59. Every object may be considered either in the real or in the ideal order. The ideal is their representation in an understanding, which has a value only inasmuch as it refers to possible or actual reality. In this manner alone can the idea have objectiveness, since otherwise it could only be a purely subjective fact, of which, excepting the purely subjective, nothing could be either affirmed or denied. The idea which we have of the triangle aids us, in so far as it has a real or possible object, to know and combine: we refer what we affirm or deny of it to its object: if this disappear, the idea is converted into a purely subjective fact, to which we cannot apply the properties of a triangular figure without an open contradiction. CHAPTER IX. IDEA OF NEGATION. 60. It is said that the understanding does not conceive nothing: this is true in the sense that we do not conceive nothing as something, which would be a contradiction; but it does not therefore follow, that we do not in any mode conceive nothing. Not-being is nothing, and yet we conceive not-being. This perception is necessary to us; without it we could not perceive contradiction; for which reason the principle of contradiction: "It is impossible for a thing to exist and not to exist at the same time:" fundamental as it is in our cognitions, would fail us. 61. It may be said that to conceive nothing, not-being, is not to conceive, but to not-conceive: this, however, is false, for it is not the same thing to conceive that a thing is not, and not to conceive it. The former involves a negative judgment, and may be expressed by a negative proposition; and the latter is the simple absence of the act of perception; the former is objective, the latter subjective. We do not when asleep perceive things; but this non-perception is by no means equivalent to perceiving that they are not. It may be said of a stone that it does not perceive another stone; but not that it perceives the non-being of the other stone. 62. The perception of not-being is a positive act; and it would be a contradiction to say that it is the very perception of being; for it would follow, that whenever we perceive being, we perceive its negation, not-being, and _vice versa_, which is an absurdity. 63. When we perceive not-being, we do, it is true, perceive it in relation to being; and it is equally true, an understanding perceiving absolute not-being, without any idea of being, is altogether inconceivable; but this does not prove the two ideas not to be distinct and contradictory.