Multiplicity (French: multiplicité) is a philosophical concept developed by Edmund Husserl and Henri Bergson from Riemann's description of the mathematical concept. It was later an important concept for Gilles Deleuze.
Bergson first unpacked the difference between qualitative and quantitative multiplicity in the second chapter of his doctoral thesis, Time and Free Will. The two senses of multiplicity are radically different, and our investigation of them lead us to mathematics and abstraction, on the one hand, and metaphysics and concrete reality on the other. Qualitative multiplicity names the manifold of differences which are nevertheless together in our entire field of sense experience, or are unified by continuity in the becoming of our inner duration. Bergson selects a few examples to highlight the unique characteristics of qualitative multiplicity: sympathy, grace, and effort. Each of these, as a "given" or "fact" of immediate consciousness exhibits what we today might call a depth of temporality, earlier phases are still present, at least virtually, in the later phases and the later phases only make sense as emerging from the events that preceded them. Sympathy is at first painful, and rather than flee from this pain as we normally do, the emotion then transforms into a yearning to be with, suffer with, and care for the one with whom we sympathize. The later moments are the progression of earlier ones and the whole ensemble is a transformation which leads to a new state of the soul, a new attitude and intention. Qualitative multiplicity names this reality which is essentially temporal; we can distinguish unique phases but we cannot abstract these phases from the indivisible whole they form as a passage through differences. While we tend to translate the continuous, "multiple unity" of duration into a totality of quantities measured and represented in empty space, quantitative multiplicity is always abstract and is derivative.
In his essay The Idea of Duration, Bergson discusses multiplicity in light of the notion of unity. Whereas a unity refers to a given thing in as far as it is a whole, multiplicity refers to the "parts [of the unity] which can be considered separately." Bergson distinguishes two kinds of multiplicity: one form of multiplicity refers to parts which are quantitative, distinct, and countable, and the other form of multiplicity refers to parts that are qualitative, which interpenetrate, and which each can give rise to qualitatively different perception of the whole.
- "It was Riemann in the field of physics and mathematics who dreamed about the notion of 'multiplicity' and other different kinds of multiplicities. The philosophical importance of this notion then appeared in Husserl's Formal and Transcendental Logic, as well as in Bergson's Essay on the Immediate Given of Awareness" (Deleuze 1986, 13).
- Bergson (2002, 49).
- Bergson (2002,72-74)