Immanuel Kant's Critique of Pure Reason — trans. F. Max Müller

concept (of a general representation) must express in the representation something that is generally valid for all possible intuitions which fall under the same concept. Thus I construct a triangle by representing the object corresponding to that concept either by mere imagination, in the pure intuition, or, afterwards on paper also in the empirical intuition, and in both cases entirely a priori without having borrowed the original from any experience. The particular figure drawn on the [p. 714] paper is empirical, but serves nevertheless to express the concept without any detriment to its generality, because, in that empirical intuition, we consider always the act of the construction of the concept only, to which many determinations, as, for instance, the magnitude of the sides and the angles, are quite indifferent, these differences, which do not change the concept of a triangle, being entirely ignored.

Philosophical knowledge, therefore, considers the particular in the general only, mathematical, the general in the particular, nay, even in the individual, all this, however, a priori^ and by means of reason ; so that, as an individual figure is determined by certain general conditions of construction, the object of the concept, of which this individual figure forms only the schema, must be thought of as universally determined.

The essential difference between these two modes of the knowledge of reason consists, therefore, in the form, and does not depend on any difference in their matter or objects. Those who thought they could distinguish philosophy from mathematics by saying that the former was concerned with quality only, the latter with quantity only, mistook effect for cause. It is owing

574 Discipline of Pure Reason v 2to the form of mathematical knowledge that it can refer to quanta only, because it is only the concept of quantities that admits of construction, that is, of a priori [p. 715] representation in intuition, while qualities cannot be represented in any but empirical intuition. Hence reason can gain a knowledge of qualities by concepts only.

No one can take an intuition corresponding to the concept of reality from anywhere except from experience ; we can never lay hold of it a priori by ourselves, and before we have had an empirical consciousness of it. We can form to ourselves an intuition of a cone, from its concept alone, and without any empirical assistancfe, but the colour of this cone must be given before, in some experience or other.

I cannot represent in intuition the concept of a cause in general in any way except by an example supplied by experience, etc. Besides, philosophy treats of quantities quite as much as mathematics ; for instance, of totality, infinity, etc., and mathematics treats also of the difference between lines and planes, as spaces of different quality, it treats further of the continuity of extension as one of its qualities.

But, though in such cases both have a common object, the manner in which reason treats it is totally different in philosophy and mathematics.

The former is concerned with general concepts only, the other can do nothing with the pure concept, but proceeds at once to intuition, in which it looks upon the concept in concreto ; yet not in an [p. 716] empirical intuition, but in an intuition which it represents a prioriy that is, which it has constructed and in which, whatever follows from the general conditions of the construction, must be valid in general of the object of the constructed concept also.