CONCLUSION 223 



and simplifications of which the Ancients had no 

 conception. 



In a quite different direction the physical and 

 natural sciences were likewise arrested in their develop- 

 ment. For the conception of finality, upon which 

 they were based by Aristotle, clashes with a difficulty 

 which is clearly emphasized by M. Brunschvicg. The 

 Aristotelian formula leaves the mind undecided between 

 two contrary tendencies : immanence and transcen- 

 dence. " On the one hand, beings develop by realizing 

 the proper form inherent to them, which is themselves 

 in what is intimate and specific in their reality. On 

 the other hand, this realization implies nevertheless 

 in each being an aspiration to pass beyond its actual 

 state, which cannot be wholly explained except by 

 an attraction towards a higher and in some measure 

 exterior end. The world of spontaneous living beings 

 forms a hierachy turned towards God and of which 

 God Himself, although He does not turn towards the 

 world, is the origin, the prime mover. The doctrine 

 of causation, as it was elaborated by the Aristotelians, 

 oscillates between two tendencies which, if singly 

 developed, would lead to two antagonistic visions of 

 God and the universe." 1 



The Greek conception of the science of axioms is 

 certainly very remarkable, for it accustoms the mind 

 to be very exacting as regards proofs and demon- 

 strations. It evidences, however, an exaggerated 

 prudence and timidity. It not only hampered the 

 progress of mathematics, but it showed itself to be 

 impracticable in the domain of physical science, for 

 the foundations which it specifies for scientific research 

 in this domain are too narrow to support the ideas 

 deduced from experience, such as those of motion, 

 continuity and indefinite divisibility. 



Now these notions inevitably appear when one comes 



1 Experience humaine etcausalite physique, p. 158, Alcan, 1922. 



