Could a philosophy exist without definitions? Or vice versa?

Both of these are hard questions. They point to the fact that definition, by itself, has not been a great object in philosophy. Aristotle wrote of categories, Frege wrote of Sinn and Bedeutung, but only lesser lights have devoted themselves to the mysteries of the definition. People like the 19th century mathematician Joseph Diez Gergonne, whose Essai sur la théorie des définitions was published in the Annales de mathématiques pures et appliquées (a journal he edited) in 1818.

Gergonne was a savant who absorbed certain of the lessons of the materialists before the revolution and the ideologues of the Napoleonic parenthesis – old clanky names like Antoine Louis Claude Destutt, comte de Tracy, whose work so influenced Stendhal. He is hailed, by Pierre Rosanvallon, for having written a prescient essay on the foundation of parties in a republic in which elections determine the governors, which Gergonne took as a partly mathematical problem: what divisions (territorial, or class, or whatever) exist in the republican set? In his essay on Political Arithmetic, Roanvallon claims, Gergonne sketched out a system whose legitimacy is enacted in our politics today:

“It is already a a vision of the democracy of parties which is sketched out in Gergonne. He was even the first to perceive the forms. “I only, he wrote in an extraordinarily anticipative fashion, “regularize the system of scissions that was in vogue under the Directorate with the difference that each fraction of the electoral college exercises here an effective right, proportioned to its mass; while at the time of the Directorate, each faction claimed for itself alone the deputies of each department.” In understanding that there is a modern and positive usage of factions and in sustaining that they did not only a deviant of pathological functioning of politics, Gergonne fully drew out the conclusions of his new reflection on politics.”

In other words, Gergonne is much more modern and up to date than the usual OPEDer in the NYT, bemoaning the lack of “consensus” nowadays – not like the old days, when every country clubber who paid his dues was basically of the same opinion!

So: Gergonne, born in 1777, before Stendhal, and outliving Stendhal by about 12 years, has a rather Stendhalian sense of the world, a sense that I would call liberal relativism. This, I think, comes out in his essay on definition. Definition, for Gergonne as a mathematician, was not simply a topic for philosophy, but a topic that allows us to advance, mathematically, in as much as it deals with systems of formalization and can, theoretically, be itself formalized as an operation. Or can it? In particular, at this time Gergonne was rather heretically advancing the idea that Descartes conjunction of algebra and geometry could be improved upon, or even, perhaps, reformulated.

The essay pokes at the different philosophical approaches to the definition, mainly as it proves something about thought itself – either the divinity of thought, its perfect tone, when it defines – as per Plato – or the fall of man written into the imperfection of this definitional capacity – as per Pascal.

Gergonne starts out defining definition on a perfectly classical note, dividing words – the things to be defined – between those that apply to one thing and those that apply to a set of things – Charlemagne being one thing, and Emperor being applicable to many things, or having many instances. This seems to be the predefinitional situation.

But of course, Charlemagne as a name of one thing implies a certain knowledge about Charlemagne – that is, a socius, or culture.

« It would be difficult to decide if individual names are less numerous than collective names. But one can remark that in as much as there is only a small portion of individual names that are used in each locality, common names, on the contrary, are used by everyone. Thus, for example, the names of the streets and places in a town, those of the individual by which it is peopled, maybe be ordinarily familiar to those who have inhabited it for a long time, but are unknown by almost everyone who does not live there, the names man, bird, fish, etc. are equally and ceaselessly in the mothers of everybody.”

The image of a language as a town, or city, in which the street names, knicknames and signifying events are unknown to the traveller is a charming one. This is 1818, and cities are, of course, getting much more interesting – a whole line of writers, from Balzac and Baudelaire to Wordsworth and Dickens are finding this out.

Interestingly, just as the city presented its horror to the writer in figural terms as a crowd – the classic man in a crowd trope that one finds in Hoffmann and Poe – the crowd also gets into the problematic of definition for Gergonne. He bumps into the possibility of the crowd nightmare in terms of this contrast between individual definitions – proper names – and collective definitions – common names – given the need, on the one hand, for terms that are more specific and complex, and on the other hand, for rooting those words in the language of ordinary uses.

All of these ways of using and inventing terms have a dimension in the passions – in “I know not what repulsion” felt in the presence of new terms. Of course, academia is a veritable factory for producing new terms – and for expressing repulsion about new terms, and a suspicion that underneath the new term there is vacancy or worse.

What interests me in Gergonne most particularly is the mention of what I’d call the Funes problem: the problem we solve, every day, by having categories and species to work with. But what if, on a deeper level, we get rid of these in some grand nominalist purge?

« Thus, even though individual names are extremely numerous, they are, in relation to each of us, as though they were a small quality, seeing that each of us, for our own use, need only a limited number. And this is how, in language, one uses incomparably more common nouns than proper one, although it could have been the case that the latter were more numerous than the former. However the case might be, one senses that there will always exist an uncountable number of objects with without proper names; and that it is as difficult to name everything as it is to know everything. And that one would be as little inclined to make them names than as might be to a real advantage. Thus, while the stars in the sky, at least those we perceive, have all received names, it is very probable that the trees in our forests and the animals that inhabit them will never be honoured with a parallel distinction.

Ah, the vertigo of the countless – or to trespass a bit on a mathematically exact term, the infinite – is always in our lives, an unconscious fear that haunts our personal cosmologies, every one of us. It is out of this that, in a stroke of genius, Borges created Funes the memorious.

‘With a glance, we perceive three glasses on a table; Funes, though, perceives all the shoots, clusters and grapes that compose a trellis. He know all the forms of the austral clouds on the dawn of April 30 1882 and could compare them to the memory of the marbling design of the page of a book he had seen one time and the lines in the foam raised by an oar on the Rio Negro on the eve of the battle of Quebracho. These memories were not simple; each visual image was tied to muscular and thermal sensations, etc.”

With names we begin the arduous process of simplifying the world, and making it our magi, our image. Science builds on the magic, but don’t think it provides any foundation. Because that is not the work of science, after all.

I have to use words when I talk to you.

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2Chris Hudson and Fred Wise