Today, I shall have to turn to a seemingly more remote topic that will fit in, however, with yesterday's and tomorrow's subjects. I have frequently mentioned that when the evolution of humanity is surveyed, people proceed too much from the premise that the general condition of human soul life has basically remained the same ever since any human development can be traced historically or in prehistory. However, this assumption simply does not correspond to the facts. It is difficult, of course, to ascertain what the successive metamorphoses of human soul evolution were like if one is merely in a position to study the facts recorded in historical documents. If, on the other hand, one is able to look back further than these facts allow, then even the historical traditions present themselves in a different light. It then becomes evident that the human soul condition was not always what it is today or what it was in the ages still discernible by external means.
Above all, people believe the following: Human beings utilize something like geometry, like arithmetic, which, as we know, is mainly the theory of counting. Furthermore, they master the art of weighing, of determining weights of given objects. People then consider what measuring and measures represent and contemplate the way one counts and weighs things today. Then people think: Surely, in the age when, according to modern, prevalent opinion, human beings were still completely childlike, they were incapable of measuring, counting, and calculating anything. But ever since human beings were capable of that, these matters have been carried out approximately in the same way we execute them nowadays.
This is not the case at all, and even though it will lead us into a more remote subject, as I said, we must acquire a more exact idea of measures, numbers, and weights before we go into the historical considerations about mankind. Even according to external historical tradition the views concerning numbers prevailing in the Pythagorean School differed somewhat from those of today. As all of you realize, the Pythagoreans connected certain ideas with the numbers one, two, three, four, and so on. They linked quite definite conceptions with an even and an odd number. In short, they spoke about numbers in a certain qualitative sense, not merely in a quantitative one.
When the underlying reason for this is considered from the standpoint of spiritual science, we arrive at the realization that the Pythagorean School, which as yet was still a kind of esoteric school, represented basically only the last vestige of a much more ancient wisdom of numbers, going back to primordial times of which only the traditions have been preserved. And what is handed down to us concerning a science of numbers by Pythagoras is in fact already a decline from a much older teaching of numbers. When these matters are pursued further with the methods of spiritual science, we arrive by way of measure, number, and weight at concepts essentially different from those we possess today. As I said, even though it might create difficulties for some of you, we must make it somewhat clear to ourselves how these concepts of measuring, counting, and weighing are constituted today.
Measuring — how do we measure? We can only have one measure and it must be assumed in some manner. We cannot claim that this measure on which we base everything, such as the metric measure today, is somehow determined absolutely. It is determined as a certain segment of the northern quadrant of the earth's meridian that passes through Paris, and this segment, the ten millionth part, is not even exactly contained in that original prototype meter located in Paris. It is assumed, however, and we say that we proceed from a certain measure. With it, we then measure other lengths or surface areas by forming a square measure out of the unit of length. Yet, the figures arrived at concerning the object being measured refer to something completely arbitrary that was at one time assumed. It is important to make it clear to ourselves that we actually take an arbitrary measure as the basis, hence, that we always arrive only at a relation of some object to this arbitrarily assumed measure when we measure an object.
It is somewhat different in the case of numbers. In the abstract manner of our life today, we count, 1, 2, 3; we do this when counting apples or people, horses or chairs. To the object that is to be determined by the number it matters not what we designate as 1. We apply our peculiar way of counting to all things we count off, which, as a unit, represent an integrated totality.
Please note that in measuring we proceed from an arbitrary measure and we then relate everything to this arbitrary unit of measure. This unit of measure is something, so to speak; it exists. It is even conceivable, as it were, almost like a thing, an object. The unit of numbers cannot be pictured in this way. The unit of number is a completely abstract concept applicable to anything. No matter whether we count years or people or stars, we are led into total abstraction, into something that cannot stand for any particular reality since it could stand for all realities. When we take the arithmetic unit as the basis, the minute objective element still retained in measuring is lost to us.
When weighing something, we do not see the whole extent of what we take as the basis of weighing. There, the whole matter escapes us even more than in the case of numbers. When we count chairs, for example, and we say, “one,” “two,” “three,” we are at least finished when we come to the third chair that stands before us as a unit. In the case of a scale, on the other hand, we place a weight on one side of the scales — a weight in itself is nothing if it is not subject to earth's gravity, as we say — and the object we weigh is equal to the weight of the weights. Here, however, we are no longer by ourselves; basically, the whole earth is involved. Our point of reference here lies somehow completely beyond the realm we oversee. We enter into a complete abstraction when we say that something weighs five kilograms. Just think what you actually picture when you say that something weighs five kilograms. You place a five kilogram weight on a scale, but this weight by itself is really nothing! We are not dealing with a property of the thing itself. When I say, “one chair,” this one is at least integrated in the chair. The five kilograms, on the other hand, must relate themselves to the earth. You merely deal with something that relates to something else the whole extent of which you do not see at all, namely, the whole body of the earth. And when weighing the other object on the scale, which is to weigh five kilograms, again, you have something that escapes you completely, belonging again to a totality that is even less than an abstraction.
Let us proceed from numbers. In former times, and here we actually go back as far as the second post-Atlantean epoch, all thinking concerning numbers was dealt with in a significantly different manner from the way we treat it today in the outside world. People then really had concepts of 1, 2, and 3. For us, 2 is nothing but the presence of two units of 1; 3 is the presence of three, 4 that of four units of 1. Thus we continue counting by always adding 1 more. hence repeating the same act of thinking. We can repeat it indefinitely.
This was not the case in the second post-Atlantean epoch. Back then, people sensed the same difference between, let's say, two and three that we today feel only between different objects. In the number 3, one sensed a significantly different element from that in the number 2. Not only was it the addition of one unit; rather, one sensed something integrated in the 3, something where three things relate to one another. The 2 had an open element, something where two things lie indifferently side by side. People recalled this indifference in lying side by side when they said “two.” They did not sense this in the number 3, but only something that belongs together, where each thing relates to all the others. Concerning 2, a person could imagine that one thing escapes to the left, the other to the right. The 3 could not be pictured that way; instead, it was felt that if one unit would disappear, the remaining two would no longer be what they had been, for then, they would exist indifferently beside each other. The 3 combined the 2 in a totality, so to speak; it made them a whole. The form of arithmetic we have today, our elementary counting, this repetition of the same act, did not exist at all in those former times. Only now, through spiritual science, we are once again directed in a certain sense to the qualitative element of numbers.
I can illustrate this with an example long since familiar to you so that you will realize that it is necessary to add not only 1 to 1, and so on, but to delve into the reality of existence with the numbers. In order to give you at least a very elementary idea of this matter, let me outline the following. In my book, Theosophy, [Note 1] the individual members of the human being are described:
1. Physical Body
2. Ether Body
3. Astral Body
4. Sentient Soul
5. Intellectual or Mind Soul
6. Consciousness Soul
7. Spirit Self
8. Life Spirit
9. Spirit Man
To list the members of the human being side by side like this, however, signifies counting them off abstractly one after the other; it means that we do not delve into reality. Because these nine do not exist, we cannot count them like that at all: “1. physical body, 2. ether body, 3. astral body, 4. sentient soul.” You cannot count like that when you wish to comprehend the human organization and observe human beings today in their reality. In fact, it must be put like this: The physical body is delimited as an integrated whole, so is the etheric body. Pass on to the third member, on the other hand, it is not something self-enclosed. In the case of the actual human being, we cannot just add the sentient soul to the astral body. Instead, these two, the astral body and the sentient soul, must definitely be combined and thereby, passing from one to two to three in reality, we can, as it were, count off realistically, not merely finding in the 3 the simple addition of 1.
What develops in us as the “astral body” and the “sentient soul,” which interact with each other, is simply a third element, abstractly speaking, but by passing in reality to this third element, a third unit can no longer merely be added to the first two. Instead, we must realize that this third element is in itself different from the first two.
Then, the fourth member is counted off, which is actually the fifth, and again, in the modern human being, we must basically add together the sixth and seventh. Thus, we arrive at the way they are actually listed in my Theosophy: 3, 4, 5, 6, 7. We have seven actual components, which, when they are abstractly counted off, are nine:
Based on reality, we learn to say: By proceeding according to their inherent rules, one thing is not indifferent to the others. Just because this is the third member (see above, 3), it is something different. Certainly, due to our customary abstract thinking about numbers, we have to illustrate this a little, for this older way of thinking about numbers is foreign to ordinary consciousness. In ancient times, on the other hand, in the first and second period of the post-Atlantean epoch, it would not have occurred to anybody to imagine an indifferent addition in progressing from one number to the next. Instead, people experienced something when they passed from, say, 2 to 3, just as we experience something here when we pass from 2 to 3 (see above list). Today you can barely sense it in this example, but not yet in the number itself. In those former times people could sense it in the numbers themselves. They spoke of numbers in reference to their mutual relationships. Anything that existed in twos, for example, was felt to have a quality of openness towards the world, of not being closed off. Something existing in threes, as an actual three, was something closed off. You might now say that depending on what is counted a distinction has to be made. When you count, one man, one woman, one child, man and woman are equal to a duality, hence not closed off to the world; the child closes this duality off, forms a totality. When you count apples, on the other hand, we can indeed not say that three apples are more closed off than two. It was true that external matters were merely sensed in this way, but the number itself was experienced quite differently.
You might recall that certain aboriginal tribes still use their ten fingers to count, comparing to them the amount of objects present in their surroundings. So we could say that if we have three apples here, this is equal to three fingers.
For 1, 2, 3, however, these primitive people would not have said — naturally in the words of their own language — “thumb,” “index finger,” and “middle finger.” Although the objects they counted off in the outside world remained undefined, what represented those objects inwardly was very clearly defined, for the three fingers differ from one another. Well, mankind has now advanced so splendidly in the fifth period of the post-Atlantean epoch — basically, it was already like this in the fourth period — that we no longer need to count by means of our fingers. Instead, we say, “one, two, three.” The genius of language is not taken into consideration anymore. For if you would listen to what is contained in the words, purely based on feeling you would say: “Eins, entzwei” (“one, in two — cut in two.”) (Translator's Note 1) It is still retained in the language, and when you say: “Drei” (“three”), and you are sensitive to the sounds, you have something closed off. Three: when pictured correctly, three things can only be imagined as lying in a circle, connected to each other; two: into two (entzwei); three: self-enclosed, the genius of language still retains that.
Well, as I said, we have “advanced so far” that we can abstractly add one unit to another. Then we feel that this is 2, that is 1; in case of 3, one more has been added, and so on. Yet, why is it that we can count in the first place? In reality, we don't accomplish it any differently from primitive peoples. Only they did it with their five physical fingers. We, too, count with the fingers, but with those of our etheric body, and we no longer know it. It takes place in our subconscious, and we leave that out of consideration. We actually count by means of the etheric body; in reality, a number is still nothing but a comparison with what is contained within us. The whole of arithmetic is in us; we brought it to birth within us through our astral body. It actually emerges from our astral body, our ten fingers being merely replicas of the astral and etheric. These two are only utilized by the external finger, whereas, when we do sums, we express in the etheric body what brings about the inspiration of numbers in the astral body; then we count by means of the etheric body, with which we think in the first place.
Therefore, we can say that, outwardly, counting is something quite abstract for us today; inwardly, the reason we count is connected with the fact that we are counted in the first place, for we are counted out of universal being and are structured according to numbers. It is most interesting to trace the various methods of counting among the different folk groups in the world — according to the number 10, the decimal system, or the number 12 — and how this relates to their different etheric and astral constitutions. Numbers are inborn into us, woven into us out of the cosmic totality. Outwardly, numbers are gradually becoming a matter of indifference to us; within us, this is not the case. Within ourselves, each number has its own definite quality. Just try and imagine that you could eliminate numbers from the universe and then see what things formed in numbers would look like if one thing were merely added to the other. Imagine the appearance of your hand, if the thumb were here, and the next finger would be added as the same unit and then the next, and so on. You would have five thumbs on your hand and five on the other! This would then correspond to abstract counting.
The spirits of the universe do not count like that. They create forms according to numbers, and they do it in the manner formerly connected with numbers during the first and even the second period of the post-Atlantean epoch. The development of abstract numbers out of the quite concrete concept of the element and quality of numbers is something that only evolved in the course of humanity's evolution. We have to realize that it has profound significance that the tradition handed down to us from the ancient mysteries relates that the gods fashioned man according to numbers. The saying that the world abounds in numbers implies that everything is fashioned according to numbers and that the human being, too, is formed on the basis of numbers. Hence, the modern way of counting did not exist in those ancient times; on the other hand, an imaginative thinking in the qualities of numbers did exist.
As I said, this leads us back to an age of long ago, namely, the first and second post-Atlantean periods, the ancient Indian and Persian eras, in which our present form of counting was not at all possible. In those times people connected something entirely different from two times one with the number 2. And likewise they associated something other than two plus one with three. As you can see, the human soul constitution has indeed changed considerably in the course of time.
Turning now to the somewhat later period of time, the third period of the post-Atlantean epoch, we find that the measure was something quite different. Today, we measure on the basis of an assumed and arbitrary unit of measurement. Even in the third post-Atlantean period, for example, people did not really refer to such an arbitrary unit of measure. In measuring, they had in mind something quite pictorial. What they focused on may perhaps become clear to you from the following. Here, for instance, we see one column, there is another one (see sketch below); we look at these two columns. If we experience things abstractly, we say that the second column is twice as high as the first one; we measure it by the first one.
That, however, is a very abstract conception. Picturing it concretely, we can interpret it in approximately the following manner: When we evoke a feeling for the column on the left, we experience it to be weak in comparison to the one on the right. We feel that it must grow, and when it grows and grows and reaches this point up here (pointing to the taller column), it has become something special. It has put so much energy into this growth that it now possesses a strength such that its two parts are both equally strong. You can sense something qualitative there. You can go further and say: I have a structure here; I measure it against the other one and thus arrive at the symmetry; the concept of the measure expands for me, entering into the picture.
In this way, we gradually come to the idea that measure actually has to do with something that is still sensed dimly when we speak of moderation (Translator's Note 2) in which case we are not thinking of measuring something. For example, when a person consumes only a certain quantity of some food, we might designate that as being moderate (maessig) without having measured the amount. We classify something else as immoderate (unmaessig). We are not measuring anything here, we make no comparison, measuring the stomach with what enters it, and so on. We don't measure the piece of meat and then eat it; we do not measure it against the size of the person. Instead, we refer to a quality when we speak of a moderate or immoderate intake of food. We arrive at something that is not so very different from what we term a measure today but it does show us that we refer to something abstract today when we speak of measure, namely, “the unit of measure contained in a certain quantity,” whereas formerly people defined it as something that was qualitatively connected with objects.
Above all, people sensed the measured symmetry of each member of man in relation to the totality of the human being without thinking at that point of a unit. One thing has remained from this, namely, that it seems abhorrent to us if, as artists, we are supposed to measure anything; for, if an artist actually has to take measurements so that the nose, for example, does not turn out to be too long or too short, this is not considered artistic. But we consider the work artistic when we see that the thing has the proper size for an organism. Therefore, we do not deal with an abstract process here but with something related to the pictorial element.
Finally, consider the unit of measure that still plays a certain role today, namely the so-called golden mean or golden section. It is not connected with measurements but only with a qualitative element. The smaller element is to the medium-sized one as the medium-sized one is to the whole. The smaller element may be any size, but it must always be to the medium-sized one as the medium-sized one is to the whole. We do not have a measurement in mind but something that reveals a certain interrelationship when we look at it. Yet, we speak of the harmonious measure that comes to expression in the golden mean. We cannot base the golden mean on any kind of unit of measure in the abstract sense as we do otherwise. Therefore, as we examine the various periods of humanity's evolution in regard to measuring, we find that in the fourth post-Atlantean period, the Greco-Roman age, this vivid awareness of measure and symmetry gradually transformed itself into abstract measuring. This was actually not the case until the fourth post-Atlantean period. In the third period people experienced the relationships of measure, the proportions, much more the way we only experience the golden mean. Likewise, as we go back into ancient times, our abstract counting can be traced back to an experience of the inner quality of numbers.
In the case of weight, human beings are already far removed from what existed in the first post-Atlantean period as an experience of weight. You need only recall a well-known phenomenon that most of you have experienced in observing an athlete who lifts a heavy weight with the inscription, “200 kilograms”; he tries and tries to lift it, sweating all the while, and you almost perspire with him. Then, when he's let you sweat long enough, he suddenly lifts it up and carries it off. The whole thing really has no absolute weight; that has only been feigned. You feel the weight because of the abstract inscription “200 kilograms.” The experience of weight is something we are deprived of nowadays. Therefore, it is one of the most profound experiences when, in regard to natural phenomena, the experience of absolute weight appears in clairvoyant consciousness, as is indeed the case.
It is really true that in the first post-Atlantean epoch, designated as the ancient Indian epoch, a human being still experienced something of weight relationships within himself. I have pointed out many times that our brain actually floats in the cerebral fluid and therefore — according to the well known law whereby a floating body seemingly becomes lighter by the amount of the weight of water it displaces — loses a considerable amount of its weight. Otherwise, the brain would crush the blood vessels lying underneath. The brain floats in the cerebral fluid, but people in their abstract awareness no longer notice this today; neither are they aware of any other relationships within themselves. We no longer experience weight, pay it no attention. There is a major difference between experiencing one's weight at age twelve, and when one is, say five times that age. Most people have forgotten, however, how heavy they appeared to themselves at age twelve, and therefore they cannot very well make the comparison. But let's assume that according to the scales you have the same weight at two ages. Yet this does not matter; what matters is the experience of the weight. This experience of weight that for people today is present only in regard to the earth, was something absolute during the first postAtlantean epoch.
Today, we experience only a remnant of that in art but there in a very pronounced manner. I need only call your attention to the following. Let us assume that I draw two figures. According to my view, this is really something unclear and unresolved, something that should not be. Two objects like that side by side induce me to draw a third one. But I can shape the third object only in such a way that it appears larger, in a sense, holding the other two together. Then I have the feeling that the three are floating in air and can mutually support each other.
When a painter nowadays draws three angels who are, after all, not viewed in connection with gravity, and he is concerned with composition, he distributes them in space in such a manner that they support each other, that one is borne by the other. Artistically, it would be the worst thing simply to draw three angels side by side on a canvas; such a painter would have no true artistic feeling. One must have a feeling for the weight of each one, how one thing carries the other. In artistic feelings, a slight touch has remained of what was mainly experienced inwardly by people in the post-Atlantean age as producing weight, as giving him weight.
The experience of weight, number, and measure developed during the first three post-Atlantean periods according to the way human beings experienced themselves within the cosmos. And based on what had shaped them from out of the cosmos, the other matters were judged, namely, what they produced. When people observed what their astral body pushed into the etheric body, they had to tell themselves that the astral body counts, counts in a differentiating way, thus forming the etheric body. Numbers are found between astral and etheric body and they are something alive and active within us.
Something else is located between etheric body and physical body. Through the inner relationships something is formed out of the etheric body that we can then behold. Basically, even our organism is structured according to the golden mean: the forehead is to a certain other part of the head as that in turn is to the whole length of the head, and so on. All this is imprinted by the etheric body into our physical body out of the cosmos and its relationships. Contained within us, measure and symmetry represent the transition from the etheric to the physical body.
Finally, in the transition from the ego to the astral body lives what can be inwardly experienced as weight. I have often pointed out that the ego was actually born in the course of human evolution. The people of the ancient Indian period did not yet experience such an ego. They did, however, experience within themselves something causing weight, the condition of possessing form; hence, they sensed this heaviness, this downward pull, as well as their buoyancy, their ascent. They sensed within themselves what is overcome when the child changes from a being that crawls on all fours to one that walks. The people in ancient India did not experience their ego, but they did sense that they were fettered by the Ahrimanic forces to the earth, that they were weighted down by them, and that, on the other hand, they were borne upwards, lifted up by the Luciferic forces. All this, they experienced as their position of equilibrium. If we were to study the ancient terms for the ego we would find that the above experience was contained in the formulation of the words themselves. Just as the words were fitted together in the verbs according to their inner configuration, so the ancient words for the ego contained the balance between floating and falling.
Weight, which isn't abstract anymore, for we confront something completely unknown; number, something quite abstract, for it is totally unrelated to what is being counted; measure, which has become increasingly abstract for us — these abstract conceptions of ours are actually projected from our inner being to the outside. Something that has very real significance within the human being since he is fashioned according to measure, number, and weight is transferred by him to the indifferent external things. In this process of abstraction the human being dehumanizes himself. It is therefore possible to say that mankind's evolution tends in the direction of losing the inner experiences of weight, number, and measure, retaining only a slight touch of them in the artistic realm. We no longer experience them in such a manner that we sense ourselves as having been formed out of the cosmos according to weight, number, and measure.
The geometry we have when we compare congruent and similar figures, when we say that an ellipse is generated by a point so moving that its distance from a fixed point divided by its distance from a fixed line is a positive constant, is something abstract. There, we basically measure the distances and find that their sum is always equal to the large axis of the ellipse. Even if it was not pictured in any way, the ellipse was nevertheless experienced by people in the third post-Atlantean period in this peculiar relationship of two different quantities. In the relationship of one to the other they already sensed the elliptic element, just as they sensed the circle during the same age. And in the same way the nature of numbers was experienced. Humanity evolved in this way from concrete experience to something abstract, developing geometry out of the ancient experience of measure, arithmetic out of the former experience of numbers, and having completely lost the ancient experience of weight and thus having utterly dehumanized themselves, human beings developed only external observation out of it.
All this slowly prepared the way for the increasing abstractness of inner human experience, a development that culminated in the nineteenth century. Thus, the human being became lost to his own conception. He can no longer comprehend himself; he no longer has any idea that he produces geometry because he has been formed according to measure out of the cosmos, that he counts through his very nature. He is surprised when the so-called savages use their fingers in order to compare external objects with them. He has forgotten that he has been fashioned according to numbers out of the cosmos. He does not know that in this regard he, too, always remains a “savage,” that his etheric body had imprinted the numbers into his astral body in accordance with the inner qualities of the numbers themselves so that he could later experience the numbers also outside himself. In the course of humanity's evolution, geometry, arithmetic, and the science of weight and weighing have all moved into the abstract domain and have contributed to the fact that the human being could henceforth only devote himself to a science and a form of scientific research that observes these matters externally.
What do we do when we are involved in scientific research today? We measure, count, and weigh. Nowadays, you can indeed read of strange definitions of existence. We already have thinkers who state that existence, being, is that which is measurable. Yet, they naturally refer only to measuring with an arbitrary unit of measure. It is odd that existence is traced back to something actually based on arbitrariness. Therefore, the human being dwells in something that has been completely detached, excluded from him and in regard to which he has utterly lost the connection with himself. Due to such influences, the human being has lost himself in modern knowledge; something I have emphasized from a number of viewpoints, particularly during this lecture course.
As I have often said, the human being has been lost in our perception of ourselves as merely the last step in the evolution of the animals. In society we have lost sight of the human being, for though we have invented extremely sophisticated machines, we are unable to integrate the significance of the people operating these machines into our social processes. We must learn to penetrate mankind's evolution; above all we must observe in this way how the process of man's intellectualization has come about. Just think how different people's frame of mind was in the first post-Atlantean period when they continuously experienced a changing equilibrium in placing one leg in front of the other. They always felt themselves become heavy, sensed a falling and floating. Picture how different it was when human beings felt that numbers permeate their own form, that they are built up according to measures. Think of how different that was from superficial measuring, counting, and weighing, leaving out the human being altogether. As I already indicated, at most it is possible for a person with a more sensitive awareness for language to gain some insight into the nature of numbers by means of what is in fact contained in the numerals, the words naming the numbers; or, from an artistic viewpoint, it is possible to sense that this, for example, in the sketch below is feasible:
but that this is impossible in this connection:
Such a person then has just a touch of the feeling for the inner condition of weight, the inner balance. If, by means of a line, I can follow some relationship in the other object, I have them balancing each other. However, if I sketch a protrusion over here, on the object on the right of second sketch, where there cannot be one, then I have no feeling for this balance. See how mankind has struggled to produce the external proportions out of its inner being, so to say, the outer appearance in contrast to the inward experience. Take a look at the painting by Raphael — it is actually true of all of Raphael's paintings but especially obvious in this one — depicting the “Marriage of Mary and Joseph,” [Note 2] and see how the figures are positioned and painted in such a way that they support each other and that the viewer thus loses the feeling that anything exerts a downward pull. In particular, however, when ancient painters drew some flying creature, study how that was motivated, how you can clearly discern from this figure that it is not pulled down by weight but, rather, supports itself somehow by means of the relationship to other elements in the painting.
So, here we have the transition from the experience of the inner weighting to the external determination of weight: thus, here we have the course of mankind in the post-Atlantean epoch from inward experience to intellectualism, this struggling ascent to the intellect where everything experienced in our concepts is divorced from the human being; where we no longer experience the tearing in the word entzweien, (“to fall out with each other”; literally: “tearing in two”) when we say Zwei (“two”).
All this comes about slowly. When this term is employed further, when we say, zweifeln, “to doubt,” we sense the derivation from entzweien. After all, one who doubts something implies: Perhaps this is correct, perhaps it is not. It is open in both directions, the feeling of entzweien is inherent in the conceptual act. It is also already contained in the word for the number 2, zwei. Three — there you cannot experience this in the same manner when you apply it to something. Apply it to a judgment, where you have the major premise, the minor premise and the conclusion: a triad, a matter enclosed within itself. Take the syllogism about the most famous logical personality, the one about Gaius Julius Caesar:
All men are mortal;
Gaius is a man;
therefore Gaius is mortal
It all belongs together, the major and minor premise and the conclusion. However, if you take merely the first two, the matter remains open.
Hereby, I only wished to indicate to you what mankind's path to abstraction was like and how, in fact, by losing himself, man brought the intellect into his evolution.
We shall continue with this tomorrow. Today's subject was intended only as an episode, but you will see how it will fit in with further considerations.
1. Translator's note: In the original German, Rudolf Steiner's example is quite clear. This is the reason the German words were retained and the English translation given in parenthesis.
2. Translator's note: In German, this example is immediately clear. Mass means “measure;” maessig and massvoll mean “moderate.”