114 THE WORLD-ENERGY 



already at the point of destination without even leaving 

 the point of departure. 



But one fallacy is not explained, still less explained 

 away,, by putting another by its side. A really valid 

 answer to the one here under consideration is found in 

 the contradiction involved in the expression, "infinite 

 number." 



Doubtless there may be, and is, a reality corresponding 

 with the expression, infinite quantity ; and mathematics 

 is commonly defined as the "science of quantity." Nev- 

 ertheless, as we have seen, mathematics deals, and from 

 its nature can only deal successfully, with the finite 

 aspects of quantity. To quantify in the mathematical 

 sense means to find a definite measure. And whenever 

 a "mathematically exact "result is reached, that result 

 is represented by some definite number. But number, as 

 a given definite number, is and can only be finite. ' Any 

 given number may be added to, or may be multiplied 

 either by itself or by any other number. Hence the ex- 

 pression, an " infinite number." has really no meaning in 

 the strict sense of the term. The infinite is beyond all 

 number, and no given number can ever represent the 

 infinite. So that the phrase, "infinite number," is an 

 "expression," indeed, but an expression of nothing more 

 than the vague conception of a quantity very great, but 

 as yet undefined ; unmeasured, but by no means absolutely 



In short, the Zenonian fallacy can possess even the 

 color of truth only so long as one fails to recognize the 

 essential relationship between the continuous and the dis- 

 crete aspects of quantity the true relation of the meas- 

 urable to the measureless. 



