lectures by gilles deleuze_ theory of multiplicities in bergson

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3/5/2014 Lectures by Gilles Deleuze: Theory of Multiplicities in Bergson

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Theory of Multiplicities in Bergson

... I wanted to propose to yo u an investigation [recherc he] into the history o f a word, a still verypartial, very localized history. That word is multiplicity. There is a very current use of

multiplicity: for example, I say : a multiplicity of numbers, a multiplicity o f acts, a multiplicity of

states of consciousness, a multiplicity of shocks [branlements]. Here multiplicity is employed as a

bar ely nominalized adjec tiv e. A nd it's true that Bergson ofte n ex pre ssed himself thus. But at other

times, the word multiplicity is employ ed in the strong sense, as a true substantive, thus, from the

second c hapter of Time and Free Will onward, the number is a multiplicity, which does not mean the

same thing at all as a multiplicity of numbers.

Why do we feel that this use o f multiplic ity , as a substant ive, is a t once unusual and important? (The

conc ept of multiplicity, Time and Free Will 224-26) It's because, so long as weemploy the adjective

multiple, we only think a predicate that we necessarily place in a relation of opposition and

complementarity with the predicate ONE: the one and the multiple, thething is one or multiple, and

it's ev en one and multiple. On the contrary , when we employ the substantive multiplicity, we already

indicate thereby that we have surpassed [dpass] the opposition of predicates one/multiple, that

we are already set up on a co mple tely d ifferent terra in, and on this terrain we are ne ce ssar ily led to

distinguish types of multiplicity. In other wor ds, the very notion of multiplicity taken as a

substantive implies a displacement of all of thought: for the dialectical oppo sition of the one and the

multiple, we substitute the typo logical difference bet ween multiplicities. And this is exac tly what

Bergson does: throughout all his work he continually denounces the dialectic as an abstract tho ught,

as a false mov ement that goes from one opposite to the other, from the one to the multiple and from

the same to the one, but which thus always lets the essenc e of the thing escape, that is the how many,

the poson [Greek term for how muc h]. That's why in c hapter three of Creative Evo lution he will

reject the q uestion: is lan vital one or multiple? For lan v ital is like duration, it's neither one nor

multiple, it's a ty pe of multiplicity. Even further: the predicates one and multiple depend upon the

notion of multiplicity , and only agree precisely with the other type of multiplicity, that is to say with

the multiplicity that is distinguished from that o f duration or lanv ital: Abstrac t unity and ab stract

multiplicity are determinations of space or c ategories of the understanding (Creative Evolution

280-81).

Therefore there are two ty pes of multiplicity: one is called multiplicity of juxtaposition, numerical

multiplicity, distinct multiplicity, ac tual multiplicity, material multiplicity, and for predicates it has,

we will see , the follo wing: the one and the multiple a t once . The other: multiplicity of penetration,

qualitative multiplicity, c onfused multiplicity , virtual multiplicity, o rganized multiplicity, and it

rejects the predicate o f the one as well as that of the same. Obv iously it's easy to re cognize behind

this distinction between two multiplicities the distinction between space and duration; but what's

important is the fact that, in the second c hapter of Time and Free Will, the space/duration theme is

only introduced as a function of the prior and more profound theme of the two multiplicities: there

are two qu ite different kinds of multiplicity , the numerical multiplicity that implies space as one of

its conditions, and the qualitative multiplicity that implies duration as one o f its conditions. Note:

Numerical multiplicities have two dimensions: space and time; the others: duration and pr e-spatial

extension.

Now Bergson begins with a study of numerical multiplicities. And his study, I believ e, includes a

very original princip le: not that the re was a multiplicity of numbers, but eac h numb er is a

multiplicity, ev en unity [unit] is a multiplicity. A nd from this three theses flow [dcoule], theses

that I will only summarize:

1. The reduction of number to ex clusively cardinal notions: the number as collectio n of units

[units], and the ordinal definition of the number of a collectio n is purely extr insic or nominal,

counting hav ing no other goal than finding the name of the number that was already thought.2. Space as co ndition of number, ev en if only an ideal space, t he time that arises in the ordinal series

arising only seco ndarily, and as spatialized time, that is to say as space of succession.

3. The divisibility of the unit; for a number is a unity only by virtue o f the cardinal colligation, that is

to say the simple act of the intelligence that considers the c ollection as a whole; but not only does

the colligation bear on a plurality of units, each of these units is one only b y v irtue of the simple act

G I L L E S D E L E U Z E

C H A P T E R S

2007 (8)

February(8)

The Body , the Meat and the

Spirit: Becoming Animal...

Capitalism: A Very Special

Delirium

Postscript on the Societies of

Control

Theory of Multiplicities in

Bergson

On Kant

On Leibniz

On Spinoza

Capitalism, flows, the

decoding of flows, capitali...

L E C T U R E S B Y G I L L E S D E L E U Z E
http://deleuzelectures.blogspot.com.au/2007/02/on-spinoza.htmlhttp://deleuzelectures.blogspot.com.au/2007/02/on-leibniz.htmlhttp://deleuzelectures.blogspot.com.au/2007/02/theory-of-multiplicities-in-bergson.htmlhttp://deleuzelectures.blogspot.com.au/2007/02/postscript-on-societies-of-control.htmlhttp://deleuzelectures.blogspot.com.au/2007/02/capitalism-very-special-delirium.htmlhttp://deleuzelectures.blogspot.com.au/2007/02/body-meat-and-spirit-becoming-animal.htmlhttp://deleuzelectures.blogspot.com.au/2007/02/theory-of-multiplicities-in-bergson.htmlhttp://deleuzelectures.blogspot.com.au/http://deleuzelectures.blogspot.com.au/2007/02/capitalism-flows-decoding-of-flows.htmlhttp://deleuzelectures.blogspot.com.au/2007/02/on-spinoza.htmlhttp://deleuzelectures.blogspot.com.au/2007/02/on-leibniz.htmlhttp://deleuzelectures.blogspot.com.au/2007/02/on-kant.htmlhttp://deleuzelectures.blogspot.com.au/2007/02/theory-of-multiplicities-in-bergson.htmlhttp://deleuzelectures.blogspot.com.au/2007/02/postscript-on-societies-of-control.htmlhttp://deleuzelectures.blogspot.com.au/2007/02/capitalism-very-special-delirium.htmlhttp://deleuzelectures.blogspot.com.au/2007/02/body-meat-and-spirit-becoming-animal.htmlhttp://deleuzelectures.blogspot.com.au/2007_02_01_archive.htmlhttp://void%280%29/http://deleuzelectures.blogspot.com.au/search?updated-min=2007-01-01T00:00:00-08:00&updated-max=2008-01-01T00:00:00-08:00&max-results=8http://void%280%29/http://deleuzelectures.blogspot.com.au/2007/02/theory-of-multiplicities-in-bergson.html


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that grasps it, and on the contrary is multiple in itself by virtue o f its subdivisions upon which the

colligation bears. It's in this sense that every number is a distinct multiplicity . And two essential

conseque nces arise from this: at once that the one and the multiple belong to numerical

multiplicities, and also the discontinuous and the co ntinuous. The one or disco ntinuous qualifies the

indivisible act by which one co nceiv es one number, then another, the multiple or co ntinuous

qualifying on the contrary the (infinitely divisible) matter co lligated by this act.

There we are, how numerical multiplicities are defined, and in a certain way these ar e the ones that

engender space: Time and Free Will, page 91-92.

But there is something quite odd. Time and Free Will appears in 1 889. In 1 891 Husserl's Philosophieder Ar ithmetik appears. There Husserl also propo ses a theory of number: he there explicitly affirms

the exc lusively cardinal character of number, the colligation as synthesis of number and the

divisible charac ter of the unit. If he differs from Bergson, it's only on the relation o f the colligation to

space, Husserl thinking that the c olligation is independent of spatial intuition; but ev en this

difference is seriou sly mitigated if one considers the no tion of ideal space in Bergson, space being in

no way a pro perty of things but a scheme of action, that is to say an original and irreducible

intellectual sy nthesis (cf. Matter & Memory 2 10 -11 ). So there is an astonishing parallelism.

Furthermore, Husserl in turn considers number as a type o f multiplicity.

Furthermore, Husserl opposes this type o f multiplicity that is number to ano ther ty pe: when I enter

a room and see that there are lo ts of people, when I look at the sky and see lo ts of stars, or lots of

trees in the forest, or a line of columns in a temple. There, actually, there is no numericalmultiplicity: it's in its very looming up [surgissement] that a sensorial aggregate presents a mark that

makes it recognizable as a multiplicity, and as a multiplicity of a totally different ty pe than the

numerical multiplicity, without any explicit c olligation: this is an implied multiplicity, a

qualitative multiplicity. Husserl speaks of quasi-qualitative charac teristics, or o f an organized

multiplicity, or of figural factors.

It's a property o f the Whole, which, as it's too easy to say , is in no way independent of its elements,

but which has c omplex relatio ns with its e lements that are c ompletely differe nt than tho se a

numerical co llection has with its elements. And Husserl doesn't fail to cite the ex ample of melody .

It's quite evident that Husserl here agrees with the work of his contempor ary Ehrenfels who, in 1890,

spoke of Gestalt qualities, distinct from the qualities proper to the elements, o f another order than

those qualities, and abov e all and explicitly the work of Stumpf who, in 1885, invo ked the notion of

Verschmelzung to designate a so rt o f passiv e (non-inte llectual) synthe sis, the apprehension of

qualities of an order superior to that of the elements.

Thus there we have what the non-numerical multiplicity is. Now this seems quite far from Bergson.

And y et it 's not so : the strokes o f the clock, in chapter two of Time and Free Will, c an enter into a

numerical multiplicity, b ut when I am distracted, what happens? They ar e based in a non-numerical

qualitative multiplicity . Multiplicity o f fusion, o f interpenetration. It's true that in Bergson it

involv es a fusion, but there's nothing of the kind in Husserl or Stumpf, who ob serv e that the more

clearly the elements, the notes of a melody are perceiv ed, the more forcefully the quality o f the set

[ensemble] affirms itself.

2 C O M M E N T S :

Prof. Ing. Ramon Oscar fernandezsaid...

UN EJEMPLO DE MULTIPLICIDAD CON SIGNIFICADO ES EL CASO DEL COLOR.. ACASO ES

POSIBLE SIGNIFI CAR EL COLOR SIN LA PRESENCIA DE LAS FORMAS QUE ELLAS

SIGNIFICAN.. EL "ROJO" ES UNA MULTIPLICIDAD EN SI MISMO.. CON PRESENCIA S DE

LOCALIZA CION MULTIPLES.. Y A QUE EL COLOR NO ESTA SITUADO EN UN LUGAR EN

PARTICULAR Y NO ES POSIBLE REDUCIR AL "ROJO" A UNAEXPERIENCIA NI CA... SOLO

AS UNA PI NTURA TIENE EL MISMO SIGNIFICADO QUE UNA MELODIA

A P RI L 2 2, 20 1 2 A T 9 :3 9 A M

Joe Danielssaid...

Good to see r elational opposites - in this case qualitative and quantitative multiplicities, if I

read y ou right - that are posited without recourse to the dialecticism that was infesting

philosophy at the time.

N OV E M BER 1 3 , 2 0 1 3 A T 5 : 3 5 P M
http://deleuzelectures.blogspot.com/2007/02/theory-of-multiplicities-in-bergson.html?showComment=1384392914498#c4187614553818884468http://www.blogger.com/profile/13813771610543530480http://deleuzelectures.blogspot.com/2007/02/theory-of-multiplicities-in-bergson.html?showComment=1335112786969#c8295778413811839060http://www.blogger.com/profile/06350275353137524349


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