Answers Provided by Anthroposophy Concerning the World and Life

GA 108 — 20 October 1908, Berlin

12. Formal Logic I

The relationship between anthroposophy and philosophy has already been discussed, albeit only briefly. Today we want to talk about fairly elementary aspects of so-called formal logic. Despite the elementary nature of our deliberations today, it may not be without use to delve into a philosophical chapter between our forays into higher worlds. It is not meant that such a lecture could directly offer anything for penetrating into the higher worlds. A logical consideration can do this no more than formal logic can enrich experience in the sensory realm. For example, someone who has never seen a whale cannot be convinced that they exist. He must make the observation himself. But it is precisely the knowledge of borderline areas that will be useful to anthroposophy, just as logic was useful to scholastics. The philosophers of the Middle Ages, who today are somewhat contemptuously grouped together under the name of scholastics, did not regard logic as an end in itself either; it did not serve to learn anything substantial. The subject-matter of teaching was either the observation of the senses or revelation, which is obtained through divine grace. But although, in the opinion of the scholastics, logic was quite powerless to enrich experience, they nevertheless regarded it as an important instrument of defense. So it should be an instrument of defense for us as well.

A distinction is made between material and formal logic. Logic as such cannot grasp anything material or substantial as its object. Concepts such as time, number, and God give a content that does not arise through logical conclusions. On the other hand, the form of thinking is the task of logic; it brings order to thoughts, it teaches how we must connect concepts that lead to correct conclusions. It is fair to say that logic was more highly valued in the past than it is today. In grammar schools, philosophy, logic and psychology used to be taught together. The aim of the teaching was to lead young people to disciplined, orderly thinking; propaedeutics means preparation. Today, however, people are trying to eliminate this kind of preparation and incorporate it into the study of silence because logic is no longer sufficiently respected. Thinking, they say, is innate in man; so why teach thinking in a special subject? But it is precisely in our time that it is very necessary to reflect on ourselves and to devote more attention to formal logic.

Aristotle is considered the founder of formal logic. And what Aristotle has done for logic has always been recognized, even by Kant, who says that formal logic has not progressed much since Aristotle. More recent thinkers have sought to add to it. We do not want to examine today whether or not such additions were necessary and justified. We just have to recognize the scope of logic here.

Anthroposophists are often reproached for not being logical. This is very often because the person making the reproach does not know what logical thinking is and what the laws of logical thinking are. Logic is the science of the correct, harmonious connection of our concepts. It comprises the laws by which we must regulate our thoughts in order to have within us a mirror reflecting the right relationships of reality.

We must first realize what a concept is. The fact that people are so little aware of what a concept is is due to the lack of study of logic on the part of the learned. When we encounter an object, the first thing that happens is sensation. We notice a color, a taste or a smell, and this fact, which takes place between man and object, we must first consider as characterized by sensation. What is in the statement: something is warm, cold and so on, is a sensation. But we actually do not have this pure sensation in ordinary life. When we look at a red rose, we not only perceive the red color; when we interact with objects, we always perceive a group of sensations at once. We call the combination of sensations “red, scent, extension, form” a “rose.” We do not actually perceive individual sensations, only groups of sensations. Such a group can be called a “perception”.

In formal logic, one must clearly distinguish between perception and sensation. Perception and sensation are two entirely different things. Perception is the first thing we encounter; it must first be dissected in order to have a sensation. However, that which gives us a mental image is not the only thing. The rose, for example, makes an impression on us: red, scent, shape, expanse. When we turn away from the rose, we retain something in our soul, such as a faded remnant of the red, the scent, the expanse, and so on. This faded remnant is the idea. One should not confuse perception and idea. The idea of a thing is where the thing is no longer present. The idea is already a memory image of the perception.

But we still have not come to the concept. We get the idea by exposing ourselves to the impressions of the outside world. We then retain the idea as an image. Most people do not get beyond the idea in the course of their lives, they do not penetrate to the actual concept. What a concept is and how it relates to the idea is best shown by an example from mathematics. Take the circle. If we take a boat out to sea, until we finally see nothing but the sea and the sky, we can perceive the horizon as a circle when it is very calm. If we then close our eyes, we retain the idea of the circle from this perception as a memory image. To arrive at the concept of the circle, we have to take a different path. We must not seek an external cause for the idea, but we construct in our minds all the points of a surface that are equidistant from a certain fixed point; if we repeat this countless times and connect these points with a line in our minds, the image of a circle is built up in our minds. We can also illustrate this mental image with chalk on the blackboard. If we now visualize this image of the circle, which has been created not by external impressions but by internal construction, and compare it with the image of the sea surface and the horizon that presented itself to our external perception, we can find that the internally constructed circle corresponds exactly to the image of external perception.

If people really think logically, in the strict logical sense, they do something other than perceive externally and then visualize what they have perceived; this is only an idea. In logical thinking, however, every thought must be constructed inwardly, it must be created similarly to what I have just explained using the example of the circle. Only then does man approach external reality with this inner mental image and find harmony between the inner picture and external reality. The representation is connected with external perception, the concept has been created by inner construction. Men who really thought logically have always constructed inwardly in this way. Thus Kepler, when he formulated his laws, constructed them inwardly, and then found them in harmony with external reality.

The concept is therefore nothing other than a mental image; it has its genesis, its origin in thought. An external illustration is only a crutch, an aid to make the concept clear. The concept is not gained through external perception; it initially lives only in pure inwardness.

In its thinking, our present-day intellectual culture has not yet gone beyond mere imagining, except in mathematics. For the spiritual researcher, it is sometimes grotesque to see how little people have progressed beyond mere imagining. Most people believe that the concept comes from the imagination and is only paler, less substantial than the latter. They believe, for example, that they can arrive at the concept of a horse by successively seeing large, small, brown, white and black horses appear in their perception; and now I take - so people continue - from the perception of these different horses, what is common to all horses and omit what is separate, and so I gain the concept of the horse. But one only gets an abstract idea, and one never arrives at the concept of the horse in the strict sense of the word. Nor does one arrive at a concept of the triangle by taking all kinds of triangles, taking what is common to them and omitting what separates them. One only arrives at a concept of the triangle by inwardly constructing the figure of three intersecting lines. With this inwardly constructed concept we approach the outer triangle and find it harmonizing with the inwardly constructed image.

Only in relation to mathematical things can people in today's culture rise to the concept. For example, one proves by inner construction that the sum of the angles in the triangle is equal to one hundred and eighty degrees. But if someone starts to construct concepts of other things inwardly, a large proportion of our philosophers do not recognize it at all. Goethe created the concepts of the “primordial plant” and the “primordial animal” by inward construction; not only was the different left out, the same was retained - as stated earlier in the example of the horse. The primordial plant and the primordial animal are such inward mental constructions. But how few recognize this today. Only when one can build up the concept of the horse, the plant, the triangle, and so on, through inner construction, and when this coincides with outer perception, only then does one arrive at the concept of a thing. Most people today hardly know what is meant when one speaks of conceptual thinking.

Let us not take mathematical concepts, and let us not take Goethe's Organik, where he created concepts in a truly magnificent way, but let us take the concept of virtue. One can indeed have a pale general idea of virtue. But if you want to arrive at a concept of virtue, then you have to construct it inwardly, and you have to take the concept of individuality to help you. You have to construct the concept of virtue as you construct the concept of a circle. It takes some effort to do this, and various elements have to be brought together, but it is just as possible as constructing mathematical concepts. Moral philosophers have always tried to give a sensuality-free concept of virtue. Some time ago, there was a philosopher who could not imagine a sensuality-free concept of virtue and thought those who claimed such a thing were fantasists. He explained that when he thinks of virtue, he imagines virtue as a beautiful woman. Thus, he still introduced sensuality into the non-sensual concept. And because he could not imagine a sensuality-free concept of virtue, he also denied this to others.

If you delve into Herbart's ethics, you will find that for him, “goodwill” and “freedom”, these ethical concepts, are not formed by taking what is common and omitting what is separate. Instead, he says, for example, that goodwill encompasses the relationship between one's own will impulses and the imagined will impulses of another person. He thus gives a pure definition. In this way, one could construct the whole of morality through pure concepts, as in mathematics, and as Goethe attempted with his organic system. The general idea of virtue must not be confused with the concept of virtue. People arrive at the concept only gradually, through an inner process.

By setting the concept of the concept before us, we distance ourselves from all arbitrariness of imagining. To do this, we must first consider the pure course of imagining and the pure course of conceptualizing. I need not say that when a person imagines a triangle, he can only imagine this or that triangle. We must now take into account the way in which mere perceptions are connected and the way in which pure concepts are connected. What governs our perceptual life? When we have the perception of a rose, the perception of a person who has given us a rose can arise quite spontaneously. This may be followed by the perception of a blue dress that the person in question was wearing, and so on. Such connections are called: association of perceptions. But this is only one way in which people link ideas together. It occurs most purely where the human being completely abandons himself to the life of ideas. But it is also possible to string ideas together according to other laws. This can be shown by an example: a boy sits in the forest under tall trees. A person comes along and admires the good-quality timber. “Good morning, carpenter,” says the bright boy. Another comes along and admires the bark. “Good morning, tanner,” says the bright lad. A third passes by and marvels at the magnificent growth of the trees. “Good morning, painter,” says the boy. So here three people see the same thing – the trees – and each of these three people has different ideas, but these are different for the carpenter, the tanner and the painter. They are different combinations of ideas, not mere associations. This is because, according to his inner element, his soul structure, man connects this or that external idea with another, not only externally surrendering himself to the ideas. Here man allows the power that rises from his inner being to work. This is called: apperception is at work in him. Apperception and association are the forces that link mere ideas through external or subjective inner motives. Both apperception and association work in the mere life of ideas. It is quite different in the life of concepts. Where would people end up if they only relied on the subject's apperception and random association in the life of concepts? Here, people have to follow very specific laws that are independent of the association of ideas and the apperception of the subject. If we look at the mere external connection, we do not find the inner belonging of the concepts. There is an inner belonging of the concepts, and we find the lawfulness for this in formal logic.

First of all, we now have to look at the connection between two concepts. We connect the concept of the horse and that of running when we say: The horse is running. - We call such a connection of concepts a “judgment.” The point now is that the connection of concepts is carried out in such a way that only correct judgments can arise. Here we have, first of all, only a connection of two concepts, quite independently of association and apperception. When we connect two ideas through their content, we form a judgment. An association is not a judgment, because, for example, you could also connect bull and horse with each other through an association. But the connection of ideas can also happen in more complicated ways. We can add judgment to judgment and thus come to a “conclusion.” A famous old example of this is the following: All men are mortal. Caius is a man. Therefore, Caius is mortal. - Two judgments are correct in these sentences, so the third one “Caius is mortal” that follows from them is also correct. A judgment is the combination of two terms, a subject with the predicate. If two judgments are combined and a third follows from them, that is an inference. We can now develop a general scheme for this: If “Caius” is the subject (S) and “mortal” the predicate (P), then in the judgment “Caius is mortal” we have the connection of the subject (S) with the predicate (P: S = P). According to this scheme, we can form thousands of judgments. But to come to a conclusion, we still need a middle term (M), in our example “human”, “all humans”. So we can set up the scheme for a conclusion:

(M = P) All humans are mortal
(S = M) Caius is a human
(S = P) Therefore Caius is mortal.

If this conclusion is to be correct, the concepts must be connected in exactly this way; nothing must be transposed. If, for example, we form the sequence of judgments: The portrait resembles a person – The portrait is a work of art – we must not conclude: Therefore the work of art resembles a person. This latter conclusion would be false. But what is the error here? We have the schema:

(M = P) The portrait resembles a person
(M = S) The portrait is a work of art
But (S) is not equal to (P):
The work of art does not resemble a person.

We have turned the universally valid schema upside down here. It depends, then, on the form of the schema, on the manner of linking, to know: the first figure of conclusion is correct, the second is false. It is immaterial how the linking of concepts otherwise proceeds in our thoughts; it must be like the first formula in order to be correct.

We shall now see how one comes to know a certain legitimate connection in order to be able to find a number of such figures. Correct thinking proceeds according to quite definite such figures of inference; otherwise it is just wrong thinking. But things are not always as easy as in this example. Merely from the fact that the conclusions are wrong, one could often find out today, from even the most learned books, that what has been said cannot be true. Thus there are inner laws of thinking like the laws of mathematics; one could say an arithmetic of thinking. Now you can imagine the ideal of correct thinking: all concepts must be formed according to the laws of formal logic. However, formal logic has certain limits. These limits must be applied to the human mind. This would lead to correct insights and recognize the nature of fallacies. By all rules of logic, it would conform to the laws of logic if we said:

All Cretans are liars (M = P)
This one is a Cretan (S = M)
Therefore he is a liar, therefore (S = P)

Now the ancient logicians had already noticed that this is true for all cases, except for the case in which a Cretan himself says it. In this case, the conclusion is certainly false. For if a Cretan says, “All Cretans lie, therefore I am a liar,” it would not be true that Cretans are liars, and so he would be telling the truth; and so on.

It is similar with all fallacies, for example with the so-called crocodile conclusion: An Egyptian woman saw how her child playing by the Nile was seized by a crocodile. At the mother's request, the crocodile promises to return the child if the mother guesses what it will do now. The mother now utters: You will not give me back my child. - The crocodile replies: You may have spoken the truth or a lie, but I do not have to give the child back. Because if your speech is true, you will not get it back according to your own saying. But if it is false, then I do not return it according to our agreement. - The mother: I may have spoken the truth or spoken falsely, but you must give me back my child. Because if my speech is true, then you must give it to me according to our agreement; but if it is false, then the opposite must be true. You will give me back my child. The same applies to the conclusion that affected a teacher and a student. The teacher has taught the pupil the art of jurisprudence. The pupil is to pay the last half of the fee only after he has won his first case. After the teaching is completed, the pupil delays the beginning of the practice of law and therefore also the payment. Finally, the teacher sues him, saying to him: “Foolish youth! In any case, you must now pay. For if I win the lawsuit, you must pay according to the judgment; if you win, you must pay according to the contract, for you have won your first lawsuit. But the student: Wise teacher! Under no circumstances do I have to pay. For if the judges rule in my favor, I have nothing to pay according to the judgment; but if they rule against me, I pay nothing according to our contract.

There are countless such fallacies, which are formally quite correct. The problem is that logic can be applied to everything except itself. The moment we refer back to the subject itself, formal logic breaks down. This is a reflection of something else: when we move from the three bodies of man to the ego, everything changes. The self is the setting for logic, which, however, may only be applied to other things, not to itself. No experience can ever be made through logic, but logic can only be used to bring order to experiences.