The Rudolf Steiner Archive

1. Probability and Chance, Fritz Mauthner's Studies of Improbability

My task today will be to discuss how hard it is for people to keep to the truth of a situation in their ordinary trains of thought. I want to convey to you how far from easy it is in thinking to keep all the factors involved so before us that the course of our thoughts doesn't go astray from reality, that we follow the thread of reality.

The theme proposed for us today is certainly more difficult than others we might choose. But there is inner moral value to be derived from the realization that truth is hard to get at and that it is very easy to go astray as we forge ahead in a train of thought in the attempt to arrive at the truth by means of strict logical reasoning.

You will find that what I am going to tell you today will make it easier to understand certain matters that will occupy us in the next lecture. I will be speaking then about the important concepts chance, necessity, and providence. And I want to begin today with an introduction that, though it has its difficulties, will nevertheless contribute something vital and significant, not only to our theoretical understanding, but to the feeling we will then be able to develop for the way to seek truth.

I have often had occasion to mention the fact that there is a contemporary philosopher by the name of Fritz Mauthner who has written a Critique of Language.^{1Fritz Mauthner, 1849–1923, German philosopher and writer. Critique of Language, 1901.} This Critique of Language was intended to provide our period with something better suited to it than Kant provided for his time with his Critique of Pure Reason.^{2Immanuel Kant, 1724–1804, German philosopher of the Enlightenment, Published Critique of Pure Reason in 1781.} For Mauthner no longer believes—if that expresses it—that people seek knowledge in the form of concepts. It is rather his conviction that it is fundamentally just language to which people attach their insights. He believes that they don't really have true concepts when they are thinking, but merely have what words convey, and that words simply suggest this or that to them. He pictures people as having certain inner experiences in connection with words, putting their faith in words, jumbling them up, putting them together, and deriving insights from these processes. This is a total misconception of the entire cognitive process, but one that was bound to emerge eventually in an age working its way through to the worst consequences of materialism.

I want to convey just a sense of how Mauthner came to hold this view by quoting a passage from his Dictionary of Philosophy,^{3Fritz Mauthner, Dictionary of Philosophy, 1909.} written after his Critique of Language. Since we will be concerning ourselves with chance, necessity and providence, I will quote a passage from his article on the word “chance.” As I read it you will see that the materialistic age has gradually learned to talk about certain things. I am not so much interested in touching on any theoretical aspects involved in what I'll be reading you as I am in getting you to examine your feelings as you are exposed to what a materialistic philosopher of the present has to say on such a subject. I'd like to have you try to sense the way he speaks. He says of chance in his treatise on it “And it would be like going back to childhood and taking out of a magic package the surprises some kindly merchant has concealed in it.” He believes that looking at all the things that happen by chance is like becoming a child again and taking out of a magic package all the surprises put into it by a kindly merchant! “As though one were to keep on making God responsible, as Spinoza, Hume, Kant, and Schopenhauer did ...” is his sense of it. Trying to explain the world by ascribing everything to a kindly God would, in his opinion, be to regress to the state of a child gradually discovering what some kind merchant has hidden in a surprise packet. The child explores its content and comes upon one lovely thing after another. That is how Mauthner sees anyone who, attempting to find a wise explanation of the phenomena of the world, makes God responsible by regarding Him as the world's Creator. And he goes on to say, “... if one wanted to follow the example of Spinoza, Hume, Kant, and Schopenhauer in making Schopenhauer's elderly Jew” (he calls Him that because the term “God of the Christians” strikes him as unsuitable) “responsible for unscrambling this confusion of chance and purpose.”

You see the type of expression into which a materialist lapses if he takes himself seriously. Of course it is true that many people do not take materialism (which inevitably is also atheism) any more seriously than did the man who exclaimed “As surely as God is in heaven I am an atheist!” But anyone who takes it seriously today has to ridicule providence and similar matters; there is really no other possibility for those who have adopted materialism.

Though Fritz Mauthner is bound to give deep offense to our feelings and our sense of the fitness of things, I have brought him up because he is an honest, upright seeker after truth in the current materialistic sense. It is not my intention to do battle with individuals who are philosophers by profession, but rather with someone who comes to philosophy out of inner necessity from a quite different professional background and attains a certain degree of competency in it. For what one misses so greatly today in the way world views are evolved is a really serious coming to grips with what the various branches of science have brought forth up to the present. Fritz Mauthner has really grown into a learned gentleman, enabling me, as I take him for my point of departure and describe the difficulties inherent in the search for truth, to base my commentary on the thoughts developed by a very learned, very brilliant man. I am not basing it on what just any person thinks, but on the thinking of a very scholarly, clever man.

To begin with, I must take a very simple concept to show you at hand of a very special example from Mauthner's work how hard the search for truth is. You all know that there has long been what is called in mathematics the calculus of probability. It's quite easy to grasp the principle involved. Let's assume, for example, that you have some dice. I don't want to lead you astray into gambling with them, but let us say you have some dice. You know that they are so arranged that there is a single dot on one side, two on another, and so on, up to six dots on one of the six sides. If you roll these dice, they can turn up any one of the six sides; there are six possibilities. Now we can ask what the chances are of turning up a \(6\). You might really want to know what the chances are of getting a \(6\) when you shake the dice cup and throw the dice. The mathematician makes his calculation and says there are six possibilities; there is thus one-sixth of a chance of turning up a \(6\) on a single throw. You see how unlikely this possibility is. You would have to run through all six possibilities to be certain of a particular outcome. The numerator and the denominator would have to be identical, since certainty would equal \(1\) (\(\frac{6}{6} = 1\)). Probability is therefore six times smaller than certainty in throwing dice.

Now we can pursue the matter further and ask what the chance is of throwing two sixes if two dice are thrown. This can also be calculated. You will get one divided by thirty-six if you calculate as follows: Throwing a \(2\) with one dice, you can get anything from a \(1\) to a \(6\) with the second. Getting a \(2\) with the first throw, you can also get anything from a \(2\) to a \(6\) with the second, and so on, until you have counted thirty-six different possible throws. The probability of getting any particular outcome is thus \(1\) in \(3\)6, or \(\frac{1}{36}\). If you wanted to calculate probability with \(3\) dice, you would get \(\frac{1}{6} \times \frac{1}{6} \times \frac{1}{6}\), or \(\frac{1}{216}\), a very unlikely event indeed. The probability gets smaller and smaller the more dice are involved. The more possibilities there are, the less probable is any particular outcome.

You see, then, that it is possible to express in mathematical formulas the degree of probability of any particular outcome, and calculations of this kind can be applied to all sorts of cases. But I don't need to explain more than this principle to you; you see that it is possible to express in mathematical formulas what one feels. One can always feel that there is a certain degree of improbability that a \(6\) will be thrown, but the actual probability is \(\frac{1}{6}\), with two dice \(\frac{1}{36}\), and so on. Such feelings can, in a sense, be expressed in mathematical terms.

Now there is a certain way of thinking about divine providence. Materialists say something like this about it: We want to examine the reasoning of those who believe in God and providence; what are their thoughts? Believers in providence say, Let us take a work like Goethe's Faust or Homer's epics. What is Goethe's Faust in the last analysis? If we think as the materialists do, picturing the world as composed of atoms or molecules, we would really have to conceive Faust in its entirety as composed of letters, of single letters, unless we wished to go deeper. People who believe in providence and also believe in atoms and molecules formulate the situation more or less like this: Let's imagine that we have a container of type and in it all the letters that make up Faust, and some machinery—not some intelligence—spreads out these letters. The believers in providence could now ask how great the probability is of Goethe's Faust emerging from a typesetting machine that simply put the letters one after the other as they happened to fall on being thrown out of the container. They ask the question, perhaps, but have to admit that the probability of such a thing happening is so slight as to be nonexistent. One cannot assume that a haphazard scattering of type could possibly result in a chance (Voltaire's “His Majesty, Chance”) printing of Goethe's Faust. Since that can't be the case with Goethe's Faust, we can scarcely think that this world, which is much, much more gloriously put together, could have been flung down so thoughtlessly and simply.

This is approximately how a person with the current atomistic outlook would think if he could not avoid accepting providence as necessary in the scheme of things because of the impossibility of the world's having put itself together out of chaos.

Now Fritz Mauthner is a thorough gentleman, so he has let himself in not just for producing this train of thought but for correctly calculating how improbable it is that, for example, Goethe's Faust could have originated from a mere scattering of the letters it consists of. He has really figured it out, and I want to show you how he did it. He makes a fairly thorough job of it. He says,

God's existence is proved by the fact that the world's beauty and order are just as improbably the product of pure chance, achieved without purpose on the part of a creator, as we would regard the production of Faust as a consequence of upsetting a huge container of type and an accidental arranging of the letters and punctuation in the sequence found in Faust. The improbability of such a production is truly vast, beyond anything fantasy could conjure up, even if one disregards the utterly nonsensical assumption that letters could arrange themselves into sentences, and assumes the probability of an immeasurably favorable special case—something, say, along the lines of a German typewriter or typesetting machine getting into the hands of a Chinaman who, totally unfamiliar with the German language and letter-symbols, nevertheless experiments tirelessly with the keys for weeks or months, handling the machine correctly, with the result of this mere experimenting producing Faust!

Mauthner goes on to say:

I entertained myself working out an approximate calculation of the probability of a chance emergence of Goethe's Faust from this experiment. There was no need to bother about a few decimal places in the decimal part of the logarithm, and I magnanimously upped the probability by allowing for one hundred typographical errors and still recognizing the product as genuinely Faust, thus giving it a more than generous benefit of the doubt. Faust contains approximately \(300,000\) letters. Now the probability of striking the right key at every touch is not exactly small; it is almost \(1\) out of \(100\), since there are about \(100\) different symbols.

So one can light upon \(100\) symbols. Blindly tapping away, the probability of getting the right one is \(1\) in \(100\), according to the principle explained at hand of the dice. Thus the probability of the Chinaman totally ignorant of the language in which Faust is written striking the right key is \(\frac{1}{100}\). “But since, according to elementary rules, the chance of accidentally producing the whole of Faust with its \(300,000\) letters equals the product of \(300,000\) partial probabilities, the probability of an accidental production of Faust must be calculated as \(1:{100}^{300,000}\).”

You see, the probability of Faust coming into existence in the above way is not \(\frac{1}{6}\) or \(\frac{1}{36}\), and so on, but equals the fraction obtained by dividing \(1\) by \(100 \times 100 \times 100\), and so on, until we have done it \(300,000\) times. That is a fraction with a gigantic denominator, as you can see; in other words, the probability is exceedingly tiny. Mauthner continues, “We have here a fraction whose numerator is \(\)1, whose denominator consists of \(600,000\) digits. Even the conceptual power of the Indians,” (which Mauthner rates very highly), “even the mathematical genius of Archimedes is not up to grasping so vast a denominator. There is not even a name for such a number. The Greeks and the Romans were right, then, when they considered the chance production of any organized whole as extremely improbable. Here we reach the limits of the possible”—but only for human conceiving, he means. One cannot obtain Faust this way.

And the Greeks and Romans would also have concluded that the meaningful production of a Faust on the part of a creator could most probably—or even quite certainly—equally prove the existence of a world-creator if the whole proof or metaphor or line of reasoning were not so unspeakably foolish. I could never even bring myself to believe that the marvelous build of a mosquito could be the product of chance in a materialistic sense. The chance material production of a mosquito is just as improbable as that of Faust. Darwinism has not really lessened the incomprehensibilities. But the headwork on the part of a God Who would have had to organize not merely \(3\) times \(100,000\) elements or letters (with repetitions) but all the elements that make up the cosmos an endless number of times (with repetitions) is, if possible, even more improbable for human conceiving (and we really have no other!) than a chance production of Faust. I have no wish to extend my calculations to figuring out the degree of the improbability of a world- dominion and providence.

You see what tremendously learned reflections one can engage in. You will have thought them quite learned enough to arrive at the logical conclusion: what must God not have had to keep in mind, if He wanted to put the world together out of all its elements, if producing Faust out of an upset typecase or the chance striking of typewriter keys represents such an improbability as to be practically out of the question? Therefore, says Mauthner, both the concept of chance and that of divine providence are inconceivable. For if the degree of probability in the case of Faust is so minuscule, one can certainly not presuppose in the world's case that it could have been the chance creation of an upsetting of a cosmic typecase, so to speak. But then, one can just as little presuppose God—for what wisdom would He not have had to possess to have built the world out of all its elements!

So one can take neither God nor “His Majesty, Chance” for granted. Mauthner therefore maintains that neither has validity, that all that is involved here is just concepts in language, and people deal with them as they do with languages themselves and with translations. And he calls this a Critique of Language! We have here a truly incisive train of thought indeed, pursued with a great deal of effort. It leads to two alternatives: one has either to presuppose that the world came into being by chance—an exceedingly tiny probability, of course—or, still less credibly, to conceive of a kind God with a head so full of wisdom that He could use it to build a world out of chaos.

Now, since we are concerned in spiritual science not only with getting to know things but with thinking correctly, taking into account all the factors involved in developing a sound train of thought, let us examine this particular train of thought in a way commensurate with the serious approach of spiritual science. Let us review again the proposition that the probability of Goethe's Faust resulting from a jumbling up of the contents of a typecase is so infinitesimal as to be represented by a fraction with a numerator of 1 over a denominator consisting of 600,000 digits. The probability of the world's coming into being as the result of a similar accident would, of course, be infinitely smaller. But the fact is that Faust did come into being in its entirety! Now did this happen because the good Goethe—not the good God in this case—had in his head the laws whereby, according to the principles of typesetting, \(300,000\) letters taken from the typecase could be set in soldierly rows to eventuate in Faust? Was Goethe thinking of the right way to reach into that container to get hold of the right letters?

Certainly not! When we think of the origin of Faust, we don't picture it as having anything to do with selecting type. The creator of Faust proceeded quite differently. It would never have occurred to him that Faust could have resulted from the placement of 300,000 letters. It was totally unnecessary for Goethe to know that Faust could be composed of 300,000 letters, and yet he composed it! We might, on the one hand—and indeed we even must—picture a chaos, with things in a state of utter disorder, but conceive on the other of a good God with all the various laws in mind according to which He would arrange the world, exactly as Goethe would have done if he had been set before a typecase to bring forth his Faust. But neither God nor Goethe went to work in this fashion. What we have to picture going on in God's soul has nothing whatever to do with the whole train of thought about composition, any more than such an incredibly cleverly conceived composition applies in the case of the creation of Goethe's Faust. In other words, this whole train of thought leads to absurdity. It is brilliant, it is well reasoned, it is conscientious—all these things; yet it ends in absurdity. That comes of a conscientious person engaging in a train of thought and pursuing it, but losing sight of the actual factors that could have led to a sound conclusion.

This is a much more important matter than we might suppose, for it demonstrates how extraordinarily difficult it can be, no matter how scientifically one proceeds, to avoid losing sight of reality as we pursue a train of thought. We must imbue our feelings with this realization and learn a great deal from just such an example. Two things are required as we mull it over. One is that we educate ourselves through an outstanding example of this kind to an awareness that the search for truth is far from easy, and that we badly need to develop a feeling for the fact that not just any thought sequence that strikes us at first glance as correct is actually a sound one. The more we can imbue ourselves with the feeling that we could err, that even at our most conscientious we might be wrong, the more easily will we avoid a rigid clinging to our own opinions, to a stubborn belief in the correctness of our views.

It is a very common thing, these days, to encounter people who declare that they think this or that to be a fact. The typical reaction one has in such encounters is how fortunate and at the same time how simple-minded such people are—fortunate, because they have no idea what it really means to believe in something they have figured out, and simple-minded because they don t have a glimmering of how far removed from reality their thoughts may be. But we should be aware that we mustn't allow this realization to depress us. It will make us very modest indeed, but not to the point of driving us into melancholia, to a sense of despair about human life because of the great difficulty of achieving truth. For we know that the life of the human soul is unending and must be a quest, that it may even be due to a wise ordaining that the quest for truth is so difficult. And we will find that life rests upon this fact.

It would be the death of our souls if the quest for truth were easy, if those people who say they have found out how to arrange things in a way to make the whole world happy were right. If, confronted by the world's complexity, it were such a simple matter to discover truth as most individuals believe it to be, that would mean the death of the soul. For the soul's life depends on our inability to find any access to the totality of truth; it requires a long slow search for truth, and the preservation of a profound degree of modesty as one progresses in it, step by step. Error is the more likely the more comprehensive the truth we seek. So it was natural for even one of the most learned men to fall into childish error such as that demonstrated in connection with solving the cosmic problem of chance and providence.

But dismay and depression over the fact that truth can be discovered only with such difficulty cannot touch us if we bear in mind that life derives from our having to seek truth. The quest is what matters. You might say, Well, if it were to mean the death of the soul not to have to search for truth, that fate is surely going to claim us now, for we have currently reached a high point in human evolution in the lack of feeling for a true quest for truth. In the whole course of history there have never been more people with programs, more individuals who believe that they can solve the whole cosmic riddle with a word or two. So we do have the very outlook right now that can be described as leading to the death of the soul. And it would indeed mean the death of the soul if what these program-people think were true. But it is not true, fortunately!

The thinking of people like Fritz Mauthner is more typical than one might assume, and there are many of them. The volumes of his Philosophical Dictionary are a perfect example of the current outlook. They really reflect the way most people think who aren't interested enough in freeing themselves from the trend of contemporary thought to move in a direction such as spiritual science has taken. People like Mauthner say, We come, on the one hand, to the untenable concept of a world that has come into being by chance (for this has the degree of improbability I have been demonstrating). But the alternative concept of an all-wise God is just as untenable since our human minds find it impossible to credit the existence of a god, a good God, who created in His head everything He needed to assemble out of initial chaos the various “letters” that compose the universe. Mauthner believes that people used to make do with concepts like chance and providence, but that we have now advanced beyond them since we realize today that they have no cosmic significance, no objective meaning; as mere figments of our human minds they hold meaning for ourselves alone. They are judged entirely on the basis of whether they are presently applicable to the world at large. People like this always say, Look how childish people used to be! They talked on the one hand of “divine providence and on the other of the concept “chance.” We must recognize the fact that both concepts exist only in the thoughts of human beings and are not even remotely applicable to the world.

And on what do they base this judgment? They say, When we survey the whole range of philosophical thought, the philosophical procedure followed by many philosophers (and Mauthner has really sat down and studied the world's philosophers and is as familiar with all of them as anyone can be in a single lifetime), we see what trouble they took to arrive at concepts. But all these are just human concepts; they can't be applied to reality. There is no reality in the concept of divine providence. And Mauthner's article on chance ends with the statement that divine providence, the cosmic order, cosmic harmony, and the beauty of the world used to be looked upon as concepts in the following context: “Yes, there are elements of chance in the world, but the world is also endowed with order and beauty.” And Mauthner ends: “But we realize that the concept of chance is man-made, and so are the concepts of beauty and order, of God, of causality.” We know, in other words, that they are all of human origin and lack objective applicability. “Thus it is the height of literal-mindedness even to ask the question whether chance or God is the origin of universal order and beauty, and worse to try to answer it with a childish simile.”

Now what have Mauthner and all the other philosophers who agree with him done to arrive at the insight that the concepts of God and chance and order are human products, and that neither order nor beauty and so on really exist outside us? You needn't believe me, but they have demonstrated with all possible philosophical incisiveness how profoundly human reason goes to work to produce such concepts and how true it is that they are human products. They have demonstrated this. He has offered proof when he says, “But we know ...” etc. He has proved it! But if we look at how he proved it, we have to say, Yes, dear Mr. Mauthner, you are right. But we are familiar with the fact that the concepts of chance, beauty, God, and the June bug are all the work of man. That is true, looked at in the right light. Now you would have to spend years making a really thorough study of it, but if you were to examine the penetrating thinking that has gone into demonstrating how all the concepts mentioned above are the fruits of human thinking, you would find trains of thought that can very properly be applied to the assertion that the June bug concept is also man-made. That is certainly true, but does that say anything about whether June bugs can fly around outside there and are real? What is childish is to say that the concept of the June bug is just a human product. One can think really penetratingly and be totally convinced of the correctness of one's conclusions, and yet have lost the thread on which the true facts are strung. All the proofs adduced in support of the finding that the above concepts are simply fruits of human thinking do not say anything about the objective existence of these things; just as calling the June bug concept a human product does not help us when its objective existence is in question.

You see what tremendous certainty the modern scientific way of thinking generates. It is reflected in such a statement as “We know that the concepts of chance, beauty, order, God, and causality are all man-made. So it seems to us to be the very height of literal-mindedness even to ask the question whether chance or God is the origin of universal order and beauty.”

Well, then, one must comment, you believe—since you can prove that the June bug concept is man-made—that it is being childish, being a victim of literal-mindedness to apply the June bug concept to an insect flying around there outside the window? It is all exactly the same thing, you simply don't notice the similarity.

What is the point of bringing up such matters? Why, to call attention to how difficult it is to get at truth by stringing logical concepts together; to show what the outcome can be, no matter how penetratingly one proceeds; to illustrate how thoroughly we must imbue ourselves with a sense of the difficulty of the quest for truth, both in great and small concerns. The more you develop a feeling for this as a result of what has been discussed today, the better it will be.

On Hegel's birthday, August 27, we will build on the foundation laid today in a spiritual scientific approach to the concepts chance, necessity, and providence.