adequately known, and the term _objective_ to what is known in such a way that a constantly increasing number of new impressions could be substituted for the idea which we actually have of it. Thus, a complex feeling will contain a fairly large number of simple elements; but, as long as these elements do not stand out with perfect clearness, we cannot say that they were completely realized, and, as soon as consciousness has a distinct perception of them, the psychic state which results from their synthesis will have changed for this very reason. But there is no change in the general appearance of a body, however it is analysed by thought, because these different analyses, and an infinity of others, are already visible in the mental image which we form of the body, though they are not realized: this actual and not merely virtual perception of subdivisions in what is undivided is just what we call objectivity. It then becomes easy to determine the exact part played by the subjective and the objective in the idea of number. What properly belongs to the mind is the indivisible process by which it concentrates attention successively on the different parts of a given space; but the parts which have thus been isolated remain in order to join with the others, and, once the addition is made, they may be broken up in any way whatever. They are therefore parts of space, and space is, accordingly, the material with which the mind builds up number, the medium in which the mind places it. Properly speaking, it is arithmetic which teaches us to split up without limit the units of which number consists. Common sense is very much inclined to build up number with indivisibles. [Sidenote: It follows that number is actually _thought of_ as a juxtaposition in space.] And this is easily understood, since the provisional simplicity of the component units is just what they owe to the mind, and the latter pays more attention to its own acts than to the material on which it works. Science confines itself, here, to drawing our attention to this material: if we did not already localize number in space, science would certainly not succeed in making us transfer it thither. From the beginning, therefore, we must have thought of number as of a juxtaposition in space. This is the conclusion which we reached at first, basing ourselves on the fact that all addition implies a multiplicity of parts simultaneously perceived. [Sidenote: Two kinds of multiplicity: (1) material objects, counted in space; (2) conscious states, not countable unless symbolically represented in space.]