Our knowledge springs from two fundamental sources of our mind; the first is to receive representations (receptivity of impressions), the second is the faculty of knowing an object through these representations (spontaneity of concepts). Through the first an object is *given* to us, through the second the object is *thought* in relation to that representation (which is a mere determination of the mind). Intuition and concepts constitute, therefore, the elements of all our knowledge, so that neither concepts without an intuition in some way corresponding to them, nor intuition without concepts can yield knowledge. Both are either pure or empirical. They are empirical when they contain sensation (sensation presupposes the actual presence of the object). They are *pure* when no sensation is mixed in with the representation. Sensation may be called the matter of sensible knowledge. Pure intuition, therefore, contains only the form under which something is intuited, and the pure concepts contains only the form of thinking an object in general. Pure intuitions and pure concepts alone are possible *a priori*, empirical intuitions and empirical concepts only *a posteriori*. We call *sensibility* the *receptivity* of our mind to receive representations insofar as it is in some wise affected, while the *understanding*, on the other hand, is our faculty of producing representations by ourselves, or the *spontaneity* of knowledge. We are so constituted that our intuition can never be other than *sensible*; that is, it contains only the mode in which we are affected by objects. The faculty, on the contrary, which enables us to *think* the object of sensible intuition is the *understanding*. Neither of these properties is to be preferred to the other. Without sensibility no object would be given to us, without understanding no object would be thought. Thoughts without content are empty, intuitions without concepts are blind. It is, therefore, just as necessary to make our concepts sensible (i.e., to add the object to them in intuition) as to make our intuitions understandable (i.e., to bring them under concepts). These two faculties or capacities cannot exchange their functions. The understanding cannot intuit anything, the senses cannot think anything. Only from their union can knowledge arise. But this is no reason for confounding their respective contributions; rather, it gives us a strong reason for carefully separating and distinguishing the one from the other. We therefore distinguish the science of the rules of sensibility in general, i.e., aesthetic, from the science of the rules of the understanding in general, i.e., logic."―Transcendental Doctrine of Elements. Transcendental Logic: The Idea of a Transcendental Logic
Spinoza formulated the profoundly important principle that *all determination is negation*. To determine a thing is to cut it off from some sphere of being and so to limit it. To define is to set boundaries. To say that a thing is green limits it by cutting it from the sphere of pink, blue, or other-coloured things. To say that it is good cuts it off from the sphere of evil. This limitation is the same as negation. To *affirm* that a thing is within certain limits is to *deny* that it is outside those limits. To say that it is green is to say that it is not pink. Affirmation involves negation. Whatever is said of a thing denies something else of it. All determination is negation.This principle is fundamental for Hegel also, but with him it takes rather the converse form that *all negation is determination*. Formal logicians will remind us that we cannot simply convert Spinoza's proposition. But it is sufficient to point out in reply that not only does affirmation involve negation; negation likewise involves affirmation. To say that a thing belongs to one class is to affirm that it belongs to some other class,—though we may not know what that class is. Positive and negative are correlatives which mutually involve each other. To posit is to negate: this is Spinoza's principle. To negate is to posit: this is Hegel's.When, therefore, we meet Hegel talking about "the portentous power of the negative," we have to consider that for him negation is the very process of creation. For the *positive* nature of an object consists in its determinations. The nature of a stone is to be white, heavy, hard, etc. And since all determinations are negations, it follows that the positive nature of a thing consists in its negations. Negation, therefore, is of the very essence of positive being. And for the world to come into being what is above all necessary is the force of negation, "the portentous power of the negative." The genus only becomes the species by means of the differentia, and the differentia is precisely that which carves out a particular class from the general class by excluding, i.e., negating, the other species. And the species again only becomes the individual in the same way, by negating other individuals. These thoughts are no causal reflections of Hegel. They underlie his entire system. We must get to understand that these three ideas, determination, limitation, and negation, all involve each other."—from_The Philosophy of Hegel_