I remember a seminar held at the University of Heidelberg, soon after Hitler came to power. Karl Jaspers, who was shortly to lose his professorship because he had committed the crime of Rassenschande—in other words, because he had married a Jewess—was discussing a student's essay on Hegel's philosophy. He said: “In these days when we hear all too much about race, I advise you to read X's book on ‘race among the herrings’. You will then see what we know about race today, when human passions are not involved.”

When I was at the lycée, I listened with passion to the lessons of my history professor and I eagerly enlarged upon his lessons by doing a great deal of reading. On the other hand, I disliked mathematics. For me, equations, theorems and logarithms were no more than cumbersome baggage for the historian I aspired to become. Worse than that, it was an obstacle which inevitably I had to surmount in order to obtain my baccalauréat. Having surmounted the obstacle, I simbolically sold my table of logarithms, for had I not freed myself forever of that which for too long had been a nightmare?… Now, about twelve years later, without my ever having deviated from my original course, I find myself once again confronted with mathematics. Of the same sort? Certainly not. What I am now confronted with is infinitely more complicated and beyond my comprehension as I lack the basis which I erstwhile ignored. What then has happened? Why is it that the historian that I became in the meantime now needs mathematics today?

As an introduction to the study which is the subject of this article, we would like to provide some definitions and make a few elementary observations, in order to make it possible for the less informed reader to understand better the origins and the raison d’être of the propositions that are under examination.

In the Biblical story of the creation we read (Gen. II): “The Lord in the exercise of His power created from the soil all the wild animals of the field and all the birds (and other animals) that fly in the sky. He brought to the Man to see what name he would give it. Whatever the Man called a living soul, that would be his name. The man gave names to all the domestic animals and to the birds of the sky and to all the wild animals of the field; but there was not found a helpmate appropriate to Man.” An early medieval commentary (Midras Beresit Raba, quoted from ed. Levin-Epstein, Jerusalem, 5712 = 1951/2) reports the following explanation (xvii, 4): “The students asked Rabi Yohanan ben Zarai: It is written (Gen. 1, 24), ‘And God said, let the earth bring forth living souls according to their species…’ What, then, is the meaning of the verse, ‘The Lord created from the soil…?’ He said to them: The first verse (1, 24) relates to the creation, whereas the second mention (II, 19) refers to the power of the humans over the animal kingdom. This can be seen from the verse (Deut. xx, 19): ‘If you will use your power against a city…’.” (This means that the word wayser should not be derived from the root ysr, to create, but from the root swr, to behave in an inimical fashion. The best translation of the verse would then be: “The Lord in the exercise of His power forced from the soil all the animals of the field… and brought them under the power of the Man under condition that he would name them.” It is to be noted that the word “he created” appears previously in II, 7 as applied to the creation of Man. There it is spelled wyysr, seemingly to exclude a derivation from swr. This is similar to the massoretic treatment of wyr’, he saw, and wyyr’, he feared. The first root is r'h, the second yr’. Naturally, biblical scholarship cannot take notice of these remarks since it must believe in a theory of sources.) The attitude underlying this commentary is that the knowledge of the right name gives power over the bearer of that name. This attitude is a well-known principle of magic in all its forms. It can be found in folk-tales like that of Rumpelstilzchen. J. G. Frazer, in The Golden Bough (quoted from 2nd ed., vol. 1, London, 1900) has made a classical study of this kind of magic. He writes of the Egyptians (p. 446): “For it was believed that he who possessed the true name possessed the very being of god or man, and could force even a deity to obey him as a slave obeys his master.” For the same reason, we are told (p. 447): “The city of Rome itself had a secret name which it was unlawful to divulge.”

Before bringing out the relationship between dialectic and logic, we must define as precisely as possible the sense in which we shall use these terms. It is well known that the words “dialectic” and “logic” have taken on very different meanings in the history of philosophical and logical thought. This ambiguity is also characteristic of their use in contemporary publications.

Moslem countries have a high birth rate (4096-50%) and a rapid rate of natural growth (28%-34%). Not even in towns where mortality has decreased does natality appear to have decreased, and not even where the family nucleus is beginning to assert itself can a drop in the birth rate be ascertained. This is attributed to a “backward attitude toward economic and social changes.”

It is true that all ideas begin with experience, in a factual, temporal sense. It is also true that the validity of many ideas does not depend upon the observations of natural experience. “Experience” is used therewith in two different senses of the term, which cannot be fused by calling them different modes of experience. The difference between the inductive and the deductive, or the empirical and the formal, is involved. It has been one of the supports for the doctrine of a priori knowledge. The difference between direct experience, in which one is “at the mercy of the object,” and reflective experience, which is regarded by some philosophers as more adequate and independent, has also been prominent. It has led to the doctrine of transcendental knowledge, in response to the understandable wish to be emancipated from the natural conditions of experience. Curiously, it does not seem to be realized that an emancipation from nature would also involve independence from all conditions of human culture. That the direction of flight is away from the limitations of the natural world is evident. Not so evident is the goal, which hardly offers the desired haven of refuge in a nonnatural world that is devoid of culture as we know it.