THE HELLENIC PERIOD 45 



is incomprehensible and therefore cannot exist. " In 

 relation to the small, there is not a least, but there is 

 always a smaller, for it is not possible for Being to be 

 annihilated by division. In the same way in relation 

 to the great, there is not a greater, and it is equal to 

 the small in plurality, and in itself each thing is at the 

 same time great and small " (Diels, Vor. I, p. 314, 16). 

 In giving these definitions, Anaxagoras was the first 

 to bring to light one of the aspects of the mathematical 

 infinite, which he wrongly connects with sensible 

 phenomena. The world is a magnitude which increases 

 beyond all limits, and matter is indefinitely divisible. 

 Thus, according as it is indefinitely divided or inde- 

 finitely added to, the same thing may be said to be 

 infinitely great or infinitely small. Only if matter 

 be infinitely continuous and divisible, how can it 

 form individual and distinct beings ? Aristotle and 

 Zeller answer this question by saying that Anaxagoras 

 believed matter to be composed of an infinite number 

 of elements all qualitatively different, and which the 

 influence of the Nous had gradually grouped according 

 to their affinities. The various groups which were 

 formed in this manner could separate, and this explains 

 the birth and death of phenomena. This conception 

 was very nearly analogous to that of Democritus. 

 Tannery judges it unacceptable as Anaxagoras 

 expressly declared that empty space does not exist. 

 According to Tannery the atomism taught by 

 Anaxagoras was essentially qualitative. The infini- 

 tesimal elements of matter are of the same nature 

 as matter taken as a whole. For example, a part of 

 the human body, however small it may be, contains 

 heat, cold, hairs, teeth, muscles, etc. Finite bodies 

 do not therefore result from a mechanical mixture of 

 atoms differing in quality, for Being, however much 

 it is divided, remains the same qualitatively. But, 

 if this be so, whence come the diversities which our 



