## 3 Feb 2009

### Bergson, Time and Free Will, Chapter 2, §54 "All Unity is the Unity of a Simple Act of the Mind. Units Divisible Only Because Regarded as Extended..."

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### [The following is summary; my commentary is in brackets.]Bergson, Time and Free WillChapter II, "The Multiplicity of Conscious States," "The Idea of Duration"Part XVI: Numerical Multiplicity and Space

§54 "All Unity is the Unity of a Simple Act of the Mind. Units Divisible Only Because Regarded as Extended in Space"

There are two ways we use the term "unit" when speaking of number:

1) Every number itself is one unit, because it is the synthesis of its constituent units.

2) Every number is a collection of units.

But it could be that we have a different meaning for each usage of "unit."

a) To say that every number is a unit means that we take it as a whole when we conceive it with a "simple and indivisible intuition of the mind." Hence, it is a unity of a whole and thus a unity that includes a multiplicity.

b) However when we think of the units making-up a number, we conceive them as "pure, simple, irreducible units." Each such simple unit is not itself a sum. However, we sum them together one-by-one to form the natural number series. (80b)

Thus there are really two kinds of units:

1) the ultimate basic simple unit that is added so to produce numbers, and

2) the "provisional" unit that is the number formed when simple units are added to one another. This sort of unit is "multiple in itself, and owes its unity to the simplicity of the act by which the mind perceives it." (80c)

In the previous two sections we discussed reasons why we mistakenly believe that we conceive number independent of space [§52, §53]. Now consider that if something is extended, it can be divided. So if it is unextended, it is indivisible. And if we conceive numbers as being made up of indivisible units, then it could be that we understand number independent of extension or space. (80d)

So for example, when making the number 2, we think of it as composed of two single units. But when dividing a unit by two, we then think of that same unit as being composed of two units. In other words, our notion of the unit's indivisibility is only something we temporarily assume in order to compose multiplicities. Otherwise, we think of the unit as being composed of multiplicities. So in other words, if we are thinking of the unit as indivisible, that is only because we want it to be a part of a divisible whole. Otherwise we think of it as being a totality of smaller indivisibles. So when we divide one into two halves, we provisionally regard each half as an indivisible unit. But these very same 'indivisible' halves can themselves become multiplicities when we divide them in half to produce fourths of the original unit. And those indivisible fourths we may divide to eights, and so on. So just as there are infinite multiplications of units, there are infinite divisions of units. The only way that we can consider any unit to be potentially divided infinitely is if we regarded it "implicitly as an extended object, one in intuition but multiple in space." (81bc) (82b)

[Next entry in this series.]

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:

http://www.archive.org/details/timeandfreewill00pogsgoog

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:

http://www.archive.org/details/essaisurlesdonn00berguoft