When it is said then that we 'localize' such and such an object at such and such a point of space, what does it mean?
It simply means that we represent to ourselves the movements it would be necessary to make to reach that object; and one may not say that to represent to oneself these movements, it is necessary to project the movements themselves in space and that the notion of space must, consequently, pre-exist.
When I say that we represent to ourselves these movements, I mean only that we represent to ourselves the muscular sensations which accompany them and which have no geometric character whatever, which consequently do not at all imply the preexistence of the notion of space.
Change of State and Change of Position.—But, it will be said, if the idea of geometric space is not imposed upon our mind, and if, on the other hand, none of our sensations can furnish it, how could it have come into existence?
This is what we have now to examine, and it will take some time, but I can summarize in a few words the attempt at explanation that I am about to develop.
None of our sensations, isolated, could have conducted us to the idea of space; we are led to it only in studying the laws, according to which these sensations succeed each other.
We see first that our impressions are subject to change; but among the changes we ascertain we are soon led to make a distinction.
At one time we say that the objects which cause these impressions have changed state, at another time that they have changed position, that they have only been displaced.
Whether an object changes its state or merely its position, this is always translated for us in the same manner: by a modification in an aggregate of impressions.
How then could we have been led to distinguish between the two? It is easy to account for. If there has only been a change of position, we can restore the primitive aggregate of impressions by making movements which replace us opposite the mobile object in the same relative situation. We thus correct the modification that happened and we reestablish the initial state by an inverse modification.