A New Philosophy

by Edouard Le Roy

The first of these artifices is that from which results the possibility of decomposition or recomposition according to arbitrary laws. For that we need a previous substitution of symbols for things. Nothing demonstrates this better than the celebrated arguments which we owe to Zeno of Elea. Mr Bergson returns to the discussion of them over and over again. ("Essay on the Immediate Data", pages 85-86; "Matter and Memory", pages 211-213, "Creative Evolution", pages 333-337.)

The nerve of the reasoning there consists in the evident absurdity there would be in conceiving an inexhaustible exhausted, an unachievable achieved; in short, a total actually completed, and yet obtained by the successive addition of an infinite number of terms.

But the question is to know whether a movement can be considered as a numerical multiplicity. Virtual divisibility there is, no doubt, but not actual division; divisibility is indefinite, whereas an actual division, if it respects the inner articulations of reality, is bound to halt at a limited number of phases.

What we divide and measure is the track of the movement once accomplished, not the movement itself: it is the trajectory, not the traject. In the trajectory we can count endless positions; that is to say, possible halts. Let us not suppose that the moving body meets these elements all ready-marked. Hence what the Eleatic dialectic illustrates is a case of incommensurability; the radical inability of analysis to end a certain task; our powerlessness to explain the fact of the transit, if we apply to it such and such modes of numerical decomposition or recomposition, which are valid only for space; the impossibility of conceiving becoming as susceptible of being cut up into arbitrary segments, and afterwards reconstructed by summing of terms according to some law or other; in short, it is the nature of movement, which is without division, number, or concept.

But thought delights in analyses regulated by the sole consideration of easy language; hence its tendency to an arithmetic and geometry of concepts, in spite of the disastrous consequences; and thus the Eleatic paradox is no less instructive in its specious character than in the solution which it embodies.

At bottom, natural thought, I mean thought which abandons itself to its double inclination of synthetic idleness and useful industry, is a thought haunted by anxieties of the operating manual, anxieties of fabrication.

What does it care about the fluxes of reality and dynamic depths? It is only interested in the outcrops scattered here and there over the firm soil of the practical, and it solidifies "terms" like stakes plunged in a moving ground. Hence comes the configuration of its spontaneous logic to a geometry of solids, and hence come concepts, the instantaneous moments taken in transitions.

Scientific thought, again, preserves the same habits and the same preferences. It seeks only what repeats, what can be counted. Everywhere, when it theorises, it tends to establish static relations between composing unities which form a homogeneous and disconnected multiplicity.

Its very instruments bias it in that direction. The apparatus of the laboratory really grasps nothing but arrangement and coincidence; in a word, states not transitions. Even in cases of contrary appearance, for example, when we determine a weight by observing the oscillation of a balance and not its rest, we are interested in regular recurrence, in a symmetry, in something therefore which is of the nature of an equilibrium and a fixity all the same. The reason of it is that science, like common-sense, although in a manner a little different, aims only in actual fact at obtaining finished and workable results.

Let us imagine reality under the figure of a curve, a rhythmic succession of phases of which our concepts mark so many tangents. There is contact at one point, but at one point only. Thus our logic is valid as infinitesimal analysis, just as the geometry of the straight line allows us to define each state of curve. It is thus, for example, that vitality maintains a relation of momentary tangency to the physico-chemical structure. If we study this relation and analogous relations, this fact remains indisputably legitimate. Let us not think, however, that such a study, even when repeated in as many points as we wish, can ever suffice.