marți, 28 iunie 2011

KORZYBSKI - Time Binding: The General Theory

ALFRED KORZYBSKI
Printed by the Graphic Press, 39 W. 8th St., N. Y. C.
Photographs by the Fernand Studios, N. Y. C.
 Presented in abstract before the International
Mathematical Congress, August, 1924, Toronto, Canada
(This paper is a summary of a larger work on Human Engineering soon to be published.)

 ALL HUMAN knowledge is conditioned and limited, at present, by the properties of light and human symbolism. The solution of all human problems depends upon inquiries into these two conditions and limitations.
Einstein's theory is a fundamental inquiry and application of the known properties of light; theirrefutable minimum of his theory results in an entirely new world conception, as beautiful and cheerful as the old ones were gloomy and despairing.
The minimum of our inquiry into the structure of human knowledge and symbolism is also irrefutable, and this beginning, imperfect as it may be, has already enormous beneficial consequences.
Einstein's theory was the application of modern scientific methods to the universe, man excluded. The present inquiry includes man in the field of modern science. As a result, both theories meet on a common ground.
The theory presented here is broader than Einstein's. It may be proved that the whole of the theory of relativity can be deduced from the application of correct symbolism to facts; so that the general theory of Time-binding includes the general theory of relativity as a particular case.

For a full understanding this essay should be read twice, at least, because the beginning presupposes the end, and vice versa. This theory is built upon the minimum of the best ascertained scientific facts of 1924. Its scientific soundness has to be judged on theoretical grounds (1924). Its working cannot be judged by arguments, only by application. Fortunately, it works with the reader who has understood it. If it does not work, the reader has not understood.
We cannot argue as to whether the sun is shining, we must go and see. In the case here presented, arguments alone are also not legitimate.
Statements containing variables are called "propositional functions"; they are neither true nor false. When values are assigned to such variables the expressions become propositions, which are either true or false. (Russell.)
Many words are names for stages of processes and are therefore variables, as for instance, "civilization", "science", "humanity", "mathematics", etc., etc. To generate a proposition with such words, we must assign to them a value through the use of co-ordinates. For our purpose, it will be sufficient to use only the time-co-ordinate, which will be indicated by the year in parenthesis, such as "science (1924)."

Obviously "science (1924)" is a different affair from "science (1500)," or "science (300 B. C.)." In the field of this investigation the term "science" means, for the majority, "science (300 B. C.)," or, at best, "science (1800 A. D.)." For such readers, this inquiry will be incomprehensible.

Most, not all, of the details of this general theory are vaguely known; it seems that the main novelty consists in the building up of an autonomous system. Such systems, if scientific, are useful; they economize thought and bring to light truths as well as fallacies. In a deeper sense fallacies, if scientific, are often as useful as truths, because they open new and unexpected fields for inquiry. Probably no system is true, although this statement does not include mathematics which does not claim to be true but to be correct.
The scientific revolution started with Geometry, and, in a deeper sense, it is carried on by Geometry. Until Gauss, Lobachevski, Bolyai, Riemann, etc., the Euclidean Geometry, beingunique, was theologically believed to be the geometry of the space. The moment a second geometry was produced, "just as good," self-consistent, yet contradictory to the old one, the geometry became ageometry. None was unique. One absolute was dead. Until Einstein (roughly) the universe of Newton was for us the universe. With Einstein it became a universe. The same happened to man. A new "man" was produced, "just as good" and a trifle better, yet contradictory to the old one.[1] Theman became a man, otherwise a conceptual construction, one among the infinity of possible ones.
Granting, for the time being, all that mathematicians say about mathematics (1924), there are two aspects of mathematics which have been neglected.
That which has symbols and propositions is a language. This aspect must be taken into account.[2] Besides, if we free mathematics entirely from theology, mathematics may be viewed as an activity of these bags of protoplasm called "Smith," "Brown," etc. This aspect makes mathematics a form ofbehaviour of man. No psychology of man can ever be valid so long as we disregard entirely this most characteristic behaviour of man. It explains the utter failure of the old mythological psychologies, and the failure of those contemporary students of psychology whose scientific standards and mental age are somewhere B. C.
Lately the natural sciences have firmly established the fact that an organism should be treated "as-a-whole" (Loeb, Ritter, etc.). The theory of relativity has established another fact, that all we know and may know is a "joint phenomenon" of the observer and the observed. Indeed there is no such thing as an "observer," without something to observe, neither such thing as the "observed," without somebody making the observation.
Any inquiry into the affairs of man with any pretense of being scientific (1924),must take into account these two fundamental principles or fail.
Our daily language, and, in most cases, our so-called scientific language together with its logic, originated mostly in a pre-scientific epoch and are largely elementalistic and absolutistic; which must hamper successful reasoning and solutions.
It has been known for some years that we cannot speak sense about man in the old language. Although Wittgenstein has proved this point, he did not show us the way out. The way out is simple. We must form a new vocabulary, which would be in accord with the above-mentioned principles.
Some authors have already used new terms successfully, yet they did not explain the importance of these new terms. For instance the late J. Loeb introduced the term "Tropism" to cover the forced movements of the organism "as-a-whole"; the present writer introduced the term "Time-binding" to cover all the factors "as-a-whole" which made man, a man. We may agree that man differs somehow from animals by the capacity for building this accumulative affair called civilization. In the old way we could argue endlessly about "what made civilization possible." Some say that "thinking" made it, others say that "speech" is responsible (Watson), or writing, etc., etc. As a matter of brute fact, all such statements, takenseparately, are false, because civilization is a joint affair of all of them and an infinity of others, as yet not abstracted.
The new words do perform the task, because they do not split what, for our purpose, should not be separated (Poincaré). This explains why the language of this paper is not our usual one.
The old subject-predicate language and logic veil the inter-relatedness of nature (Whitehead); the new, brings these relations to a sharp focus (Korzybski).
There is a profound difference, indeed, between a man-made green leaf and a non-man-made green leaf. In the first, green color wasadded, it is a "plus" affair, it was "made." In the second, color wasnot added, it is a functional affair, it was not made, it "happened," "became."
Quite obviously, a subject-predicate "plus" language and logic can cover man-made "plus" affairs, but cannot cover functional affairs, "happenings," "becomings"—where, for instance, the natural greenness of the leaf is inherent in the leaf itself, which is not the case with a man-made leaf.
Only a functional logic and language can cover functional natural phenomena (Korzybski). Such logic and language have been built by modern mathematical discoveries (Whitehead, Russell, Keyser, etc.). To treat man at least as fairly as we treat a green leaf, the same methods must be used.
Universal Peace—(be it family, school, industrial, economic, political, scientific, personal, international and what not) depends ultimately on Universal Agreement.
Universal Agreement—is finally based on Rigorous Demonstration. Rigorous Demonstration—absolutely depends on Definitions.
Definitions—are ultimately conditioned by
Correct Symbolism.
So, if we want universal agreement, we must start with correct symbolism. Before a theory of correct symbolism may be written down it must already have started with correct symbolism. It must be felt instinctively. A prototype of correct symbolism we may find in mathematics.
A word is a symbol. Before a sign may become a symbol something must exist for this sign to symbolize, else the sign has no meaning; it is not a symbol, not a word, but a noise. For our purpose we may speak, in the rough, of two kinds of existence, namely, the physical existence, somehow connected with persistence, and logical existence. By logical existence we mean in this case a thinkable thought, otherwise free from self-contradiction (Poincaré). A "word" which labels a self-contradictory "idea" is not a word, not a symbol, because it symbolizes nothing; if spoken, it is a noise, or if written, a blot of black on white; it is meaningless, no matter how many thousands of volumes have been written about it.
If we use such noises as significant words, it is a fraud played on the other fellow. Such acts should and will be some day, listed in the criminal codes of civilized countries as among the most harmful crimes against civilization.
With this introduction permanently in mind we may proceed, provided we agree that we will try to talk sense about "man." If this unusual request is granted, our task is not difficult; without it, it is impossible.
Let us imagine a genetic series, father-son-grandson, etc. We start with "Amoeba I" (A1), and end the series with "Albert Einstein" (AE). Somewhere near the end there is an individual, "Adam" (A). All individuals are very "real," and every one of them is different. According to one of the important rules of correct symbolism we label every individual with a different name, so that every individual has one and only one name.
We wish, (it is only our pleasure) to produce two other words "man" and "animal." I said "We wish"; it is so because there is no such thing in the world as "a man" or "an animal." These labels are names for abstractions of high order, for "ideas" and not things. Smith, Brown, Jones, etc., are "realities," objects, but they all are different, and the collective name "man" is given to an idea and not a thing. This point is extremely important, and I would suggest to the reader to be entirely convinced on this point before he proceeds, otherwise he will not be able to follow the rest.
Incidentally we see that the naturalistic, as well as anti-naturalistic creeds are false, because both are based on the false assumption that "a man" or "an animal" is a thing.
If we want to talk sense about the ideas "man" and "animal", wemust have them sharply defined, otherwise confusion must follow. We do not want to produce unnecessary new words; we inquire whether the old terms in which we used to speak about the terms "man" and "animal" will serve our purpose, which is to talk sense. There is one condition, among others, which must be fulfilled, namely the terms must be sharp. We pick any of the old terms, let us say, for instance, the term "thinking."
How do we get this term? We find that we watched the behaviour of Smith, Brown, Jones, etc.; we passed through a mental process of abstraction, generalization, assumption, inference and what not, and in this way we got our term "thinking." We do the same with, let us say, "Fido" (I select Fido because the majority of us know and like dogs). We watch the behaviour of different dogs, Fido I, Fido II, Fido III, etc.; we pass through the same processes of abstraction, etc. and we conclude, "Fido thinks." Obviously the term "thinking" isnot sharp, and because it is not sharp, we must abandon it as useless. We may retain this term for family use, but science is a public activity, and for public use nicknames will not do.
The problem now is such that we want to keep the useful terms "man" and "animal" and we have no terms in which we could talk sense about them. There is only one way out, namely, to produce new terms which will be sharp. As "man" and "animal" are not things but logical entities, the finding of those sharp definitions is a problem of ingenuityonly.
We observe again our genetic series; we note that "man" is an accumulative class of life with a special high rate, in that the son may start where the father ended, and that "animals" are not accumulative, or, if accumulative, they are so with a different and slower rate. With Korzybski we label these two different rates of accumulation "Time-binding" for "man," and "Space-binding" for "animals."
                            Amoeba I
           Adam
    Albert Einstein
III
animal
man
Non-accumulative class of life or
if accumulative, with a different
and slower rate, which we label:
"Space-binding"
accumulative class of life, with
a rapid rate, which we label:
"Time-binding"
                                                                      These differences are sharp.

            The foundation for a deductive science of man is thus laid down.

If we inquire into the mechanism of this rapid accumulation (Time-binding, PRt) we should be entitled to expect that we will strike the very core of our problem. This actually happens with most unexpected results.
We must stop here to emphasize, and it cannot be over-emphasized, namely, the power of the method. We cannot talk sense in the old "psychological" terms, therefore we deliberately avoid such terms; we carry on our inquiry in a "queer" engineering way and language, yet the results are deeply psychological. This inquiry unravels to us the deepest secret of man as man, a secret which neither psychology nor philosophy had ever disclosed and capitalized (the last three words representone idea). The explanation is simple: This could not be done before the physico-mathematical revolution of modern science.
THE reader is warned about an extremely important principle entirely disregarded in practice, namely, that what can be shown cannot be said (Wittgenstein). If we show something which we call "a pencil," it is an entirely different affair than when we speak of "a pencil." The content of the first is inexhaustible, the second is a concept, with finite content, fixed by a definition.
The following applies to things, and therefore the actual thing should always be shown.
We take something (anything) let us say a pencil; we show it and ask, "What is this?" This is a process, a chunk of nature, a clog of electricity, a mad dance of electrons; this is something acted upon by everything else, and reacting upon everything else; this is something which is different all the time, something which we can never recognize, because when it is gone, it is gone, etc.
This something which we can never recognize we call an event (Minkowski, Lorentz, Einstein, Whitehead, Planck, Millikan, etc.). The number of characteristics an event has, is infinite.
Yet in this event which we cannot recognize there is something fairly permanent which we can recognize. This we call an object (Whitehead). We label our object with a special symbol which we call a word.

The accompanying picture represents the Anthropometer, a plastic diagram to illustrate what has been said.

C represents the "event"; it is a broken-off paraboloid which indicates extension to infinity, while the holes represent characteristics, infinite in number.
B is the object of finite size with a large, yet finite, number of characteristics.
A is the label—a word. The holes, also, represent characteristics.
What is an object? An object is a first abstraction, a first rough summary, a first integration, etc., of the infinite number of characteristics of the event, into the few characteristics of the object. This process of abstracting is indicated by lines F.
We get the meaning of our symbol by defining it, that is by abstracting a second time (F1) from the many characteristics of the object into the still fewer characteristics of the label. The symbol is a second order abstraction. Then follow abstractions of higher orders.
How about Fido? We defined objects in terms of recognition, therefore "who recognizes has objects." It means, by definition, that Fido "has objects." Are his objects the same as ours? Similar, but not the same (D). For instance, we can not recognize our own gloves among a thousand of gloves, but Fido can. Has Fido "symbols"? Yes, he barks at a cat and another Fido "knows" somehow, something. But his symbols are not articulate (E).
We see that Fido's objects (D) are first-order abstractions; what he lacks is the second and higher-order abstractions. It must be remembered that the new language of orders of abstractions has the flexibility and exactness of number series. We could ascribe to Fido many orders of abstractions, but man would have still higher. I take here the simplest case; the other refinements would not alter the method, and this is important.
We see that the difference between "Fido" and "Smith" is in the order of abstractions, and this difference issharp.
Here a crucial question arises. No doubt Fido did the abstracting; does Fido know, and can Fido know that he abstracts? The answer is positive (due to the method): Fido does not know andcannot know
that he abstracts, because it takes science to know that we abstract, and Fido has no science, as a matter of brute fact.
This faculty for building higher and higher abstractions is the mechanism of the characteristic rapid accumulation, which makes man a man.
If, for instance, we could see an electron in its flight, the world would be a maze; no law, no order, no intelligence would be possible.
The first nerve, the first dynamic gradient (Professor Child) (a) was not stimulated by all of (b) but only by a small part (c). (a) got the experience of (b) by exploring, summarizing, abstracting the (c's), and so it goes all through life, man included.
Life and "intelligence" and abstracting start together, this being the result of the physico-chemical structure of living organisms. The function builds the organ (Professor Child). The mechanism of the rapid human accumulation is the faculty for higher and higher abstractions, which accelerate its progress at a permanently increasing rate.
The term "abstracting" is used here in the "organism-as-a-whole" way, where "senses" and "mind" are not divided; we know that the old elementalistic methods are not valid.
The complexities of life and of the organism become intelligible in terms of orders of abstractions, and it must be repeated again, that it is immaterial how many orders of abstractions we ascribe to an organism—the method remains the same.
We may illustrate what was said by a simple experimental fact. We all know an electric fan. When the fan is rotating rapidly we do not see the separate blades (a) but we see a disk, a shield (b). "Matter" and "objects" are such shields or disks; in other words a "joint phenomenon" of therotating blades and our abstracting organism. We cannot put our finger through the disk, although itis a fiction, because the rotation of the blades is much more rapid (for one of the reasons) than the velocity of our finger. Similar reasons explain why we cannot put our finger through a table; it takes an X-ray to be able to do so, in some instances.

The Anthropometer shows to the physical eye, that in human economy (A) is not (B) and (B) is not (C) (this must be shown on the Anthropometer); in animal economy (A) is (B) and (B) is (C); in other words, the animal does not discriminate between the three. If man omits to discriminate,he copies the animals in thinking.
This simple fact is the solution of practically all human troubles. The reader should not be misled by the childish simplicity of this all-important issue. As a matter of fact we nearly all, until this day copy Fidos in our thinking, by not being conscious that we abstract. This habit so permeates our old theories and practice, that one has to have the Anthropometer before him for some time to overcome this pernicious habit. Those who copy Fido must be dogmatists, categorists, absolutists, "know-alls"; they must be fanatics, intolerant; when they meet others of their kind, a fight must follow, etc. They do not want to think, they are not interested to investigate, for why should they? They "know it all," they are self-satisfied in their ignorance, they "know" that they "know all," which is all there is to know about it. They will persecute others who think. For them thinking and science are crimes, or, at best, unnecessary waste of time; and, if forced to think, it is a serious pain to them. They take everything for granted, critical thought and the spirit of inquiry is entirely foreign to their makeup.
Man to be a man and think as a man must be a relativist, which is an inevitable consequence of the application of correct symbolism to facts. He knows that he does not know, butmay knowindefinitely more, that his knowledge is only limited by his own ingenuity and nothing else. This feeling liberates his creative faculties, arouses his interest, his energy, builds up his character and puts his strivings on a very high level. His sporting spirit is aroused; he wants to know more; he wants to inquire and think; in fact, with the understanding of the Anthropometer he must think, there is no escape for him, and thinking becomes a pleasure to him as well as a necessity.
This explains, also, the well-known fact that with the Fido-way imposed upon mankind, it was impossible to make a man think. But with the Anthropometer introduced into homes and elementary schools, it is impossible to stop man from thinking.
A man who understands and applies the Anthropometer will never take a word for granted; instead, he will ask indefinitely, "What do you mean?" and this, ultimately, leads to inquiry into facts, correct symbolism, and universal agreement. The important thing is to get the feeling that we abstract, firmly rooted into the minds of the children.
This achieved, the rest follows automatically.
All disputes such as the fight between the vitalists and the mechanists; the modernists and the fundamentalists; naturalists and anti-naturalists; the Newtonians and the relativists, etc., evaporate, since these are mostly due to the objectification of higher abstractions, the Fidoism in our thinking processes.
The elimination of the Fido-ways would affect, in an extremely beneficial manner, our old economic system; it would bring sanity where, at present, there is none.
What is money? Money is a symbol. A symbol for what? For all human Time-binding faculties; animals have it not. No doubt bees producegoods—honey, but these goods of the bees are not wealth until man puts his hands on them. Money is not edible or habitable, it is worthless if the other fellow refuses to take it. The reality behind the symbol is human agreement, or else the value behind the symbol isdoctrinal. Fido does not discriminate between A and B, and B and C (see the Anthropometer). He worships the symbol alone. "In Gold we trust" is his motto, with all its destructive consequences. Man must not forget the reality which is behind the symbol. It is amusing to see how the so-called "practical man" deals, mostly, with fictitious values, for which he is willing to live and die. When he has the upper-hand and ignorantly plays with symbols, disregarding the realities behind the symbols, of course, he drives civilization to disasters. Life is full of them.
We see also the utter folly of anyone making a race to accumulate symbols, worthless in themselves, destroying the mental and moral values which are behind them. For it is useless toown a mentally disorganized world, such "ownership" is a fiction, no matter how stable it may look on paper. Commercialism, as a creed, is such a folly.
Some day even economists, bankers and merchants will understand that such "impractical" works, as the present one, for instance, on the stabilization of doctrinal values, are directly working toward the stabilization of an economic system; which the former, in their ignorance, do their best to keep unscientific and, therefore, unbalanced.
But such thoughts are beyond the Fidos, and the world is drifting rapidly toward further catastrophes.[3]
We may outline a few more, important consequences. The understanding and the training with the Anthropometer would help scientists in all lines of research, for there are no "facts" free from some "doctrine." There are only "facts" with bad logic and facts with good logic. Gross empiricism is a delusion, and he who professes it as a creed is probably more mistaken than the old metaphysicians were.
Deduction worksrelatively until we bump our nose on these particulars left out.
Deduction worksabsolutely, if correct. We never can bump our nose, because no particular is left out.
Mathematical abstractions differ from our daily abstractions by the fact that mathematical abstractions include the particulars, in mathematics we go byremembering (Lambert, Cassirer); the opposite is the case with our daily language, wherein abstractions leave the particulars out. We go by forgetting, until we bump our nose in our deductions on some particular left out.
The majority of our disasters is due to the not knowing or neglecting of this all important issue. The Anthropometer, giving the consciousness that we abstract, brings these issues forcibly home.
We mostly all (mathematicians included) objectify our high abstractions, which is a confusion oforder of abstractions. But mathematics is unique in this respect, that mathematical abstractions have all particulars included, and therefore these objectifications are not dangerous. This explains why mathematicians very seldom show "practicality" in life; they objectify daily abstractions with great assurance in the same way they do with mathematical abstractions, and disastersmustfollow.
The objectification of high abstractions is a terrible danger, because of these particulars left out, but the moment we realize this, we are conscious of it, the danger is over.
If the event has an infinity of characteristics, then, obviously, from an event we can build up an infinity of higher-order abstractions. Because of it the old "negative facts" become a much more fundamental source of knowledge than the old "positive facts" (conventional). Einstein's theory is a brilliant example. When we speak about something, what we actually do, is to exhibit the behaviour of a system of symbols, rather than to say much about this world (Ogden). When the system misbehaves, then we learn something important about this world.
The realization of it, the feeling of it, gives us these wings Couturat was speaking of, and Poincaré was laughing at. It sets man free. The Anthropometer releases man from the old limitations of Fidoism, when shown (not only said. A "knowing class of life" begins with "knowing," therefore, scientific method and science is not a luxury for the privileged few; it is the very thing which differentiates "Smith's" "thinking" from Fido's "thinking." The consciousness of abstracting which is so fundamental for man, is the awareness of a faculty, and inthis special case we can use thisfaculty only when we are aware that we have it.
The Anthropometer shows that the event is an absolute variable, different all the time; the object is arelative variable, different for every observer, the label is a constant, when posited by a definition. It follows that we cannot agree (theoretically) about an object, and cannot disagree on the label.
These undeniable facts lay down the foundation for a positive theory of universal agreement, inherent in the structure of human knowledge. From an event we can abstract an infinite number of abstractions of first and higher orders. Only folly can make us fight for these abstractions, which are only poor selections among the infinity of possible ones. We do not need to doubt human reason, we should distrust our language. There is a world of difference between these two conceptions and attitudes.
The Anthropometer is built upon two fundamental primitive feelings, namely: that we abstract, showing on the Anthropometer "This (A) is not this (B), and this (B) is not this (C)"; while for Fido "This (A) is this (B) and this (B) is this (C)"; all three are one. And that of difference and of countingthe differences (we do not need actually to count them, the feeling is there just the same). Exactness here is not required, although it is always desirable; the feeling that we abstract is all that is needed. This feeling, I repeat again, is the awareness of a circular faculty, and is, therefore, necessary for its exercise.
As a result, universal agreement becomes a possibility. We can give the "scientific temper" to the masses in a very short time. The dreams of Bertrand Russell may become true.
The modern physico-mathematical discoveries become very simple when explained on the Anthropometer. Einstein simply refused to copy Fido, and objectify higher abstractions such as "space" and "time" (Minkowski) and "matter" (Whitehead).
III
AS SHOWN before, the meaning of a label must be given by a definition. This fact gives us the means to investigate the structure of all human knowledge.
Whenever and wherever we start, we must start with a set of words which are undefined, because we have, by assumption, no more words to define them. This means that human knowledge, at every stage, presupposes knowledge of these few undefined words. This is called, in logical terms, the circularity of human knowledge.
We have never before faced this issue candidly, and it has ever been responsible, as it is today, for most of all intellectual gloom and skepticism. This inherent structure of human knowledge was called the "weak spot" of knowledge, which, of course, it is not.
It cannot be theoretically denied that human knowledge is a faculty such that the son can start where the father ended; therefore it always should start from the latter-end (1924) and not from the beginning. This fact, as yet entirely ignored theoretically, shows that the naturalistic philosophies should be reversed as to logic and order when they tackle the problem of man.
The gross empiricists, overwhelmed with horror against the old metaphysics, went to the other extreme, into a mythology equally false to facts.
When we inquire indefinitely, "What do you mean?" accidentally we spoil every nice "talky-talk"; but we also come to a set of undefined terms, which are postulates. All the rest of our vocabularies (not names for things) are theorems, logical necessities of the starting set of terms strictly interwoven with the metaphysics of the maker of the vocabulary. It may be mentioned that a babe, before he begins to understand anything and to revise his feelings about the world around himself, has alreadyhis metaphysics aggravated by the metaphysics of his parents, teachers, etc., away back to our savage ancestors. Of course, these metaphysics are false to facts, but just the same it is first as to order.
We see that all human knowledge is geometrical in structure (I might say mathematical, but for serious reasons, I prefer to say geometrical). Somewhere at the border line there is the metaphysics. The system is strictly interdependent and bound up by "Logical Destiny," to use this beautiful expression of Professor Keyser.
The expression "circularity of human knowledge," was used here in its logical sense, which is misleading if taken literally. We muststart somewhere, somehow, anywhere, anyhow, with a set of undefined terms, then go ahead, come back, revise our base (a) for (b), go ahead again, revise our base (b) for (c), go ahead again, and so on endlessly. Human knowledge is inexhaustible. No set is undefined absolutely, but only relatively so.
In practice, things are much more complicated because we seldom, if ever, have one vocabulary. But we must untangle first the simplest theoretical issue. The vocabularies (silent postulates) imply the theorems, the theorems imply the postulates. He who accepts uncritically the vocabulary made by X, accepts unwillingly and unbeknowingly X's metaphysics. This fact is of very great importance. If we accept the vocabulary made by X and the metaphysics made by Y, we are lost in inconsistency, the world is an ugly mess, unknown and unknowable. This mess, which is nearly always followed up by rampant pessimism, is the necessary consequence of the misunderstanding of what is here explained. With understanding, our troubles vanish, the world remains unknown (because the Fidos have so long persecuted science) but it becomes knowable.
With all of this permanently in mind, it is easy to understand anybody else, just as a mathematician when he hears a theorem, he knows usually from which geometry it is taken.
If we do not understand the above, we are slaves; if we know it, we are free, because we can select our master (Keyser, Poincaré).
The geometrical structure of human knowledge shows that man is extremely logical, if we grant him his conscious and unconscious premises (language). Whoever has any doubts about all of the mentioned issues should visit an asylum, where he would see the working of this general theory in its nakedness. In daily life and in semi-insane cases the issues are veiled by customs, habits, overlapping vocabularies, and other doctrinal complications. It is known that "insane" people are extremely logical. In many instances "insanity" is cured by making the unconscious premises conscious. Psychiatry, as yet, has no preventive methods. The Anthropometer is such a preventive educational method against many cases of insanity and different unbalanced states, due to inherited or inhibited false doctrines. A man full of false doctrines cannot be a perfectly normal, healthy and useful man; neither can he copy Fido in his thinking processes without somehow registering it to the detriment of society and himself.
When someone claims to be a "Napoleon" we lock him up. How about the majority of us? Do we not fancy that we are what we are not? That is rather a serious question.
The psychiatrists have all the time to fight "absolutism" and "dogmatism," which in many instances are responsible for different forms of insanity. They do so without the full understanding of the mechanism of it.
The whole advancement of science and civilization shows that this theory is true, but as we did not know explicitly the structure of human knowledge, every revision from (a) to (b) and from (b) to (c) (see page 21) etc., was always painful and slow. We see that, as the structure of the atom is reflected in a grandiose manner in the structure of the universe, so is the structure of the knowledge of the individual man reflected in the collective knowledge of mankind called science, and vice versa.
IV. Consequences and Applications
AT THE present stage of our inquiry it is impossible to foresee all the consequences and applications of this general theory by means of the Anthropometer, but some of them are manifest from the beginning, and are manifold and weighty. I will summarize them, roughly only, as material for thought and further analysis.
It must be emphasized again that merely talking about the Anthropometer will not help much. This prototype of the event and the object and the label must be shown. The moment we point our finger at them and say "this," it cannot be covered by words, and it economizes thousands of words at once. Whoever disregards this positive condition and misses the benefit of it, should not blame the theory and the Anthropometer, but his disregard of a vital condition and issue. The old Fido-way is so deeply rooted in our theories, practice, habits, systems, etc., that although I have had it on my desk for more than a year, my own Fidoism shocks me far too often. In a century or so, of course, we shall not need it, but such is not the case at present.
Some of the consequences are educational and scientific, some are suggestions for activities. We will start with the educational and scientific ones.
The inherent circularity and geometrical structure of human knowledge proves the interconnection of our vocabularies with our metaphysics. We see, that if we want humans to be humans and think as humans, we must start our education from the latter-end (1924) by beginning with modern "metaphysics" of Planck, Einstein, Whitehead, Russell, Keyser, etc., made possible by the understanding of the Anthropometer and the structure of human knowledge.
We would then find, at once, the interest of the masses aroused, and thinking would start on an unprecedented scale, with all its beneficial results. The "scientific temper" would overrun mankind in a few years, facts and correct symbolism would count, and the exponential law PRt would begin to work properly.
Man is ultimately a doctrinal being. Even our language has its silent doctrines, and no activity of man is free from some doctrines, so that the kind of metaphysics a man has, is not of indifference to his world outlook and his behaviour.
We cannot expect when we force a dynamic being into the patterns of Fido static doctrines, that we will get anything else but an unbalanced being in an unbalanced civilization.
The Anthropometer should be introduced into elementary schools and we should start our education with it, everywhere. We must teach a small modern scientific vocabulary and train our children to think habitually in these new terms; which automatically carry with them a new non-absolutistic world conception. Such simple and mechanical means (they must be mechanical and simple if we hope to give them to the masses) would impart to all mankind, not the knowledge, but thecultural results of university training. Such methods, the complete reversal of the old, would stop Fido-ways in theory and practice.
The language of "concepts" is very difficult because that is an elementalistic, absolutistic term (as auxiliary it may be useful) and will not do as our fundamental term. This doctrine is very difficult to teach even to university students, to say nothing of the masses. The language of "abstractions of different orders" is not an elementalistic term; it is a "joint-phenomenon," "organism-as-a-whole" modern new term; it is natural to man, it can be shown to him, and is easily grasped by children and people of very low mentality when shown on the Anthropometer.
We see that modern philosophers have heavy duties and responsibilities toward mankind; heavier, perhaps, and more important than the duties and responsibilities of engineers and doctors. With the modern physico-mathematical discoveries and mathematical discoveries, as those of Whitehead, Russell, the "doctrinal function" of Keyser, etc., "philosophy" has ceased to be a divertisement of the few, it has become as vital an inherent factor in all human life, as air, water, and sunshine. There are communities who have very little to do with engineers or doctors, but no community in the world is free from some kind of "philosophy." Among savage tribes we see how doctrines have prevented entirely any progress at all. The more civilized races have advanced simply because they were more rebellious, and never could stick to an unrevised doctrine for too long.
This is why we have had this semblance of civilization at all! It is not enough to discard philosophy entirely, on the ground that most of it is foolish. Granted our old philosophies were foolish enough, whoever thinks he can discard them entirely without supplanting them by others, sometimes equally foolish, deludes himself. The problems at hand require philosophy, and ignorant vagaries will not do. It is about time that mankind should hold the philosophers responsible. Ignorance is not an excuse.
It may as well be admitted that our old educational methods would have to be reversed. Babies should start their education playing more with microscopes than toys. Before they learn to spell they should firmly feel, at least, the structure of "matter," the structure of human knowledge, and the mechanism of human symbolism. Then they would be equipped to be humans.
Science is not a luxury for the few, but as it leads to the consciousness that we abstract, science and scientific method is precisely that, which makes man think and behave as man.
Non-scientific, half-education (in the sense of 1924, which we could, maybe, consider "scientific education" in the sense of 300 B.C.) is not a boon to mankind in 1924, far from it. That is very natural in the meantime. The conditions, environment, social inheritance, racial experience, other complications, with all accompanying andnovel nervous and mental pressure upon man in 1924, are entirely different from these in 300 B. C. Is his mental, nervous resistance and health properly taken care of? Are our educators and doctors themselves modern men? Sad to say the answer is NO. We still educate man, drug him with doctrines thousands of years old, doctrines which are inconsistent and false to facts. We still keep him in a savage-made universe. This deep discrepancymust unbalance him, and periodically unbalance his institutions. The sooner we understand this and modernize the antiquated branches of knowledge, the better for all of us. There is hope for us, if we stop folly. Our old doctrines do not work even with savage tribes, as practice shows. From the modern point of view the savage tribes do not gain anything by passing from one kind of savage-made doctrines to another set of savage-made doctrines. Experiments should be made, by taking some newly-born from different savage tribes, placing such children in highly cultured scientific families and give them full scientific education, and see what would happen. The new doctrines would work maybe, where the old failed.
The Anthropometer presents a synthesis of modern scientific strivings in a form ready for application.
In the old way we delude ourselves talking about the "education of the masses," and in the old way it is hopeless. What we need most at present and what could be accomplished very quickly is the re-education of the educated. A proper insistence by the scientists, and a few books for this purpose would perform the task. The understanding of the Anthropometer shifts the center of gravity from something which is impossible to something which is possible.
With a re-educated educated class the world would soon become a different place to live in.
The benefits of new terms are that occasionally they throw a new light on old problems, or quite often they help in settling, in a positive way, old controversies. When some controversial questions are settled the world accepts them quickly. What was roughly known but ignored, because veiled by the old language is brought by the new language to a sharp focus. After the results are obtained, they may be explained in any language, but the results, in most cases, could not be gotten in another way.
As a matter of fact, civilization has advanced in the shape of the diagram given on page 21, but as we did not know that this was the inherent structure of human knowledge, every revision of our assumptions was slow and accomplished with great suffering and bewilderment. The creative scientists and teachers were persecuted and hampered, mankind has paid a hideous price. The new understanding will stop persecution and propaganda of any kind.
The popular introduction of the Anthropometer would also prevent the publication of nine-tenths of books and the delivery of the majority of speeches, inasmuch as most of them are based on Fido-ways. Such elimination would relieve us of a great amount of useless ballast.
We must repeat here that the theories of relativity have a still more general underlying theory, namely, the general theory of time-binding. As this theory is so general it is therefore easy to grasp and teach, even to children. It explains the refusal to accept high-order abstractions, such as "matter," "space," and "time," for first order abstractions, which they are not. This is the minimum of science (1924) with which each babe should start its education.
There are a few interesting points about "matter," "space" and "time." Taken separately they are abstractions of high order and not objects, or abstractions of first order. If we objectify the high abstraction, we get a fanciful universe, self-contradictory, a nature which is against human nature. Being logical, we invent something supernatural to account for a nature against human nature. If "time" is an object, if it has objective existence, then, obviously, it must have, as all objects have, a beginning and an end; then the universe was made, it must have a "beginning of the beginning" (old "essences"), etc., etc., and the whole old anthropomorphic mythology follows, by a purely logical process.
But if "time" is an abstraction of high order and not an object (first order abstraction), otherwise, if it does not exist as an object, then, obviously, something which does not exist cannot have a "beginning," or a "beginning of the beginning," the universe was not "made," etc. It just was, is, and will be. Obviously the "primal substance" may quite happily be a myth in such a universe of transformation; we cannot exhaust it in either direction.
Our universe is timeless. In another language, it is eternity in time, or, still in another language, infinity of times (this is a generalization of experimental time). When times are very rapid we nervously summarize times, and feel "time," a "duration." The "infinity of times" is nothing else, when translated in still another language, than the law of conservation of energy. Incidentally it proves the existence of actual infinity.
The above explanations were given because the old Fido-ways are omnipresent. In a way they permeate all mankind, and they must lead us to most acute mental disorders, reflected in behaviour. I do not know any other phase of science in the whole history of civilization which would have a more profound and beneficial influence upon the daily life of the man on the street, than the modern advancement of mathematical and physico-mathematical sciences, when given to the masses and applied in education.
This understanding clears up another old fallacy. We are accustomed to hear that the old mythologies are somehow "primary" with man. We see clearly that it is not true. Those mythologies are "secondary" with man. What was primary is the objectification of high abstractions, the Fido-ways in our thinking processes. Once this is eliminated by the Anthropometer, all the old vicious fictions automatically vanish.
If we confuse the orders of abstractions; if we fancy that the high abstractions are first-order abstractions, which they are not, then we get "absolute matter," "absolute space," and "absolute time." If the world is made up of "absolute matter," "absolute space," "absolute time" then of course such a structure cannot account for "mind" and what not. The number of possibilities in such a universe are too limited, etc., etc., and all the rest follows. But if the world is made up of "quanta," "fields," etc., then all we see, we feel, we know and can know are averages, summaries, abstractions of different orders, etc., etc. Only a language of processes, transformations, variables, functions, integration, abstractions of different orders, probabilities, etc., etc., can account for such a universe. Mathematics considered as an activity of the human organism, reflects in its structure and form the structure and form of the universe. Being a language, it is the universal tongue.
In such a universe all we deal with are combinations of high orders ("Matter" made up of molecules, molecules of atoms, atoms of electrons, and so on, probably).
How the combinations of high order grow, as to numbers of possibilities, an instance taken from the Principles of Science by Jevons will show. This simplest possible case which is far, far away from any "simplicity" in nature, will show.
"The successive orders of the powers of two have, then, the following values, so far as we can succeed in describing them:
First order ......................................................... 2
Second order ..................................................... 4
Third order ........................................................ 16
Fourth order ................................................ 65,536
Fifth order number expressed by 19,729 figures.
Sixth order number expressed by figures, to express the number of which figures would require about 19,729 figures."
By way of contrast Jevons gives us "that the almost inconceivably vast sphere of our stellar system if entirely filled with solid matter, would contain more than about 68•1090 atoms, that is to say, a number requiring for its expression 92 places of figures. Now, this number would be immensely less than the fifth order of the powers of two."
Due to the modern knowledge of the structure of the world we see that practically everything becomes possible, and may be understood, no matter when. The feeling of these issues, with the lack of understanding of the simple law of growth of the higher order combinations, gives, I think, the base for mystical feelings, which vanish as such, once these issues are understood. We can know, never mind when; all the rest is a matter of method and science. In this way the unknowable becomes knowable. Correct symbolism covers all these facts, also, and leads to the same conclusions.
The concept of order is fundamental, not only because it underlies all mathematics but, also, because it is easily and obviously translated in terms of senses. This gives a base for a scientific vocabulary.
The savage-made language of "cause" and "effect" has also order in it, only it is a very short series—it is a two-term relation. Yet, in the world around us, there is no such thing in existence as a two-term relation, and therefore when we use a two-term relation, cause-effect, these two terms are overloaded with non-crystallized "thought" (emotion), hence metaphysics of the wildest kind. Science expands the series into an indefinite number of members. Old ignorance and metaphysics go.
The expansion of this series is the coefficient of our knowledge.
The theory, as expounded in this paper, seems to suggest directions in which some activities could be started.
There seems to be no doubt that the recent physico-mathematical and logic-mathematical advancement of science is affecting all branches of human knowledge in many unexpected directions. It seems without question, that the scientists could not deal with these problems without the help of professional mathematicians. If the mathematicians refuse to cooperate with other branches of science, Human Engineering included, it will probably take one or more generations before the whole beneficial effect of modern discoveries would be felt in education and life.
The situation today is such that, in many serious instances, naturalists who know "facts" speak nonsense quite happily, about them. The mathematicians who alone speak sense, know very little or nothing about facts. The results are: slow advance, groping in the dark, thousands of false doctrines, and endless arguments in vacuo. Science is a joint phenomenon of logic and "facts"; as there are no "facts" free from some doctrine, therefore science should be carried on as a joint phenomenon. Experimentalists, for example, should have very able and creative mathematicians who would work at logic and language, and they should work together, jointly. Life is too short for one to be a specialist in several lines at once; science has outgrown the individualistic epoch, it must become a group activity.
All our doctrines should be revised and correct symbolism should be applied to facts. The old philosophy is dead in disgrace, the world is without co-ordinating guidance. To be fair to philosophers, no single person nowadays could perform this co-ordinating work alone. It again must become a group activity.
If we want to avoid complete mental anarchy, which must be followed up some day by grave disturbances in our behaviour, this problem of revision and co-ordination must be our urgent and immediate task. The people of the world have lost the old faiths in their theories, their leaders, and themselves; this state, again is another phase of other creeds as yet not crystallized. Only heroic measures can save us from still worse turmoils.
When, for instance, biologists make statements about mathematics, or mathematicians make statements about biology, such statements are always short somewhere on knowledge, they never are competent. Statements should be made by biologists on biology, but with the full understanding of other branches of knowledge; by mathematicians on mathematics, but also withfull understanding of other achievements.
Such work could be done only and exclusively by a permanent body of the world's best scientists being relieved from all other duties who, after getting acquainted with each other's specialities, would work together on the revision of language and doctrines, and would prepare this co-ordination of knowledge. Such a permanent body could issue a yearly or quarterly journal which would give to mankind the revised and co-ordinated doctrines of each "present" day.
Such a method would allow mankind to start every generation where the last one left off, and the progress of civilization would follow the exponential law PRt. A copy of this general doctrinal summary should be placed in the hands of every teacher throughout the world, by legislation if need be. There is no doubt that if scientists themselves insist upon some such plan, mankind would accept it. After all, a united opinion of those who, in the major part, are the driving force of civilization, is irresistible. Scientists would start with such an institution a new period of human history which would be called the "scientific era." This body might be called the "Senate of Humanity" (this name was suggested to me by Professor A. Vasiliev, and I gratefully acknowledge it).
If the peoples of the world were told that the best scientists of the world are working on their problems they would settle down and wait, some hope would be restored, otherwise they will not wait. The publications of the "Senate of Humanity" would be stripped of technicalities so that the general public would understand them. They would save an enormous amount of work to scientists and laymen by giving short, yet reliable, informations in an already co-ordinated andrevised form. With these budgets of knowledge, not of paradoxes, mankind would come gradually out of the Fido era, into the scientific era.
We need not delude ourselves. The most important hindrances, in the old ways, are found in language and the logics; these problems would remain the most important for a long time to come, and the mathematicians would have to play nolens volens, a most conspicuous rôle, a rôle worthy of their science.
It follows from the geometrical structure of human knowledge, that the solution of all human problems lies in frankly putting all branches of human endeavor upon a postulational base. Postulational treatment gives us unique benefits, among others, it facilitates inspection, gives clarified systems of doctrines, and unifies all other methods. Our debates would become limited to experimental testing of our sets of postulates.
It may be mentioned that such a library is being established in New York City under the name of "International Library of Human Engineering" (Principia Scientiæ Hominis), which will originate a deductive science of man, and deductive natural and other sciences.
This library will be at present under the editorship of one mathematician and one engineer, with an advisory board of scientists from all countries in all branches of science. For geographical and linguistic reasons, local national boards of co-editors will also be formed.
Until the Senate of Humanity is organized, this library with its international scientific boards, will be the research and organizing center for the future permanent international body of scientists. Its publications would be the handbooks for the future chairs of Human Engineering which sooner or later must be established in all important universities of the world. Human Engineering, as every other branch of engineering, would be based on mathematical methods.
Such is the outline of immediate constructive steps which could be taken. The problems at hand are manifold, weighty, and difficult, beyond the power of any single man to deal with. A great deal of responsible preparatory work must also be accomplished. Such work of course must be a group activity, and it is hoped that the international advisory boards of the library will be able to accomplish a good deal of this preparatory work.

 

 

A SHORT BIBLIOGRAPHY
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PATON, S. Education in War and Peace. New York.
ROBACK, A. A. Behaviorism and Psychology. Cambridge.
ROBERTSON, T. B. The Chemical Basis of Growth and Senescence.Philadelphia.
RITTER, W. E. The Unity of the Organism. Boston.
SHERRINGTON, C. S. The Integrative action of the Nervous System.London.
WATSON, J. B. Behaviour. An Introduction to Comparative Psychology. New York.
WHEELER, W. M. Social Life Among The Insects. New York.

HUMAN ENGINEERING
CARMICHAEL, R. D. Logic of Discovery. (Forthcoming book.)
KEYSER, C. J. Mathematical Philosophy. E. P. Dutton. New York.
KORZYBSKI, ALFRED. Manhood of Humanity, The Science & Art of Human Engineering. E. P. Dutton. New York. Time-Binding: The General Theory. (Forthcoming book.)
POLAKOV, W. N. Man and his Affairs. (Forthcoming book.)
RUEFF. Des Sciences Physiques aux Sciences Morales.Paris. (English translation forthcoming.)
[1] See my "Manhood of Humanity." The Science and Art of Human Engineering. E. P. Dutton & Co., N. Y. C.
[2] See my "Fate and Freedom," in Mathematics Teacher, May, 1923.
[3] See the chapter on "Wealth" in my "Manhood of Humanity".


SECOND PAPER

Nearly two years have elapsed since its publication, and I am happy to find that I have nothing to retract. I find it wise, however, to amplify that former outline to furnish those who use the Anthropometer (to be referred to as the A.), which is now available, with more adequate information.
The present paper is written for a very limited class of readers, namely, those already familiar with my work and who are willing to look over the references indicated in the G. T. and here. I assume therefore that the reader is acquainted with quite a number of subjects. Both papers are outlines and far from exhaustive. I emphasize only special points which are known but disregarded in general, or else not known. Usually all the additions that an intelligent and unprejudiced reader can make to this outline are foreseen and legitimate; most of the possible objections of the old kind are also not disregarded, but the theory takes care of them in the form and by the method in which it is expressed. Quite often I use at present words admittedly vague; it would be impossible to make them more exact without expanding this paper into many chapters. In most cases this vagueness is intentional, to be eliminated in a fuller exposition to be published later.
It should never be forgotten that the G. T. as outlined in this and in the preceding works is deliberately treated as a branch of natural science; it is descriptive, but in a language allowing fewer incorrect inductions and deductions than the older forms of representation. It is not a speculation, which gives me more freedom in handling and adjusting, the system to facts known in1926. The main difficulties encountered by the mature reader are precisely in this new, non-familiar form of representation, while he has already a mature and established habit of thinking in the old terms of his language, which may give quite different characteristics, or emphasis. Quite often objections in one form of representation are eliminated in another form because they are purely verbal and due to habits hundreds of thousands of years old, and to unrevised premises and creeds.
My work is deliberately a non-aristotelian system, to follow up which, to the point of familiarity, is inherently difficult—as difficult perhaps as the study of the non-euclidian systems. The Greek gods are still potent, firmly rooted in our habits and in the structure of the generally accepted form of representation.
Historically non-aristotelian attempts have been even more numerous than the non-euclidian, but no system has been built as yet to the best of my knowledge. The primitive form of representation which Aristotle inherited, his metaphysics, and his philosophical grammar, which we call "logic," are strictly interconnected, so much so that one leads to the other.
In my non-aristotelian system I reject Aristotle's metaphysics (circa 350 B. C.) and accept modern science (1926) as my metaphysics. I reject his postulate that man is an animal, the postulate of uniqueness of subject-predicate representation, the postulate of cause in the form he had it, the elementalism of "percept" and "concept," his theory of definitions, his postulate of cosmical validity of grammar, his predilection for intensional methods, etc., etc.
I accept man as a man, use functional representation whenever needed, expand the two-term relation cause-effect into a series, introduce organism as-a-whole form of representation in the language of time-binding, orders of abstractions, accept postulational methods as the foundation for a theory of definitions and therefore of meaning. which bridges the conscious with the unconscious, introduce modern "logical existence," relations, differential and four dimensional methods, use the extensional methods, etc., etc., and so build up my system.
One extremely important and disregarded problem arises in connection with introversion and extroversion, which is of crucial significance in preventive mental hygiene. Plato was an introvert, Aristotle an extrovert, and so their systems are permeated by these tendencies. Until the einsteinian revolution we did not know, neither did we suspect, or could know, that the normal man (1926) ought to be an introverted-extrovert, or if we prefer, an extroverted-introvert. The disregard of this problem leads to a peculiar and very common mild form of some kind of splitting of personality, further aggravated by a lack of consciousness of it. We see instances of double personality practically everywhere, but clearest of all in some writers. One instance is the scientist who, on the one hand, may be an epoch making individual in his special line, while on the other hand, when he deals with human problems, let us say, he is no longer the scientist, but in fact seems to have forgotten about science, and his split personality then makes its appearance.
It need hardly be added that these problems should be of supreme interest to educators, psychiatrists, parents, etc., as the disregard of them can not lead to the education of a whole man,but leads rather to the production of two distinct half-men or some other multiple personalities, mild in the beginning, but which easily can become morbid under the stress of life.
One of the aims of the G. T., and of training with the A., is precisely the building up of this extroverted-introvert type, the normal man, a whole man, a time-binder; avoiding the splitting of personality, which if avoided in childhood, may be of preventive value, increasing the resistance, and so facilitating future adjustment. Such education leads to an entirely different outlook upon the world and ourselves, and so favors adjustment, mental health, and happiness.
The characteristic that a language is a form of representation, one out of an infinity of possible forms is obvious to any one who has taken the bother to understand the G. T. and A. I therefore prefer the term "form of representation" to the familiar term "language" because "form of representation" is more correct, more general, and much more full of implications. Although the term "form of representation" is taken from mathematics the reader who analyses it will discover that my more general use of it is not only legitimate but obviously fully justified; into the details of such an analysis I cannot enter here.
Does the G. T. and the A. represent something new? This question is rather of some importance, and on entirely impersonal grounds. The study of man is as old as man himself; a great many things have been said about man—true, false, and meaningless. The present inquiry aims to be independent, an enterprise which on psychological grounds is very difficult. As the subject is very old and much analysed it is unavoidable that in our independent inquiry we should "discover" quite often the well known, often the "obvious," so obvious indeed that we have all disregarded it. Einstein for instance "discovered" the "obvious" and well known fact of the identity of gravitational and inertial mass, completely disregarded by the older scientists, yet this "old" fact has proved of new and enormous. importance when analysed.
I use the term "discovery" in quotation marks for lack of a better word. My "discoveries" are often neither discoveries (without quotation marks) nor re-discoveries. Re-discoveries are common in science and no one is shy about them. A re-discovery is mostly characterised by the fact that an individual A did not happen to know that an individualB had discovered the same thing before him. Under such circumstances, A's ingenuity is perfectly equivalent to the amount B has displayed. In my case it is not re-discovery because usually I know what has been done before by B; such knowledge is necessary in my field. I do not need to use the same ingenuity as the re-discoverer; my "discoveries" are less than re-discoveries from the point of view of ingenuity displayed. At the same time, although less ingenious, "discoveries" in my system are more important.
I attempt to establish a "science of man"—"Humanology," as I call it. I use a new form of representation, not primitive but modern, 1926, and I do this deliberately. Forced by the form of representation I have to explore my subject independently and carry on my inductions and deductions in a purely formal manner. In this process I am led automatically by this new form to certain results independently of others, and that with practically no display of personal acumen or ingenuity. I am willing to admit that any moron, not of the lowest type, if properly trained to master the new form of representation could reach approximately the same result. These are made obvious and simple by the new form of representation. But when I am led automatically by this modern method to "discover" without difficulty and effort what has been actually discovered before and which is already admitted by mankind to be important, sometimes very important, it is a fact of the deepest significance. It shows that the application of modern scientific methods, involving abandonment of primitive forms of representation, opens a new field of most startling possibilities. Each of such "discoveries" is an indication that the method and the new form of representation are fundamentally sound as judged by their inner consistency and fertility. Even in this short paper there will be displayed quite a number of such "discoveries," to justify the claim that the G. T. is not only sound but also extremely fertile and workable.
Let me give a few examples of re-discoveries. Frege discovered what numbers are. Russell, independently and without knowing the work of Frege, made the same discovery. The same honor to both! The achievement was very important; the caliber of mentality, no doubt was first class in both cases. There are also the instances of Newton and Leibniz and the calculus; and of Gauss, Lobachevski and Bolyai and the non-euclidian geometries. Theirs also were re-discoveries.
My own case, however, is different. In my independent inquiry I came across difficulties and had to solve them or quit. My solution is given in the G. T. and the A. It is found that this theory covers the theory of mathematical types invented by Russell, but in a different garb, a garb which makes it much more general and workable. Was this discovery or re-discovery? To my mind, neither. It was "discovery" because I knew about the theory of types long before, so it cannot be re-discovery. I could not accept the theory of types because it is not general enough and does not fit in my system; as far as my work is concerned I had to dismiss it. Scientific method led automatically to a solution of my difficulties; and perhaps no one was more surprised and happy than myself when I found that the G. T. covers the theory of types. The conclusion which follows is reassuring: the G. T. with the A. appear to be sound and fundamental if they can lead to solutions which cover such important achievements as Russell's theory of types.
Some one might say: perhaps it is the same thing. There are empirical proofs that it is not the same, and that the G. T. is more general. Bertrand Russell and myself write books (empirical fact) and are interested in human affairs. If the theory of types, of Russell were the same as the G. T., Russell, and not I, would have discovered the thesis developed in my Manhood of Humanity and the present General Theory. Yet he did not discover them; his theory of types did not work that way, and could not; it was therefore obviously not the same thing. In his Analysis of Mind and in other books of a sociological, non-scientific character he repeats the usual errors illustrated on pages 45 and 46 of the present paper; he accepts the logical blunder that man is an animal, an aristotelian, pre-scientific fallacy, an error which Russell of all men should have been first to avoid. We see that the theory of types did not work outside of mathematics; it wasn't general enough. Although Russell's theory and my own are strikingly similar, they are not at all the same thing; one works outside of mathematics, where the other does not. It would be extremely interesting and instructive to inquire as to what extent Principia Mathematica itself pays tribute to Aristotle. This important problem looms in the foreground the moment we have the pluck to face non-aristotelianism candidly.
If we were to apply the G. T. and the A. in the realm of physics we should be led, without Einstein's genius, to Einstein's theory.
The G. T. is, among other things, a theory of what Eddington, without formulating it, called the "standpoint of relativity," obviously a psychological affair. Quite naturally the "standpoint of relativity" precedes the formulation of the theory of Einstein, which applies to Einstein as well as to others. If called "big names" for this particular "achievement," I should disclaim them, as I disclaim them for the "discovery" of the "theory of types" as such; but what I should claim is this: the G. T. of Time-Binding as explained in my writings seems to be sound and very fertile, leading to many far reaching consequences, some of which are already worked out, others not.
After all, the reader who is familiar with it should not be surprised that the General Theory of Time-Binding leads to a psychology of discovery, which I cannot prove otherwise than by making "discoveries" over and over again. I claim, for instance, a theory of universal agreement; how can this be "proved"? Again, only by showing in special cases how disagreement can be eliminated. On theoretical grounds the old animalism and aristotelianism are rampant everywhere, even in science and philosophy. The older theories of knowledge which are based on "percepts" and "concepts" are to the fullest extent elementalistic theories of universal disagreement. With such prevailing doctrines, one should really wonder that we do not behave still more  disgustingly. No hyena can surpass Smith in viciousness; nevertheless Smith, when one considers the set of savage doctrines that make up his superficial culture, is by comparison a "saint." Theoretically he is fully entitled to be worse. Eliminate the vicious theories and much is accomplished at once, but such a revision cannot be a gloss on Aristotle any longer. It must be a non-aristotelian system. I had wide experience in this field during the War. The conditions of life at the front contradicted accepted doctrines of sociology, economics, politics, morals, etc. The new standards were far from perfect in any sense, yet I saw a great many men who in daily life behave disgracefully, behave totally differently at the front. Why?
To return to the question of "discoveries." We "discover" in the present paper the "scientific, or public unconscious"; it is similar to the "preconcept" of Dr. H. S. Sullivan, with which I became acquainted recently, and whose work I respect highly. Again, it is not as yet the same thing. The situation is similar to the case of types of Russell. A system has its own requirements and a form of representation has its own implications.
THE reader should not miss the point that this work is a non-aristotelian system, a general theory, and that not in name only; something which at present does not exist to my knowledge. It is not a compilation. Compilations lack the organic unity which a system has, and which has made systems so useful through all history. This theory is easily understood and remembered and therefore workable.
This work is not in animalistic competition with existing branches of science, but a human, Time-Binding, co-operative enterprise and might be of assistance to specialists in those branches; in general it is in full sympathy with all and each of them. With daily increasing numbers of special facts, systems are becoming increasingly rare and increasingly difficult and laborious to formulate. Some day they must become group activities requiring special training and devotion; because of this we can foresee the necessity of establishing a new science for which the name "Humanology" is suggested. This science of course must be non-aristotelian in structure.
Science after all is the highest form of adjustment, and is displayed by no organism except man; therefore no study of human adjustment can be free from fundamental errors without the study of science and mathematics as the highest forms of adjustments as yet on record. In them we find the highest order of abstractions, which account for the rapid rate of accumulation of the being called man. (See pp. 10, 11 of the G. T.)
Quite naturally, since I make it my business to study all forms of human behavior and adjustment, not excluding psychiatry, mathematics and science in general, the G. T. must differ from all special sciences, for which reason its author, necessarily, must work at present in an uncomfortable isolation. The problem of adjustment is strictly dependent on the organism's power of abstracting. An organism without eyes and ears is much more handicapped in a world of continuous happenings than an organism with them, etc., etc. Since man has the unique power of extending his orders of abstractions indefinitely, his power of adjustment also increases indefinitely, provided he uses this power. It is therefore possibly of some use to inquire into the mechanism of it; perhaps we shall be better equipped to use it more effectually.
The use of a new form of representation also has important consequences. Occasionally such a new form of representation brings to light characteristics which another form would not reveal and quite often brings problems to a sharp issue where formerly the same issues were not sharp; also it usually throws a new light on old problems. It is very difficult, if at all possible, to decide a priori if such or such a form of representation will be particularly important; such things show themselves in practice, and the justification of a new form is its fertility. Thinking in unfamiliar terms is bothersome, yet it forces us to think anew, and so diminishes the influence of old preconceived and unconscious notions upon us. The usefulness of new forms of representation is usually quite important.
To give an example. Every line, except theX axis, through a point O, which is the intersection of a parabola with its X axis, cuts the curve a second time. This fact, important for us to know, appears clearly in the polar co-ordinate form of representation but does not appear in the rectangular form of equations. In my own case the whole theory is an example, and many issues have already been emphasized, as on pages 7, 8, 9, 11, 13, 14, 15, 19, 21, 25, 26, 28 of the G. T., and in my Manhood of Humanity (E. P. Dutton, 1921). We find there that issues not sharp and controversial often become sharp and not controversial, and quite often also new characteristics appear.
In quite a number of cases the importance is in emphasis. Issues disregarded, although supposedly known and never analysed because considered such "commonplaces" as not to be worthy of analysis, are re-valuated and appear extremely important, all of which leads in my case to empirical verification.
I am not trying to prove some special creed, but to apply as rigorously as possible the modern (1926) scientific standards to the study of the behavior of Smith, Brown, etc. With this aim in view, I had to reject the older forms of representation and build up a new form. Having done this, I take a handful of labels in my pocket, so to say, look around anew and label as I go, the results being all the time independent, because of this new form of representation. Here an interesting mathematical analogy arises. The characteristics which appear in this new form, and yet are the same as in the older ones, are perhaps characteristics intrinsic in our subject, as they have survived the transformation of our form of representation. Such transformation is the only method by which we may be sure that the characteristics are intrinsic, independent of our accidental form of representation. So the fact that we discover in our new form of representation many characteristics which appeared also in the older forms is in itself a fact not only of interest, but also an indication that these characteristics common to different forms of representation, may be intrinsic in our object, and are not extrinsic, or read into our analysis by the form we use. The fact that quite often we "discover" the "obvious" has in itself a scientific value.
After formulating the G. T., I made a search of the germane literature and found that my analysis differs considerably, as a whole, from others. First of all I have never come across a system of such a deliberate non-aristotelian character, of such ramification requiring so many special studies, nor having the same structure. I have never seen or heard of anything similar to the Anthropometer and its application. Details, even, are frequently so different from the old that quite often the reference to existing works are given for sake of contrast. The above explanations are given because often a superficial reader who says "That is old," not only misses the subtle differences, the constant iteration of which would make the writing unreadable, but also because such a reader misses the fact that this theory claims to be experimental and should therefore be applied and tried out, not merely verbally criticised. The statement "That is old," said hastily and often impatiently, carries the unconscious implications: "It did not work for thousands of years, so it will not work now." Such an implication totally prevents application and experimentation and so becomes seriously obstructive to this work. If this work were a mere speculation and not an empirically verifiable theory, I should never have published it. There are already too many speculations on the bookshelves.
My personal experience has made it obvious that there is some obscure psychological process involved in training with the A. which until recently I was unable to explain or formulate. All my experience convinced me that in spite of the approval of the A. and the G. T. given sometimes in the form "that's all known" or "platitudes," the very person saying so the next time he opens his mouth bluntly refutes in fact all he formerly admitted and called, perhaps, "platitudes." This experience appears to me to be without a single exception; at least I have not met any one of this class doing otherwise. My main difficulty has seemed to be not with people who could not understand the G. T. and the A. at once, but with those who seemingly understood and approved it, but considered it a matter of "platitudes." Quite naturally having such experience with trained and rigorous thinkers, the importance and difficulties of this work were brought forcibly home to me. It became more and more evident that at the bottom of it there was some fundamental difficulty affecting all mankind, some pernicious, old, very old, habits of thought, unconscious in the main, "fossils" of our savage ancestry. I found myself dealing with the field of paleopsychology, to use the excellent term of Dr. Jelliffe.
How to connect my own work with that of the psychologists became my next problem. After much meditation I selected psychiatry for that purpose and not psychology, and that for serious reasons. All science is the study of some behavior; even mathematicians study the behavior of the entities which they invent or posit. In order to study "psychology" we would need to study the behavior of man as-a-whole, and all the forms of his behavior. At present, this branch of science does not exist. Of course, to name some branch of research "behaviorism" does not make it psychology. The behavior of Smith, Brown, Jones, etc., consists not only of sleeping, eating, fighting, cheating, etc., but embraces also all of science, mathematics, and "insanity." As yet no psychologist has ever attempted to study all forms of human behavior. I am compelled to conclude, surprising as this may be, that the science of human psychology does not exist at present.
Usually we think of psychiatry as a science of mental illness, or "morbid psychology," the term "psychology" being reserved for the study of the so-called "normal" man as-a-whole. Before we can orient ourselves in these matters we must see what we label what, otherwise "normal" has no meaning. Everybody's observation shows that extremely few people are free from some kind of mental deficiency, because extremely few can follow any kind of rigorous thought, so that statistically "normal" means "mentally deficient." From this point of view, and in agreement with Dr. Malinowski, the anthropologist, I conclude that psychiatry is the study of the "normal" man, since it deals with the mentally deficient, the Fido, the savage, the baby within us. Perhaps the "copying of animals in thinking" (see G. T., p. 15.) is more serious and universal than I stated in my outline.
The implications of the last mentioned fact are very different from those involved in the false statement that we are animals. If you and I and Fido are the same thing, then of course there is nothing to be done about it; but if we merely copy Fido we can stop that at our pleasure, the moment we realise it, which is very different. The hopeless on one level becomes hopeful on another.
I grow more and more convinced that the claims of the G. T. were not exaggerated. A number of actual experiments with the A. have shown the most astonishing and beneficial results, and many claims of the G. T., even many which were only implied, have been confirmed empirically. If such results accumulate, so that we learn that the few initial ones were not accidental, but actually due to training with the A. and the G. T., it would mean that mathematics, which among other achievements makes a business of unraveling unconscious assumptions, may be considered as "higher psychiatry," essential for human thought and mental hygiene, with extremely far reaching consequences for human life and happiness. It would mean also that the "scientific, or public unconscious" (if we may call it so) with which mathematicians deal may in certain cases be morbid in character, hence the appellation "higher psychiatry," embracing the mental hygiene of all mankind.
The above does not mean that mathematicians now get this psychological benefit out of their work. The great majority of them do not know what was said here, or else know it vaguely, and believe that mathematics has very little, if anything to do with human life and happiness, an attitude representing creeds false to facts and which therefore may be morbid in character.
The present outline may be of interest to those mathematicians who are concerned with the broader aspects of their science, and the psychology and methods of teaching it; and to educators in general. Psychiatrists in especial might find the work important, because of the pointing out of preventive methods where at present there are none, and suggesting perhaps new methods, more general and therefore perhaps more fundamental, which might throw new and unexpected light on problems, particularly where the older methods failed, or did not give entirely satisfactory results. There seems to be little doubt that the "scientific, or public unconscious" is a more fundamental, deeper level underlying the private unconscious. Perhaps the clarifications on the private level do not clear up the public, or scientific, level which represents the creeds of a certain epoch, and so might be in agreement with the general development of the race. It is interesting to note that "epoch-making discoveries" are seldom if ever isolated; usually they come in bundles, being discovered by several individuals independently; they are "in the air," as we say—perhaps they are in the protoplasm more than in the air. With the dynamic theory of "matter," and the difference between the world of man and the animal as indicated by the G. T., the term "evolution" is gaining a much broader meaning. This public unconscious, by its very character, is such that we can deal with it on a wholesale base, through public education. My experience seems to show that this is the case, although more facts in this field are necessary.
In this border land—this no man's land, as yet—between psychiatry and mathematics we deal with the "unconscious" and therein we find the common ground where they meet. In using the word "unconscious" we touch one of the taboos. Psychiatrists as well as mathematicians know what they mean by this term in their own work, but each usually is innocent of its meaning in the other's field and there is a necessity for each to become acquainted with the other's work. The usual meanings given to this word in these respective sciences are not the same, and we must make up our mind in what sense to use it. Investigation shows that the mathematical meaning is more general and, therefore, more fundamental. I accept the mathematical meaning, as amplified by the G. T., which, in the meantime, includes the psychiatrical meaning.
To explain a little.
Two assumptions are said to be absolutely equivalent when each of them can be deduced from the other without the help of additional new assumptions. For instance, (a) the fifth postulate of Euclid: "If a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles," (b) "Two straight lines parallel to a third are parallel to each other," (c) "Through a point outside a straight line one and only one parallel to it can be drawn." Each assumption silently, unconsciously presupposes the others, so that they can be deduced from each other. They actually are different forms of the same proposition. Another case is equivalencerelatively to a fundamental set of assumptions A, B, C,..... M. It might happen that in diminishing the fundamental set two assumptions which were equivalent before cease to be so. For instance, the following assumptions are mutually equivalent and also equivalent to the fifth postulate of Euclid. (a) The internal angles, which two parallels make with a transversal on the same side, are supplementary (Ptolemy). (b) Two parallel straight lines are equidistant. (c) If a straight line intersects one of two parallels, it also intersects the other (Proclus). (d) A triangle being given, another triangle can be constructed similar to the given one and of any size whatever (Wallis) (e) through three points, not lying on a straight line, a sphere can al ways be drawn (W. Bolyai), etc. The following assumptions are only equivalent to the euclidian fifth postulate if we retain the postulate of Archimedes: (a) The locus of the points which are equidistant from a straight line is a straight line; (b) The sum of the angles of a triangle is equal to two right angles (Saccheri). (See Bonola, pp. 1, 19, 23, 118, 119, 120. The titles of the books are given in the G. T.)
The crucial point of this discussion is that all of what was said is not obvious even to an attentive and intelligent reader. It took nearly two thousand years and some of the efforts of the best thinkers of the world to discover these connections and implications. Here we have a glimpse of the "scientific, or public unconscious," a problem of great importance to be worked out by mathematicians and psychiatrists in the light of the G. T. In this paper I am only pointing out this problem and no attempt is made to analyse it.
Let us assume that the fifth postulate of Euclid is a false assumption seriously detrimental to human life, comparable to some of the false doctrines that underlie the morbid symptoms with which psychiatry deals every day. Let us assume, further, that a doctor innocent of the structure of human knowledge and the equivalence of assumptions would succeed after painful and laborious efforts in eliminating from the system of a patient this vicious assumption, but because of his innocence pays no attention to some other assumption, equivalent to the first, and would not eliminate it. (See G. T, pp. 26, 27.) In such a case rationalisation about the first false doctrines would probably make the treatment a failure, as the other unconscious and equivalent doctrine would in virtue of the extremely logical character of the unconscious perform its task and make the treatment ineffective. Of course, all possible degrees of failure might happen. The tangle of equivalent assumptions in daily life is still entirely unanalysed yet it seems that what is given on pp. 26, 27 of the G. T. is of the most fundamental importance. The semi-failures so common in the practice of psychiatrists seem to indicate that the fundamental structure of "human knowledge" as explained in the G. T., gives a clue to the explanation of them.
The scientific, or public unconscious would be the implications which, far from obvious, are silently hidden behind some set of postulates, "unconscious" because totally unknown and unsuspected,unless uncovered after painful research. Any form of representation has its own assumptions at the bottom, and when we accept a form of representation we unconsciously accept sets of silent assumptions of which we become victims in the long run. This explains why for so long a time we have been victims of the unconscious assumptions which underlie the aristotelian, euclidian and newtonian systems; and also the importance of the revision of these systems and their form of representation culminating in non-euclidian, non-newtonian and non-aristotelian systems. These last systems are characterised not by the introduction of new assumptions, but by making these unjustified, primitive, unconscious assumptions conscious, and so helping us in eliminating these undesirable elements of the older systems. To the best of my knowledge the G. T. and the A. are the first to formulate this problem explicitly, and to take it into consideration as the foundation of a theory. I have already attempted to show how other fallacies and taboos can be manufactured unconsciously by logical processes, starting with some more general, more natural and more fundamental errors, due to pre-human ways of thinking, which I have called Fidoism (see pp. 26, 27 of G. T.)
This scientific, or public, unconscious seems to be more fundamental than the private (psychiatrical) one because the very structure of human knowledge is such. As the reader may recall (see p. 14 ff. of G. T.) life, intelligence and abstracting of different orders start together; without abstracting, recognition and, therefore, selection would be impossible. The world of the animals as well as the world of man is nothing other than the result of abstractions without which life itself would be totally impossible. But man alone has the power of extending the orders of his abstractionsindefinitely. When Smith produces an abstraction of some order, perhaps by making a statement, he has the faculty of analysing and contemplating this statement which meanwhile has become a fact on record (potentially, anyway) and so he can abstract himself to a still higher order, or level, and so on endlessly. It is this power which crowds the world of Smith with endless "facts" belonging to very different orders or levels of abstractions, and which constitutes the extremely complex world of man. The animals' power of abstraction ceases on some level, and is never extended without change in their structure (evolution), as the diagram on page 35 makes obvious. So their world is comparatively simple, the world of man being by comparison indescribably more complex. It is for this reason that veterinary science is so "simple" as compared with humanmedicine, in spite of the fact that the higher animals and man differ very little anatomically. The "facts," which are the result of abstraction ("not-all-ness") differ in number as well as in complexity according to the power of abstracting. Now the human faculty for expanding indefinitely its orders of abstractions must by necessity be inherently stratified; it is a product of evolution just as rocks are. This stratification is a fact of crucial significance completely disregarded, except in mathematics (theory of types, space-time) and psychiatry. (See White, Foundation of Psychiatry.) This stratification, which is conveyed with simplicity by the G. T. and the A., is not only the base for a theory of universal agreement, but also explains why the older disregard of it led always to universal disagreement with all its dismal consequences.
I RECALL a vivid argument I had with a young and very gifted mathematician. We were discussing the dropping and introduction of assumptions. Our conversation was about the geometries of Euclid and Lobachevski. I maintained that Lobachevski introduced an assumption; he maintained that Lobachevskidropped an assumption. On the surface it might have appeared that this is a problem of "fact" and not of preference. The famous fifth postulate of Euclid reads: "If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely meet on that side on which are the angles less than two right angles." (We must note in passing that a straight line is assumed to be of infinite length, which involves a definite type of metaphysics of "space," common to the aristotelian and older systems). This postulate of Euclid can be expressed in one of its equivalent forms, as, for instance: Through a point outside a straight line one and only one parallel to it can be drawn. Lobachevski and others decided to build up a geometry
without this postulate, and in this they were successful. Let us analyse further the activity of Lobachevski (what he did). To do this we go to a deeper level, where we discover that what on his level had been the dropping of an assumption becomes on our deeper level the introduction of an assumption, namely, the assumption that through a point outside a straight line there passes more than one parallel line.
Now such a process is inherent in all human knowledge; more than this, it is a most unique characteristic of the structure of human knowledge. We always can do this. The problem is the passing to a higher order of abstraction, and situations, seemingly "insoluble," "matters of fact," quite often become matters of preference. This problem is of extreme importance and of indefinitely extended consequences for all science, psychiatry and education in particular. The A., by giving the means to train mankind in this stratification, facilitates the passing to higher and higher orders of abstractions, a capacity unique with man as man; it builds up human "mind," and engages the activity of the higher centers of the nervous system.
The same could be said about the psychiatrical "complexes." On some level they might exist; on another, a higher order of abstraction, a deeper level of analysis, they do not exist. What actually happens is that a doctrinal being, the baby, reacts to the inherited and inhibited doctrines of his parents, teachers, etc., to be explained later. As a matter of fact all human life is a permanent dance between different orders of abstractions. Similar analysis of the lowest developed tribes of savages would confirm this conclusion. But as yet mankind as a whole (not a few academicians perhaps) is totally unaware of the extreme benefit as well as dangers of this "dance." The mechanism of our rapid accumulation is thus revealed (see p. 11, G. T. ) and it also explains why we are, as a whole, on such a low level, with artificial difficulties hampering us everywhere.
The G. T. and the training with the A. aims at making these benefits as well as dangers conscious, formulated in a workable way. The expected results should be in both directions. One, exercising the beneficial side of it, which leads to a high development of "mentality," which after all is nothing else than passing to higher orders of abstractions; the other, the avoiding of the dangers which can be expressed in the form of avoiding the confusion of orders of abstractions, which would be preventive of unhappiness, insanity, imbecility, wars, revolutions, and what not. All of this works automatically the moment we are trained in the consciousness that we abstract, which is the secret of all "thinkers" and "geniuses." It might be objected that there are many men who are conscious that they abstract and yet do not escape the "ugly" side of "human nature." My whole limitedexperience shows that even those men who are conscious that they abstract do so only in some and not all lines; besides, I have yet to meet a man who could avoid the dangers without special training. An enormous amount of material to prove this contention can be found in the biographies of thinkers, as well as in daily intercourse with one's associates. I do not except myself. The discoverer of the G. T. and the A. might be supposed immune, but such is not the case. The A. catches me quite too often.
A very interesting point should be noted. One and the same question can be answered sometimes both yes and no, depending on the order of abstractions; this diminishes to a very large degree the old sharp field of "yes" and "no." This restricts the possible field of human conflict, a consequence which is of importance, and which alone would save billions of dollars spent unnecessarily because people, scientists, manufacturers and so on, cannot agree on some subject, owing to their innocence of the above. Any executive knows too well what enormous trouble and expense little disagreements involve.
The use of the A. in homes, schools, offices, courts, parliaments, etc., would save mankind considerable trouble and expense—countless efforts which at present are spent unproductively. Men somehow have learned to manage their live stock scientifically, but the management of human affairs is still on a savage plane, owing, in the final analysis (1926), to Fidoism.
There is something more than the elimination of disagreements. There is a satisfaction, mental, emotional, etc., when things run smoothly. Many problems of "fact" on one level become problems of "preference" on another, thereby helping to diminish the field of disagreement.
It is important to throw some light on the problem of "preference." Let us take the case analysed above: which statement or attitude is preferable? The one claiming that Lobachevski dropped a postulate, or the one claiming that Lobachevski introduced a new postulate? Both are "facts," but on different levels, or of different orders. The "dropping" is an historical fact; the "introducing" is a psychological fact, inherent in the structure of human knowledge. The preference is fairly indicated: the psychological fact is of the utmost generality (as all psychological facts are), and therefore more useful, since it applies to all human endeavors and not merely to what one mathematician did under certain circumstances.
This psychological fact is of unrealised importance, particularly in the study of the enormous field of the unconscious, which embraces not only the individual's history or the race's history but practically the history of all life. Here comes the importance of our new conceptions of "space," "time," "matter," "infinity," etc., as indicated on pp. 26 and 27 of the G. T. The old mythologies are not "primary" but secondary, based on Fidoism, our inheritance from the pre-human ways of "thinking." The same could be said about such problems as the one of Lobachevski, or about "complexes," or about a great many others, of similar import.
The faculty for higher and higher abstractions, no matter how high or low they may be, is a most characteristic faculty of man which can be found even among the most primitive people. The potentiality for passing from one level to a deeper one, from one order of abstractions to a higher one, is inherent in man. Whenever and wherever he stops the unconscious begins.
Until recently we did not suspect that the scientific, or public unconscious might be as morbid as the private unconscious with which psychiatry deals. My experiences with the A. and the G. T. seem to show that this is the case.
It is no mystery that maladjustment to the "environment" (including doctrines) is the origin of the majority of mental ills. In helping this adjustment we directly help mental, and therefore physical, well being; that these mutually affect each other is a commonplace of present day psychiatry. The G. T. and the A. give us not only the means for training in the consciousness that we abstract, but formulate a method by which unconscious doctrines are made conscious; the whole G. T. is based on this principle.
In this connection we see the importance of the circularity of human knowledge, which circularity is not a matter of speculation but is a fact of natural history. This directs our attention to a deeper point of analysis, a higher abstraction, namely, it will no more be the older and usually accepted standard demanded of you by existing science that you "define your terms," but a deeper, more fundamental one, inherent in all human knowledge, which starts with undefined terms, which as undefined represent creeds, mostly unconscious. As these undefined terms can always be defined in some terms which at present do not exist, or which are not suspected to be connected by implication, they imply a totally unknown material (see p. 21 of the G. T.)
In this work we are in complete agreement with mathematics, considered as a form of human behavior, the only science which starts deliberately with undefined terms. This characteristic of the G. T. is one which appears to be novel, as I am not aware that this has ever been done before. Of course, the undefined terms which I use as the base of my work represent "creeds" which in other disciplines are, and remain, unconscious: I make them conscious by frankly stating them.
There is no escape from the inherent structure of human knowledge; the choice is between having unconscious, unaccessible, unrevisable, and therefore extremely dangerous, creeds; or making these creeds, postulates, undefined terms conscious, and so giving one the liberty of analysing them or even of abandoning them. This diminishes the enormous field of the unconscious, the silent records of all past life, and so expands the field of the conscious which might be expected to be useful.
In the G. T., I accepted the ordinary names for things, making individual names with the help of indexes, as for instance Fido', Fido'', or Fido I, Fido II, etc. But as a class of names makes no proposition and cannot express a meaning, I accept as my set of undefined terms such terms as "order" (in the sense of betweenness), "relation," "difference," and a few others. The actual process is by necessity symbolic and is not indicated here. To develop it in a full system will be the task of years.
In analysing the structure of human knowledge and its inherent circularity, owing to the fact that we must start with undefined terms, we came to the conclusion that all human knowledge is postulational in structure and therefore mathematical in which we find the link between the conscious and the unconscious. Mathematicians have been inclined to claim in general that all of mathematics is "logical" in structure. Both statements may be said to amount to the same thing.
It is of no small importance which form we accept, so that a few words about it will not be amiss. Mathematicians discovered some time ago that the form of representation they use is not of indifference to the results they obtain. Speaking roughly, they found that in one form, let us say, they obtained characteristics a, b, c, d,...... m, n,......; in another, a, b, c, d...... p, q,......; in still another, a, b, c, d,...... s, t,........; etc. In some cases direct inspection was possible and they found that by checking up predicted characteristics some of them, such as a, b, c, d, in our example, actually belong to the subject of our analysis, whereas the characteristics m, n,...... p, q,...... s, t,........, etc., do not belong to our subject at all, but vary from one form to another, and depend on the form of representation. They are read into our analysis by the form of representation. Mathematicians came to distinguish between characteristics which are intrinsic, which actually belong to the subject independently of the form of representation; and those which are extrinsic, which do not belong to the subject but to the form. The mathematicians solved their difficulties by inventing absolute calculuses which automatically eliminate the extrinsic characteristics. The same story repeats itself in a much more vicious way in our daily life, because the issues are not so sharp. It is not of indifference which form of representation we accept. We do not have as yet a tensor calculus to orient ourselves in daily life, but this does not mean that we should be unmindful of these issues.
Let us apply correct symbolism to some of these issues, logic for example. We find that "logic" by definition is the science of the "laws of thought." How could such a thing be produced at all? Someone would have to observe all possible forms of "thought," abstract himself from the study of those facts and generalise them, and so formulate the "laws of thought." He would have to study all forms of "thought" and therefore he should make not only studies of the activities of the average man, but also of "geniuses," the "insane," and particularly mathematicians. Because mathematics is free from material content it represents "pure thought" in action. If we take definition seriously, as the little word "must" on p. 13 of the G. T. seems to compel us to do, then we conclude that such a thing as "logic" does not exist at present. What passes for "logic" is only a philosophical grammar of a pre-scientific, primitive form of representation, which Aristotle and his followers did not even make but inherited from primitive ancestors, uncritically accepted, generalised, and put into a system. Correct symbolism tells us unmistakably that we have no such thing at present as logic true to its definition.
We must look in another direction. We can survey the achievements of mankind which have proved to be the most beneficial and of lasting value, study them, and try to train ourselves in repeating the mental processes which have made them. In this way we are led to the study of mathematics and science and acquire the habit of rigorous thought. Naturally, such a way is wasteful; it would be simpler to have a general theory true to the definition of the term "logic," and study this short, ready-made formulation, rather than the actual performance of rigorous thought, and formulate those generalisations for ourselves. At present, this cannot be helped. Such generalisations from actual performance by the best thinkers is called "scientific method," or "applied logic."
As an historical fact mathematics has proved of the very highest value; its structure admits of being perfect. Again applying correct symbolism we see that by definition whatever has symbols and propositions is a language. Mathematics is therefore a language. What kind of language is it? We see that it is a perfect language but at its lowest development—lowest simply because it is not a language in which we can speak about everything.
How about our daily language? We know that with it we can speak about everything, but unfortunately cannot speak sense about anything except by accident. We conclude that language is the highest of mathematics, because all-embracing, but it is at its lowest development—lowest because we cannot speak sense in it.
The result of this analysis is that mathematics and language are different stages of one and the same process, mathematics being the lowest in its development but at the perfect end of the process. Quite naturally it is wiser to start with the perfect product and make it fundamental. For the same reason it is more expedient to consider the whole of human knowledge mathematical in structure, because in such a way we start from something which actually exists, is on record, can be studied, etc., than to start from something which as yet does not exist, like a "logic" true to its definition. From the foregoing it is obvious that any general theory which might be called "psychology" or "logic" still awaits formulation, and would have to start with mathematics as a foundation.
It is impossible in this paper to elaborate upon the influence a form of representation has upon the characteristics we find. Let us say briefly that we are saddled with a "plus," a primitive-made language and its implications; and with it, it is impossible to analyse adequately the universe, ourselves included, which are not "plus" affairs. We see, for instance, how psychiatry has been seriously hampered and is still struggling with the "soul," a "plus" affair, and yet psychiatrists persist uncritically in calling man an animal! Of course the "soul" is not something intrinsic with Smith or Jones but it is a characteristic which depends on the aristotelian form of representation. If we accept man as man, as we should do, it leaves us free from "plus" verbal implications. If we think of man as an animal or a god, we are at once saddled with "plus" or "minus" aristotelian implications, which lead to errors. It seems that persisting in pre-human (Fido) attitudes toward our own thinking processes is much more serious and disastrous than would appear to a casual reader.
The world around us is a dynamic affair; human thought for its best working has to deal with static pictures. Again arises the problem of the form of representation. If we select a dynamic form of representation such as we inherited from our primitive ancestry, rigorous rationality is impossible. Such paradoxes as those made famous by Zeno will prevent it. (See Russell under Zeno). This primitive inheritance culminated in science with the system of Sir Isaac Newton and his followers, and in philosophy with the bergsonian and similar systems. They were the first approximations as far as the primitive form of representation could make it possible. Curiously enough the notion that the earth is flat has governed our speculations for ages, and it was a primitive approximation. Only with the Einstein theory, in our own days, do we abandon the other corresponding primitive notion of the flatness of the world of stars!
What is the way out? The way is so simple when once discovered, so simple, indeed, that we can only wonder that it was not discovered long ago. The facts are of course not changed, the world around us remains dynamic; our minds remain static for their best working. The way out is the invention of new forms of representation that would account in static terms for dynamic events. In such forms the human intellect would feel at home, able to represent dynamic events in static terms, so as to satisfy rationality. We would be justified in expecting that such inventions might have been made by psychologists or philosophers; as a fact, they were made by mathematicians in the differential calculus and the four dimensional geometries. (See Keyser Math. Phil. pp. 176, 177). Future "logicians" and "psychologists" will find there most of what they need. It is not to be forgotten that all said here applies to our daily language, and the same transformations of form of representation can be accomplished in it. As a matter of fact my own researches are an attempt in this direction. A non-aristotelian system may prove to be as revolutionary as the non-euclidian and non-newtonian systems are proving to be. Perhaps more! The aristotelian doctrines pervade and shape our daily lives much more fundamentally than the euclidian ever did, hence the difference. Two sharply contrasted world views emerge. On the one side is the world represented by Aristotle, Euclid and Newton; on the other is the world represented by non-euclidianism (Lobachevski, Riemann, etc.), non-newtonianism (Einstein, etc.) , and finally non-aristotelianism. On the outcome hangs the issue of the future.
HERE should follow a disregarded chapter on the development of science. Unfortunately a few suggestions only can be given here.
The atomistic principle—the principle of individualisation—has been extremely fruitful in science. We introduced this principle in the study of substance, electricity and finally applied it to processes themselves, as in the quantum theory. This principle has far reaching consequences; it implies dealing with separate individuals, which again carries with it the extensional attitude, the naming of individuals, and so leads to correct symbolism. The same could be said about mathematics which began with the extensional attitude from which all the rest followed by implication. As the reader already knows, my own work is consistent with this; it requires a new form of representation, which carries also important unconscious elements in it. It diminishes the field of the unconscious by making many of the unconscious assumptions conscious. It seems to the writer that these methodological, and therefore psychological considerations give us a glimpse into the larger values of science, and account also for the extraordinary importance and validity of mathematics. The wider application of these principles would throw a considerable light on many other problems which at present cannot be reduced to the orthodox mathematical treatment. That mathematical treatment should remain the goal.
The "organism as-a-whole" is also a principle which involves a new form of representation. The parallel to it will be found in the einsteinian mathematics. Psychologically Einstein made up his mind to talk sense or stop talking. He decided to see the world anew. He had to abstract himself to a very high order and free himself as much as possible from preconceived ideas, which are always implied by the accepted form of representation. He decided to see facts and to label them anew. Helped by mathematical method and symbolism he succeeded. This involved a thorough-going behavioristic attitude. But it was a new behaviorism, a mathematical behaviorism in which the rôle of the observer is not disregarded. The implications which the observer carries with his form of representation are considered. Other attitudes are fallacious; they disregard the share of the observer in the observation, an error avoided by the G. T. and the A. By labeling correctly as he went along, Einstein found that by no hook or crook can we divide "space" and "time" (we might add "matter"). "Such a thing is impossible," he said, "therefore let us stop talking about it as if it were possible." Minkowski, his follower, formulated the necessary form of representation and worked out the language in which he does not attempt to divide that which cannot be divided. So the world geometry of four dimensions of Minkowski came into existence. It makes the Einstein general theory possible and it opens a new era in which mankind acquires a static representation for dynamic events. All this enables us to be rational and in accord with the world and with ourselves.
Mathematical space-time (with a hyphen) is the mathematical counterpart of the naturalist's "organism as-a-whole." In my work I follow the same impulses, I refuse to divide what cannot be divided and so I am obliged to establish a new form of representation in the language of "time-binding" and "orders of abstractions." The results are astonishingly similar; the old absolutism goes. But the system is no longer aristotelian.
There is here an important point to be noted, namely, the psychology of this process. The attitude is new and requires a long training. In the old way we took our language (labels) for granted, never suspecting that some mischief might be there. We had our words in our heads and hearts, so to say, and used them automatically and unconsciously. The new attitude—and this is the only attitude which will enable us to understand modern science as well as the present work—is the consciousness that we abstract and carry our labels, so to say, in our pocket, and therefore are able to use them consciously as conveniences and not as some kind of magic. My experience teaches me unmistakably that the average intelligent reader has little difficulty in reading these "platitudes," but when he begins to apply them for some time he becomes completely confused and the whole thing does not stick together. The whole thing is circular, of course. The aim of this work is to give means to train students to the consciousness that we abstract, yet before he gets this consciousness he cannot fully understand this work, so the process requires training, and finally is achieved only after some effort. The work is then simple and understood fully. The reason for these difficulties is to be found in different attitudes toward labels. He usually carries them most intimately with himself as a part of himself; he never doubts his form of representation which he uses instinctively and unconsciously, and forgets usually that the moment he opens his mouth to say something he is never on the level of the object but on the level of the label, that talky-talk is just talky-talk and not an object. My attitude is different. I carry my labels in my pocket, so to say, as a convenience. When confronted with any problem my first unconscious attitude is, "I do not know; let us see"; then I look at the situation and begin to label and see what can be said about the situation. The A., by the way, has labels which we may put in our pockets actually and not only figuratively.
A few words more regarding the form of representation. When a donkey kicks a donkey there may be a broken bone but the complications are few and of no great consequence. But when Smith kicks Brown the situation at once becomes much more complicated. If Smith and Brown happen to be kings, the kick might be considered as a "deadly offense of a nation by a nation," and without even a broken royal bone a war might follow and hundreds of thousands of non-royals might die. In this case we see where complications of a symbolic, doctrinal character enter when doctrinal beings are involved. The problem is still more complex when the problem is not the activity itself but talky-talk about it. In our talk we might consider that the leg of Smith to reach Brown has to pass an "infinity" of "places" in an "infinity" of "times"; it includes "movement," "continuity," and what not. We see that the simplest of statements involves a full-fledged metaphysics of "space," "time," "infinity," etc., and here the human tragedy begins.
The point in question is that to understand "space," "time," "infinity," etc., we need asymmetrical relations, which are totally excluded by the aristotelian subject-predicate "plus" form of representation. In other words, if we accept the primitive-made language—a "plus" form—under no circumstances shall we be able to give an account of any asymmetrical relation and therefore of "space," "time," "infinity," etc., and so will not be able properly to analyse such a simple statement as "Smith kicks Brown." (See Russell under relations.) The powers and dangers of forms of representation are ever present with a doctrinal, symbolic class of life; in it we find the ready source of our unique powers and as well as our maladjustments.
Consider a striking example of what a form of representation means. In a paper presented before the American Mathematical Society and printed in the Proceedings of the National Academy of Science February, 1926, Doctor Rainich, the mathematician, tried to introduce "mass" into space-time, each belonging to a different form of representation. He succeeded but at the price of splitting space-time into the original space and time. It is to my knowledge the first proof of how intimately a form of representation is inwardly interconnected, and does not allow much tampering. This fact is of extraordinary importance for psychologists and psychiatrists who always deal with symbolism of some sort. It would be of great interest to have these problems worked out by them.
The circularity of human knowledge has its physiological counterpart. It is an established fact that circularity exists in the physical structure of the human organism. We find in many cases that doctrines which provoke "emotions" are the result of some glandular secretions; these glandular secretions are affected in their turn by emotions, which in turn affect still more the emotions, and so on in a vicious circle. It is a known fact that often some trouble which began as "mental" ultimately leads to somatic disorders where only a surgeon's knife can help, and vice versa.
All the parts of the nervous system are not of the same age; some, as for instance the vegetative system, are older than others. The same can be said about the brain; the brain stem and cerebellum are older than the cerebral cortex. The brain stem and cerebellum are devoted chiefly to reflex and instinctive activities; the cerebral cortex is devoted to the higher associations. The vegetative nervous system is intimately connected with the vital primitive functions of the organism and also with the affective (emotional) and unconscious. The inter-connections within the systems and between the older and newer systems are unspeakably complex and every kind of deviation in the connections is possible, all of which is not sufficiently known at present. It is interesting to note how the consideration of this phylogenetic age difference between different parts of the nervous system may throw some light on problems in connection with "mental age," not only as tested by psychologists but also in the sense I use it in the G. T., where "mental age" is considered according to the amount of information one has. The primitive, the pre-human, the Fidoism, the emotional, and vast unconscious (not necessarily repressions) go together and indicate a low mentality, insufficient use of the cerebral cortex, and the prevalence of the control by the more primitive and older systems.
Mathematics is the leading discipline among all sciences and the only one which—because of its postulational structure—might be perfect. Because of this structure mathematics virtually abolishes the field of the scientific unconscious by making all assumptions, as expressed even in undefined terms, conscious. Quite naturally this shifts the neurological activities by engaging the higher centers, the cortex.
We should not be surprised that, under such circumstances, the "motional" and "emotional" systems of science and philosophy, systems which make rigorous rationality impossible, are the remains of the pre-human, pre-cortex epoch of development. The above considerations explain also why we are governed and swayed so easily by unconscious doctrines; there is such predominence of emotionalism, imbecility, moronism, etc., why the mathematical methods of making the unconscious doctrines conscious, the discovery of static means to account for dynamic events, etc., culminating in the modern developments of science might be considered as an epoch in which mankind will finally abandon Fido-ways and enter into manhood, its cortex age. But to accomplish this, a new understanding of these problems is necessary and above all new methods of training and education. Perhaps we can train the cortex just as effectually as we train our muscles for a boxing match. Perhaps the A. and the G. T. will prove to be a device for bridging the gap between the old and the new, for engaging and stimulating the activity of the cortex.
In the rough, men can usually be divided into four types. Some of us "think" better in visual terms (visile type); some in auditory terms (audile type); some are motile type, and finally some are tactile type. Extreme cases in which individuals belong wholly to one class or another are rare; with the majority of us as a rule all of these propensities are brought into play. It may be suspected that individual peculiarities found in this respect in life are the results of individual peculiarities in the interconnections between the older and the newer nervous systems. The main difficulty is to affect the unconscious, the affective, which in physiological terms means to affect the vegetative nervous system. Psychiatrists know well that quite often a patient is fully aware of his situation, understands thoroughly the mechanism of his trouble and yet nothing happens; the morbid symptoms persist. The foregoing might suggest why rationalisation alone is quite often not sufficient; equivalent doctrines play the havoc because they are disregarded. It seems, however, that the main difficulty is always somehow connected with the equivalence between the dropping of one assumption on one level and the introduction of another on a deeper level. After serious efforts a patient may be induced to drop some assumption, but the patient's very logical unconscious will not stop there; this dropping which is achieved by rationalisation is not enough, as there remains a most intimate connection of this assumption with others on a deeper level which have not been eliminated or clarified. The conflict remains. As a rule this cannot be so easily helped; the inherent structure of all human knowledge being such that a man can pass to higher and indefinitely higher orders of abstractions, deeper and deeper levels, and usually does—this last being at present beyond the control of the psychiatrist. I said "at present" because this can be controlled also when psychiatrists learn to take care of the scientific, or public unconscious, which is at the base of the private unconscious. Very interesting facts begin to accumulate in this field, to be published elsewhere.
We are able now to give a suggestion concerning the solution of the "obscure" psychological process involved in training with the A. and the G. T. The fact is that all claims and suggestions expressed in the G. T. become empirical facts only and exclusively after a training with the A.; mere talking about it and rationalising without training, no matter how well done, usually remains practically valueless. This surely was a puzzling situation, which some time ago made me feel almost hopeless about the whole problem. I had very little doubt that the majority of people would ask an explanation of such a fact (for them it was just a claim on my part and not a "fact") and if an explanation were not forthcoming they would drop the whole matter and never start training with the A. The explanation is found in the very complicated interconnections between the nervous systems of different ages, the older ways of "thinking" being unconscious, habitual already in permanent effect upon the older nervous system. The problem was and is to affect the older systems, the affective, the unconscious, or quit. Seemingly this is precisely what the A. does. Being made in relief, with movable pegs, strings, and, particularly, labels which also are movable it is somehow better fitted than any other device I know to drive home this G. T., because it operates through all known channels, the visile, the audile, the motile, the tactile, thus giving us the maximum opportunity to deal with the vegetative nervous system, and therefore the unconscious and affective.
We know that a piano player or a car driver is never a good player or driver unless he plays and drives unconsciously; the same applies to the A. It seems that the eye, which in reality is a part of the brain itself (as we know from embryology), is one of the oldest organs of life and somehow is closer connected with the vegetative system than the ear. Because of this it may be that although the G. T. is an intellectual affair it may reach the affective side of man because training with the A. is a physical affair by which all available channels are called into activity. What is said here of the A. might be said of any other model; however, though the physiology would remain the same, the psychology of it would differ since it depends entirely on the character of the doctrines which utilise a model and these physiological channels.
A few words about the "complexes" of the older psychiatry. We quite often speak about "complexes" as we might speak about a table or a chair or a house; this certainly is an objectification of higher abstractions, very vicious in effect. If we apply correct symbolism to the facts, we see that a human baby is born, not only with its natural propensities and impulses, largely connected with its structure and functions, quite few and simple to observe and analyse, but also is born into a full doctrinal surrounding built of the creeds of his parents, teachers, and what not. He is taught a language which, being a form of representation of a definite kind in the main primitive-made, also carries with it full-fledged metaphysics and by implication distorts and colors observation and "thought" with preconceived and transmitted false creeds.
Having no knowledge of the past or future conditions the baby is from birth under full dominance of the doctrinal set in which it happens to be born. The old animalistic standards begin their deadly work. We begin to repress the baby instead of enlightening it and so from the beginning the future mental disturbances are already implanted. In all actuality there is no such thing as a "complex"; it is simply an extremely complex reaction of a complex doctrinal being to complex doctrinal follies of other complex doctrinal beings. I said "follies" and do not apologise! Underlying this whole situation, due in the main to Fidoism all through, is the complete incapability of the parents and teachers for sound doctrinal orientation, due again to the lack of a scientific treatment of doctrines which involve human daily lives, and particularly the lack of elaboration of methods by which such orientation may be had. On the level of this inquiry the errors are of omission; in life they become errors of commission. The main aim of this work is to fill this gap.
We have here another example of fundamental circularity. Each "cause" is already an "effect"; each "effect" another "cause," strictly interwoven and operative with great precision, in spite of bewildering possibilities. This precision gives us means to investigate the situation to a still deeper level and so we can come to a point where, and when, we can control it. There is little doubt that this chain is practically endless, but there is a short cut in this field. If introduced into homes and schools the A. and the G. T. would give individual means to the individual Mr. Smith and Mrs. Smith to revise their own creeds and doctrines and so would enable them to behave without so much detriment to themselves and others. Eventually, in a generation or two we could expect a civilization graduated from Fido to Man. There is a joy in life if we know how to live, and science as always helps us.
THE accompanying diagram gives a suggestive sketch as to how the strings and the labels of the A. should be most effectively arranged as shown by my practice. It is not to be supposed that this arrangement is the only one possible.
It is important that in explaining the A. we should use our hands freely, follow up the lines with our hands, play with the labels, speak about the different levels, orders of abstractions, by showing them actually, hanging them, taking them off, etc. This labeling with our hands teaches us the most important essentials of our attitude towards words, and cannot be overstressed. In explaining the A. we should give a general idea of the G. T.; we should explain the event a, how the object b is already an abstraction of some order, which we call here "first order"; and should label the object b with a label c. Then the statement c and its level becomes a fact, and we can look at it, contemplate it, and abstract ourselves still further to a higher order, or deeper level, concentrate our attention on this new fact and speak about it; and so we produce a statement on a different level d. We repeat the same procedure with d and so reach e, etc. It is important in the training not to be shy of repetitions; they help greatly. By such training we exercise the inherent faculty of man, as man, to pass to deeper and deeper levels, or higher and higher orders of abstractions, a characteristic which might be considered as a definition of "human mind" as distinguished from the activities of animals. This peculiar power—it is the secret of the rapid accumulative power of man—we label the time-binding power. We use a new label since the old terms are not sharp. In this way we find two entirely different worlds; the world of Fido, which is comparatively simple however complex it may appear; and the world of Smith, with its endless series of facts on different levels or orders of abstraction, and corresponding complexity. It is extremely interesting to note that the power of Smith to pass to higher and higher abstractions not only populates his world with endless "facts" on different levels but also gives him means to simplify endlessly his older "facts."
It is important to remember constantly that it is the feeling of the described processes which matters most. The labels are used in three ways; one, as labels, names; the second, to indicate levels; the third, to illustrate the fundamental circularity of human knowledge as indicated by the arrow in the diagram on page 35. Each "characteristic" being one of the highest abstractions man of a certain epoch has produced, or will produce. The present descriptions are far from exhaustive and perhaps even far from satisfactory, but any intelligent reader will be able to amplify this rough sketch.
The higher the order of abstraction, the deeper the level of our analysis, the simpler and more all-embracing the higher abstractions become. The lower abstractions are always made by necessity from a very limited number of observations; they are non-satisfactory in extent; connections are blurred or unknown; generality is impaired, and so the corresponding theories become difficult and in conflict. To teach science to the masses it is perhaps not best to "popularise" something which probably never can be done satisfactorily, but to formulate theories of higher orders of abstractions, on deeper and deeper levels. Such theories would become extremely general, all-embracing and so ultimately very easy to grasp. This might give the man on the street the benefit of modern science.
The above statements run counter to accepted creeds—so much must be granted—but the legitimacy of these creeds has never been investigated. It is an empirical fact in the meantime that the opposite is true, namely, that we all somehow start, and always have, from the latter end (see p. 20 of the G. T.). That mythology precedes science is an empirical fact. On a very low level of development mythology was all that man knew; the troubles began to accumulate when his knowledge began to grow; yet he kept his old mythology, and conflict began. At present we see this conflict becoming more and more acute, and among more advanced races it has come to the point of mental and physical break downs. Man from the dawn of the human era had always had some feelings, some vague notions, about "infinity," "space," "time," "number," etc., and has unconsciously littered his systems with these vague notions and feelings. In the meantime these notions can be made clear only through the application of non-aristotelian methods (mathematical methods) and this has been accomplished with noted success only in our own lifetime. Examples abound everywhere; indeed, they seem so obvious that once stated we can only wonder why we did not discover them long before.


The principle of least action, for instance, as called by Silberstein in his Theory of Relativity the "Variational Principle," originated fundamentally in metaphysical principles that some supernatural rule reveals itself in nature. Leibniz formulated it in the form, that of all the worlds that may be created the actual world is that which contains, besides the unavoidable evil the maximum good. Yet this principle in its mathematical formulation, called also the hamiltonian, principle appears of extreme generality and therefore usefulness; it allows us to derive the fundamental equations of electro-dynamics and electron theory. It has survived the einsteinian revolution, and is one of the invariants of nature, independent of the system of reference of the observers (see Max Planck, A Survey of Physics).
It takes hundreds of pages of Principia Mathematica, for another instance, to establish the proposition that "one and one are two," yet some savages know it; and we begin the education of our children with such advanced knowledge. Somehow it seems easier to start from a very advanced stage of mathematics.
To give more examples. The euclidian system involves several "infinity" assumptions; in it a line has infinite length; the space constant is infinite; and the natural unit of length is also infinite. In the newtonian system the velocity of light is assumed unconsciously to be infinite, which is an assumption false to facts (see Bonola 46ff, 74, 94. Chap. V; Sommerville 58, 162, 203, and Einstein).
The aristotelian system and allied systems are equally belittered with such "infinity" assumptions. It is extremely interesting to note that in the aristotelian systems as well as in the euclidian and newtonian systems the same mechanism exists for the introduction of these different "infinities"; namely, such an "infinity" when introduced in the denominator makes the whole expression vanish. When in life we miss some characteristic entirely it leads to the introduction of "infinity" somewhere. In other words, faulty, insufficient observation leads to the introduction somewhere in our systems of some fanciful "infinities."
Modern progress does not consist only of the discovery of new knowledge but in the clarification of the ideas involved and the elimination of fallacious or unjustified silent unconscious assumptions which have crept into these primitive systems, and vitiated them, through the disregard of facts, facts unknown to the founders of those older systems. We see why the old mythologies are so dangerous. They all disregard facts, and therefore lead directly to false creeds about this world and ourselves, and so must lead to maladjustment with all its serious consequences. It is very characteristic and significant that the non-euclidian and non-newtonian systems elucidate or eliminate some of these undesirable primitive notions, which also permeate the aristotelian systems and therefore the structure of our language, a defect which again the present non-aristotelian system helps to clarify.
The fact that primitive man unconsciously littered his form of representation with these vague or fallacious feelings of "infinity" is due perhaps to the fact that he could not help but feel (not knowing it explicitly) that his power for higher and higher abstractions is unlimited, and he was using this power constantly though he did not clearly understand what he was doing.
It would not be an exaggeration to say that the aristotelian, euclidian and newtonian systems have one most interesting characteristic in common, namely, that they all have a few "infinities" too many. The, modern non-euclidian, non-newtonian and finally non-aristotelian systems, after analysis, eliminate these unjustified notions; new systems arise, quite different from the old ones, which again have this characteristic in common that they have a few "infinities" less, an important characteristic which is especially important in the non-aristotelian system as it helps to clarify our older mythologies. If I am not mistaken the present theory is an example of this.
In my work I deliberately tried to acquaint myself with many more "facts" than the usual generalisations involve (all forms of human behavior, not omitting "insanity," science and mathematics); I tried to give a description of these facts on different and proper levels; then, by deliberately passing to a higher order of abstractions I tried to generalise these "facts." Thus this theory was born.


No one will doubt probably that it is easy and simple to train a child with the A. using an apple or an orange; asking him to tell "all" about it, and then when he has finished his tale to show him experimentally, using the microscope if need be, that he did not say "all," which is an impossibility, because all we know and may know are abstractions of different orders—the word "abstraction" meaning "not all." Having conveyed this to him experimentally it is easy to train him habitually to remember unconsciously, that in the whole series of human "facts," "this is not this, and this is not this," as shown by the A., and so all through. This simple and childish training is the psychological key not only to the understanding of modern science but also ourselves; a key for the unlocking of the tangle of doctrines from which human life is never completely free. This accomplished—and it can always with patience be accomplished—the individual Smith becomes an entirely different person; his whole attitude is changed, in general; most of his difficulties vanish. Modern achievements in science are due to the same psychological attitude, but the modern scientists seldom keep this professional attitude outside of their specialty. Usually in private life and particularly in discussions of human problems the Fido predominates, and so the refute in practice what they ought to know from science. My observation shows me that this is the case practically everywhere, so that trainingwith the A. might be of use even to scientists. Originally I did not think so, but observation has forced me to change that opinion.
It is an historical fact that a few men have contributed more to mankind than others. We call this class "geniuses." Analysing their activities we find that the great majority of them have a peculiar characteristic noticed by Leibniz, a power to see the old anew. This power can be found in most of them. What does it mean? No more and no less than that "geniuses" are freer somehow from Fidoism and preconceived ideas; they mistrust unconsciously the old forms of representation and build up new forms and invent new languages to describe old facts. By using a method by which we can train ourselves to the consciousness that we abstract we build up an unconscious attitude which will help us in "seeing the old anew," the characteristic of those we call "geniuses." In other words training with the A. develops in us the psychology of discovery, which seems useful if we are to be time-binders.
A significant fact should be noticed about the G. T. and the A. One general and simple rule applies to three most fundamental errors, which are more destructive of human endeavors than we have ever dreamed of: the rule is, "This is not this, etc.," as shown on the A., which means that b is not a, and c is not b, and d is not c, and e is not d, and f is not e, and g is not f; which is to say that an object is not an event, that a word is not an object, and a statement about a statement is not the same statement, nor is it on the same level.
It should never be forgotten that the A. conveys also something which it is impossible to convey by words at all, and which is extremely difficult to master habitually. Whenever we use a word we are never on the level of the object but always on the level of the label; to reach the level of the object we must point to it with our finger and be silent. Those critics who burst into speech all the time never succeed in being on the level of the object; and all their activity is on the level of talky-talk which without the A. they hardly realise or can realise. This realisation when acquired makes a rather profound and very subtle difference in attitude, which in the meantime is an exceedingly valuable psychological acquisition, it teaches us to observe. It explains also why the art of criticism is such a difficult one; the majority of critics defend some creed, silent or explicit, instead of making an impartial analysis of the subject in hand, which ought to be always a higher order of abstractions.
If we have not the sense for this inherent stratification of all human knowledge we are entirely unaware of the mixing of our levels, the confusion of orders of abstractions, and so the two fundamental errors arise. One is the mistaking of a label—a word—for an object. This error is very common and usually very difficult to avoid. It is the origin of the savage magic of words. Some call it "hypostatization" or "reification" of the older philosophers; others, like Whitehead, use the term "misplaced concreteness." I call this error "objectification of higher abstractions," it is a confusion of orders of abstractions. I select the common word "object" instead of some other high-sounding word because the error is common; besides, I wish to imply the fact that every objectification is vicious and makes errors habitual, the opposite of which is believed in some academic quarters. The implications of the term used by Whitehead are vicious. His "concreteness," placed or misplaced, is already very abstract, the object itself being already an abstraction of some order, according to modern knowledge, and in my form of representation. The other fundamental error is mixing the orders of abstractions other than the first and the second; it is the origin of other endless fallacies, which often have very tragic consequences. These must be explained briefly.


When Whitehead and Russell were working at the foundations of mathematics they found themselves confronted by a very serious difficulty, namely: they came across endless paradoxes and self-contradictions, which of course would make mathematics impossible. After many efforts they found that all of these paradoxes had one general source, in the rough, in expressions that use the word "all," as, for example, "a proposition about all propositions." They found that such totalities, or such "all," were not legitimate, as they involved a self-contradiction to start with, namely: a proposition cannot be made about all propositions without some restriction since it would have to embrace the very proposition being made. So they had to invent the theory of mathematical types for the purpose of avoiding such fallacies. The theory of types solved the problems of the mathematical paradoxes and self-contradictions. That theory is rather difficult, but at present it is indispensable if we are to have mathematics without self-contradictions. Nevertheless, for reasons that cannot be here given, the theory is somehow distrusted and disliked by most, the authors included. Please note that the G. T. and the A. are built upon "non-allness."
In my researches in Humanology I came across the same difficulties and had somehow to solve them. My solution is given in the G. T. and the A. It is very interesting, instructive and, it seems to me, important to notice that the G. T. and the A. cover also the theory of types. It gives it in a different garb, perhaps one more sympathetic and more effective in form, for the application to daily life and not only to mathematics. It seems that the theory of types, although of purely mathematical origin, has in its new garb the most unusual and constant application to daily life.
As I said above the secret of training with the A. is the childish training to the effect "this is not this, etc."; Fido's "thinking" considers "this is this" and fights and dies for it. To reiterate. A statement about a statement is not the same statement, but is already the product of higher abstraction. From this we see that a proposition about other propositions belongs to a different level of abstractions and should not be put alongside the original set of propositions. The term proposition is such that it can be applied to all levels except the first order of abstractions. The other developments are very similar to the theory of types but cannot be explained in this short paper, and the reader must be referred to the Principia Mathematica (Chapter 11 of the Introduction).
How about the application of it to life? It seems unnecessary to enlarge upon the acknowledged fact that human beings are completely immersed in symbolic dealings with each other and ultimately with themselves, because our habits of speech become parts of our data, and represent already preconceived ideas. What we talk, and how we talk, and our attitudes toward our own and other people's talk, our personal life, community life, national and international life, institutions, customs, habits, etc., depend on what we talk, how we talk, what the other fellow talks, and our attitudes toward these endless talks. How can one revise or correct the statements of himself and others that he might "feel" are somehow wrong, when he himself has not the capacity for clear thinking and does not know the dangers of speech?
The same problems remain perhaps in a more acute form in psychiatry. A baby is born; his parents not only talk over their problems and begin to talk to the baby, but the whole life of the parents, embracing all of their creeds, customs, habits, institutions, taboos and what not, is entirely and thoroughly colored not only by all the talky-talk of all their family, friends, prophets and what not, but also by their attitude toward the talky-talk they are hearing constantly, etc., etc. Of course there is a short cut across this endless tangle, namely: let us assume that a baby is educated in a proper way, has explained to it and is shown the structure of human knowledge, and is trained in the way more or less outlined here. Would it be as easy to wreck his life?
Would it be as, easy to sway him by ignorant doctrines, customs, or slogans? I venture to say, no; he would be immune to the dangers of senseless talky-talk. He would have to think for himself.
IN this short space it is possible to show only one, though most important, application of the A. to the confusion of higher order abstractions, which corresponds to the confusion of types of Russell. Before we make a decision we usually make a more or less hasty survey of happenings, this survey being a foundation for our judgment, which is the base of our action. This statement is fairly general as the elements of it can be found by analysis practically everywhere. Our problem is to clear the general case no matter on what level. Let us follow up roughly the process.
Let us assume a hypothetical case of an ideal observer who would observe correctly and would give an impersonal, unbiased account of what he had observed. Let us assume that he has seen happenings †, ‡, *, ¶ occur, and then a new happening  occurs. He gives a description of the facts in the case, let us say in the form a, b, c, d,........x; and then he makes an inference from facts, or reaches a conclusion, or forms a judgment about these facts. Obviously we are on at least three different and distinct levels of abstraction. We assume further that facts unknown to him, which always exist, are of no importance in this case. Let us assume that his conclusions are correct and the action which this conclusion motivates is proper.
Let us now take another individual Smith, ignorant of what was said here, a politician let us say, who habitually jumps his levels (mixes his orders of abstractions) and rather makes a business out of it. Let us assume that he is observing the "same happenings." What would happen? He would have witnessed the happenings so and so †, ‡, *, ¶, and the new happening would be also a new happening to him. His process would be as follows: the happenings †, ‡, *, ¶, he would describe in the form a, b, c, d, from which he would form a judgment, reach a conclusion B, which means that he would pass to another order of abstractions, another level. When the new happening would occur he would handle it with an already formed opinion B and so his description of the happening  would be colored, and no longer the x of the ideal observer but B(x)=y. His description of "facts" would not be a, b, c, d,........x, of the ideal observer but a, b, c, d,........B(x)=y. Again he would abstract himself to a higher level, form a new judgment about facts a, b, c, d,........B(x)=y, which would be, let us say, C. We see how the trick has been done. The happenings were "the same" yet the unconscious jumping of levels brought finally an entirely different conclusion to motivate a quite different action.
A diagram will make it clearer, as it is very difficult to explain this merely by words. On the A. it is shown without difficulties.
IDEAL OBSERVERSMITH
Seen Happenings,
First order abstractions
†, ‡, *, ¶, . . . 
†, ‡, *, ¶, . . . .
      ..... 
      . . . . 
Description,
Second order abstractions
a, b, c, d,... x

A
a, b, c, d,... B(x)=y

C
Inference, conclusions,
and what not.
Third order abstractions
Creeds

A'

C'
Action

A"

C"

Let us illustrate the foregoing with two clinical cases. In one, a young boy refused persistently to get up in the morning; in another, a boy persistently took money from his mother's pocketbook. In both cases the actions were undesirable. In both cases the parents jumped the levels; they mixed their orders of abstractions. In the first case they concluded that the boy was lazy; in the other, that the boy was a thief. They added these inferences to every new description of facts, so that their new "facts" became more and more distorted and colored, and the actions more and more detrimental to all concerned. The general conditions in the family became worse and worse until a final break-down followed. The psychiatrist dealt with the problems as shown in the diagram of the ideal observer. The net result was that the one boy was not "lazy" nor the other a "thief" but both were ill. After medical attention, of which the first step was to clarify the symbolic situation, though not in such a general way as given here it is true, everything went smoothly. Two families were saved from wreck.
It seems unnecessary to enlarge upon this subject. Every one of us can supply endless examples of this kind from our own observation or experience. Naturally, the generality of our method is a powerful asset and because of its generality it can be given to everybody; it can be taught in homes and schools. It is a preventive method in the millions and millions of cases where human life is wrecked through the lack of a working educational theory concerned with these matters. It is not enough to preach these "platitudes," if one wishes to call them so; they must be practised as well, otherwise the talky-talk and preaching is a farce. If the parents of the boys mentioned above had been trained as children with the A. would the situation have become as acute? For years?
The diagram on p. 44 explains also the difference between this work and other works. Because I understand the G. T. and the A. and have trained myself with it, I am able to avoid the mistakes indicated, on any scale, no matter how large, mistakes which as a matter of record have not been avoided at present, even by scientists.
Let us go to the consideration of orders of abstractions on the A. We naturally are on three levels. On one, the first level, we see with our eyes, let us say; we could give a moving picture of them. We would see what humans do (even writing a book, which is also behavior). In this case we would have to have an ideal moving picture in every conceivable detail. At a second order of abstraction we describe our facts, that they (a) eat, sleep, etc.; (b) cheat, murder, etc.; (c) love, sacrifice, etc.; (d) moralise, philosophise, legislate, etc.; (e) scientifise, mathematise, etc.
What we usually do however is this: we abstract on a higher level facts (a); jump a level; form a conclusion "man is an animal," etc. With this conclusion we jump the level again and color the description of our facts (b), (c), (d), etc., jump again to a higher level, and build conclusions from descriptions (a) and distorted, colored descriptions (b), (c), (d) and so get the prevailing doctrines in all fields, which again lead us in the field of action to the mess we are all in. In this dervish dance between the levels we entirely disregarded facts (e). The ideal observer would observe all facts of human behavior not leaving out facts (e); then without mixing conclusions with descriptions he would reach his higher order of abstractions properly, with very different resultant doctrines, which would again motivate entirely different action. We are able to understand at present why we must constantly revise our doctrines, and why static doctrines (static by intent) must be vicious. The above analysis throws a considerable light on the fact that scientists need training with the A. as much as other mortals (the author included); history shows that they have not officially checked themselves up in this habit of "holy jumpers." In this respect, this work tries to differ from others.
It might appear at first glance that all being said here is simple and easy. On the contrary it is not. In all my studies and experience I have never found anything more difficult. It involves the uprooting of old habits, taboos, philosophies and private doctrines, the worst being our primitive-made aristotelian language, all of which is deeply rooted in us, working unconsciously. Therefore rationalisation, lip-service to the "understanding" of it, will not do whatsoever. Patient and persistent training is the only way to acquire this special sense, the habit for sensing the mixing of orders of abstractions. This sense is difficult to acquire, as difficult perhaps as learning to spell correctly, but when acquired we can never miss the continuous jumping of levels of abstractions, and so utilise it consciously and become immune to its dangers. Most of the important terms apply to all levels, except the first one, a fact impossible to avoid ("ambiguous to type" of Russell), and which makes this special sense uniquely important. It seems needless to repeat that all said here applies in the fullest extent to our social, political, economical and international problems. Before any sanity can be brought into these problems, before they can be rationally analysed at all, the very investigators would have to be trained first to avoid these verbal pitfalls, without which training and re-education older Fido debates on all sides are a waste of time and effort. I say "waste of time" simply because there is no end
 to the paradoxes which, with a little cleverness we can build up when we begin to gamble with the jumping of levels. Any doctrine, no matter how true and beneficial, can be defeated, confused or delayed with the help of such methods. As a fact all of us do this continuously but at present the enormous majority are entirely innocent of this danger with the net result that usually we only sneer at each other. At present I have no doctrines to offer; what I offer and suggest is a method for the beginning of the revision of doctrines, which after years to come might lead to some feasible revisions.
A word of warning will not be amiss. Experience has taught me that the training with the A. and the G. T. are painful and disagreeable for grown-ups. It requires such an amount of persistence and effort, as much as to learn spelling or grammar, that unless a man is unhappy and looking for help I would not attempt to train him. Children as a rule have no difficulties in getting it. They have less to unlearn.
The theory of types was invented by mathematicians to solve their troubles; but in mathematics when a trouble is solved successfully it remains solved, disposed of for good. Not so in human life in general; "troubles" arise continually. The G. T. and the A. help to solve them, and because they deal with life, they are bound to have continuous application in all degrees, wherever human life is.
In the beginning psychiatrists and some mathematicians probably will be first to experiment with the A., the psychiatrists because they will find that with the G. T. and the A. they will be able to unravel that still more general and universally present form of the unconscious which I call the scientific or public unconscious, and which underlies a great many mental troubles. They will find in it methods of education by which to influence surroundings of the patients so often responsible for breakdowns; and methods to deal with equivalent assumptions; and finally a preventive method in general education where to my knowledge there is none at present. The training with the A. and the G. T. should theoretically improve what we call "mentality." It might even help imbeciles and morons; but as yet I have no experimental material in this field. That it helps super-morons I have many examples.
Mathematicians will find perhaps psychological means by which their own subject could be more easily understood and mastered. It is a known fact, little appreciated as yet, that the main difficulties in modern mathematics (the Einstein theory included) are really psychological; the problem is either to find simple yet effective means to train mankind to a new attitude, or else give up the hope for a general understanding. It seems that there is a very close relationship between the systems of Aristotle, Euclid and Newton, on the one hand, and the non-aristotelian, non-euclidian and non-newtonian systems on the other, a problem of very serious importance for mankind which can be analysed only when we come to pay more attention to non-aristotelianism. In a non-aristotelian system we might find a psychology and logic of discovery, to which perhaps the G. T. and the A. may serve as an introduction, and which might stimulate research as well as discovery in mathematics. Modern mathematics has developed to the point where we can expect, with confidence, that the gap between the two ends of the process of elaboration of better and better forms of representation will become bridged.
The methods of training are obvious. First of all the student ought to understand the G. T. Then he should keep the A. before his eyes; look at it; handle the labels and strings, and thus become thoroughly acquainted with it; tentatively explain it to friends and so slowly acquire the habit of it, thus keeping the labels in his pocket, so to say. In this way the consciousness that we abstract, which is the main issue, will become a permanent acquisition. Whenever he hears an argument of any kind, or reads one in the papers, some political speech for example, he should try to apply the A., which means to trace the confusion of orders of abstractions (Fidoism in our language) and the underlying assumptions. Of the confusion of orders of abstractions two at present are the most important; first, the objectification of higher abstractions; second, the reading of inferences into descriptions. If this is done, the student will find abundant material, some of it astonishing enough for further inquiry. It is useful to take actual arguments because after some training with the G. T. and the A. the student may lose the capacity for inventing hypothetical cases. They will seem too stupid to him.
Personally, I have lost this capacity, so that in my work I must depend on the arguments of other people for material.
Literature, the speeches of politicians, lawyers, reformers, propagandists of every description, and family quarrels usually give the best examples of Fidoism. In countries having parliaments a week's proceedings will supply usually enough material for a life time. One may usually get such a record for the asking. After training with such rough material it is useful to pass to scientific controversies in which the same material is found but in a more refined form. In this last case some previous training is necessary since the controversies in science are usually very subtle; but in the main they are of the same character. It should be expected that such analysis of scientific controversies, and the verbal classification of such cases would be a definite contribution to our knowledge. In the old days philosophers amused themselves with writing books on the art of controversy; it is equally amusing to study the reverse—the art of abolishing controversy. Which one is more useful, more human? Which more animalistic? To accelerate our rate of accumulation which makes man a man? Or to diminish that rate? The reader may judge for himself. Such application and explanations should be periodically repeated and applied at every suitable occasion.
When this preliminary training is fairly well advanced and the student has acquired a more or less habitual consciousness that he abstracts, it is time for him to pay attention to the other important points of the theory, which, because they depend on this consciousness that we abstract, will present no difficulty whatsoever. When this full re-education is completed the student will find himself psychologically equipped to understand Einstein and modern science. After Einstein is understood it is extremely useful to read one or two works in which Einstein is attacked, or in which rival theories are propounded. It is only after such work is done that the student will be able to appreciate fully the generality of the G. T.
Einstein's theory has many aspects: some are mathematical, some are physical, some psychological, some methodological, etc.; there is at present a serious confusion in these matters, due in the main to the lack of appreciation of the many aspects this theory represents. Einstein himself stresses the physical side, which may be true or false accordingly to experiment. No "philosophical" generalisation taken from this particular field has any validity or excuse; it leads to the old "relativism" of which Greek children were talking two thousand years ago, and which is shot through with false and vicious implications. That old "relativism" is so different from Einstein's "relativism" that it might better be called by some other name, such as "comparativism," a term suggested to me by H. L. Haywood. The mathematical, psychological, and methodological sides of Einstein's theory are of enormous importance and are independent of experiments in physical and astronomical laboratories; they represent irreversible progress, which mankind has already cashed in, regardless of whether the physical theory proves to be true or false. Here is an endless field for higher abstractions and generalisations and analysis, which mankind has not yet had time to do. The non-technical understanding of Einstein is fundamental to every modern man, perhaps even to every man, but it requires a new psychology, a new theory of knowledge, etc., and the author hopes that he has perhaps scratched the surface of this wide field.
Our world in 1926 is an entirely different world from what it was a few years ago. The problems of human life are problems of adjustment, and to adjust ourselves to anything we men have first to know something about this "something" we have to adjust ourselves to. Happiness is becoming increasingly rare among modern men, and will remain so as long as we persist in applying animal standards to ourselves. Now, such an error has also different levels. Before the error as such is discovered on a higher order of abstractions (deeper level) it is not "error" but "truth," or "fate," or anything we please. It is a necessity. When the error is discovered by a new analysis on a deeper level it ceases to be "truth" or "fate" or "cruel necessity"; it becomes simply error. The problem of compulsion on the older level becomes a problem of preference on the new level. We have two ways open before us (not only one any more); we can select either way we please. If we decide that we like the old miseries and the eventual extinction of the human race let us suit ourselves. It is our pleasure and no more a necessity. If we decide otherwise, again it is our pleasure. In this matter the author has nothing to say except that "necessity," "fate" are bluffs, plain and simple, although we may do whatever we please. What will mankind do? I really do not know. Our Fido ways are so unspeakably deep-
rooted that perhaps our future is hopeless. It is not unknown to scientists that the world is mostly managed by extremely ignorant men, and organised for the survival of the unfit, which of course means ultimately misery and extinction for all.
There is indeed a tremendous power, unrealised as yet in the application of correct symbolism to facts and in the understanding of the structure of human knowledge! Let us take for instance the problem of adjustment. I use, for sake of illustration, a pencil. If we believe (creed, 1000n B. C.) in the "absolute concreteness" of it (whatever this could mean) then of course we deal with fiction; but if we believe (a creed just the same, 1926 A. D.), as explained in the G. T., that the pencil we see and hold in our hands is an abstraction of a certain order which we call the first, then we deal with reality. In the first case we deal with fictions and we cannot adjust ourselves to such a fictitious world and so we may break down. In the second case, we deal with reality; we can adjust ourselves; we do not break down. Psychiatrists will probably be interested in this transformation of different "realities." It is a problem which is intimately connected with mental ills.
Similarly, in parlor conversations we ascribe to the theory of Relativity the principle that "everything is relative"; if we analyse such a statement on a deeper level we come to the conclusion that this statement if true would be an absolute statement. It is important to note that these statements have very little to do with the external world; they reflect in the meantime the structure of human knowledge and so again what is relative on one level might become absolute on another, an instance where the field of human disagreement is diminished and two opposites can be reconciled. The understanding of this mechanism is of great importance in our lives.
THE reader should understand that this work is a limited inquiry, into a limited subject, with limited results. The metaphysician need not become alarmed; as Whitehead has put it, I stop where he begins to become excited. The present work is not a speculation but an inquiry (1926) into the natural history of man as-a-whole, and all his activities. Such an enterprise seems to be novel, and because of that fact naturally it must be full of weak spots which future inquiries will correct or eliminate. In my case I attempt to build deliberately a non-aristotelian system; also I take seriously the preaching of the naturalists about the organism as-a-whole; and the results, whatever their value, are the direct consequence of following both principles all through, they necessitate the rejection of the majority of our pet terms because these are subject-predicate and elementalistic. New terms had to be invented in accord with these principles, or the principles had to be abandoned. The attitude is frankly behavioristic but it is a new behaviorism, different from the classical one, and embraces all forms of human behavior; and therefore mathematics and psychiatry are included. In this case the study of mathematics is of fundamental importance because mathematics can be considered as a prototype of a non-aristotelian system. In this short exposition I take quite a number of informations on the part of the reader for granted, and stress only those points which either have been neglected or which are of unusual importance in this system, so that this inquiry is far from exhaustive.
In closing I wish to draw the attention of the reader to a desideratum, much emphasised of late by the best educators, psychiatrists, neurologists, etc., and all men of experience and wisdom. It might be expressed somehow as follows. The first aim of scientific pedagogy should essentially be the prolongation of the plasticity of childhood, the preservation of mental youth, so to say. It seems to the author that this desideratum is a very serious and useful one, and if only we could do a little in this direction a great deal would thereby be accomplished. It seems that the present theory and the A. give the means to build up such plasticity. The consciousness that we abstract is the psychological key to this plasticity; the fact that all human knowledge is postulational in structure (mathematical) is another important step in this direction. All of this when understood and habitually acquired, affects our unconscious attitudes which are essential for such plasticity. It involves automatically a psychological attitude and philosophy of "as if."
This non-aristotelian theory aims to be very general in its limited field, which happens to be rather wide, and applies to all talky-talk, no matter who does it. I stress the talky-talk; it is a self-imposed limitation to delete the old metaphysics from the problem, as there is no way out with it. The reigning metaphysics are neither true nor false as investigation shows; they are meaningless at bottom and in such a case there is nothing to argue about them, as all such arguments are equally senseless. Words to be words must be symbols, and symbols must stand for something, otherwise they are not symbols but meaningless noises. Meaningless questions are equally not questions at all; they also are mere noises and cannot be answered. Metaphysics indeed is human misbehavior as one of my friends calls it.
The attitude of the writer is neither that of "materialism" nor "idealism" of the old, "materialism" being a hypocritical "idealism"; "idealism" in its turn being some kind of elementalism. Instead of cleaning up a mess I select to start anew, as a matter of economy of time.
If we must label this system, non-aristotelian would probably be the most appropriate. In my Manhood of Humanity and other writings I have already begun an independent non-aristotelian inquiry.
My claims are conservative and often merely suggestive. The grief in such work as this comes from trying to originate a science of man. In this unique subject we all somehow assume that we are experts; we jump to criticism (higher order abstraction!) before we know what we are talking about. No field of human inquiry is equally unpleasant and ungrateful—and seemingly more important. Another great difficulty is found in the fact that, at present, such a non-aristotelian line of inquiry is novel and that therefore I have to work practically unaided. In my experience I have found that many scientists (not all) when they are outside their own field of specialty, are just the same narrow, innocent, blind followers of prejudices and vicious habits of thought as average men: their opinions in such matters are just as little valid. When I say to one of these that I try to establish a "science of man" he usually tells me cordially, "fine enterprise"; but when it comes to face the issues of this "fine enterprise," he often is no more the scientist, his personality splits somehow, and he talks usually as a hurt and naughty baby; quite often he is not willing even to grant to me the most orthodox standards of fairness universally applied in science. Fortunately he who will go through with the training will discover for himself whether my claims are exaggerated. If he will not pay the price he cannot be a competent judge; his judgment could not be fair because the theory is experimental, and talky-talk alone is not enough.
The reader cannot miss that the present work, as well as future similar works where all forms of human behavior will be studied and which will be non-aristotelian in character, will require not only special training but also cannot be classified under any one of the older branches of science, although dealing practically with all of them as forms of human behavior. We had even to look into metaphysics, apply correct symbolism to it to find that it has no meaning, which is the only legitimate statement which can be made about it. The metaphysicians try to speak about the unspeakable, which in parlors is misbehavior, but in life becomes a fraud, it is an attempt to make noises pass for words, which they are not.
My attempt is as yet without academic pigeon hole, academic sanction, chair, or bread and butter, blessed with all academic and non-academic prejudices, all of which is a serious handicap to the author and to future workers. Is it useful? Is it worth while? Is it important? Those who will study it and apply it will know for themselves. I am eager for practical experimental results and would greatly appreciate reports of the same.
Because of the misuse of the term "Human Engineering," I have been compelled to abandon this label and have returned to another name already coined in my Manhood of Humanity, namely, "Humanology."
The material presented here so roughly is being worked out in a book form under the title Time-Binding; The General Theory, An Introduction to Humanology, to be published shortly.

I AM deeply indebted to Professors C. J. Keyser, E. T. Bell and R. D. Carmichael, Doctors W. A. White, H. S. Sullivan, P. S. Graven, and a few other personal friends for their kindness in reading this paper in MS. and for their valuable criticisms and suggestions. I owe much also to Mr. H. L. Haywood for editorial assistance. At the same time, as I need not say, I assume entire responsibility for these pages, especially since I have not always followed the suggestions made.