“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

Denotation

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.

Manifestation

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.

Signification

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.