168 THE GENESIS OF SCIENCE. 



riences of quantitative relations which men have gathered 

 from surrounding bodies and generalized (experience? 

 which had been scarcely at all generalized at the beginning 

 of the historic period) we find these generalized expe 

 riences, these intellectual abstractions, elevated into con 

 crete actualities, projected back into Nature, and consid 

 ered as the internal frame- work of things the skeleton by 

 which matter is sustained. But this new form of the old 

 realism, is by no means the most startling of the physio- 

 philosophic principles. We presently read that, 



&quot; The highest mathematical idea, or the fundamental 

 pi-inciple of all mathematics is the zero 0.&quot; * * * 



&quot; Zero is in itself nothing. Mathematics is based upon 

 nothing, and, consequently, ai-ises out of nothing. 

 , &quot; Out of nothing, therefore, it is possible for something 

 qo arise ; for mathematics, consisting of propositions, ia 

 something, in relation to 0.&quot; 



By such &quot; consequentlys&quot; and &quot;therefores&quot; it is, that 

 men philosophize when they &quot; re-think the great thought 

 of creation.&quot; By dogmas that pretend to be reasons, noth 

 ing is made to generate mathematics ; and by clothing 

 mathematics with matter, we have the universe ! If now 

 we deny, as we do deny, that the highest mathematical idea 

 is the zero ; if, on the other hand, we assert, as we do 

 assert, that the fundamental idea underlying all mathemat 

 ics, is that of equality ; the whole of Oken s cosmogony 

 disappears. And here, indeed, we may see illustrated, the 

 distinctive peculiarity of the German method of procedure 

 in these matters the bastard d, priori method, as it may 

 be termed. The legitimate a priori method sets out with 

 propositions of which the negation is inconceivable ; the d 

 priori method as illegitimately applied, sets out either with 

 propositions of which the negation is not inconceivable, or 

 with propositions like Oken s, of which the affirmation is 

 inconceivable. 



