SOMETHING. 11 



manifested, it is either a positive or negative. The whole 

 of arithmetic is nothing else than a ceaseless act of posit- 

 ing and negating, of affirming and denying. 



All realization is nothing else than the act of positing 

 and negating. The act of positing and negating of the 

 Eternal is called realization. 



49. Positing and negating is, however, an act or 

 function. Arithmetic is, therefore, a ceaseless process of 

 acting or performing. Numbers are ads of the primary 

 idea, or, properly speaking, stationary points of its func- 

 tion, and hence proceeds a division into the two ideas 

 + and _. If these remain always alone nothing is 

 added to them. They alone produce the whole science of 

 arithmetic, and simply because they are never exhausted 

 by the act of positing themselves repeatedly, but capable 

 after this of again elevating themselves in power. Since 

 + is in essence nothing else than a simple positing, a 

 mere affirmation, and a mere suppression of this 

 affirmation, a negation ; so is the positive unity = 1 no- 

 thing but an affirmation once declared, and the whole 

 series of numbers is a reiterated affirmation. The act 

 of affirmation alone gives the number, and the latter is 

 thus the definite quantity devoid of intrinsic value. Bare 

 affirmation alone without reference to any substance is 

 unity, duality, &c. 



SOMETHING. 



50. Still, however, there must be something, which is 

 posited and negatived. The form must have a substance. 



This something is the primary idea, or the very Eternal 

 of mathematics, the zero ; for + is = 0. The + is 

 naught else than zero affirmed ; the naught else than 

 this + negatived = 0. Now since an affirmation 

 once declared is = 1, so are unity and zero identical. 

 Zero differs only from finite unity in that it is not affirmed. 



51. The is not simply the want of affirmation, but 

 its explicit abstraction. The + presupposes the ; the 



. the + and ; the 0, however, presupposes neither 

 + nor . Purely negative quantities are, as is known, a 

 nonentity, because they can only bear reference to positive 



