A Challenge to Modern Logic !

MODERN logic may have begun with Aristotle, but it will not end with him. For 2000 years Aristotle's two-valued system has been so engrooved upon our mind that any other way of thinking is difficult and painful. A fact is either true or false - can there be any other possibility? In a pre-atomic universe perhaps there couldn't, but now we discover uncomfortable moments when a fact may be neither true nor false, but something else. Just as Euclidean physics, which explained nothing, had to yield to Einsteinean physics which once grasped are self-evident, so two-valued logic must yield to three.

The series of articles initiated here by Dr. G�nther, eminent metaphysician, are genuinely trail-blazing. Most of what he offered as the latest word in science is a rehash of stuff old to any conscientious researcher. This material is new, the first new concept in 2000 years of philosophical thinking. Trying it on my hurt like a pair of new shoes but once broken in you will find it more serviceable. And you may never think in alternative values again.

- The Editor

- part 1 of 4 -

You must have wondered what would happen if a terrestrial space-ship, traveling to some distant portion of our galactic universe, were to encounter strange beings with absolutely alien minds. How would the two parties react, and how would they establish communication - if any? We meet people with supposedly "alien" mentality even on this planet. You have only to make a world tour to see the pygmies in equatorial Africa, the Weddas in Ceylon or the Dravidian races in India. But it's easy to talk to a Dravida - if you know Tanil, Kanarese or any other of the Dravidian languages. 

Some people draw the line even closer. I know a Texan for whom all non-Texan inhabitants of the United States are beings with foreign tastes and alien minds. But even a Texan can talk to a New Yorker - if he wants to. And if you want to talk to a Dravida you buy yourself a Kanarese grammar and dictionary. You'll get along somehow. Misunderstandings can be corrected, and are sometimes amusing. I recall once in Italy when I wanted cold water and ordered the waiter to bring me "aqua caldo". He returned with a pot of warm water. I shook my head and repeated: "caldo, caldo!" He brought me steaming water. When I refused again and shouted "caldo" at the top of my lungs I got boiling water. A look in the dictionary told me that "aqua calda" in Italian means warm water. "Cold" is "freddo" (frigid). 

Such mentalities are not alien at all. They produce identical thoughts, but convey them by different languages. Human ideas are the same everywhere on this planet. Only the vocal and written expressions of them are different. That is why we use the general term "man-kind". Man is spiritually of the same kind wherever you find him on this planet. Incidentally, though the modes of expression might differ to a far greater degree than they do among peoples of our world, the mind acting behind the alien system of expression might still be the same as ours. 

Murray Leinster's fine story "First Contact" describes the encounter between a terrestrial spaceship and an alien vessel from unknown regions of our galaxy. The members of that alien crew possessed bodies physiologically unlike our own. They saw by heatwaves, and breathed through gills. Moreover, they were unable to produce vowel and consonant sounds in vocal speech. They communicated instead by frequency-modulation of variable wave lengths. Consequently any "language" communication went directly from brain to brain without the help of any acoustic, tactile, olfactory or visual medium. This poses quite a problem for translation. But as this system of frequency-modulation with variable wave lengths is still a language system - even though of non-terrestrial origin - the problem is simply one of translation and is fundamentally no different from translating Shakespeare into German or Newton into Chinese. Leinster takes care to point out that the intellects behind the two different systems of communication - terrestrial and non-terrestrial - are basically the same. During the attempts to establish communication, Leinster writes, one terrestrial crew member "essayed a mild joke". It had to be translated into code numerals, then into cryptic groups of short-wave, frequency-modulation impulses; these went to the other ship and into heaven-knows-what to become intelligible. A joke which went through such formalities would not seem likely to be funny. But the alien saw the point. There can be no doubt that if people enjoy the same jokes their mentalities must be structurally identical, and only the mode of communication differs. Leinster finds this issue, important enough to bring up again at the end of his story. Before the two spaceships part, an alien reports to his own skipper, "You see, sir, spent those two hours telling dirty jokes". This is fairly profound. Only if two intelligences are akin to each other down to the very root of procreation are they really alike. 

Obviously the aliens in Leinster's story are "alien" in the same way as the Dravidas are to us or a New Yorker is to a Texan. Actually they belong to a larger cosmic concept of man-kind because they are spiritually the same kind as the terrestrial man, and form together with him a greater community of rational life within our universe. This raises the interesting question: May we ever encounter rational intelligences of extraterrestrial origin which do not belong to that greater community of cosmic mankind ? Intelligent beings outside of that community would have a truly alien mind. In such a case more than the system of rational expression and communication would differ. Even the mind activating its language would be different and capable of producing thoughts which mankind never having conceived could never grasp in all the future history of our universe.

Understandably, the author of this article knows no more about the existence of such alien intelligences than anybody else. It is still possible, however, to answer the question of whether theoretically at least, the existence of such alien minds is possible, and, if the answer is affirmative - as it will be - how such a mind must differ from our own. 

To find out whether the existence of genuine alien intelligences (so alien that mere language translation would never establish a common understanding) is theoretically possible, we must first ask the following question: what are the basic conditions of existence for the human mind and all the other hypothetical extraterrestrial minds which follow the same rational system of thinking as we do? The answer is simple: in order to work and to recognize the world intelligently the mind must - in its own structure - repeat the basic properties of general physical existence.

Let me illustrate: if our world contained only the two colors "green" and "blue", and if our retina could react only to the colors "red" and "yellow", then we would not perceive our surroundings at all and would have no conception of what they are really like. In order to obtain true knowledge, our eyes must "repeat" the objective properties blue and green. Let us generalize from this and switch from the specific color situation to the comprehensive relation between general physical existence and the human mind. Everybody knows that the world is made up of matter. If you have more detailed knowledge - and readers of science fiction usually have -then you know that matter consists of elementary particles called protons, electrons, neutrons and positrons. To these, we can add photons, gravitons, neutrinos, and many others. The number of these particles is not important for us. However what is important is that all these particles, and any as yet unknown corpuscles, display three fundamental energetic properties. They carry either:

    • a positive electric charge
    • a negative charge
    • no charge at all.

It stands to reason that if the human mind produces its knowledge by repeating the basic properties of the world around it, it will also repeat in its own brain mechanism the energetic qualities of physical existence. Consequently, our brain is made up of a system of neurons that are equipped for two - and only two reactions a positive and a negative one. Now, don't stop my argument with the objection that if physical existence has three fundamental energy states then the repeating neurons of the human brain should be capable of three reactions. There's a flaw in such reasoning. Our mind is supposed to repeat the basic qualities of physical existence. These qualities are energetic. There are only two definable ones - positive and negative charge - and there is a third electrically undefinable one: no electric quality at all. Manifestly, while our brain can, in its functions, repeat definite qualities, it cannot repeat no quality in any definite way. This is why consciousness judges matter as impenetrable. There is something in matter the mind does not repeat. That is why the metaphysician says that the very core of matter is transcendental. 

Our organic brain repeats in its own functional organization the two active properties of physical existence. That is a first and physical repetition. But if we observe the rational laws according to which our brain works and describe them in a theory of logic we repeat this basic structure of physical existence a second time in one consciousness. We say then: our intelligence works with basic concepts of thought which have two fundamental qualities. They are either positive or negative. True or false. Objective or subjective. Individual or general. These alternatives may be continued endlessly and they are referred to when we say that the human mind uses a two-valued logic. These two values (no matter what you call them) repeat in their turn the "on" and "off"' positions of the neuronic switches in our brain. The latter repeats (as we pointed out before) the positive and negative electric charge of the particles of which our physical world is composed. 

We can see that all rational beings - terrestrial or galactic - must necessarily have the same brain-structure and use the same logic if they face the same universe and are physically composed of the same matter. The two-valued logic which corresponds exactly to the structure of physical existence as we know it, is Aristotelian logic. All rational beings - provided they inhabit our universe - are therefore "Aristotelian" intelligences. If we meet a foreign race, let us say in the neighborhood of the Crab Nebula, the difficulty of translating their language may be technically extreme. Nevertheless, the task will not be impossible because the mind which functions behind any bizarre pattern of language is still the same as our own. It is two-valued and follows precisely the rational laws that govern the terrestrial mind. Our friend from the Crab Nebula may have tentacles and breathe through gills, but his mind will follow Aristotelian patterns just the same. He is, spiritually speaking, the same kind as terrestrial man. The philosophic concept of mankind is not confined to Terra. It comprises all rational beings in a universe that is composed of one single type of physical matter. 

This, however, is but half, the story. There exists a theoretical possibility of contraterrene matter - c/t or, for convenience, "seetee". Contraterrene matter is a state of material existence where the elementary particles have reversed their electrical charges. Electrons which, are known to have a negative charge in terrene matter will carry a positive charge if they belong to seetee matter, and protons would display the properties of negative electricity if they occur contraterrene forms of physical existence. Rational beings living in a seetee world must have a seetee organism and a brain with reversed neuronic reactions. As their logic repeats the functional characteristics of their brain-matter, the thinking of the hypothetical seetee intelligence must be determined by an inverted system of logical values. Where in Aristotelian thought processes the positive logical value is attached to a certain concept, a seetee being must treat the same concept as negative, and where the terrene minds use negations, the being from a contraterrene world will introduce positive terms of thought. The seetee mind is the total contradiction of the terrene mind. It is two-valued too, but it is contra-Aristotelian /1/.

Let us ignore the fantastic physical difficulties of ever meeting seetee intelligences. But if we succeeded in contacting a seetee race, no mere language translator would be adequate. Seetee jokes would not be our jokes, and seetee logical conclusions would not have validity for our mind. In addition to the language translator, we would need an infinitely more intricate gadget - genuine thought translator.

The seetee mind would be based on total reversal of logical values. We are all familiar with a so-called partial reversal of logical values. This is a tacit way of saying that we are all liars when the occasion demands it. In practical the logical values are "true" and "false". In a statement, if I replace the true predicate with its negation, the statement becomes false. Five minutes ago the telephone rang. I did not wish to be interrupted. Since I am able to imitate little girls� voices over the telephone the party at the other end was greeted by a child's voice: "Mister G�nther is not in." This of course was a plain case of lie - pardon me - of reversal logical values. The positive predicate was replaced by its negation "not in".

The being with the contraterrene mind is in relation to us and on truth-conception "the absolute liar". But don't jump to conclusions. It may be relatively true that if you ring the bell and the seetee butler in a seetee world tells you that "Mr. So-and-so is not at home", he is sitting right in his study and expecting you to come in. Such a simple case is exceptional, and your own experience in lying makes simple to find out what is (for you) the true statement. But if things become a little more involved, you will not be able to keep up with the statements of the seetee butler. The reason for this is that we are only partial liars and use only unconnected simple alternatives when we intend to make a false statement. The interrogation technique of the police is based on the fact that we are only capable of incomplete lies. Our statements are always an inextricable mixture of true and false terms and therefore logically inconsistent. The seetee mind, so far as we are concerned, is the complete and consistent "liar". All his statements are - judged by terrene standards - untrue. Truth, however, is more systematic consistency than anything else. It is the total absence of contradictions. The "lies" of a contraterrene intelligence are "true" to a seetee being as long as they do not contain inherent contradictions. They do not deny each other. They simply deny our terrene viewpoint. 

I once discussed this question in a course on formal logic at a New England college. A bright young thing in the classroom said, "Oh, it must be easy to adopt an alien mentality. If I never forget to lie I shall actually be thinking in terms of a non-human intelligence."

"You are mistaken", I said. "The question is not whether or not you forget to lie, but whether you actually know the consistent lie in instance. What, for instance is the exact reversal of logical values in the statement: This color is green? It is �not green' of course. We all know that. But what is �not green�? Is it orange, red, blue, yellow or what? As this case is still very simple I happen to know the right answer which would be given by the �total liar'. It is �This color is purple�. 

This is the only answer which will not involve you in contradictions, but to find it you will have to have very specific knowledge about our color-system. In order to lie about everything consistently you would have to know all about everything. This, however, is the prerogative of the divine mind. To know that purple is the logical opposite of green you need only know enough about one single system - that of color. The task of finding a seetee predicate becomes impossible for any human being if the array of negative predicates that contradict a positive statement is distributed over an unknown number of systems with different semantic characteristics. You want, for instance, to obtain two complete statements - one in terrene and one in contraterrene terms. The array of predicates is as follows:








The defendant is :







not guilty











. . .

. . .

Now the statement: guilty-fat-intelligent Republican, may be the terrene viewpoint. Then it seems that the contraterrene series of predicates is: not guilty-lean-stupid-Democrat /2/. This, however, is a serious mistake. Unless we know all the predicates for the terrene viewpoint we cannot establish a single predicate for the seetee mentality because one as yet unknown terrestrial predicate might cancel out any of the alternatives. Let us assume one of the later predicate, not in the above array, to be "Russian". This would automatically cancel the alternative:



There ain't no such animal in Russia! But as we will never know all the predicates that are implied for a certain sentence by terrene mentality, it is impossible for us to establish even one pertinent predicate that belongs to the contraterrene intelligence. The difficulty is that the series of possible predicates implied by a single statement is infinite, and to find the negation of a whole series you must first negate each predicate individually.

 This is patently impossible. 

It follows that all negations are indefinite and equivocal. This is amusingly illustrated by the famous "proof" of a medieval logician that a cat has three tails. It goes as follows:

No cat has two tails

One cat has one more tail than no cat.

One cat has three tails.

The infinite range of possible negations of a single statement is demonstrated by the fact that you could "prove" your case for any number of tails, because it is equally true that no cat has seven or seven-hundred tails. A similar problem of negation is illustrated by the following anecdote. An irate reporter once wrote: "Half the members of our parliament are imbeciles." He was taken to court and the judge ordered him to publish a retraction of his statement.

He next wrote: "My previous statement is untrue - half the members of our parliament are not imbeciles." 

What I want to emphasize is this: The capacity for logical negations which we possess does not carry us across the immeasurable gulf that exists between an Aristotelian mind and an inverted Aristotelian intelligence. And no other type of alien mentality can possibly exist, in terms of our present understanding of the nature of matter. The seetee mind is the only physical possibility. Its whole range of thoughts would be a total negation of our thoughts. However, we can never reach that hypothetical seetee mind by negation of our thoughts because any negation we perform remains partial and therefore equivocal and indefinite. Our negations simply remain inside our own terrene range of thought. We are not capable of that radical step of total negation which carries across the gulf from the Aristotelian to the contra-Aristotelian mind. No rational being can consciously perform a total negation because in order to perform it the intelligence in question would have to negate not only all its statements, but in addition negate the existence of its own mind. This radical reversal would be meant: suicide.

Total negation, then, is that which not only negates all the contents of a certain mind but also the mind itself. In fact total negation is the logical definition of death. 

Our instinct of self-preservation always prompts us to minimize negation and to split them up into weaker form of negative statements. For instance, restaurant diner orders a cup of coffee without cream. The waiter returns saying, "Sorry, sir, we are out of cream - how about a cup of coffee without milk?" The diner implied that he wanted neither. This is the stronger negation. The waiter split it up into two weaker forms. 

It is absolute death that separates the terrene Aristotelian from the contra Aristotelian seetee mind. The conclusion seems unavoidable that the twin shall never meet. But this issue is not quite settled. The purpose of this article was to demonstrate that no direct contact between such minds is possible. No contact, that is, between a terrene and contraterrene ego in which the Aristotelian self intuitively recognizes the spiritual alter ego of the seetee mind. But what about the mechanical brain as a mediator? This brings us to a technical problem: would it be possible to design a mechanical brain on the basis o a three-valued logic which would contain the Aristotelian and the contra-Aristotelian viewpoint as subordinate terms of a specific robot logic? This necessitates an analysis of the idea of three-valued, non-Aristotelian logic. That will be the subject of my next article "Aristotelian and non-Aristotelian Logic".




/1/ For the idea that personal subjects can only think in two-valued terms I am indebted to John W.   Campbell, Jr.-G.G. to text

/2/ Note: the distribution of the predicates does not reflect the political convictions of the author. to text



G�nther Web

vordenker Contact: [email protected]
Copyright � Gotthard G�nther 1959
Issued: September 2, 1997