¹ We are concerned here not with the extent to which the Nazis’ claim to Hegel and Nietzsche is justified, but simply with the fact that they make this claim. Cf. Herbert Marcuse: Reason and Revolution. Hegel and the Rise of Social Theory. Oxford University Press, 1941. Also: Karl Loewith: Von Hegel bis Nietzsche. New York, 1941.

² I am not quite certain whether it would not be truer to Aristotle to say that it is artifacts, and not living beings, from which the fundamental categories of hylomorphism are gained. The living beings are the sphere of preferred application of the categories, but not their place of origin. They originate with a phenomenological description of artifacts. However, this would make no difference to our contention, the chief objective of which is to show the dependence of classification upon some ontology—quite apart from naming the particular stratum (life or artifacts) to which this ontology is indigenous.

³ We shall henceforth use the term “explanation” as always meaning “causal explanation.”

⁴ Cf. Anaximandros, in Diels, die Fragmente der Vorsokratiker, Vol. I. Berlin, 1934 (5. edition).

⁵ Herman Kelsen, Die Entstehung Des Kausalgesetzes Aus Dem Vergeltungsprinzip. The Journal of Unified Science (Erkenntnis) Vol. VIII. No. 1-3.

⁶ Cf. John Wild, the Cartesian Deformation of the Structure of Change and Its Influence on Modern Thought. The Philosophical Review, Vol. L, 1.

⁷ Mathematization may be, and has been, united also with classification. An example is Aristotle's analogy of the powers of the soul with geometrical figures. A modern example: the system of chemical elements.

⁸ The characteristic quality of beings is, therefore, in the modern beginning of this process of mathematization, extensio. The applicability of geometry to nature is based upon res being extensa. The secondary qualities are to be dismissed altogether, or shown to be rooted in primary qualities, i. e. in mathematizable properties. The mathematical determinations make up what a thing really is. The secondary qualities are mere appearance. Furthermore, insofar as a science is mathematical, it is demonstrated science. Demonstration seems to illustrate most clearly the victory of autarchic reason over the factuality and the contigency of the given.

⁹ Cf. Herman Weyl's latest public lectures in Princeton, N. J.

¹⁰ Cf. Aristotle, De Anima.

¹¹ May I stress again that I use this term not in the sense which James Harvey Robinson gave it, but in the sense defined on page 3.

¹² Contemporary Existenz Philosophie limits the term “existence” to man's particular beingness. The peculiarity of man's beingness we have found to lie in his essentiality. Man has not only the relation to existence, which any animal has, i. e. to preserve his existence; he has also a relation to this relation. He knows, however inarticulately, that he exists as preserving his existence. His reality is noein ten ousian.

¹³ This non-rationality of the basic decision will be analyzed more fully on page 28.

¹⁴ This statement anticipates the following section C, and will be fully understood only only in its later context. But it had to be mentioned here in order to explain our not dealing with the content and the history of the issue. The general formulation of the material issue as given on pages 2 and 26 will do for our purposes. And, as to the historical background of the warring ideologies, it suffices to know that the Nazis claim Hegel and Nietzsche as their spiritual ancestors, while the democrats claim to build on the great rational tradition of philosophy from Aristotle through the doctors of the church to Kant and the Neo-Stoics of the Enlightenment. Cf. W. T. Stace, The philosophical issues involved in this war, Philosophy Vol. XVI, No. 63.

¹⁵ We shall call rationalist anybody who, directly or indirectly, implicitly or explicitly, upholds the value of reason above and against the value of race. Even the empirical scientist would be a rationalist in our use of the term.