AND ITS SELF-CONSERVATION. 115 



A valid reason is found, as I think, for the attention 

 here given to the fallacies of the Zenonian dialectic, in 

 the re-appearance of those fallacies under varying forms 

 in modern science. In this connection it will suffice to 

 mention the mathematical theory of "variables and lim- 

 its"; in which it is supposed to be shown, for example, 

 how a polygon may actually become a circle;* and, as a 

 typical case in physical science, that of work done by 

 weight with a lever of infinite length. Mathematics 

 struggles courageously toward the infinite, and produces 

 magnificent results within its appropriate domain of 

 the finite. 



In contrast with the Eleatic doctrine that "Being 

 alone is and non-being is not," Heraclitus declared that 

 "Being no more is than non-being." In the former the 

 conception of "being" is equivalent to that of absolute 

 reality, while by "non-being" is evidently meant the 

 absolutely unreal; that is, mere nothing. In the latter or 

 Heraclitean doctrine, on the contrary, the term "being" 

 evidently represents the present state in which any given 

 phase of reality is, while the term "non-being" stands 

 for any state that a given phase of reality may assume 

 other than that which it now is in. That is, Heraclitus 

 seems to have been the first to see clearly that nothing in 

 the finite world is ever at any one moment all that it is 

 possible it should be the first to see at all clearly the 

 true distinction between the real and the potential. Thus, 

 according to his doctrine, any individual object has being 

 at any given moment in just so far as its potentialities 



*In some mathematical works it is, indeed, explicitly stated that the 

 "limit" can never be actually reached; though the conception of a number 

 " becoming infinite " seems to present no difficulties. 



