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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, 



" The highest mathematical idea, or the fundamental 

 principle of all mathematics is the zero = 0." * * * 



" Zero is in itself nothing. Mathematics is based upon 

 nothing, and, consequently^ arises out of nothing. 



" Out of nothing, therefore^ it is possible for somethmg 

 to arise ; for mathematics, consisting of propositions, is 

 something, in relation to 0." 



By such " consequentlys" and "therefores" it is, that 

 men philosophize when they " re-think the great thought 

 of creation." 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 c?o 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- 

 ic;s, 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 a. iTi^iori 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 ia 

 inconceivable. 



