4 Feb 2009

Bergson, Time and Free Will, Chapter 2, §57 "Two Kinds of Multiplicity"

by Corry Shores
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[The following is summary; my commentary is in brackets.]

Bergson, Time and Free Will

Chapter II, "The Multiplicity of Conscious States," "The Idea of Duration"

Part XVI: Numerical Multiplicity and Space

§57 "Two Kinds of Multiplicity: (1) Material Objects, Counted in Space; (2) Conscious States, not Countable Unless Symbolically Represented in Space"

Previously we discussed how we have two ways of conceiving number:

1) as indivisible, in a common sense way, and

2) as divisible, in a mathematical and scientific way.

Based on these two conceptions of number, Bergson now explains that we have two ways of conceiving multiplicity:

a) Material objects are divisible multiplicities: we localize material objects in space. Even if we are merely speaking of them, we still consider it possible that we see and touch them somewhere in space. When building-up numbers, we needed partly to think of them "abstractly," because we had to juxtapose the units in "ideal space." But when dealing with material objects, we do not have to artificially place them in imaginary space. We only need to examine them in the space that already contains them: "no effort of the inventive faculty or of symbolical representation is necessary in order to count them." (85d)

However, sense data from smell and touch are non-spatial. Likewise, mental states are also not spatially locatable. (85-86) But we can only count these non-spatialized terms by symbolically representing them in a way that gives them places.

Now imagine we are walking down a dimly-lit street at night. We hear footsteps. But it is too dark to see anyone walking. Nonetheless, we might have a "confused vision" of someone pacing in the darkness where the footsteps make their sound. And each of the following sounds of foot-steps are "localized at a point in space where the passer-by might tread." (86b) So in this way we give a spatialized representation to visual images when their actual place in our visual field is not apparent.

Or imagine that we hear a tower bell toll the hour.

Toll One: We see in our minds the shuddering bell. It fades somewhat as the sound begins dying-off.

Toll Two: The bell flashes again vividly in our imaginations. The remnant of the last one still hovers nearby in another place in "ideal space." We thus imagine two juxtaposed bells. We count two tolls.

Toll Three: This time we do not add a third image. We still keep two spatially distinct ones in our mind. But we recall the first one. This way we may add more terms without overburdening our imaginations.

So, we place the bell images in "ideal" space as they each appear one-after-the-other successively in time. And we also consider many of them implicitly rather then imagine all 12 tolls at noon, for example. For these two reasons we might think that we are really counting the tolls in pure duration.

Bergson has us consider two possible ways we count the images.

1) When we are feeling the rhythm of music, we are not keeping a running-tally of all the beats. Rather, we retain the successive sensations of the beats so to arrange them in a group. But, because we continue to retain the sense-impressions of the beat, we might at the end of one song have the feeling that it had so much of a relative quantity of beats. Then when we hear a shorter song, we will have the feeling that it had a lesser quantity of beats. So we are not counting the images in this case. Rather we are "gathering, so to speak, the qualitative impression produced by the whole series." (86d) This way we can still gauge one song to be longer than another. Or,

2) We separate each beat and give them different ideal places. When we put them in this homogeneous ideal medium, we strip them of their qualities, leaving only "traces of their presence which are absolutely alike." Then we may give each its own numerical value by counting them.

Now, this ideal medium in which we place the images can either be a spatial or temporal medium.

[Time passes. The bell's resonance dies off. So too does that moment of duration fade away. But imagine a sound that hits a crystal glass' resonant frequency. It shatters to bits. The sound then fades. Likewise, the crystal glass's duration has disappeared. But we can still put another glass in its place. Time fades, but space remains. Thus, ] moments in time cannot persist in a way that allows them to be added to each other. Each beat of the drum is separated by an empty interval of time. When we count the beats, we count the intervals. But how can the intervals remain if sounds die off? The only way is if we place the sounds or intervals in an ideal space so that they may be juxtaposed and counted. So even in order to count non-spatialized durations, they must first be spatialized.

Now also consider the "confused multiplicity" of constituent sensations and feelings making-up one of our mental states. These states do not have spatial place. But we may still count them one-by-one. Each time we count one, we do so during a moment that is distinct from the moments when the other parts were counted. Thus when we count constituent mental states, we are adding moments. But as we just saw, the only way to add moments is by giving them places in idea space. Hence we need space to count our mental states.

Bergson then concludes that there are two types of multiplicity:

1) the multiplicity of material objects. To them we may directly apply our conception of number. And,

2) the multiplicity of states of consciousness. These we cannot consider numerically unless we represent them symbolically. This requires that we place them in ideal space.

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Images from the pages summarized above, in the English Translation [click on the image for an enlargement]:

Images from the pages summarized above, in the original French [click on the image for an enlargement]:

Bergson, Henri. Time and Free Will: An Essay on the Immediate Data of Consciousness, Transl. F. L. Pogson, (New York: Dover Publications, Inc., 2001).

Available online at:


French text from:

Bergson, Henri. Essai sur les données immédiates de la conscience. Originally published Paris: Les Presses universitaires de France, 1888.

Available online at:


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