Answers Provided by Anthroposophy Concerning the World and Life

GA 108 — 28 October 1908, Berlin

13. Formal Logic II

Of course, it is not possible to cover this topic of logic as fully as one would wish in the time available. If you wanted to cover the subject exhaustively, you would have to hold a kind of course. Therefore, please take what is said here only as a few sketchy suggestions. I do not intend to proceed systematically either, but only to present some of the elementary logical truths to you, so that you may have something that you can perhaps make use of right now.

We have formed a concept of the concept itself, have heard what a judgment is and how a conclusion arises, namely through the connection of judgments. It has been said that there are certain inner laws of the technique of thinking that determine how to connect judgments if one wants to reach correct conclusions. We have given the original form of the conclusion in the first form of the conclusion using the example: All men are mortal. Caius is a man. Therefore Caius is mortal. In the major premise, “All men are mortal,” we have the first judgment; and in the minor premise, “Caius is a man,” we have a second judgment. The point now is to let a new judgment follow from the connection of these two judgments, through inner conformity to law: “Therefore Caius is mortal.” We call this last judgment the conclusion. We see what this concluding sentence is based on: we have two sentences that are given, that must be present; we know what they state. The point now is to omit the middle term from these two given sentences. The subject term of the antecedent was: “all men”, the predicate term “mortal”. In the consequent we had the subject term “Caius” and the predicate term “man”. In the final sentence, the two terms that were present in both sentences are omitted, namely the term “human”. The fact that we can form the final sentence depends on how this middle term “human” is included in the upper and lower sentences. Our scheme was: (M = P); (S = M); (S = P).

The fact that we are allowed to construct the conclusion in this way depends on the distribution of the concepts in the antecedents. If it were different, we would not be able to conclude as we did in the example given above: Photography resembles man (antecedent); photography is a mechanical product (subordinate clause). If we were to omit the middle term, which is contained in both sentences, then no valid conclusion could be formed here. This is because in both sentences the middle term is connected to the predicate in the same way as the subject. The middle term must be at the beginning in one case and at the end in the other; only then can we form a valid conclusion. Logic is a formal art of forming concepts. It is already evident in the arrangement of the concepts how one can arrive at valid conclusions. We must acquire as laws the way in which the concepts must be combined. We could also say that formal logic comprises the doctrine of concepts, judgments, and conclusions.

Now we will deal with judgments in a few remarks. Certain laws can be established about judgments. The laws of inference will only be understood once the tenets about the concepts and judgments have been established. So today we will first deal with the laws of judgments and concepts.

If we start with the law of concepts themselves, we can compare a concept such as “lion” with the concept of “mammal”. Both are concepts that we can form. They differ in the following ways. Think about what all falls under the concept of “mammal”. It is a large group of individual objects, for example, monkeys, lions, marsupials, and so on; that is much more than we summarize under the term “lion”, which gives us only a small part of the “mammal” concept. Thus, all concepts differ from each other in that some concepts cover a great deal and some only a small area. Here we say: The concepts differ in their scope; but they also differ in other respects. To define the concept of “lion”, many characteristics are needed, many features such as head, color, paws, teeth, and so on. All these things that are listed to get to the concept of “lion” are called the content of the concept. The concept of “mammal” has considerably fewer characteristics than the concept of “lion”. If you were to subsume animals with a certain hair color under the concept, that would no longer be correct. When you form the concept of “mammal”, you have to have as few characteristics as possible, a small content, for example, only the characteristic that it gives birth to live young and that it suckles them. Thus, in “mammal” we have a concept with little content and great scope, and in “lion” the opposite. There are therefore concepts with great scope and little content, and concepts with little scope and great content. The greater the scope of a concept, the smaller its content; the greater the content, the smaller the scope. Thus, concepts differ in content and scope.

Let us now consider judgments in a similar way. When you pronounce the judgment: All men are mortal, you have a different judgment than: The crocodile is not a mammal. The difference between the two is that in the first case something is affirmed, the concepts are brought together in such a way that they are compatible. In the second case, the concepts do not agree; they exclude each other; here we have a negative judgment. Thus, we distinguish between affirmative and negative judgment. There are still other differences with respect to judgment. All men are mortal - the judgment is such that something quite different is given with it than with: Some flowers are red. In the first case, the statement of the property applies to the entire scope of the subject concept; in the second case, other characteristics can be added. The latter judgment is called a particular judgment, in contrast to the first, a general judgment as opposed to a universal judgment. So we have affirmative and negative, universal and particular judgments. Other distinguishing features can also be found in judgments. For example, a judgment can be made in such a way that it is along the lines of “All men are mortal,” or a judgment can be pronounced in such a way as “When the sun shines, it is light.” The first judgment unites the subject and predicate concepts unconditionally, whereas the second unites the subject and predicate concepts not unconditionally, but only conditionally. It only states that the predicate term is there when the subject term is also there, nothing else. The first - All men are mortal - is an absolute or unconditional judgment, the second - When the sun shines, it is light - is a hypothetical judgment. So there are absolute or unconditional judgments and hypothetical or conditional judgments. Many more such characteristics of judgments could be cited; but the point is to show that some of the knowledge depends on these differences. One must master the technique of concepts in order to be able to draw correct conclusions.

If, for example, you take our conclusion after the first conclusion figure: All men are mortal. Caius is a man. Therefore Caius is mortal – we have a general judgment in the major premise and a singular judgment in the subordinate premise, because it is applied to only one individual, to Caius. This is a subform of the particular judgment. This arrangement of the judgments is permissible; it leads to a correct conclusion. But let us try a different arrangement. Take, for example, the proposition: Some women have red dresses – this is a particular judgment. And now let us say: Mrs. NN is a woman. – Now I must not conclude: Therefore Mrs. NN has a red dress. – I must not do that because it is impermissible to conclude according to this figure of speech when the antecedent contains a particular judgment. Only when the antecedent is a universal judgment is this figure of speech correct. Thus certain laws can be established here again. We could now also cite other properties of judgments. We have said that a judgment can be affirmative or negative. Let us take a negative judgment: The crocodile is not a mammal. This animal is a crocodile. Here we may conclude: Therefore this animal is not a mammal. The subordinate clause may thus be affirmative as well as negative.

So there is a certain technique of thinking, a law of thinking, which is formal, that is, quite independent of content. If we observe this formal technique, we think correctly, but otherwise we think incorrectly. We have to follow this technique of thinking, this law of thinking, in order to come to the right conclusions.

We now have a famous classification into analytical and synthetic judgments, which was originally proposed by Kant. Today, people who do a little philosophy can very often come across this classification. What is the difference in the Kantian sense? An analytic judgment is one in which the concept of the predicate is already contained in the concept of the subject. In a synthetic judgment, on the other hand, the concept of the subject does not necessarily contain the concept of the predicate. For example, the sentence “the body is extended” is an analytic judgment, because one cannot think of a body without also thinking of its extension. “Extended” is only one characteristic of the concept “body”. A synthetic judgment, however, is one in which the concept of the predicate is not yet contained in the concept of the subject. Subject and predicate are brought together by an external cause. For example: “The body is heavy” is, according to Kant, a synthetic judgment. For he believes that the concept of heaviness is connected with the concept of the body only through external reasons, through the law of attraction. In the synthetic judgment, therefore, the concepts are more loosely connected.

Much nonsense has been made of the concepts of analytical and synthetic judgments in recent philosophy. It always seemed to me that the most enlightening thing was the story that is said to have happened to an examinee at a German university. He came to a friend on the evening before the exam and asked him to quickly teach him a few more logic terms. But the friend realized the futility of such an undertaking and advised him to leave as he was and take his chances. The next day, the examinee was asked: Do you know what an analytical judgment is? The sad answer was: No. To which the professor replied: That's a very good answer, because I can't say either. And what is a synthetic judgment? The student, growing bolder, answered again: “I don't know.” The professor said, very pleased: “You have grasped the spirit of the matter. I congratulate you, you will get a good grade!” In a certain respect, the matter seems to me to be indeed shedding light. For the difference between the two types of judgment is indeed a floating one: it depends on what one has thought with the concept. For example, one person adds the concept of extension to the body; on the other hand, the person who adds the concept of gravity brings more to the concept from the outset than the other person. The point now is for us to recognize what is really real in the combination of concepts into judgments, or rather what the secret goal of all judgment is. Judgment is in fact purely formal at first.

But there is something connected with judging that will become clearest to you if you compare the following two judgments with each other. Let us assume – not that we are going to leave the physical plane – we have the judgment: The lion is yellow. When you form this judgment, it can be correct. But let us assume that someone imagines some concept out of his head, an animal half lion, a quarter whale and a quarter camel. He could quite well imagine it together; he calls it, let us say, “Taxu”. He could now form the judgment: This animal is beautiful. - This judgment is valid in a formal respect just as the judgment: The lion is yellow. - How do I distinguish valid judgment from invalid judgment? - Now we come to a chapter in which we have to find the criterion for the ability to form a judgment at all. You can change the judgment: “The lion is yellow” at any time, namely by saying, “A yellow lion” or “The yellow lion is”. - But we cannot say, “A beautiful taxu is”. This leads to a criterion for the validity of a judgment: one must be able to include the predicate concept in the subject concept and make an existential judgment out of it. The transformation of a formal judgment into an existential judgment by adding the predicate to the subject thus forms the criterion for validity. In the first case, [empirical] necessity unites the concept “yellow” with “lion”; in the second case, it is assumed when forming the concept that the subject has been taken from an existential judgment, whereas in fact it only arose from a formal judgment.

This is a criterion for the validity of every judgment. The formal correctness of a judgment depends only on the correct connection of the concepts, but the validity of a judgment depends on the existential judgment. A formal judgment is transformed into an existential judgment by adding the predicate to the subject; one enriches the subject. And that is precisely the goal of judging and also of concluding: the formation of such concepts that have validity. Form the judgment: A yellow lion is - then you have thought not only in terms of formal correctness, but also in terms of validity. Now you see that formal logic does indeed offer us the possibility of filling ourselves with correct concepts, so to speak, but that the formation of valid judgments is what we must have in mind; and valid judgments cannot be gained from mere formal logic. The existential judgment in our example – The yellow lion is – was gained from external sense observation. Formal logic gives us the possibility of arriving at correct concepts; with its help we can create quite fruitful concepts. But for the validity of judgments, logic will have to be fertilized by content-related aspects. People usually do not really realize what logic is at all. But if one has learned to grasp the concept correctly, independently of content, it is extremely important.

The validity and the formality of a judgment are two different things. Because people do not really understand the connection between these things, they spin out very grand theories, which some people regard as irrevocable, but which would collapse of their own accord if people were to realize the difference between “formal correctness” and “validity”. You know that there is a modern school of psychology that strictly denies the freedom of the human will. Every human action, it says, is strictly determined by previous events. There are certain methods of proving this, and these play a fateful role today in statistics, for example. For example, someone is investigating how many people in France die by suicide. That's easy, you don't even have to think about it; you just note the numbers over a period of about five years, then you examine it for another five years and so on. Then the person finds that there is a certain difference between these numbers. Now he takes larger numbers, compares twenty to twenty years and finds that here the suicide numbers are almost the same; of course not the same, because the circumstances change, - say, they increase in a certain proportion. A numerical law can be found according to which one can predict how many suicides will occur within a certain period, how many people will die by suicide in a certain period of time. Now there are people who say: if you can calculate in advance how many people would commit suicide, how can one still speak of human freedom? It is the same with estimating future crimes. According to an immutable causality - so they say - so many people would have to become criminals. It is not to be said here that the law is not valid. In a way, it is perfectly applicable in practice to certain cases. But the moment the law is applied, the worst misunderstanding will result, the essence of things or the human being will be investigated and fathomed.

Let us think of insurance companies that work with probability calculations. They arrive at very specific formulas by deducing from experience that a certain number of every hundred married twenty-year-olds will lose the other spouse to death over the course of thirty years. They check the percentage rate within a certain period of time and use it to determine the insurance premiums. It is quite practical to apply such laws in the insurance business; they are true, these laws; but they do not go to something deeper. The matter becomes strange when we take the laws more deeply! Let us imagine that someone is presented with the material of such an insurance company and finds: There is still a spouse alive who should have died by now; but this person is healthy and, according to his inner being, it does not even occur to him to die yet. Nevertheless, the insurance company still has a right to its money, because the formal laws apply very well in the world, but one cannot see into the inner being of a person through such laws. And so it is with all the laws of nature, which are only gained through the collection of external observations. One only gains a concept of the external course of events, but cannot draw conclusions about the inner essence of a thing or a person, for example, whether it is healthy or sick. In the same way, you can never gain a concept of the essence of light by observing its phenomena. You have to keep this in mind, otherwise you will come to results such as those of Exner in his last rectorate speech in Vienna.

External facts are not indicative of the inner essence of a thing. There is still a great deal of confusion in the thinking of humanity in this regard. It cannot be claimed that one can learn to think through logic; that is just as impossible as becoming a musician through the study of harmony. But logic is necessary for correct thinking, just as the study of harmony is necessary for composing for the right musician. One must know how judgments and conclusions are formed. But we must always remain in the same region if we want to make formally correct judgments. For example, the conclusion is: All men are mortal. I am a man. Therefore I am mortal - apparently no fallacy, because here we fall back on the subject. However, the laws of logic only apply if you stay on the same level. The conclusion “Therefore I am mortal” refers only to the body. However, our ego belongs to another level; it is not mortal. The conclusion: “Therefore the ego is mortal” is therefore false. Such formal errors are frequently found in the work of today's scholars.