What I tell you three times is true.
– LEWIS CARROLL, The Hunting of the Snark


Chapter 2, "Every Schoolboy Knows . . ." has introduced the reader to a number of basic ideas about the world, elementary propositions or verities with which every serious epistemology or epistemologist must make peace.

In this chapter, I go on to generalizations that are somewhat more complex in that the question which I ask takes the immediate, exoteric form: "What bonus or increment of knowing follows from combining information from two or more sources?"

The reader may take the present chapter and Chapter 5 "Multiple Versions of Relationship" as just two more items which the schoolboy should know. And in fact, in the writing of the book, the heading "Two descriptions are better than one" originally covered all this material. But as the more or less experimental writing of the book went on over about three years, this heading aggregated to itself a very considerable range of sections, and it became evident that the combination of diverse pieces of information defined an approach of very great power to what I call (in Chapter 1) "the pattern which connects." Particular facets of the pattern were brought to my attention by particular ways in which two or more pieces of information could be combined.

In the present chapter, I shall focus on those varieties of combination which would seem to give the perceiving organism information about the world around itself or about itself as a part of that external world (as when the creature sees its own toe). I shall leave for Chapter 5 the more subtle and, indeed, more biological or creatural combinations that would give the perceiver more knowledge of the internal relations and processes called the self.

In every instance, the primary question I shall ask will concern the bonus of understanding which the combination of information affords. The reader is, however, reminded that behind the simple, superficial question there is partly concealed the deeper and perhaps mystical question, "Does the study of this particular case, in which an insight developed from the comparison of sources, throw any light on how the universe is integrated?" My method of procedure will be to ask about the immediate bonus in each case, but my ultimate goal is an inquiry into the larger pattern which connects.



Of all these examples, the simplest but the most profound is the fact that it takes at least two somethings to create a difference. To produce news of difference, i.e., information, there must be two entities (real or imagined) such that the difference between them can be immanent in their mutual relationship; and the whole affair must be such that news of their difference can be represented as a difference inside some information-processing entity, such as a brain or, perhaps, a computer.

There is a profound and unanswerable question about the nature of those "at least two" things that between them generate the difference which becomes information by making a difference. Clearly each alone is – for the mind and perception – a non-entity, a non-being. Not different from being, and not different from non-being. An unknowable, a Ding an sich, a sound of one hand clapping.

The stuff of sensation, then, is a pair of values of some variable, presented over a time to a sense organ whose response depends upon the ratio between the members of the pair. (This matter of the nature of difference will be discussed in detail in Chapter 4, criterion 2.)



Let us consider another simple and familiar case of double description. What is gained by comparing the data collected by one eye with the data collected by the other? Typically, both eyes are aimed at the same region of the surrounding universe, and this might seem to be a wasteful use of the sense organs. But the anatomy indicate that very considerable advantage must accrue from this usage. The innervation of the two retinas and the creation at the optic chiasma of pathways for the redistribution of information is such an extraordinary feat of morphogenesis as must surely denote great evolutionary advantage.

In brief, each retinal surface is a nearly hemispherical cup into which a lens focuses an inverted image of what is being seen. Thus, the image of what is over to the left front will be focused onto the outer side of the right retina and onto the inner side of the left retina. What is surprising is that the innervation of each retina is divided into two systems by a sharp vertical boundary. Thus, the information carried by optic fibers from the outside of the right eye meets, in the right brain, with the information carried by fibers from the inner side of the left eye. Similarly, information from the outside of the left retina and the inside of the right retina is gathered in the left brain.

The binocular image, which appears to be undivided, is in fact a complex synthesis of information from the left front in the right brain and a corresponding synthesis of material from the right front in the left brain. Later these two synthesized aggregates of information are themselves synthesized into a single subjective picture from which all traces of the vertical boundary have disappeared.

From this elaborate arrangement, two sorts of advantage accrue. The seer is able to improve resolution at edges and contrasts; and better able to read when


Figure 4

the print is small or the illumination poor. More important, information about depth is created. In more formal language, the difference between the information provided by the one retina and that provided by the other is itself information of a different logical type. From this new sort of information, the seer adds an extra dimension to seeing.

In Figure 4, let A represent the class or set of components of the aggregate of information obtained from some first source (e.g., the right eye), and let B represent the class of components of the information obtained from some second source (e.g., the left eye). Then AB will represent the class of components referred to by information from both eyes. AB must either contain members or be empty.

If there exist real members of AB, then the information from the second source has imposed a sub-classification upon A that was previously impossible (i.e., has provided, in combination with A, a logical type of information of which the first source alone was incapable).

We now proceed with the search for other cases under this general rubric and shall specifically look in each case for the genesis of information of new logical type out of the juxtaposing of multiple descriptions. In principle, extra "depth" in some metaphoric sense is to be expected whenever the information for the two descriptions is differently collected or differently coded.


Human sense organs can receive only news of difference, and the differences must be coded into events in time (i.e., into changes) in order to be perceptible. Ordinary static differences that remain constant for more than a few seconds become perceptible, only by scanning. Similarly, very slow changes become perceptible only by a combination of scanning and bringing together observations from separated moments in the continuum of time.

An elegant (i.e., an economical) example of these principles is provided by the device used by Clyde William Tombaugh, who in 1930, while still a graduate student, discovered the planet Pluto.

From calculations based on disturbances in the orbit of Neptune it seemed that these irregularities could be explained by gravitational pull from some planet in an orbit outside the orbit of Neptune. The calculations indicated in what region of the sky the new planet could be expected at a given time.

The Object to be looked for would certainly be very small and dim (about 15th magnitude), and its appearance would differ from that of other objects in the sky only in the fact of very slow movement, so slow as to be quite imperceptible to the human eye.

This problem was solved by the use of an instrument which astronomers call a blinker. Photographs of appropriate region of the sky were taken at longish intervals. These photographs were then studied in pairs in the blinker. This instrument is the converse of a binocular microscope; instead of two eyepieces and one stage, it has one eyepiece and two stages and is so arranged that by the flick of a lever, what is seen at one moment on one stage can be replaced by a view of the other stage. Two photographs are placed in exact register on the two stages so that all the ordinary fixed stars precisely coincide. Then, when the lever is flicked over, the fixed stars will not appear to move, but a planet will appear to jump from one position to another. There were, however, many jumping objects (asteroids) in the field of the photographs, and Tombaugh had to find one that jumped less than the others.

After hundreds of such comparisons, Tombaugh saw Pluto jump.



Synaptic summation is the technical term used in neurophysiology for those instances in which some neuron C is fired only by a combination of neurons A and B. A alone is insufficient to fire C, and B alone is insufficient to fire C; but if neurons A and B fire together within a limited period of microseconds, then C is triggered (see Figure 5). Notice that the conventional term for this phenomenon, summation, would suggest an adding of information from one source to information from another. What actually happens is not an adding but a forming of a logical product, a process more closely akin to multiplication.

Figure 5

What this arrangement does to the information that neuron A alone could give is a segmentation or sub-classification of the firings of A into two classes, namely, those firings of A accompanied by B and those firings of A which are not accompanied by B. Correspondingly, the firings of neuron B are subdivided into two classes, those accompanied by A and those not accompanied by A.


Macbeth is about to murder Duncan, and in horror at his deed, he hallucinates a dagger (Act II, scene I).

Is this a dagger which I see before me,
The handle toward my hand? Come, let me clutch thee.
I have thee not, and yet see thee still.
Art thou not, fatal vision, sensible
To feeling as to sight? Or art thou but
A dagger of the mind, a false creation,
Proceeding form the heat-oppressed brain?
I see thee yet, in form as palpable
As this which now I draw.
Thou marchall’st me the way that I was going;
And such an instrument I was to use.
Mine eyes are made the fools o’ the other senses,
Or else worth all the rest: I see thee still;
And on thy blade and dudgeon gouts of blood,
Which was not so before. There’s no such thing:
It is the bloody business which informs
Thus to mine eyes.

This literary example will serve for all those cases of double description in which data from two or more different senses are combined. Macbeth "proves" that the dagger is only an hallucination by checking with his sense of touch, but even that is not enough. Perhaps his eyes are "worth all the rest." It is only when "gouts of blood" appear on the hallucinated dagger that he can dismiss the whole matter: "There’s no such thing."

Comparison of information form one sense with information from another, combined with change in the hallucination, has offered Macbeth the metainformation that his experience was imaginary. In terms of Figure 4, AB was an empty set.



In many cases, an increment of insight is provided by a second language of description without the addition of any extra so-called objective information. Two proofs of a given mathematical theorem may combine to give the student an extra grasp of the relation which is being demonstrated.

Every schoolboy knows that (a + b)2 = a2 + 2ab + b2, and he may be aware that this algebraic equation is a first step in a massive branch of mathematics called binominal theory. The equation itself is sufficiently demonstrated by the algorithm of algebraic multiplication, each step of which is in accord with the definitions and postulates of the tautology called algebra – that whose subject matter is the expansion and analysis of the notion "any."

But many schoolboys do not know that there is a geometric demonstration of the same binomial expansion (see Figure 6). Consider the straight line XY, and let this line be composed of two segments, a and b. The line is now a geometric representation of (a + b) and the square constructed upon XY will be (a + b)2; that is, it will have an area called "(a + b)2."

This square can now be dissected by marking off 




the length a along the line XY and along one of the adjacent sides of the square. The schoolboy can now think that he sees that the square is cut up into four pieces. There are two squares, one of which is a2 while the other is b2, and two rectangles, each of which is of area (a x b) (i.e., 2ab).

Thus, the familiar algebraic equation (a + b)2 = a2 + 2ab + b2 also seems to be true in Euclidean geometry. But surely it was too much to hope for that the separate pieces of the quantity a2 + 2ab + b2 would still be neatly separate in the geometric translation.

But what has been said? By what right did we substitute a so-called "length" for a and another for b and assume that, placed end to end, they would make a straight line (a + b) and so on? Are we sure that the lengths of lines obey arithmetic rules? What has the schoolboy learned form our stating the same old equation in a new language?

In a certain sense, nothing has been added. No new information has been generated or captured by my asserting that (a + b)2 = a2 + 2ab + b2 in geometry as well as in algebra.

Does a language, then, as such, contain no information?

But even if, mathematically, nothing has been added by the little mathematical conjuring trick, I still believe that the schoolboy who has never seen that the trick could be played will have a chance to learn something when the trick is shown. There is a contribution to didactic method. The discovery (if it be discovery) that the two languages (of algebra and of geometry) are mutually translatable is itself an enlightenment.

Another mathematical example may help the reader to assimilate the effect of using two languages.*

Ask your friends, "What is the sum of the first ten odd numbers?"

The answers will probably be statements of ignorance or attempts to add up the series:

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

Show them that:

The sum of the first odd number is 1.
The sum of the first two odd numbers is 4.
The sum of the first three odd numbers is 9.
The sum of the first four odd numbers is 16.
The sum of the first five odd numbers is 25.

And so on.

Rather soon, your friends will say something like, "Oh, then the sum of the first ten odd numbers must be 100." They have learned the trick for adding series of odd numbers.

But ask for an explanation of why this trick must work and the average nonmathematician will be unable to answer. (And the state of elementary education is such that many will have no idea of how to proceed in order to create an answer.)

What has to be discovered is the difference between the ordinal name of the given odd number and its cardinal value – a difference in a logical type! We are accustomed to expect that the name of a numeral will be the same as its numerical value.*2 But indeed, in this case, the name is not the same as the thing named.

For example, the sum of the first five odd numbers minus the sum of first four odd numbers must equal 52 – 42. At the same time, we must notice that, of course, the difference between the two sums is indeed the odd number that was last added to the stack. In other words, this last added number must be equal to the difference between the squares.

Consider the same matter in a visual language. We have to demonstrate that the next odd number will always add to the sum of the previous odd numbers just enough to make the next total square of the ordinal name of that odd number.

Represent the first odd number (1) with a unit square:


Represent the second odd number (3) with three unit squares:


Add the two figures together:

1 + 3 = 4

Represent the third odd number (5) with five unit squares:


Add this to the previous figure:

1 + 3 + 5 = 9

Figure 7

That is, 4 + 5 = 9.

And so on. The visual presentation makes it rather easy to combine ordinals, cardinals, and the regularities of summing the series.

What has happened is that the use of a system of geometric metaphor has enormously facilitated understanding of how the mechanical trick comes to be a rule or regularity. More important, the student has been made aware of the contrast between applying a trick and understanding the necessity of truth behind the trick. And still more important, the student has, perhaps unwittingly, had the experience of the leap from talking arithmetic to talking about arithmetic, Not numbers but numbers of numbers.

It was then, in Wallace Steven’s words,

That the grapes seemed fatter.
The fox ran out of his hole.



Von Neumann once remarked, partly in jest, that for self-replication among machines, it would be a necessary condition that two machines should act in collaboration.

Fission with replication is certainly a basic requirement of life, whether it be fore multiplication or for growth, and the biochemists now know broadly the process of replication of DNA. But next comes differentiation, whether it be the (surely) random generation of variety in evolution or the ordered differentiation of embryology. Fission, seemingly, must be punctuated by fusion, a general truth with exemplifies the principle of information processing we are considering here: namely that two sources of information (often in contrasting modes or languages) are enormously better than one.

At the bacterial level and even among protozoa and some fungi and algae, the gametes remain superficially identical; but in all metazoa and plants above the fungal level, the sexes of the gametes are distinguishable one from the other.

The binary differentiation of gametes, usually one sessile and one mobile, comes first. Following this comes the differentiation into two kinds of the multicellular individuals who are the producers of the two kinds of gametes.

Finally, there are the more complex cycles called alternation of generations in many plants and animal parasites.

All these orders of differentiation are surely related to the informational economics of fission, fusion and sexual dimorphism.

So, returning to the most primitive fission and fusion, we note that the first effect or contribution of fusion to the economics of genetic information is presumably some sort of checking.

The process of chromosomal fusion is essentially the same in all plants and animals, and wherever it occurs, the corresponding strings of DNA material are set side by side and, in a functional sense, are compared. If differences between the strings of material from the respective gametes are too great, fertilization (so called) cannot occur.*3

In the total process of evolution, fusion, which is the central fact of sex, has the function of limiting genetic variability. Gametes that, for whatever reason, be it mutation or other, are too different from the statistical norm are likely to meet in sexual fusion with more normal gametes of opposite sex, and in this meeting, the extremes of deviation will be eliminated. (Note, in passing, that this need to eliminate deviation is likely to be imperfectly met in "incestuous" mating between gametes from closely related sources.)

But although one important function of the fusion of gametes in sexual reproduction would seem to be the limitation of deviance, it is also necessary to stress the contrary function: increasing phenotypic variety. The fusion of random pairs of gametes assures that the gene pool of the participating population will be homogeneous in the sense of being well mixed. At the same time, it assures that every viable genic combination within that pool shall be created. That is, every viable gene is tested in conjunction with as many other constellations of other genes as is possible within the limits of the participating population.

As usual in the panorama of evolution, we find that the single process is Janus-like, facing in two directions. In the present case, the fusion of gametes both places a limitation on individual deviance and ensures the multiple recombination of genetic material.


Interesting phenomena occur when two or more rhythmic patterns are combined, and these phenomena illustrate very aptly the enrichment of information that occurs when one description is combined with another. In the case of rhythmic patterns, the combination of two such patterns will generate a third. Therefore, it becomes possible to investigate an unfamiliar pattern by combining it with a known second pattern and inspecting the third pattern which they together generate.

The simplest case of what I am calling the moiré phenomenon is the well-known production of beats when two sounds of different frequency are combined. The phenomenon is explained by mapping onto simple arithmetic, according to the rule that if one note produces a peak in every n time units and the other has a peak in every m time units, then the combination will produce a beat in every m x n units when the peaks coincide. The combination has obvious uses in piano tuning. Similarly, it is possible to combine two sounds of very high frequency in order to produce beats of frequency low enough to be heard by the human ear. Sonar devices that operate on this principle are now available for the blind. A beam of high-frequency sound is emitted, and the echoes that this beam generates are received back into an "ear" in which a lower but still inaudible frequency is being generated. The resulting beats are then passed on to the human ear.

The matter becomes more complex when the rhythmic patterns, instead of being limited, as frequency is, to the single dimension of time, exist in two or more dimensions. In such cases, the result of combining the two patterns may be surprising.

Three principles are illustrated by these moiré phenomena: First, any two patterns may, if appropriately combined, generate a third. Second, any two of these three patterns could serve as base for a description of the third. Third, the whole problem of defining what is meant by the word pattern can be approached through these phenomena. Do we, in fact, carry around with us (like the blind person's sonar) samples of information (news of regular differences) that comes in from outside? Do we, for example, use our habits of what is called "dependency" to test the characteristics of other persons?

Do animals (and even plants) have characteristics such that in a given niche there is a testing of that niche by something like the moiré phenomenon?

Other questions arise regarding the nature of aesthetic experience. Poetry, dance, music, and other rhythmic phenomena are certainly very archaic and probably more ancient than prose. It is, moreover, characteristic of the archaic behaviors and perceptions that rhythm is continually modulated; that is, the poetry or music contains materials that could be processed by superposing comparison by any receiving organism with a few seconds of memory.

Is it possible that this worldwide artistic, poetical, and musical phenomenon is somehow related to moiré? If so, then the individual mind is surely deeply organized in ways which a consideration of moiré phenomena will help us to understand. In terms of the definition of "explanation" proposed in section 9, we shall say that the formal mathematics or "logic" of moiré may provide an appropriate tautology onto which these aesthetic phenomena could be mapped.



Among human beings, description and explanation are both highly valued, but this example of doubled information differs from most of the other cases offered in this chapter in that explanation contains no new information different from what was present in the description. Indeed, a great deal of the information that was present in description is commonly thrown away, and only a rather small part of what was to be explained is, in fact, explained. But explanation is certainly of enormous importance and certainly seems to give a bonus of insight over and above what was contained in description. Is the bonus of insight which explanation gives somehow related to what we got from combining two languages in section 6, above?

To examine this case, it is necessary first briefly to indicate definitions for the three words: description, tautology, and explanation.

A pure description would include all the facts (i.e., all the effective differences) immanent in the phenomena to be described but would indicate no kind of connection among these phenomena that might make them more understandable. For example, a film with sound and perhaps recordings of smell and other sense data might constitute a complete or sufficient description of what happened in front of a battery of cameras at a certain time. But that film will do little to connect the events shown on the screen one with another and will not by itself furnish any explanation. On the other hand, an explanation can be total without being descriptive. "God made everything there is" is totally explanatory but does not tell you anything about any of the things or their relations.

In science, these two types of organization of data (description and explanation) are connected by what is technically called tautology. Examples of tautology range from the simplest case, the assertion that "If P is true, then P is true," to such elaborate structures as the geometry of Euclid, where "If the axioms and postulates are true, then Pythagoras' theorem is true." Another example would be the axioms, definitions, postulates, and theorems of Von Neumann's Theory of Games. In such an aggregate of postulates and axioms and theorems, it is of course not claimed that any of the axioms or theorems is in any sense "true" independently or true in the outside world.

Indeed, Von Neumann, in his famous book,*4 expressly points out the differences between his tautological world and the more complex would of human relations. All that is claimed is that if the axioms be such and such and the postulates such and such, then the theorems will be so and so. In others words, all that the tautology affords is connections between propositions. The creator of the tautology stakes his reputation on the validity of these connections.

Tautology contains no information whatsoever, and explanation (the mapping of description onto tautology) contains only the information that was present in the description. The "mapping" asserts implicitly that the links which hold the tautology together correspond to relations which obtain in the description. Description, on the other hand, contains information but no logic and no explanation. For some reason, human beings enormously value this combining of ways of organizing information or material.

To illustrate how description, tautology, and explanation fit together, let me cite an assignment which I have given several times to classes. I am indebted to the astronomer Jeff Scargle for this problem, but I am responsible for the solution. The problem is:

A man is shaving with his razor in his right had. He looks into his mirror and in the mirror sees his image shaving with its left hand. He says, "Oh. There's been a reversal of right and left. Why is there no reversal of top and bottom?"

The problem was presented to the students in this form, and they were asked to unravel the muddle in which the man evidently is and to discuss the nature of explanation after they have accomplished this.

There are at least two twists in the problem as set. One gimmick distracts the student to focus on the right and left. In fact, what has been reversed is front and back, not right and left. But there is a more subtle trouble behind that, namely, that the words right and left are not in the same language as the words top and bottom. Right and left are words of an inner language; whereas top and bottom are parts of an external language. If the man is looking south and his image is looking north, the top is upward in himself and is upward in his image. His east side is on the east side in the image, and his west side is on the west side in the image. East and west are in the same language as top and bottom; whereas right and left are in different language. There is thus a logical trap in the problem as set.

It is necessary to understand that right and left cannot be defined and that you will meet with a lot of trouble if you try to define such words. If you go to the Oxford English Dictionary, you will find that left is defined as "distinctive epithet of the hand which is normally the weaker." The dictionary maker openly shows his embarrassment. If you go to Webster, you will find a more useful definition, but the author cheats. One of the rules of writing a dictionary is that you can not rely on ostensive communication for your main definition. So the problem is to define left without pointing to an asymmetrical object. Webster (1959) says, "that side of one's body which is toward the west when one faces north, usually the side of the less-used hand." This is using the asymmetry of the spinning earth.

In truth, the definition cannot be done without cheating. Asymmetry is easy to define, but there are no verbal means – and there can be none – for indicating which of two (mirror-image) halves is intended.

An explanation has to provide something more than a description provides and, in the end, an explanation appeals to a tautology, which, as I have defined it, is a body of propositions so linked together that the links between the propositions are necessarily valid.

The simplest tautology is "If P is true, then P is true."

A more complex tautology would be "If Q follows from P, then Q follows from P." From there, you can build up into whatever complexity you like. But you are still within the domain of the if clause provided, not by data, but by you. That is a tautology.

Now, an explanation is a mapping of the pieces of a description onto a tautology, and an explanation becomes acceptable to the degree that you are willing and able to accept the links of the tautology. If the links are "self-evident" (i.e., if they seem undoubtable to the self that is you), then the explanation built on that tautology is satisfactory to you. That is all. It is always a matter of natural history, a matter of the faith, imagination, trust, rigidity, and so on of the organism, that is of you or me.

Let us consider what sort of tautology will serve as a foundation for our description of mirror images and their asymmetry.

Your right hand is an asymmetrical, three-dimensional object; and to define it, you require information that will link at least three polarities. To make it different from a left hand, three binary descriptive clauses must be fixed. Direction toward the palm must be distinguished form direction toward the back of the hand; direction toward the elbow must be distinguished from direction toward the fingertips; direction toward the thumb must be distinguished from direction toward the fifth finger. Now build the tautology to assert that a reversal of any one of these three binary descriptive propositions will create the mirror image (the stereo-opposite) of the hand form which we started (i.e., will create a "left" hand).

If you place your hands palm to palm so that the right palm faces north, the left will face south, and you will get a case similar to that of the man shaving.

Now, the central postulate of our tautology is that reversal in one dimension always generates the stereo-opposite. From this postulate, it follows – can you doubt it? – that reversal in two dimensions will generate the opposite of the opposite (i.e., will take us back to the form from which we started). Reversal in three dimensions will again generate the stereo-opposite. And so on.

We now flesh out our explanation by the process which the American logician, C. S. Peirce called abduction, that is, by finding other relevant phenomena and arguing that these, too, are cases under our rule and can be mapped onto the same tautology.

Imagine that you are an old-fashioned photographer with a black cloth over your head. You look into your camera at the ground-glass screen on which you see the face of the man whose portrait you are making. The lens is between the ground-glass screen and the subject.

On the screen, you will see the image upside down and right for left but still facing you. If the subject is holding something in his right hand, he will still be holding it in his right hand on the screen but rotated 180 degrees.

If now you make a hole in the front of the camera and look in at the image formed on the ground-glass screen or on the film, the top of his head will be at the bottom. His chin will be at the top. His left will be over to the right side, and now he is facing himself. You have reversed three dimensions. So now you see again his stereo-opposite.

Explanation, then, consists in building a tautology, ensuring as best as you can the validity of the links in the tautology so that it seems to you to be self-evident, which is in the end never totally satisfactory because nobody knows what will be discovered later.

If explanation is as I have described it, we may well wonder what bonus human beings get from achieving such a cumbersome and indeed seemingly unprofitable rigamarole.

This is a question of natural history, and I believe that the problem is at least partly solved when we observe that human beings are very careless in their construction of the tautologies on which to base their explanation. In such a case, one would suppose that the bonus would be negative; but this seems not to be so, judging by the popularity of explanations which are so informal as to be misleading. A common form of empty explanation is the appeal to what I have called "dormitive principles", borrowing the word dormitive from Molière. There is a coda in dog Latin to Molière’s Le Malade Imaginaire, and in this coda, we se on the stage a medieval oral doctoral examination. The examiners ask the candidate why opium puts people to sleep. The candidate triumphantly answers, "Because, learned doctors, it contains a dormitive principle."

We can imagine the candidate spending the rest of his life fractionating opium in a biochemistry lab and successively identifying in which fraction the so-called dormitive principle remained.

A better answer to the doctors’ question would involve, not the opium alone, but a relationship between the opium and the people. In other words, the dormitive explanation actually falsifies the true facts of the case but what is, I believe, important is that dormitive explanations still permit abduction. Having enunciated a generality that opium contains a dormitive principle, it is then possible to use this type of phrasing for a very large number of other phenomena. We can say, for example, that adrenalin contains an enlivening principle and reserpine a tranquilizing principle. This will give us, albeit inaccurately and epistemologically unacceptably, handles with which to grab at a very large number of phenomena that appear to be formally comparable. And, indeed, they are formally comparable to this extent, that invoking a principle inside one component is in fact the error that is made in every one of these cases.

The fact remains that as a matter of natural history – and we are as interested in natural history as we are in strict epistemology – abduction is a great comfort to people, and formal explanation is often a bore. "Man thinks in two kinds of terms: one, the natural terms, shared with beasts; the other, the conventinal terms (the logicals) enjoyed by man alone." *5

This chapter has examined various ways in which the combining of information of different sorts or from different sources results in something more than addition. The aggregate is greater than the sum of its parts because the combining of the parts is not a simple adding but is of the nature of a multiplication or a fractionation, or the creation of a logical product. A momentary gleam of enlightenment.

So to complete this chapter and before attempting even a listing of the criteria of mental process, it is appropriate to look briefly at this structure in a much more personal and more universal way.

I have consistently held my language to an "intellectual" or "objective" mode, and this mode is convenient for many purposes (only to be avoided when used to avoid recognition of the observer’s bias and stance).

To put away the quasi objective, at least in part, is not difficult, and such a change in mode is proposed by such question as: What is this book about? What is its personal meaning to me? What am I trying to say or to discover?

The question "What am I trying to discover?" is not as unanswerable as mystics would have us believe. From the manner of the search, we can read what sort of discovery the searcher may thereby reach; and knowing this, we may suspect that such a discovery is what the searcher secretly and unconsciously desires.

This chapter has defined and exemplified a manner of search, and therefore this is the moment to raise two questions: For what am I searching? To what questions have fifty years of science led me?

The manner of the search is plain to me and might be called the method of double or multiple comparison.

Consider the case of binocular vision. I compared what could be seen with one eye with what could be seen with two eyes and noted that in this comparison the two-eyed method of seeing disclosed an extra dimension called depth. But the two-eyed way of seeing is itself an act of comparison. In other words, the chapter has been a series of comparative studies of the comparative method. The section on binocular vision (section 2) was such a comparative studies of one method of comparison, and the section on catching Pluto (section 3) was another comparative study of the comparative method. Thus the whole chapter, in which such instances are placed side by side, became a display inviting the reader to achieve insight by comparing the instances one with another.

Finally, all that comparing of comparisons was built up to prepare author and reader of thought about problems of Natural Mind. There, too, we shall encounter creative comparison. It is the Platonic thesis of the book that epistemology is an indivisible, integrated meta-science whose subject matter is the world of evolution, thought, adaptation, embryology, and genetics – the science of mind in the widest sense of the word.*6

The comparing of these phenomena (comparing thought with evolution and epigenesis with both) is the manner of search of the science called "epistemology."

Or, in the phrasing of this chapter, we may say that epistemology is the bonus from combining insights form all these separate genetic sciences.

But epistemology is always and inevitably personal. The point of the probe is always in the heart of the explorer: What is my answer to the question of the nature of knowing? I surrender to the belief that my knowing is a small part of a wider integrated knowing that knits the entire biosphere or creation.

* I am indebted to Gertrude Hendrix for this, to most people, unfamiliar regularity: Gertrude Hendrix, "Learning by Discovery," The Mathematics Teacher 54 (May 1961): 290-299. [Back to text]

*2 Alternatively, we may say that the number of numbers in a set is not the same as the sum of numbers in the same set. One way or the other, we encounter a discontinuity in logical typing. [Back to text]

*3 I believe that this was first argued by C.P. Martin in his Psychology, Evolution and Sex, 1956. Samuel Butler (in More Notebooks of Samuel Butler, edited by Festing Jones) made a similar point in discussion parthenogenesis. He argues that as dreams are to thought, so parthenogenesis is to sexual reproduction. Thought is stabilized and tested against the template of external reality, but dreams run loose. Similarly, parthenogenesis can be expected to run loose; whereas zygote formation is stabilized by the mutual comparison of gametes. [Back to text]

*4 Von Neumann, J., and Morgenstern, O., The Theory of Games and Economic Behavior (Princeton: Princeton University Press, 1944.) [Back to text]

*5 William of Ockham, 1280-1349, quoted by Warren McCulloch in his Embodiments of Mind, M.I.T. Press, 1965. [Back to text]

*6 The reader will perhaps notice that consciousness is missing from this list. I prefer to use that word, not as a general term, but specifically for that strange experience whereby we (and perhaps other mammals) are sometimes conscious of the products of our perception and thought but unconscious of the greater part of the processes. [Back to text]


II     Every Schoolboy Knows …

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