THE VALUE OF SCIENCE 527 



we now have two laws which express the relations of A and A', of B and 

 B', and a principle which expresses that of A' with B' . It is the aggre- 

 gate of these principles that is called geometry. 



Two other remarks. We have a relation between two bodies A 

 and B, which we have replaced by a relation between two figures A' 

 and B' ; but this same relation between the same two figures A' and B' 

 eould just as well have replaced advantageously a relation between two 

 other bodies A" and B", entirely different from A and B. And that 

 in many ways. If the principles and geometry had not been invented, 

 after having studied the relation of A and B, it would be necessary to 

 begin again ab ovo the study of the relation of A" and B" That is why 

 geometry is so precious. A geometrical relation can advantageously 

 replace a relation which, considered in the rough state, should be 

 regarded as mechanical, it can replace another which should be re- 

 garded as optical, etc. 



Yet let no one say: But that proves geometry an experimental 

 science; in separating its principles from laws whence they have been 

 drawn, you artificially separate it itself from the sciences which have 

 given birth to it. The other sciences have likewise principles, but 

 that does not preclude our having to call them experimental. 



It must be recognized that it would have been difficult not to 

 make this separation that is pretended to be artificial. We know the 

 role that the kinematics of solid bodies has played in the genesis of 

 geometry; should it then be said that geometry is only a branch of 

 experimental kinematics? But the laws of the rectilinear propagation 

 of light have also contributed to the formation of its principles. Must 

 geometry be regarded both as a branch of kinematics and as a branch 

 of optics? I recall besides that our Euclidean space which is the 

 proper object of geometry has been chosen, for reasons of convenience, 

 from among a certain number of types which preexist in our mind 

 and which are called groups. 



If we pass to mechanics, we still see great principles whose origin 

 is analogous, and, as their ' radius of action,' so to speak, is smaller, 

 there is no longer reason to separate them from mechanics proper and 

 to regard this science as deductive. 



In physics, finally, the role of the principles is still more diminished. 

 And in fact they are only introduced when it is of advantage. Now 

 they are advantageous precisely because they are few, since each of 

 them very nearly replaces a great number of laws. Therefore it is 

 not of interest to multiply them. Besides an outcome is necessary, 

 and for that it is needful to end by leaving abstraction to take hold 

 of reality. 



Such are the limits of nominalism, and they are narrow. 



M. LeBoy has insisted, however, and he has put the question under 

 another form. 



