222 CREATIVE EVOLUTION 



CHAP. 



automatically, as the remainder of a subtraction 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 themselves 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. 

 But, as geometry is necessarily prior to them (since 

 these operations have not as their end to construct 

 space and cannot do otherwise than take it as given), 

 it is evident that it is a latent geometry, immanent 

 in our idea of space, which is the mainspring of our 

 intellect and the cause of its working. We shall be 

 convinced of this if we consider the two essential 

 functions of intellect, the faculty of deduction and that 

 of induction. 



Let us begin with deduction. The same move- 



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

 \byos, as P .otinus understands it. For while the X.^/os of this philosopher 

 is a generating and informing power, an aspect or a fragment of the faxy, 

 on the other hand Plotinus sometimes speaks of it as of a discourse. More 

 generally, the relation that we establish in the present chapter between 

 &quot;extension&quot; and &quot;detension&quot; resembles in some aspects that which 

 Plotinus supposes (some developments of which must have inspired M. 

 Ravaisson) wnen 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 consequences 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 recognise the real function 

 and scope of the intellect. 



