4 Feb 2009

Bergson, Time and Free Will, Chapter 2, §56 "It Follows that Number is Actually Thought of as a Juxtaposition in Space"

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

§56 "It Follows that Number is Actually Thought of as a Juxtaposition in Space"

Previously we saw that our act of constructing numbers regards them as indivisible, but our subsequent acts of conceiving numbers consider them as infinitely divisible.

Bergson notes that our minds construct numbers through simple indivisible acts. So common sense tells us to build-up numbers with indivisible units. Arithmetic, however, teaches us that numbers are infinitely divisible quantities. Yet, our minds are more concerned with their own acts rather than with the conceptual "material" they are working-on. Thus part of us holds-on to the view that numbers are made-up of indivisibles. But, consider that science quantifies space in order to make physical measurements and calculations. So science has us focus on the numerical "material" so that we can transfer a spatialized sense of quantity onto actual space itself. Also, when adding numbers, we simultaneously perceive a multiplicity of parts, and each part must take-up a different place so they all may co-exist. Hence for the purposes of science and mathematics, we are inclined to think of number in terms of a juxtaposition in space. (84-85)

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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).

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French text from:

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

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