In the former part of our transcendental logic, we defined the understanding to be the faculty of rules; reason may be distinguished from understanding as the faculty of principles.
The term principle is ambiguous, and commonly signifies merely a cognition that may be employed as a principle, although it is not in itself, and as regards its proper origin, entitled to the distinction. Every general proposition, even if derived from experience by the process of induction, may serve as the major in a syllogism; but it is not for that reason a principle. Mathematical axioms (for example, there can be only one straight line between two points) are general a priori cognitions, and are therefore rightly denominated principles, relatively to the cases which can be subsumed under them. But I cannot for this reason say that I cognize this property of a straight line from principles—I cognize it only in pure intuition.
Cognition from principles, then, is that cognition in which I cognize the particular in the general by means of conceptions. Thus every syllogism is a form of the deduction of a cognition from a principle. For the major always gives a conception, through which everything that is subsumed under the condition thereof is cognized according to a principle. Now as every general cognition may serve as the major in a syllogism, and the understanding presents us with such general a priori propositions, they may be termed principles, in respect of their possible use.
But if we consider these principles of the pure understanding in relation to their origin, we shall find them to be anything rather than cognitions from conceptions. For they would not even be possible a priori, if we could not rely on the assistance of pure intuition (in mathematics), or on that of the conditions of a possible experience. That everything that happens has a cause, cannot be concluded from the general conception of that which happens; on the contrary the principle of causality instructs us as to the mode of obtaining from that which happens a determinate empirical conception.
Synthetical cognitions from conceptions the understanding cannot supply, and they alone are entitled to be called principles. At the same time, all general propositions may be termed comparative principles.
It has been a long-cherished wish—that, (who knows how
