“Each singular substance expresses the whole universe in its own way, […] even if [somewhat] confusingly,” writes Leibniz in his Discourse on Metaphysics (§ 9).
Let’s risk a gloss: There is no-one who has not received at least once, no matter how briefly, Athena’s or Eros’s or Ares’s visit (i.e. there is no-one who has not experienced, at least once, some degree of clarity of thought, some kind of desire, or some sort of irritation), even if only to deny it. Make it extensive to all the other gods, which designate but life’s ever-living forces, i.e. the same forces that sustain the universe and keep it turning, and to everything that may fall in between (the gods) them(selves), i.e. beyond their acknowledged jurisdiction.(*)
Upon close examination, Leibniz’s intuition proves here, then, to be identical to the one which, in the domain of mathematics, lead him to discover what is called (infinitesimal) calculus independently from Newton (despite the tendentious claims to the contrary initially made by The Royal Society). For to say that each singular substance expresses the whole universe in its own way, no matter how confusingly (or else distinctly, one may add), amounts to say that X, Y, and Z (you, dearest reader, and two any other persons whom you may be acquainted with) have approached in the past, do approach now, or will approach Eros in the future – and something similar could be said about Ares, Athena, etc. – in any imaginable proportion, e.g. 0.73918 (= X), 8.00009 (= Y), and 5.24445 (= Z), respectively, where 0 would mean not to approach Eros ever and 10 would mean to approach Eros fully and permanently.
But this means that Leibniz’s philosophy, in addition to being “perspectivist,” as it is often labelled, is, first and foremost, approximationist.
Consider too § 24 of the Discourse on Metaphysics:
“distinct knowledge” of that which is otherwise confusingly known to us, we read, has “many degrees,” for “all notions comprised in a definition are in turn susceptible of being defined” (lit. “in need of being defined”),
and §§ 36–37 of the Monadology (as per Köhler’s proposed subtitle for the first German edition of a work that, most likely, Leibniz himself thought of titling Principles of Philosophy):
the analysis of whatever notion and of all the notions implied in turn in its definition could result in an “endless detail” given nature’s “variety” and “division.”
On the one hand (on the “division” side), every notion can be infinitely decomposed into smaller notions, e.g. any circle can be said to be a spatial distribution of multiple contiguous points in such a manner that they all remain equidistant, in turn, from a point that constitutes its centre. Even the notion of point, which might look like a “primitive notion” (i.e. like a non-decomposable one) presupposes, and thereby comprises, other notions: that of space, minimal unity, place, dimensions, and the negation of these, and so on and so forth.
On the other hand (on the “variety” side), any definable notion presents infinite conceptual ramifications, e.g. a plant is a multicellular (which means…) photosynthetic (that is, …) living being (in opposition to… and in relational contrast to…) that produces oxygen which is a chemical element (or, in other words, …) of a certain atomic value (which is how … is called, but it was not until… that the periodic table was established… for, in Antiquity…, and during the Middle Ages…, all this, of course, if one periodises time according to Western standards, Western meaning here…) that moreover represents the highest percentage of the earth’s biomass, the earth itself being a planet (i.e. …) of the solar system (which is…), etc.
A double vertigo thus accompanies any process of knowledge (i.e. what Leibniz calls “analysis,” whose goal is the production of “distinct knowledge”), menacing it to collapse twice: in relation to the infinitely small and in relation to the infinitely vast, one may say (to anticipate Hegel). Yet knowledge stands half way between both subtractive poles, or, rather, in any of the infinite points (read: “degrees”) comprised between them: again, 0.73918, 8.00009, and 5.24445 (for example).
Michel Serres sees very well that with this Leibniz opposes Descartes’s law of “everything or nothing” (= “one must doubt of everything one may not be absolutely certain of”),(**) and hence too – one may infer – dogmatists and skeptics alike (in respect to whom Descartes, suggests Serres, traces a merely “diagonal line”).
One can easily understand, thus too, Leibniz’s personal interest in, and commitment to, diplomacy, which may be defined as the art of bringing together different political viewpoints – Leibniz might have said different “possible worlds” – into a possible and possibly fruitful dialogue. Or Leibniz, the anti-ideologist.
Interestingly enough, Leibniz epistemological diplomacy – Leibniz’s relativism, if you wish – does not dispense with epistemological rigour. For Leibniz is strictly Platonic (cf. his defence of Plato, against “Aristotle” [= Locke?], in the Discourse, §§ 26–27), since he knows well that while what things are is what we eventually come to know, the object of our knowledge are the ideas we have about them, be they more or less refined, more or less distinct, and the more refined the better.
There are other aspects of Leibniz’s philosophy that prove less appealing to us, e.g. the need to find a limiting external reason for the world’s hyper-complexity, which Leibniz moreover identifies with “God,” the notion of a “pre-established harmony” granted by the latter, the view that we live in “the best of all possible worlds,” the thought that all the events that describe a lifetime could be ideally foretold, etc.
Leibniz’s approximationism, though, is superb – like the fractal qualities of his multivocal and multifocal universe (cf. the allusion in Monadology, § 67 to the “gardens with plants” and the “ponds with fishes” found in “every portion of matter”).
(*) Whether that in betweenness must be seen as the place for the “demons” that “operate in the intervals between the gods’ fields of action,” as Deleuze contends in Difference and Repetition (p. 37), or the paradoxical locus dedicated in Athens to an ἄγνωστος θεός (agnostos theos, “unknown god”) external to and different from the gods known to the Greek (a supplementarity that Christianity perverted in its own profit), is something on we can not discuss here.
(**) Michel Serres, Le Système de Leibniz et ses modèles mathématiques (3rd ed.; Paris: PUF, 1990), pp. 127ff.
Image by Polymorph. (Ours are all translations, as well.)