658 SCIENCE AND HYPOTHESIS 



represent them to ourselves in geometrical space. So what charac- 

 terizes change of position, what distinguishes it from change of state, 

 is that it can always be corrected by this means. It may therefore 

 happen that we pass from the aggregate of impressions A to the aggre- 

 gate B in two different ways. First, involuntarily and without ex- 

 periencing muscular sensations which happens when it is the 

 object that is displaced; secondly, voluntarily, and with muscular 

 sensation which happens when the object is motionless, but when 

 we displace ourselves in such a way that the object has relative motion 

 with respect to us. If this be so, the translation of the aggregate A 

 to the aggregate B is only a change of position. It follows that sight 

 and touch could not have given us the idea of space without the help 

 of the " muscular sense." Not only could this concept not be derived 

 from a single sensation, or even from a series of sensations; but a 

 motionless being could never have acquired it, because, not being 

 able to correct by his movements the effects of the change of position 

 of external objects, he would have had no reason to distinguish them 

 from changes of state. Nor would he have been able to acquire it if 

 his movements had not been voluntary, or if they were unaccompanied 

 by any sensations whatever. 



Conditions of Compensation. How is such a compensation possible 

 in such a way that two changes, otherwise mutually independent, may 

 be reciprocally corrected? A mind already familiar with geometry 

 would reason as follows : If there is to be compensation, the differ- 

 ent parts of the external object on the one hand, and the different 

 organs of our senses on the other, must be in the same relative position 

 after the double change. And for that to be the case, the different 

 parts of the external body on the one hand, and the different organs 

 of our senses on the other, must have the same relative position to each 

 other after the double change; and so with the different parts of our 

 body with respect to each other. In other words, the external object 

 in the first change must be displaced as an invariable solid would be 

 displaced, and it must also be so with the whole of our body in the 

 second change, which is to correct the first. Under these conditions 

 compensation may be produced. But we who as yet know nothing of 

 geometry, whose ideas of space are not yet formed, we cannot reason 

 in this way we cannot predict a priori if compensation is possible. 

 But experiment shows us that it sometimes does take place, and we 

 start from this experimental fact in order to distinguish changes of 

 state from changes of position. 



Solid Bodies and Geometry. Among surrounding objects there 

 are some which frequently experience displacements that may be thus 

 corrected by a correlative movement of our own body namely, solid 

 bodies. The other objects, whose form is variable, only in exceptional 

 circumstances undergo similar displacement (change of position with- 

 out change of form). When the displacement of a body takes place 



