53. Zero _must_ be _endlessly_ positing itself, for in every respect it is indefinite or unlimited, eternal. The number of finite singularities must, therefore, pass into the Infinite. 54. The whole of Arithmetic is nothing but the endless repetition of nothing, an endless positing and suppressing of nothing. We can become acquainted with nothing but the nothing, for the Original of our knowledge is the 0. There is no other science than that which treats of nothing. Every Real, if it were such in itself, could not be known, because the possibilities of its properties would pass into the Infinite. The nothing alone is cognizable, because it has only a single property, namely, that of having none; concerning which knowledge no doubt can be entertained. A.--_PNEUMATOGENY._ PRIMARY ACT. 55. The + - or, in other words, numbers are acts or functions. Zero is, consequently, the primary act. Zero is, therefore, no _absolute_ nothing, but an act without substratum. Generally speaking there is, therefore, _no_ nothing; the mathematical nothing is itself an _act_, consequently a something. The nothing is only postulate. 56. An act devoid of substratum is a spiritual act. Numbers are, accordingly, not positions and negations of an absolute nothing, but of a spiritual act. 57. The zero is an eternal act; numbers are repetitions of this eternal act, or its halting points, like the steps in progression. With zero the Eternal therefore originates directly, or both are only different expressions for one and the same act, according with the difference of the science wherein they are employed. Mathematics designates its primary act by the name of zero; Philosophy by that of Eternal. It is an error to believe that numbers were absolute nothings; they are acts and consequently realities. While numbers in a mathematical sense are positions and negations of Nothing, in the philosophical they are positions and negations of the Eternal. Everything which is real, posited, finite, has become this out of numbers; or, more strictly speaking, every Real is absolutely nothing else than a number. This must be the sense entertained of numbers in the Pythagorean doctrine, namely, that everything or the whole universe had arisen from numbers. This is not to be taken in merely a quantitative sense, as it has hitherto been erroneously, but in an intrinsic sense, as implying that all things are numbers themselves, or the acts of the Eternal. The essence in numbers is naught else than the Eternal. The Eternal only is or exists, and nothing else is when a number exists. There is, therefore, nothing real but the Eternal itself; for every Real, or everything that is, is only a number and only exists by virtue of a number. Every Singular is nothing for itself, but the Eternal is in it, or rather it is itself only the Eternal, though not the Eternal in itself, but affirmed or negatived. The existence of the Singular is