SPACE 657 



representative space. II is also just as impossible for us to repre- 

 sent to ourselves external objects in geometrical space, as it is impos- 

 sible for a painter to paint on a flat surface objects with their three 

 dimensions. Bepresentative space is only an image of geometrical 

 space, an image deformed by a kind of perspective, and we can only 

 represent to ourselves objects by making them obey the laws of this 

 perspective. Thus we do not represent to ourselves external bodies in 

 geometrical space, but we reason about these bodies as if they were sit- 

 uated in geometrical space. When it is said, on the other hand, that 

 we " localize " such an object in such a point of space, what does it 

 mean ? It simply means that we represent to ourselves the movements 

 that must take place to reach that object. And it does not mean that 

 to represent to ourselves these movements they must be projected into 

 space, and that the concept of space must therefore pre-exist. When I 

 say that we represent to ourselves these movements, I only mean that 

 we represent to ourselves the muscular sensations which accompany 

 them, and which have no geometrical character, and which therefore 

 in no way imply the pre-existence of the concept of space. 



Changes of State and Changes of Position. But, it may be said, 

 if the concept of geometrical space is not imposed upon our minds, and 

 if, on the other hand, none of our sensations can furnish us with that 

 concept, how then did it ever come into existence? This is what we 

 have now to examine, and it will take some time; but I can sum up 

 in a few words the attempt at explanation which I am going to develop. 

 None of our sensations, if isolated, could have brought us to the con- 

 cept of space; we are brought to it solely by studying the laws by which 

 those sensations succeed one another. We see at first that our im- 

 pressions are subject to change ; but among the changes that we ascer- 

 tain, we are very soon led to make a distinction. Sometimes we say 

 that the objects, the causes of these impressions, have changed their 

 state, sometimes that they have changed their position, that they have 

 only been displaced. Whether an object changes its state or only its 

 position, this is always translated for us in the same manner, by a 

 modification in an aggregate of impressions. How then have we been 

 enabled to distinguish them ? If there were only change of position, 

 we could restore the primitive aggregate of inpressions by making 

 movements which would confront us with the movable object in the 

 same relative situation. We thus correct the modification which was 

 produced, and we re-establish the initial state by an inverse modi- 

 fication. If, for example, it were a question of the sight, and if 

 an object be displaced before our eyes, we can " follow it with 

 the eye/' and retain its image on the same point of the retina by 

 appropriate movements of the eyeball. These movements we are 

 conscious of because they are voluntary, and because they are accom- 

 panied by muscular sensations. But that does not mean that we 



