There is, in fact, almost no formal theory dealing with analogue communication and, in particular, no equivalent of Information Theory or Logical Type Theory. This gap in formal knowledge is inconvenient when we leave the rarefied world of logic and mathematics and come face to face with the phenomena of natural history. In the natural world, communication is rarely either purely digital or purely analog. Often discrete digital pips are combined together to make analog pictures as in the printer’s halftone block; and sometimes, as in the matter of context markers, there is a continuous gradation from the ostensive through the iconic to the purely digital. At the digital end of this scale all the theorems of information theory have their full force, but at the ostensive and analog end they are meaningless.
— Gregory Bateson
Consider, for a moment, this famous line from the poem Sacred Emily by Gertrude Stein: “Rose is a rose is a rose is a rose.” If I were to pluck one of these for you, and spell it out — the letters, R-O-S-E — I could draw your attention to the fact that the order of the letters of this word, or any word, is in large part determined by the probabilistic constraints of [a] language. Almost 50 per cent of English is, in fact, redundant: “about half of the letters or words we choose in writing or speaking are under our free choice, and about half (although we are not ordinarily aware of it) are really controlled by the statistical structure of the language.”
The Danish Spinozist geologist, Hjelmslev, that dark prince descended from Hamlet … Hjelmslev was able to weave a net out of the notions of matter, content, and expression, form, and substance. These were the strata, said Hjelmslev. Now this net had the advantage of breaking with the form-content duality, since there was a form of content no less than a form of expression. Hjelmslev’s enemies saw this merely as a way of rebaptizing the discredited notions of the signified and the signifier, but something quite different was actually going on.
—Gilles Deleuze & Félix Guattari
The following is intended as a guide for reading Louis Hjelmslev’s groundbreaking 1943 work, Prolegomena to a Theory of Language. In time, I will write a full introduction to the text, as well as an ‘interactive’ (i.e. hyperlinked, as anachronistic as that sounds) glossary as befits a book of such dazzling systematic rigor. Hjelmslev’s sole intention is to analyze the “as yet unanalyzed text in its undivided and absolute integrity” (12) into definitions, and the book does not, by and large, deviate from this arc. By laying bare the steps in his argument, I do not intend to simplify, but rather to reveal the combinatory richness and complexity of what could potentially be mistaken for an abbreviated dictionary. What is it that led Deleuze to look past Hjelmslev’s characterization of his own work as merely preliminary and recognize something even more profound?
How to found the metric of physical space? If this space were discrete, a natural class of metric would impose itself immediately, since the discrete tolerates only a limited proximity for each of the elements. But space is given as continuous multiplicity in mathematical physics, if one admits the possibility of communication between monads, a communication realized by the transmission of signals that follow the most proximate path. Around me, the radiance of geodesics assures the liaison with the neighboring egos, and founds the ‘reality’ of representations obtained from within my reference frame. ‘Where’ does it come from, then, this proximity that founds all communication (and coexistence)? When space is Euclidean, distance is that which remains invariant under the Galilean group that exchanges the inertial reference frames. Although one may affect a different reference frame for each concrete ego, a unique model (clock and universal rule) can represent the class of privileged reference frames. A type of contract between the transcendental Ego and the experience of mathematics-physics allows the founding of ‘pure’ geometry in this model. If space is ‘curved’ (as Riemann suggests…), no reference is privileged a priori, no ambient Space plays host to concrete egos. The foundation of ‘pure geometry’ in this space becomes problematic”1
Leibniz reproached the systems of [George] Dalgarno and [John] Wilkins for being insufficiently philosophical. He dreamt of a language that was, in addition to being an adequate expression of thought, an “instrument of reason.” The internationality of such a language was to be the least of its advantages: the words not only had to translate the definitions of ideas, but also render their connections (and consequently the truths about these ideas) visible, so as to be able to deduce by way of algebraic transformations and replace reasoning by calculation. This language proceeds directly from the concept of the characteristica universalis, that is to say, a logical algebra applicable to all ideas and all objects of thought.
“[A] new synthesis of the analysis/synthesis duality is the order of the day.”1
When this bold declaration suddenly emerges out of Fernando Zalamea’s quilt of academic biographies, fragmentary ontological sketches, and compilations of triadic concepts, it sticks out as the sort of thing that would be easy to champion and difficult to substantiate. What meaning could synthesis even have outside of its contrast to analysis? It is this separation and promotion of synthesis that creates some problems for Zalamea: on the one hand, he wants to distinguish contemporary mathematics as surpassing the set-theoretical limits that analytic philosophy has prescribed for itself, but the pragmatic directives that Zalamea gives himself explicitly favor the relative over the absolute, and analysis is the analysis of what is relative. There doesn’t seem to be anything particularly objectionable about the idea that synthesis orients analysis, except for the fact that Zalamea lays down a maxim affirming the “power to orient ourselves within the relative without needing to have recourse to the absolute.”1.1 If synthesis (or mathematical creativity) is separated out as that which orients analysis, is it not reduced to functioning as an absolute? Perhaps a glance at Zalamea’s adherence to pragmatic principles and how these principles cohere can offer more insight into what this synthesis of synthesis and analysis looks like for Zalamea.
Given the tremendous ambiguity of the question of whether there is a philosophical language, it is necessary to first specify our interpretation. We do not read this question as asking whether it is true that the project of a lingua universalis has been accomplished—while Gottfried Leibniz began this project in earnest amidst a flurry of scholarly interest in establishing an a priori philosophical language, he eventually came to realize the sheer scale and difficulty of the task. However, his idea of a ‘universal character’ (characteristica universalis), a universal conceptual language and general theory of signs, would be taken up two centuries later by Gottlob Frege in his Begriffsschrift, written in 1879. The Begriffsschrift, which translates to “concept script,” was intended by Frege to be a ‘calculus of reasoning’ (calculus ratiocinator)—the ‘formal’ aspect of the characteristica universalis, as we shall see—but in order to distinguish his own logic from that of George Boole, he claimed that it should be understood as a lingua characterica,1 a phrase that does not appear in Leibniz but is rather taken from Trendelenburg, who uses the expression lingua characterica universalis in his own commentary on Leibniz.2