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1.6. EMPTY TERMS

Classes in logic are not only represented by circles with a hard firm outline, whereas in fact they have no such definite limits, but also there is a constant disposition to think of all names as if they represented positive classes. With words just as with numbers and abstract forms there have been definite phases of human development. There was with regard to number, the phase when man could barely count at all, or counted in perfect good faith and sanity upon his fingers. Then there was the phase when he struggled with the development of number, when he began to elaborate all sorts of ideas about numbers, until at last he developed complex superstitions about perfect numbers and imperfect numbers, about threes and sevens and the like. The same was the case with abstract forms; and even to-day we are scarcely more than heads out of the vast subtle muddle of thinking about spheres and ideally perfect forms and so on, that was the price of this little necessary step to clear thinking. How large a part numerical and geometrical magic, numerical and geometrical philosophy have played in the history of the mind! And the whole apparatus of language and mental communication is beset with like dangers. The language of the savage is I suppose purely positive; the thing has a name, the name has a thing. This indeed is the tradition of language, and even to-day, we, when we hear a name are predisposed – and sometimes it is a very vicious disposition – to imagine forthwith something answering to the name. WE ARE DISPOSED, AS AN INCURABLE MENTAL VICE, TO ACCUMULATE INTENSION IN TERMS. If I say to you Wodget or Crump, you find yourself passing over the fact that these are nothings, these are, so to speak mere blankety blanks, and trying to think what sort of thing a Wodget or a Crump may be. You find yourself led insensibly by subtle associations of sound and ideas to giving these blank terms attributes.

Now this is true not only of quite empty terms but of terms that carry a meaning. It is a mental necessity that we should make classes and use general terms, and as soon as we do that we fall into immediate danger of unjustifiably increasing the intension of these terms. You will find a large proportion of human prejudice and misunderstanding arises from this universal proclivity.

1.7. NEGATIVE TERMS

There is a particular sort of empty terms that has been and is conspicuously dangerous to the thinker, the class of negative terms. The negative term is in plain fact just nothing; “Not-A” is the absence of any trace of the quality that constitutes A, it is the rest of everything for ever. But there seems to be a real bias in the mind towards regarding “Not-A” as a thing mysteriously in the nature of A, as though “Not-A” and A were species of the same genus. When one speaks of Not-pink one is apt to think of green things and yellow things and to ignore anger or abstract nouns or the sound of thunder. And logicians, following the normal bias of the mind, do actually present A and not-A in this sort of diagram: —

(the letter A inside a circular boundary, together with the words Not A, all inside a bigger circular boundary.)

ignoring altogether the difficult case of the space in which these words are printed. Obviously the diagram that comes nearer experienced fact is: —

(the word Not, followed by the letter A inside a circular boundary, followed by the letter A)

with no outer boundary. But the logician finds it necessary for his processes to present that outer Not-A as bounded (Vide e.g. Kayne’s “Formal Logic” re Euler’s diagrams and Immediate Inferences.), and to speak of the total area of A and Not-A as the Universe of Discourse; and the metaphysician and the commonsense thinker alike fall far too readily into the belief that this convention of method is an adequate representation of fact.

Let me try and express how in my mind this matter of negative terms has shaped itself. I think of something which I may perhaps best describe as being off the stage or out of court, or as the Void without Implications, or as Nothingness, or as Outer Darkness. This is a sort of hypothetical Beyond to the visible world of human thought, and thither I think all negative terms reach at last, and merge and become nothing. Whatever positive class you make, whatever boundary you draw, straight away from that boundary begins the corresponding negative class and passes into the illimitable horizon of nothingness. You talk of pink things, you ignore, as the arbitrary postulates of Logic direct, the more elusive shades of pink, and draw your line. Beyond is the not-pink, known and knowable, and still in the not-pink region one comes to the Outer Darkness. Not blue, not happy, not iron, all the NOT classes meet in that Outer Darkness. That same Outer Darkness and nothingness is infinite space and infinite time and any being of infinite qualities; and all that region I rule out of court in my philosophy altogether. I will neither affirm nor deny if I can help it about any NOT things. I will not deal with not things at all, except by accident and inadvertence. If I use the word “infinite” I use it as one often uses “countless,” “the countless hosts of the enemy” – or “immeasurable” – “immeasurable cliffs” – that is to say as the limit of measurement, as a convenient equivalent to as many times this cloth yard as you can, and as many again, and so on and so on until you and your numerical system are beaten to a standstill.

Now a great number of apparently positive terms are, or have become, practically negative terms and are under the same ban with me. A considerable number of terms that have played a great part in the world of thought, seem to me to be invalidated by this same defect, to have no content or an undefined content or an unjustifiable content. For example, that word Omniscient, as implying infinite knowledge, impresses me as being a word with a delusive air of being solid and full, when it is really hollow with no content whatever. I am persuaded that knowing is the relation of a conscious being to something not itself, that the thing known is defined as a system of parts and aspects and relationships, that knowledge is comprehension, and so that only finite things can know or be known. When you talk of a being of infinite extension and infinite duration, omniscient and omnipotent and perfect, you seem to me to be talking in negatives of nothing whatever.

1.8. LOGIC STATIC AND LIFE KINETIC

There is another infirmity of the mind to which my attention has been called by an able paper read this spring to the Cambridge Moral Science Club by my friend Miss Amber Reeves. In this she has developed a suggestion of Mr. F.C.S. Schiller’s. The current syllogistic logic rests on the assumption that either A is B or it is not B. The practical reality, she contends, is that nothing is permanent; A is always becoming more or less B or ceasing to be more or less B. But it would seem the human mind cannot manage with that. It has to hold a thing still for a moment before it can think it. It arrests the present moment for its struggle as Joshua stopped the sun. It cannot contemplate things continuously, and so it has to resort to a series of static snapshots. It has to kill motion in order to study it, as a naturalist kills and pins out a butterfly in order to study life.

You see the mind is really pigeon-holed and discontinuous in two respects, in respect to time and in respect to classification; whereas one has a strong persuasion that the world of fact is unbounded or continuous.

1.9. PLANES AND DIALECTS OF THOUGHT

Finally; the Logician, intent upon perfecting the certitudes of his methods rather than upon expressing the confusing subtleties of truth, has done little to help thinking men in the perpetual difficulty that arises from the fact that the universe can be seen in many different fashions and expressed by many different systems of terms, each expression within its limits true and yet incommensurable with expression upon a differing system. There is a sort of stratification in human ideas. I have it very much in mind that various terms in our reasoning lie, as it were, at different levels and in different planes, and that we accomplish a large amount of error and confusion by reasoning terms together that do not lie or nearly lie in the same plane.

Let me endeavour to make myself a little less obscure by a flagrant instance from physical things. Suppose some one began to talk seriously of a man seeing an atom through a microscope, or better perhaps of cutting one in half with a knife. There are a number of non-analytical people who would be quite prepared to believe that an atom could be visible to the eye or cut in this manner. But any one at all conversant with physical conceptions would almost as soon think of killing the square root of 2 with a rook rifle as of cutting an atom in half with a knife. One’s conception of an atom is reached through a process of hypothesis and analysis, and in the world of atoms there are no knives and no men to cut. If you have thought with a strong consistent mental movement, then when you have thought of your atom under the knife blade, your knife blade has itself become a cloud of swinging grouped atoms, and your microscope lens a little universe of oscillatory and vibratory molecules. If you think of the universe, thinking at the level of atoms, there is neither knife to cut, scale to weigh, nor eye to see. The universe at that plane to which the mind of the molecular physicist descends has none of the shapes or forms of our common life whatever. This hand with which I write is, in the universe of molecular physics, a cloud of warring atoms and molecules, combining and recombining, colliding, rotating, flying hither and thither in the universal atmosphere of ether.

You see, I hope, what I mean when I say that the universe of molecular physics is at a different level from the universe of common experience; – what we call stable and solid is in that world a freely moving system of interlacing centres of force, what we call colour and sound is there no more than this length of vibration of that. We have reached to a conception of that universe of molecular physics by a great enterprise of organised analysis, and our universe of daily experiences stands in relation to that elemental world as if it were a synthesis of those elemental things.

I would suggest to you that this is only a very extreme instance of the general state of affairs, that there may be finer and subtler differences of level between one term and another, and that terms may very well be thought of as lying obliquely and as being twisted through different levels.

It will perhaps give a clearer idea of what I am seeking to convey if I suggest a concrete image for the whole world of a man’s thought and knowledge. Imagine a large clear jelly, in which at all angles and in all states of simplicity or contortion his ideas are imbedded. They are all valid and possible ideas as they lie, none incompatible with any. If you imagine the direction of up or down in this clear jelly being as it were the direction in which one moves by analysis or synthesis, if you go down for example from matter to atoms and centres of force and up to men and states and countries – if you will imagine the ideas lying in that manner – you will get the beginnings of my intention. But our instrument, our process of thinking, like a drawing before the discovery of perspective, appears to have difficulties with the third dimension, appears capable only of dealing with or reasoning about ideas by projecting them upon the same plane. It will be obvious that a great multitude of things may very well exist together in a solid jelly, which would be overlapping and incompatible and mutually destructive when projected together upon one plane. Through the bias in our instrument to do this, through reasoning between terms not in the same plane, an enormous amount of confusion, perplexity, and mental deadlocking occurs.

The old theological deadlock between predestination and free will serves admirably as an example of the sort of deadlock I mean. Take life at the level of common sensation and common experience and there is no more indisputable fact than man’s freedom of will, unless it is his complete moral responsibility. But make only the least penetrating of scientific analyses and you perceive a world of inevitable consequences, a rigid succession of cause and effect. Insist upon a flat agreement between the two, and there you are! The instrument fails.

So far as this particular opposition is concerned, I shall point out later the reasonableness and convenience of regarding the common-sense belief in free will as truer for one’s personal life than determinism.

1.10. PRACTICAL CONCLUSIONS FROM THESE CONSIDERATIONS

Now what is the practical outcome of all these criticisms of the human mind? Does it follow that thought is futile and discussion vain? By no means. Rather these considerations lead us toward mutual understanding. They clear up the deadlocks that come from the hard and fast use of terms, they establish mutual charity as an intellectual necessity. The common way of speech and thought which the old system of logic has simply systematized, is too glib and too presumptuous of certainty. We must needs use language, but we must use it always with the thought in our minds of its unreal exactness, its actual habitual deflection from fact. All propositions are approximations to an elusive truth, and we employ them as the mathematician studies the circle by supposing it to be a polygon of a very great number of sides.

We must make use of terms and sometimes of provisional terms. But we must guard against such terms and the mental danger of excessive intension they carry with them. The child takes a stick and says it is a sword and does not forget, he takes a shadow under the bed and says it is a bear and he half forgets. The man takes a set of emotions and says it is a God, and he gets excited and propagandist and does forget; he is involved in disputes and confusions with the old gods of wood and stone, and presently he is making his God a Great White Throne and fitting him up with a mystical family.

Essentially we have to train our minds to think anew, if we are to think beyond the purposes for which the mind seems to have been evolved. We have to disabuse ourselves from the superstition of the binding nature of definitions and the exactness of logic. We have to cure ourselves of the natural tricks of common thought and argument. You know the way of it, how effective and foolish it is; the quotation of the exact statement of which every jot and tittle must be maintained, the challenge to be consistent, the deadlock between your terms and mine.

More and more as I grow older and more settled in my views am I bored by common argument, bored not because I am ceasing to be interested in the things argued about, but because I see more and more clearly the futility of the methods pursued.

How then are we to think and argue and what truth may we attain? Is not the method of the scientific investigator a valid one, and is there not truth to the world of fact in scientific laws? Decidedly there is. And the continual revision and testing against fact that these laws get is constantly approximating them more and more nearly to a trustworthy statement of fact. Nevertheless they are never true in that dogmatic degree in which they seem true to the unphilosophical student of science. Accepting as I do the validity of nearly all the general propositions of modern science, I have constantly to bear in mind that about them too clings the error of excessive claims to precision.

The man trained solely in science falls easily into a superstitious attitude; he is overdone with classification. He believes in the possibility of exact knowledge everywhere. What is not exact he declares is not knowledge. He believes in specialists and experts in all fields.

I dispute this universal range of possible scientific precision. There is, I allege, a not too clearly recognised order in the sciences which forms the gist of my case against this scientific pretension. There is a gradation in the importance of the individual instance as one passes from mechanics and physics and chemistry through the biological sciences to economics and sociology, a gradation whose correlations and implications have not yet received adequate recognition, and which does profoundly affect the method of study and research in each science.

Let me repeat in slightly altered terms some of the points raised in the preceding sections. I have doubted and denied that there are identically similar objective experiences; I consider all objective beings as individual and unique. It is now understood that conceivably only in the subjective world, and in theory and the imagination, do we deal with identically similar units, and with absolutely commensurable quantities. In the real world it is reasonable to suppose we deal at most with PRACTICALLY similar units and PRACTICALLY commensurable quantities. But there is a strong bias, a sort of labour-saving bias, in the normal human mind, to ignore this, and not only to speak but to think of a thousand bricks or a thousand sheep or a thousand Chinamen as though they were all absolutely true to sample. If it is brought before a thinker for a moment that in any special case this is not so, he slips back to the old attitude as soon as his attention is withdrawn. This type of error has, for instance, caught many of the race of chemists, and ATOMS and IONS and so forth of the same species are tacitly assumed to be similar to one another.

Be it noted that, so far as the practical results of chemistry and physics go, it scarcely matters which assumption we adopt, the number of units is so great, the individual difference so drowned and lost. For purposes of enquiry and discussion the incorrect one is infinitely more convenient.

But this ceases to be true directly we emerge from the region of chemistry and physics. In the biological sciences of the eighteenth century, common-sense struggled hard to ignore individuality in shells and plants and animals. There was an attempt to eliminate the more conspicuous departures as abnormalities, as sports, nature’s weak moments; and it was only with the establishment of Darwin’s great generalizations that the hard and fast classificatory system broke down and individuality came to its own. Yet there had always been a clearly felt difference between the conclusions of the biological sciences and those dealing with lifeless substance, in the relative vagueness, the insubordinate looseness and inaccuracy of the former. The naturalist accumulated facts and multiplied names, but he did not go triumphantly from generalization to generalization after the fashion of the chemist or physicist. It is easy to see, therefore, how it came about that the inorganic sciences were regarded as the true scientific bed-rock. It was scarcely suspected that the biological sciences might perhaps after all be TRUER than the experimental, in spite of the difference in practical value in favour of the latter. It was, and is by the great majority of people to this day, supposed to be the latter that are invincibly true; and the former are regarded as a more complex set of problems merely, with obliquities and refractions that presently will be explained away. Comte and Herbert Spencer certainly seem to me to have taken that much for granted. Herbert Spencer no doubt talked of the unknown and unknowable, but not in this sense as an element of inexactness running through all things. He thought, it seems to me, of the unknown as the indefinable Beyond of an immediate world that might be quite clearly and definitely known.

There is a growing body of people which is beginning to hold the converse view – that counting, classification, measurement, the whole fabric of mathematics, is subjective and untrue to the world of fact, and that the uniqueness of individuals is the objective truth. As the number of units taken diminishes, the amount of variety and inexactness of generalization increases, because individuality tells for more and more. Could you take men by the thousand billion, you could generalize about them as you do about atoms; could you take atoms singly, it may be that you would find them as individual as your aunts and cousins. That concisely is the minority belief, and my belief.

Now what is called the scientific method in the physical sciences rests upon the ignoring of individualities; and like many mathematical conventions, its great practical convenience is no proof whatever of its final truth. Let me admit the enormous value, the wonder of its results in mechanics, in all the physical sciences, in chemistry, even in physiology, – but what is its value beyond that? Is the scientific method of value in biology? The great advances made by Darwin and his school in biology were not made, it must be remembered, by the scientific method, as it is generally conceived, at all. His was historical research. He conducted research into pre-documentary history. He collected information along the lines indicated by certain interrogations; and the bulk of his work was the digesting and critical analysis of that. For documents and monuments he had fossils and anatomical structures and germinating eggs too innocent to lie. But, on the other hand, he had to correspond with breeders and travellers of various sorts; classes entirely analogous, from the point of view of evidence, to the writers of history and memoirs. I question profoundly whether the word “science,” in current usage anyhow, ever means such patient disentanglement as Darwin pursued. It means the attainment of something positive and emphatic in the way of a conclusion, based on amply repeated experiments capable of infinite repetition, “proved,” as they say, “up to the hilt.”

It would be of course possible to dispute whether the word “science” should convey this quality of certitude, but to most people it certainly does at the present time. So far as the movements of comets and electric trams go, there is no doubt practically cock-sure science; and Comte and Herbert Spencer seem to me to have believed that cock-sure could be extended to every conceivable finite thing. The fact that Herbert Spencer called a certain doctrine Individualism reflects nothing on the non-individualizing quality of his primary assumptions and of his mental texture. He believed that individuality (heterogeneity) was and is an evolutionary product from an original homogeneity, begotten by folding and multiplying and dividing and twisting it, and still fundamentally IT. It seems to me that the general usage is entirely for the limitation of the word “science” to knowledge and the search after knowledge of a high degree of precision. And not simply the general usage; “Science is measurement,” Science is “organized commonsense,” proud in fact of its essential error, scornful of any metaphysical analysis of its terms.

Now my contention is that we can arrange the fields of human thought and interest about the world of fact in a sort of scale. At one end the number of units is infinite and the methods exact, at the other we have the human subjects in which there is no exactitude. The science of society stands at the extreme end of the scale from the molecular sciences. In these latter there is an infinitude of units; in sociology, as Comte perceived, there is only one unit. It is true that Herbert Spencer, in order to get classification somehow, did, as Professor Durkheim has pointed out, separate human society into societies, and made believe they competed one with another and died and reproduced just like animals, and that economists following List have for the purposes of fiscal controversy discovered economic types; but this is a transparent device, and one is surprised to find thoughtful and reputable writers off their guard against such bad analogy. But indeed it is impossible to isolate complete communities of men, or to trace any but rude general resemblances between group and group. These alleged units have as much individuality as pieces of cloud; they come, they go, they fuse and separate. And we are forced to conclude that not only is the method of observation, experiment, and verification left far away down the scale, but that the method of classification under types, which has served so useful a purpose in the middle group of subjects, the subjects involving numerous but a finite number of units, has also to be abandoned in social science. We cannot put Humanity into a museum or dry it for examination; our one single still living specimen is all history, all anthropology, and the fluctuating world of men. There is no satisfactory means of dividing it, and nothing else in the real world with which to compare it. We have only the remotest ideas of its “life-cycle” and a few relics of its origin and dreams of its destiny.

This denial of scientific precision is true of all questions of general human relations and attitude. And in regard to all these matters affecting our personal motives, our self-control and our devotions, it is much truer.

From this it is an easy step to the statement that so far as the clear-cut confident sort of knowledge goes, the sort of knowledge one gets from a time-table or a text-book of chemistry, or seeks from a witness in a police court, I am, in relation to religious and moral questions an agnostic. I do not think any general propositions partaking largely of the nature of fact can be known about these things. There is nothing possessing the general validity of fact to be stated or known.