In his study Das Prinzip der Infinitesimal methode und seine Geschichte (1883), he tries to prove that the concept of the "infinitely small," as it was established in the Leibnizian differ ential calculus, and in the Newtonian calculus of "fluxions," is, at the same time, the indispensable and basic intellectual means for any scientific cognition of "reality." Reality is never "given" in any sense, neither in sensation nor in mere intuition, but it must be produced by means of pure thought. The various ways and directions in which thought moves in this "production of the object" are the problems which logic has to trace.
This idea found its development in Cohen's main systematic work, the Logik der reinen Erkenntnis (1902, 2nd ed. 1914), to which were added, as a second and third part of his system of philosophy, the Ethik des reinen Willens (1904), and the Aes tlzetik des reinen GefiAls (1912) .
Riehl, too, emphasizes that the question of the objective stock and the objective validity of knowledge should not be con founded with the question of the formation of ideas within the subjective consciousness. Kant's decisive achievement, according to Riehl, consists just in this, that he distinguished clearly the two questions, the "transcendental" and the "psychological," that he separated the problem of the objective significance of knowl edge from the genetic question of its derivation.
But this idealism of the general forms of pure intuition and pure understanding constitutes, according to Riehl, only one phase of the Kantian doctrine, which has its counterpart in another equally legitimate and equally indispensable one. For the particulars of experience, the definite spatial and temporal order of empirical phenomena, as well as the specific causal laws sub sisting between them, are never to be deduced from those general forms. Here we find ourselves necessarily referred to that other factor which Kant called the "material" factor of knowledge. The concepts of understanding as well as the pure forms of space and time give only the universal and necessary form of experienced reality, while its content can never be given to us otherwise than through sensation, through immediate sense-per ception. Thus the latter forms the specific and indispensable basis of our conviction regarding the reality of things.
Riehl characterizes this view as "critical realism" and sees in it the specific kernel of Kant's teaching. "For the specific and definite forms of things as given in empirical intuition, that is, the position, shape, size, the definite and determinate duration and sequence of things, there must be, according to the explicit teaching of Kant, a source in the things themselves. For they cannot be derived from the universal form of intuition which originates solely in the mentality of the subject. . . . The things in-themselves, with their proportions as expressed in the specific forms of intuition and the empirical laws of nature, are for Kant a presupposition just as essential as the a priori elements of cog nition. The necessary combination of both, their union in ex perience, is the upshot of his teaching. Our knowledge of things is a mediate cognition of the things themselves through the appearances of the things to our senses" (Zur Einffihrung in die Philosophie der Gegenwart, 4th edition, 1913, p. 090.