General semantics

Just like any other new idea that differs radically from what has gone before, General Semantics has undergone criticism. Because General Semantics has had, up to now, little influence, the criticism had been relatively mild, and the best known version is that of science journalist Martin Gardner, in one of the chapters of his book Fads & Fallacies in the Name of Science. This has been for most observers, and for many still is, a definite demise of General Semantics, and so much so, that it is mentioned at almost every occasion General Semantics itself is mentioned at any length.
     However, the fact that this is so is not due to the substance of the criticism, but to the rhetoric skills of Gardner, as we will presently show. We will follow this with a short analysis of the relevant work of another major critic, Max Black.
    Because of the method of popularized writing used by Gardner, it seemed most appropriate to do the analysis section by section, intertwining the comments (in italics) with the original text.

From: Fads & Fallacies in the Name of Science, by Martin Gardner (Dover publications)

General Semantics, Etc.

After discussing orgonomy and dianetics, a description of any other cult in which psychiatric techniques are prominent is certain to be anticlimactic. Nevertheless, our survey would be incomplete if it did not touch upon the "general semantics" of Polish-born Count Alfred Habdank Skarbek Korzybski, and the "psycho drama" of the Rumanian-born psychiatrist, Jacob L. Moreno. Neither movement, it should be stated, approaches the absurdity of the two previously considered cults. For this reason, general semantics and psychodrama must be regarded as controversial, borderline examples, which may or may not have considerable scientific merit.

If one takes that Gardner's  analysis is a serious, objective, scientific, criticism of the value of General Semantics, this first section also contains the first rhetoric trick: GS is being placed among other theories that are characterized as unscientific and cult-like. This is done in advance of any analysis of its contents.

    Korzybski was born in 1879 in Warsaw. He had little formal education. During World War I, he served as a major in Russia's Polish Army, was badly wounded, and later sent to the United States as an artillery expert. He remained in the States, and for the next ten years drew on his personal fortune to write Science and Sanity, the 800-page Bible of general semantics. The book was published in 1933 by the Count's International Non-Aristotelian Library Publishing Company. It is a poorly organized, verbose, philosophically naive, repetitious mish-mash of sound ideas borrowed from abler scientists and philosophers, mixed with neologisms, confused ideas, unconscious metaphysics, and highly dubious speculations about neurology and psychiatric therapy.

These are all qualifications that have a value only when they refer to the contents of the book, which has not been the case until now - rather, their appropriate place would be in a 'Conclusions' section. At his point, without these references, they are completely baseless and unjustified. Usually such remarks have the effect of creating prejudices in the mind of the reader. Having mentioned these effects, they should instead serve as a warning towards Gardner's prejudgments.
   This is Gardner's second rhetoric trick: putting conclusions before proof.

    Allen Walker Read, in two scholarly articles on the history and various meanings of the word "semantics" (Trans/formation, Vol. 1, Numbers 1 and 2, 1950, 1951), disclosed that the word had not been used in the Count's original draft of Science and Sanity. Before the book was published, however, the word had been adopted by several Polish philosophers, and it was from them that Korzybski borrowed it.
    Most contemporary philosophers who use the word "semantics" restrict it to the study of the meaning of words and other symbols. In contrast, the Count used the word so broadly that it became almost meaningless. As Read points out, Korzybski considered a plant tropism, such as growing up instead of down, a "semantic reaction." In Science and Sanity he discusses a baby who vomited to get a second nursing, and writes, "Vomiting became her semantic way of controlling 'reality.' " Modern followers of the Count tend to equate "semantic" with "evaluative," defining "general semantics" as "the study and improvement of human evaluative processes."

The first attempt at a remark about GS itself. However, the name given to something is, especially when it is something novel, is at best only a vague reflection of what it is, and in no way a reflection of its value.
    Also note that Gardner's introduces his third major rhetoric trick, by changing the way he addresses his subject: the person formerly addressed as "Korzybski" is from now on mostly called "the Count". This is not a change in the objective connotation, which is both cases one and the same person, but in the emotional connotation - the use of an title of nobility is, in the context of an discussion about the scientific writings of the person, has a highly derogatory value.

    Korzybski never tired of knocking over "Aristotelian" habits of thought, in spite of the fact that what he called Aristotelian was a straw structure which bore almost no resemblance to the Greek philosopher's manner of thinking. Actually, the Count had considerable respect for Aristotle (one of the many thinkers to whom his book is dedicated). But he believed that the Greek philosopher's reasoning was badly distorted by verbal habits which were bound up with the Indo-European language structure,¹ especially the subject-predicate form with its emphasis on the word "is." "Isness," the Count once said, "is insanity," apparently without realizing that such concepts as "isomorphic," which he used constantly, cannot be defined without assuming the identity of mathematical structures.

The objections of GS against "is" are centered on the fact that "is" is usually seen as meaning "is identical to", in fact so common a habit that one hardly notices it. Since the inception of GS it has become quite well known that "is identical to" is a concept that is valid only in the realm of mathematics (more correct: formal languages), and invalid in normal language and the real world it describes - in these realms there is only one meaning for "is", which is "is approximately".
    Gardner does not dare to contradict this, because he is quite familiar with the history of mathematics (he also has written books on mathematical puzzles), and knows that these are irrefutable facts. However, he tries to convey the impression that he criticizes GS, and has made a valid criticism. This is a totally false impression.

    Another "Aristotelian" habit against which the Count inveighed is that of thinking in terms of a "two-valued logic" in which statements must be either true or false. No one would deny that many errors of reasoning spring from an attempt to apply an "either/or" logic to situations where it is not applicable, as all logicians from Aristotle onward have recognized. But many of the Count's followers have failed to realize that there is a sense in which the two-valued orientation is inescapable. In all the "multi-valued logics" which have been devised, a deduction within the system is still "true" or "false. To give a simple illustration, let us assume that a man owns a mechanical pencil of a type which comes in only three colors-red, blue, and green: If we are told that his pencil is neither blue nor green, we then conclude that it is red. This would be a "true" deduction within a three-valued system.² It would be "false" to deduce that the pencil was blue, since this would contradict one of the premises. No one has yet succeeded in creating a logic in which the two-valued orientation of true and false could be dispensed with, though of course the dichotomy can be given other names. There is no reason to be ashamed of this fact, and once it is understood, a great deal of general semantic tilting at two-valued logic is seen to be a tilting at a harmless windmill.

The non-existence of a two-valued logic is also one of the cornerstones of GS. However, this statement is meant in the same context as the one on "is-ness": it is non-existent in the real, material, world.  It does exist in the mathematical world, and probably Gardner is even correct in stating that in the mathematical world it cannot be replaced. So Gardner's criticism may be correct in his, mathematical, world, but the rest of us are living in the real world - where GS's statement is correct.

    One finds in Science and Sanity almost no recognition of the fact that the battle against bad linguistic habits of thought had been waged for centuries by philosophers of many schools. The book makes no mention, for example, of John Dewey (except in bibliographies added to later editions), although few modern philosophers fought harder or longer against most of what the Count calls "Aristotelian." In fact, the book casts sly aspersions on almost every contemporary major philosopher except Bertrand Russell.

When one takes a look at the index of 'Science and Sanity', one sees an ample amount of references. However, these reference are to scientists, not to philosophers. The short explanation of this has been given by Wendell Johnson's, cited in Hayakawa's 'Language in Thought and Action', who describes the efforts of the kind of philosophers Gardner refers to as using 'words cut loose from their moorings'. Gardner's claim that there has been a long battle against these linguistic habits seems incorrect, and even if it were correct, this battle has apparently been utterly ineffective, and there is every reason for someone to try anew.
    Even in making this remark, it is still the duty of Gardner to substantiate his criticism, and point to specific omissions Korzybski has made. Not doing so, makes this criticism invalid.

    Korzybski's strong ego drives were obvious to anyone who knew him or read his works carefully. He believed himself one of the world's greatest living thinkers, and regarded Science and Sanity as the third book of an immortal trilogy. The first two were Aristotle's Organon and Bacon's Novum Organum. Like Hubbard, he was convinced that his therapy-would benefit almost every type of neurotic, and was capable of raising the intelligence of most individuals to the level of a genius like himself. He thought that all professions, from law to dentistry, should be placed on a general semantic basis, and that only the spread of his ideas could save the world from destruction. In the preface to the second edition of Science and Sanity, he appealed to readers to urge their respective governments to put into, practice the principles of general semantics, and in the text proper (unchanged in all editions) expressed his belief that ultimately his society would become part of the League of Nations.
    The Count's institute of General Semantics, near the University of Chicago, was established in 1938 with funds provided by a wealthy Chicago manufacturer of bathroom equipment, Cornelius Crane. Its street number, formerly 1232, was changed to 1234 so that when it \Vas followed by "East Fifty-Sixth Street" there would be six numbers in serial order. The Count-a stocky, bald, deep-voiced man who always wore Army-type khaki pants and shirt-conducted his classes in a manner similar to Kay Kyser's TV program. Throughout a lecture, he would pause at dramatic moments and his students would shout in unison, "No!" or "Yes!" or some general semantic term like "Et cetera!" (meaning there are an infinite number of other factors which need not be specified.) Frequently he would remark in his thick Polish accent, "I speak facts," or "Bah - I speak baby stuff." He enjoyed immensely his role of orator and cult leader. So likewise, did his students. In many ways the spread of general semantics resembled the Count's description, on page 800 of Science and Sanity, of "paranoiac-like semantic epidemics" in which followers fall under the spell of a dynamic leader.

This quite large section consists of nothing else but ad hominems: addressing the person instead of his message. As a method of criticism utter bunk, and pointing to ill-faith.

    According to the Count, people are "unsane" when their mental maps of reality are slightly out of correspondence with the real world. If the inner world is too much askew, they become "insane." A principal cause of all this is the Aristotelian mental orientation, which distorts reality. It assumes, for example, that an object is either a chair or not a chair, when clearly there are all kinds of objects which mayor may not be called chairs depending on how you define "chair." But a precise definition is impossible. "Chair" is simply a word we apply to a group of things more or less alike, but which fade off in all directions, along continuums, into other objects which are not called chairs. As H.G. Wells expressed it, in his delightful essay on metaphysics in First and Last Things:
 

The non-Aristotelian mental attitude is, in essence, a recognition of the above elementary fact. There is no such thing as pure "chairishness." There are only chair 1, chair 2, chair 3, et cetera! This assigning of numbers is a process Korzybski called "indexing." In similar fashion, the same chair changes constantly in time. Because of weathering, use, and so forth, it is not the same chair from one moment to the next. We recognize this by the process of "dating." We speak of chair 1952, chair 1953, et cetera! The Count was convinced that the unsane, and many insane, could be helped back to sanity by teaching them to think in these and similar non-Aristotelian ways. For example, a neurotic may hate all mothers. The reason may be that a childhood situation caused him to hate his own mother. Not having broken free of Aristotelian habits, he thinks all mothers are alike because they are all called by the same word. But the word, as Korzybski was fond of repeating, is not the thing. When a man learns to index mothers-that is, call them mother 1, mother 2, mother 3, et cetera - he then perceives that other mothers are not identical with his own mother. In addition, even his mother is not the same mother she was when he was a child. Instead there are mother 1910, mother 1911, mother 1912, et cetera. Understanding all this, the neurotic's hatred for mothers is supposed to diminish greatly.

From the context one must assume that this is meant as criticism. In fact, it is precisely the opposite. The ideas in this section have served as the general ideas behind the psychological therapies named rational-emotive therapy, and cognitive therapy (both have become better known since the 80's, well after the publication of Gardner's book). Both of these therapies try to solve the psychological problems of their clients by looking for corresponding cognitive problems, and treating the latter. The different versions of cognitive therapy are now recognized as the most effective therapies for most of the more common psychological problems. Just this single application of Korzybski's ideas justifies taking his work seriously.

    Of course there is more to the non-Aristotelian orientation than just indexing and dating. To understand levels of abstraction, for example, the Count invented a pedagogical device called the "structural differential." It is a series of small plates with holes punched in them, connected in various ways by strings and pegs. The "Semantic Rosary," as it was called by Time magazine, is impressive to anyone encountering epistemology for the first time.
    Obviously there is nothing "unsane" about the various general semantic devices for teaching good thinking habits. In psychiatry, they may even be useful to doctors of any school when they try to communicate with, or instruct, a patient. But Korzybski and his followers magnified their therapeutic value out of all sane proportions. At conventions, general semanticists have testified to semantic cures of alcoholism, homosexuality, kleptomania, bad reading habits, stuttering, migraine, nymphomania, impotence, and innumerable varieties of other neurotic and psychosomatic ailments. At one conference a dentist reported that teaching general semantics to his patients had given them more emotional stability, which lessened the amount of acid in their mouths. As a consequence, fillings stayed in their teeth longer.
    Korzybski's explanation of why non-Aristotelian thinking has therapeutic body effects, was bound up with a theory now discarded by his followers as neurologically unsound. It concerned the cortex and the thalamus. The cortex was supposed to function when rational thought was taking place, and the thalamus when emotional reflexes were involved. Before acting under the impulse of an emotional response, Korzybski recommended a "semantic pause," a kind of counting-to-ten which gave the cortex time to arrive at an integrated, sane decision. For a person who developed these habits of self-control there was a "neuro-semantic relaxation" of his nervous system, resulting in normal blood pressure, and improved body health.
    It is interesting to note in this connection that a special muscular relaxation technique also was developed by the Count after he observed how often he could ease a student's worried tenseness by such gestures as a friendly grasp of the student's arm. The technique involves gripping various muscles of one's body and shaking them in ways prescribed in The Technique of Semantic Relaxation, by Charlotte Schuchardt, issued by the Institute of General Semantics in 1943.

The phenomenon whereby the creators of a new idea or theory try to apply their idea or theory beyond their boundaries of validity is such a frequent one, that one might even think that it is normal - it is of the same kind as a mother that states that her child is the most beautiful one in the whole world. So even if Gardner's observations were correct, it is in no way an devaluation of the original idea itself. And the idea itself is again absent from Gardner's analysis.  More poignantly: the unreferenced utterances of a dentist are of course completely irrelevant, and the reproduction of them another substantiation of the ill-faith Gardner apparently harbors.

    Modern works of scientific philosophy and psychiatry contain almost no references to the Count's theories. In Russell's technical books, for instance, which deal with topics about which Korzybski considered himself a great authority, you will not find even a passing mention of the Count. This is not because of stubborn prejudice and orthodoxy. The simple reason is that Korzybski made no contributions of significance to any of the fields about which he wrote with such seeming erudition.³ Most of the Count's followers admit this, but insist that the value of his work lies in the fact that it was the first great synthesis of modern scientific philosophy and psychiatry.

As mentioned before, this statement has been overtaken by later developments. This is a regular occurrence with new ideas: the more radical they depart from the known, the longer it takes before they can get any appreciation or foothold.

    But is it? Few philosophers or professional psychiatrists think so. On matters relating to logic, mathematics, science, and epistemology, Science and Sanity is far less successful as a synthesis than scores of modern works. It is more like a haphazard collection of notions drawn from various sources accessible to the Count at the time, and bound together in one volume. Many of the Count's ideas give a false illusion of freshness merely because he invented new terms for them. For example, his earlier book, The Manhood of Humanity, 1921, describes plants as "energy binders," animals as "space binders," and men as "time binders."⁴ When this is translated, it means that plants use energy in growing; animals, unlike plants, are able to move about spatially to meet their needs; and man makes progress in time by building on past experience. All of which would have been regarded by Aristotle as a set of platitudes.
    It is true that Korzybski made a valiant attempt to integrate a philosophy of science with neurology and psychiatry. It is precisely here, however, that his work moves into the realm of cultism and pseudo-science. Teaching a patient general semantics simply does not have, in the opinion of the majority of psychiatrists, the therapeutic value which followers of the Count think it has. Where the Count was sound, he was unoriginal. And where he was original, there are good reasons for thinking him "unsane."

The fourth rhetoric trick: the continuous repetition of unsubstantiated opinions, thereby creating the impression of having given them substance (through the earlier versions). These again are Gardner's opinions and not facts, and where he states a fact, in this section on GS not having practical applications, he has been proven wrong.

    Samuel I. Hayakawa, in many ways a saner and sounder man than the Count, is still waving the banners of general semantics in Chicago, even though he made a break with Korzybski .. shortly before the Count moved his headquarters to Lakeville, Connecticut, in 1946. Hayakawa continues to edit his lively little magazine, Etc.,  ...

If Gardner would have been consistent, this section would have read:
 

Because where Korzybski is a Count, Hayakawa is of Japanese origin (of American birth). Of course his descent is totally  irrelevant - but so is Korzybski's, yet Gardner uses it profusely. Again, this demonstrates the high degree of ill-faith behind Gardner's opinions. His words therefore need only be taken seriously as long as they point to directly observable facts - and there is very little of that in his analysis of GS.

... and work with the International Society of General Semantics, founded in Chicago in 1942 and not connected with the Lakeville group. His Language in Action, 1941 (revised in 1949 as Language in Thought and Action) remains the best of several popular introductions to Korzybski's views. One night in a Chicago jazz spot-Hayakawa is an authority on hot jazz-he was asked what he and the Count had disagreed about. Hayakawa paused a few moments (perhaps to permit a neurological integration of reason and emotion), then said, "Words."

Of course the mutual personal opinions of two of its progenitors is totally irrelevant to the value of their discipline. If this were a valid criticism, one could write off every science known to man. This is the well-known phenomenon of ad hominem again.

    Since the Count's death in 1950, the cult seems to be diminishing in influence. An increasing number of members, including Hayakawa himself, are discovering that almost everything of value in Korzybski's pretentious work can be found better formulated in the writings of others.

The fourth rhetoric trick, again: repeating unsubstantiated opinions.

Then too, many of its recruits from the ranks of science fiction enthusiasts, especially in California, have deserted general semantics for the more exciting cult of dianetics.
    The case of A. E. van Vogt of Los Angeles suggests the new trend. Van Vogt is the author of many popular science-fiction novels of the superman type, including one called The World of A, the action of which involves a future society that has adopted A, or Korzybski's non-Aristotelian orientation. A few years ago, van Vogt was proposing that general semantics go underground on a cellular basis. The United States might have another great depression, he feared, and fall into the hands of the Communists, who do not care for Korzybski's views. He even toyed with the notion of a General Semantic Church, with its own sacred literature, but this idea proved abortive and nothing came of it. At the moment, van Vogt has lost his former enthusiasm for semantics and Dr. Bates' eye exercises. ...

And Gardner ends his "analysis" with some final insults.

Conclusions
Gardner's criticisms of on the substance of GS, are, in order of appearance:
1:  On the use of the verb "is".
2:  On the value of two-valued logic.
3:  On having no real applications.
All these points have been dealt with in the sense that they provide no basis for a negative judgment on the value of General Semantics. 

Martin Gardner has repeated his criticisms of GS in later writings (so much so that it has been described as somewhat of an obsession), in which he also refers, like many other critics, to the writings of the other prominent critic of GS: the philosopher Max Black. In a chapter of his Language and Philosophy: Studies in Method, Black limits himself to the theoretical aspects of GS, which greatly contributes towards the objectivity of his analysis. Black's criticism is here analyzed only in summary, because an extensive review has already been done by Bruce Kodish, see here. 

Black limits his analysis to the contents of Science and Sanity, and divides it into three parts:
1:  Aims and approach
2:  The view of Aristotelianism.
3:  Theory of abstraction.

Point 1 of Black corresponds more or less to Gardner point 3. The central point of GS is that the use of language is highly connected to the working of the human psyche and the resulting working of society, and aims to improve the latter two by improving the former. This places GS high up the ladder of human intellectual effort, on top of disciplines like psychology and sociology, because psychology and sociology use words to convey their theories, i.e. use the field at which GS operates as a tool.
    Having psychology and sociology below it before it can reach lower, more practical, levels, the results of GS are difficult to show, and even more difficult to measure. However, the examples of rational-emotive therapy and cognitive therapy do show this relationship exists. Because these therapies do work, they show that GS works - but however true this is, it remains an indirect result.
    With these remarks in hand, it is easier to read Kodish's analysis of Black, since it ties all of his detailed remarks together.

Point 2 of Black is largely the same as point 2 of Gardner 2. Black and Kodish provide much more detail, but the net result remains almost the same as the much shorter analysis above.

Point 3 of Black can be seen as a much more detailed version of point 1 of Gardner. The fact that the word "is" does work less than ideally, is due to the fact that all words that point to the real world represent only an finite number of aspects of objects in this real world, the process called "abstraction". And since there is no way to check or guarantee that the first abstraction is identical to the second, two things denoted by the same word might not be the same thing: cow 1 need not be cow 2 so the statement "cow is cow" need not be true - in contrast to "A is A" if A is a mathematical object (it could even be used the other way a round: if "A" is identical to "A", then "A" is an abstract, mathematical, object).
    This being so, the "debate" between Black and Kodish provides valuable insight in the intricacies of this process, while proving GS to be largely correct - in such an extend anyway, that it does not distract in any way from its worth as an valuable addition to the description of reality.

All in all the conclusion of Kodish's analysis is that, although Black does operate at a much higher level than Gardner does, at that level he makes comparable mistakes - comparable because careless citing and selective citing from someone else's work, which Kodish show that Black does, are in the field of scientific analysis quite serious errors.

In our conclusions we have up to now concentrated on the arguments on substance. One might think: OK, the arguments as given by Gardner and Black may not have been correctly formulated, but our gut feeling, our intuition, says that GS is wrong, or even something bad - this kind of argument may even be valid at some times. And while it cannot really be refuted and should therefore be discarded if one takes Popper seriously, frequently things do work this way, and some attention has to be paid to it. Luckily, even this part of human thinking lends itself to rationally formulated considerations. Totally within the spirit of GS, we do this by going to the lowest level of this process: its expression in factual statement, for which we choose the total body of arguments given by Gardner and Black against GS. These arguments were shown not only to be incorrect, but also to use incorrect methods, Gardner's case being the easy one, e.g. by his use of numerous ad hominems. This methods are not merely incorrect, they are wrong - they signify negative emotions towards the subject while maintaining a front of being objective, i.e. it is a kind of deceit - or: the honest thing to do is to say: "I do not like this thing". Which leads to the following conclusion: where people stoop to these methods, their intuitions need not to be trusted in any way either.

In search for a cause of these violations of decent reasoning, one may note that frequently, or even usually, these repulsive emotions are caused by a conflict between internal ideas and what comes from outside, as illustrated in the expression: "Why can't they be more like us?", when it is about people. Gardner and Black do not like GS, because it is an idea not like their own. And because it is an idea not like their own, they do not like it, and because they do not like it, they try to find arguments against it. And when you try to find arguments in a certain direction, you are bound to made mistakes, like the one of overlooking arguments that point in another direction. (Note: look carefully at the role the noun "like" plays in this section, and one sees it works like: "to experience a correspondence between what is outside and what is inside", or in even more detail: "to experience a correspondence between what is newly perceived from the outside world and what is already there on the inside based on earlier perceptions")

In the case of Gardner it is not hard to find some clues as to where the ideas of GS differs with his own: first of all is GS critical about the role of mathematics with its absolute two-valued reasoning, and mathematics is one of Gardner's hobby's. Secondly, Gardner is somewhat into religion, as this quote shows. And while GS does not make any statements about religion, this mere fact plus the fact that is an explicit effort to improve upon human nature, a field that religion fervently wants to keep for its own, makes that religiously oriented people will readily see it, consciously or unconsciously, as a threat to their beliefs.

As far as Black is concerned, he is working in a field, philosophy, that GS is highly critical about, and moreover: threatens to take over. Because as stated above: the natural place of GS is above disciplines like psychology and sociology, a place formerly taken by philosophy. The enthusiasm of people from the fields of psychology and sociology will also not be very high, since GS tries to improve on their efforts too, an attitude usually not very much appreciated by the established forces in any discipline.

So the criticisms of the kind of Gardner and Black are no more than is to be expected, and can in fact be considered mild, as demonstrated by the fact that they stem from the forties and fifties. As things stand now, writing in 2007, GS has a quiet little life of its own, and is not disturbed too much by the destructive forces of the established disciplines and their followers. Meanwhile, its offspring in the field of psychology is doing quite well, and one finds some use of the ladder of abstractions in the field of writing and rhetoric. This analysis of the criticisms of Gardner and Black stems from a website that uses General Semantics, and especially the abstraction ladder, to construct a detailed analysis of the relation between human thinking and the workings of society, showing its potentials in this field; see here.

Notes to Gardner:

1. A point of view held chiefly by philologists and cultural anthropologists who like to imagine that their subject-matter (words or culture) underlies logic and mathematics. See "Words, Logic, and Grammar," by H. Sweet, Transactions of the Philological Society, 1876. Because Aristotelian logic rests upon grammatical rules peculiar to the Aryan language. Sweet argues, the "whole fabric of formal logic falls to the ground."

2. Strictly, this is a three-valued logic with two-valued functions. But even in the more exciting multi-valued logics that have multi-valued functions, deductions remain two-valued in the sense that they must be either valid or invalid in terms of the rules of the system.

3. Dr. Ernest Nagel, in a letter to the New Republic, Dec. 26, 1934 (replying to protests against his unfavorable review of Science and Sanity in the Oct. 24 issue), expresses this point as follows:

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