[1] I had already completed the present work when I read in the _Critique philosophique_(for 1883 and 1884) F. Pillon's very remarkable refutation of an interesting article by G. Noël on the interconnexion of the notions of number and space. But I have not found it necessary to make any alterations in the following pages, seeing that Pillon does not distinguish between time as quality and time as quantity, between the multiplicity of juxtaposition and that of interpenetration. Without this vital distinction, which it is the chief aim of the present chapter to establish, it would be possible to maintain, with Pillon, that number may be built up from the relation of co-existence. But what is here meant by co-existence? If the co-existing terms form an organic whole, they will never lead us to the notion of number; if they remain distinct, they are in juxtaposition and we are dealing with space. It is no use to quote the example of simultaneous impressions received by several senses. We either leave these sensations their specific differences, which amounts to saying that we do not count them; or else we eliminate their differences, and then how are we to distinguish them if not by their position or that of their symbols? We shall see that the verb "to distinguish" has two meanings, the one qualitative, the other quantitative: these two meanings have been confused, in my opinion, by the philosophers who have dealt with the relations between number and space. [2] Évellin, _Infini et quantité._ Paris, 1881. CHAPTER III THE ORGANIZATION OF CONSCIOUS STATES FREE WILL [Sidenote: Mechanism, dynamism and free will.] It is easy to see why the question of free will brings into conflict these two rival systems of nature, mechanism and dynamism. Dynamism starts from the idea of voluntary activity, given by consciousness, and comes to represent inertia by gradually emptying this idea: it has thus no difficulty in conceiving free force on the one hand and matter governed by laws on the other. Mechanism follows the opposite course. It assumes that the materials which it synthesizes are governed by necessary laws, and although it reaches richer and richer combinations, which are more and more difficult to foresee, and to all appearance more and more contingent, yet it never gets out of the narrow circle of necessity within which it at first shut itself up. [Sidenote: For dynamism facts more real than laws: mechanism reverses this attitude. This idea of spontaneity simpler than that of inertia.]