TIME-BINDING:
The General Theory

BY

ALFRED KORZYBSKI

(Second Paper)

Presented before the Washington Society for Nervous and Mental Diseases,
June 25, 1925; and the Washington Psychopathological Society, March 13, 1926.

WASHINGTON, D. C.
THE PRINTING HOUSE OF JAS. C. WOOD
2021 NICHOLS AVENUE S. E.

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Copyright, 1926 by
ALFRED KORZYBSKI
Warsaw, Poland, and New York City
All international rights reserved.

Printed by The Printing House of Jas. C. Wood
2021 Nichols Avenue S. E., Washington, D. C.

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TIME-BINDING:
The General Theory

BY

ALFRED KORZYBSKI

(SECOND PAPER)

Presented before the Washington Society for Nervous and Mental Diseases,
June 25, 1925; and the Washington Psychopathological Society, March 13, 1926.

 

THE present paper is the outline of a further elaboration of Time-Binding, The General Theory. presented before the International Mathematical Congress of 1924 in Toronto, Canada, to be referred to here as the General Theory (G. T.).

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 in

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1926. 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

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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

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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 individual B 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

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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;

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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

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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

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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 the X 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,

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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

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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

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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

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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

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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 equivalence relatively 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

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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

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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 abstractions indefinitely. 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 human

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medicine, 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 Lobachevski dropped 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.

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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 limited

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experience 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

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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 rep-

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resent 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

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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 un-

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mistakably 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

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"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

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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

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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.

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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

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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 af-

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fected 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 pre-

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dominence 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 ab-

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stractions, 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

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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

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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

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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

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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

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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 mathe-

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matics); 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 conscious-

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ness 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