whole process? A denotation: Mama. Without denotation the signified would never be divided by the signifier.

“From denotation to manifestation, then to signification, but also from signification to manifestation and to denotation, we are carried along a circle, which is the circle of the proposition.”
(Deleuze, 2004, pg.20)

To this we would just add the additional jump from signification to denotation we have demonstrated. The task, then, is how to unravel this groundless situation whereby each dimension of the proposition is using the others as support.


“Sense is the fourth dimension of the proposition”
(Deleuze, 2004, pg.22)

To unravel the circle of the proposition Deleuze adds the dimension of sense. Sense is, roughly, “the expressed of the proposition”. Frege, at perhaps the birth of modern philosophy of language, introduced sense for similar reasons: that is, the pragmatic avoidance of paradox.

The paradox Frege was dealing with in On Sense and Reference (1892) was that if the only relationship that propositions had with objects was denotation (reference), statements of identity were ipso facto uninteresting, when in fact they can be interesting. When we say, in his famous example, “The Morning Star is the Evening Star” we are expressing a speculative identity that has a difference to a statement of mere logical identity (i.e. “The Morning Star is the Morning Star”). However, if the only relationship of these propositions to objects is denotation, both speculative identity statements and logical identity statements have the same value, because the objects involved are the same: Venus, in the example. To stop words collapsing back into things such that a difference could persist between varying names of the same object, the dimension of sense (Sinn) was added. Each name has a sense, even if their references are the same, and it is in virtue of this sense that the different names denote the same object by so many different paths such that two names, being related via identity (A is B) can tell us something interesting. The layer of sense stops words falling into things, without it “The Morning Star is the Evening Star” would be identical to “Venus is Venus”.

In a similar way, Deleuze adds the dimension of sense as distinct in a purely pragmatic move to stop the proposition collapsing back into itself. But what is sense? “The expressed of the proposition”. But what is that?

A useful case to get to the bottom of this is poetry. A scientific proposition hopes to be ambivalent to the differences between the names “morning star” and “evening star” and “Venus” and “the second planet from the sun”, and so on, but a Poet cannot share this ambivalence. Such substitutions, though not effecting what is denoted, manifested, or signified by a poem, radically alters what is expressed in the process of reading or hearing or reciting it. It is important, in order for sense to be a unique dimension of the proposition, that there be worthwhile reasons to believe that signification or manifestation cannot account for what happens to a poem when we substitute synonyms. And this is precisely why Deleuze selects Lewis Carroll as his dialogue partner to explore the realities of sense.

Henry Holiday, “Fit the First”, from “The Hunting of the Snark”, (1876)
“For the Snark was a Boojum, you see?”

Now, this proposition has sense, because, as Frege argued back in 1892, sense is said of (is ambivalent to) existing and non-existing things alike (otherwise it is no different from denotation, and no solution to his problem).

It denotes a state of affairs that does not hold (there are no Snarks who are Boojums because there are no Snarks, nor Boojums). But, being a poem, it’s futile to merely say “but that’s not true”. Literature and poetry obviously do not function via denotations of objects within states of affairs that actually hold, yet they still express. Sense is ambivalent to truth and falsity, so is ambivalent to denotation.

We may say that sense is a function of manifestation, the expressed of the proposition is the intention of the writer, until we realize that such a line of poetry as the above could have been not only the product of a typo, but of a cat sitting on a keyboard. A randomly generated string of letters that stumbles upon a proposition by chance is still bestowed with sense. Sense is ambivalent to intentions and points of enunciation, so is ambivalent to manifestation.

Now we might say poetry takes place within the field of signification — the expression is engendered by the form of poetry as such, as well as the differential relationships existing between words and names, sentence structures, and so on. In this way, when the poet uses the name “The Morning Star” we can get at what is expressed by asking why they didn’t choose the other names that “Morning Star” is opposed to in the same semantic class: “Evening Star”, “Venus”, etc. Deleuze hovers over this point, of perhaps attributing sense to a function of signification. Unfortunately (fortunately?) Carroll forecloses the possibility:

For the Snark was a Boojum, you see?

What is “Snark” or “Boojum” opposed to? In what semantic class do these signs differentiate themselves? Snark is opposed to Smark, or Shnark, or any other phonetically similar mush of sounds. None of these substitutions influence the sense, what is expressed, by the line. We could say that the Snark is a portmanteau of Snake and Shark, and that it signifies in relation to these names. However, this misses the effect of the portmanteau word: the Snark is not a Snake-Shark, that is, chimerically expressing the conjunction of the physical characteristics of both animals. To take it in this way is to take it in a different sense. The Snark is not a Sharktopus, or Sharknado. The Snark is first and foremost a Snark, and a Boojum.

What is a Snark, (or a Boojum for that matter)? It has no existence beyond the expression of the poem. “Snark” as a word signifies The Hunting of the Snark by Lewis Carroll, or, more precisely, what this poem expresses, a hunt. The poem deliberately frustrates the aims of signification, the endless divisions of the total signified by the signifier: the Snark is a thing to be hunted, that doesn’t enjoys puns, that takes its breakfast at 5pm, it’s a verb that can affect a boat being used to hunt it, it’s the only idea the Dunce of the crew has ever had, it tastes like a Will-O’-Wisp… This is why the Snark is not depicted (by Carroll’s request) in the original illustrations by Henry Holiday. A Snark is not a thing, nor is it a word that forms part of a symbolic system of mutually exclusive signifiers, it is a pure expression that the entire poem, and its characters and adventures, orbit.

Etymology even places a close match with an antiquated verb “to snark” meaning to snort, the actual origin of our modern adjective “snarky”. It is unclear if this bares on Carroll’s inspiration (he refused to define “Snark”), but even if it does it is incredibly apt: the sudden, short exhalation of air through the nose as a stand in for a pure expression beyond denotation, manifestation, and signification.

Sense is the fourth dimension of the proposition. It stands between words and things in the dimension of denotation (as Frege showed), and between the signification of language and the asymptotic point of a word that signifies its own expression (Snark), as Deleuze has argued apropos Carroll. It cuts the circle of the proposition.

The Status of Sense

However, once sense is established as a fourth dimension of the proposition we are faced with the bizarre status of Sense itself.

Sense is always mobile and ungraspable: I can never say the sense of what I am saying, but I can make the sense of a previous statement the object (denotation) of a following one. What I mean by that is that sense is always, in its explication, then, doubled. And what I mean by that is…

Furthermore, sense is not only indifferent to truth or falsity, its also indifferent to contradiction and paradox. Within the expression of a paradox denotation fails and signification short circuits, yet sense goes rumbling on: paradoxes of the type “following is a lie, preceding is a truth” express themselves perfectly well despite folding signification back in on itself and flipping denotation around in an endless refraction. Sense is dispassionately portioned out to the absurd, as well as the true, the false, and even the unfinished. Accordingly it is indeterminate in the extreme.

Sense is a pure effect or phantasm. Whereas signification creates the conditions of truth for denotation, and denotation deals in truth and falsity, and manifestation creates a point-of-enunciation occupied by a subject, sense merely and effervescently floats off of produced propositions, ungraspable, silent, and ambivalent. Sense engenders nothing beyond its own effect, expression, which cannot be grasped immediately but only indirectly by freezing it and making of it a denotatum for another proposition. On its own it is completely impotent.

However, it is completely indispensable in the process of meaning.

Functionally, then, Sense has the strange honor of being completely useless but absolutely indispensable. Indispensable in that it separates words from things, and unfolds the circle of the proposition, useless in the sense that it cannot engender anything but itself. But, how is it, then, to ground the circle of the proposition?

Well, it’s important to think of what it is opposed to: nonsense. Nonsense shouldn’t be taken here as (in the sense of) a failure of signification or denotation (as Lewis Carroll showed, sense still permeates this form of non-denoting, non-signifying nonsense), but in the sense of expressing nothing, being devoid of the property of expression. We see here how sense precedes the other dimensions of the proposition, that the condition for all of the other dimensions is that the effervescent effect of sense is at least produced.

For example:

oa976dgihae oeu%h i[u ‘fe h-ui fl@e98y3hozzze

This string obviously denotes nothing, possesses no dimension of signification, and fails to manifest a narrator (cat on the keyboard is a better hypothesis). It also fails to create an effect of sense. It expresses less on its own than a stone, or the space between two trees. But now look at this:

Oanqiliu dzihau oeper ch-i, yu fe h’ui flae etba yizhose.

This version, though still being meaningless, denoting nothing, possessing only the barest of signification (the notion of consonant-vowel structure, words-spaces, and “foreign languages”) and not being the intended attempt to do anything by anyone, begins to create an effect of “sensefulness”. This very effect might drive archaeologists, in vain, to discover its significations and denotations, the hopes and intentions of its author, where in fact there are none. This little example hopes to show how sense precedes the other dimensions of the proposition, without engendering them. Any piece of meaning takes place, first and foremost already within sense, it forming the condition of meaning as such. That a minimal effect of sense has been created is the minimal condition for the other three dimensions of the proposition.

Sense is the thus the ungraspable, indistinguishable, impotent effect of meaning that, in a paradoxical reversal, is meaning’s very ground.

Next, we will look at the structure of meaning in general, and the key role that sense plays within it:

About the author: John Brady is a perennial student of philosophy and educator situated in Beijing. He gets most of his reading done in traffic jams. He is also a co-editor of this magazine, by way of full disclosure.

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