210 CREATIVE EVOLUTION [chap. 



the growing multiplicity of the symbolic elements into 

 which the scattering of the attention has decomposed 

 it. A comparison of this kind will enable us to understand, 

 in some measure, how the same suppression of positive 

 reality, the same inversion of a certain original movement, 

 can create at once extension in space and the admirable 

 order which mathematics finds there. There is, of course, 

 this difference between the two cases, that words and letters 

 have been invented by a positive effort of humanity, while 

 space arises automatically, as the remainder of a sub- 

 traction arises once the two numbers are posited. 1 But, 

 in the one case as in the other, the infinite complexity 

 of the parts and their perfect coordination among them- 

 selves are created at one and the same time by an inversion 

 which is, at bottom, an interruption, that is to say, a 

 diminution of positive reality. 



All the operations of our intellect tend to geometry, 

 as to the goal where they find their perfect fulfilment. 



1 Our comparison does no more than develop the content of the term 

 Xoyos, as Plotinus understands it. For while the Mfos of this phi- 

 losopher is a generating and informing power, an aspect or a fragment 

 of the <pL>xy> on ^ ie °ther hand Plotinus sometimes speaks of it as of a 

 discourse. More generally, the relation that we establish in the present 

 chapter between "extension" and "detension" resembles in some 

 aspects that which Plotinus supposes (some developments of which 

 must have inspired M. Ravaisson) when he makes extension not indeed 

 an inversion of original Being, but an enfeeblement of its essence, one 

 of the last stages of the procession, (see in particular, Enn. IV. iii. 9-11, 

 and III. vi. 17-18). Yet ancient philosophy did not see what con- 

 sequences would result from this for mathematics, for Plotinus, like 

 Plato, erected mathematical essences into absolute realities. Above 

 all, it suffered itself to be deceived by the purely superficial analogy 

 of duration with extension. It treated the one as it treated the other, 

 regarding change as a degradation of immutability, the sensible as a 

 fall from the intelligible. Whence, as we shall show in the next chapter, 

 a philosophy which fails to recognize the real function and scope of the 

 intellect. 



