My dear ——,

You ask me to pass to the consideration of knowledge of a new kind, knowledge of mathematical truth. “Here at least,” you say, “severe reasoning dominates supreme, and Imagination has no place.” “Two and one make three,” “The angles at the base of an isosceles triangle are equal:” “surely we may assume that Imagination has nothing to do with these propositions. They must be decided by pure Reason.” Never was assumption more grotesque. Excuse me; but by what other adjective can I characterize the statement that the Imagination has “nothing to do with” propositions for the very terms of which we are indebted to the Imagination? I maintain without fear of contradiction that the knowledge of these propositions requires an effort of the Imagination so severe that the very young and the completely untrained cannot attain to it.

For, in the first place, what do you mean by “one,” “two,” and “three”? I have never had any experience of such things; nor have you; nor can you. “Two” oranges, “two” apples, and the like, we have had experience of, and can realize; but to think of “one” or “two” by themselves (“one” or “two” with “anythings”, or with “nothings” after them), “one” or “two” as “abstract ideas”—this really is a most difficult or rather (I am inclined to say) an impossible task. When I say “one” and “two,” I think I see before me dimly “one” or “two” dots or small strokes, and I perceive that two and one of these dots or strokes make up three dots or strokes. When I speak of “twenty” and “thirty,” I do not see any images of these existences; and when I say that “twenty” and “thirty” make “fifty,” I do not realize the process of addition at all visibly; I merely repeat the statement on the authority of previous observations and reasonings mostly made by others and not by myself. But so far as I approximate to the realization of an abstract number, I do it by a kind of negative imagination. And in any case we can hardly deny that all arithmetical propositions, since they employ terms that denote mere imaginary ideas, must be regarded as based on the imagination.

It is the same with Geometry. The whole of what we call “Euclid” is based upon a most aerial effort of the Imagination. We have to imagine lines without thickness, straightness that does not deviate the billionth part of an inch from perfect evenness, perfectly symmetrical circles, and—climax of audacity!—points that have “no parts and no magnitude!” Obviously these things have no existence except in the dreams of Imagination; yet Euclid’s severe reasoning applies to none but these things. If you step from your ideal triangle in Dreamland into your material triangle in chalk-land, you step from absolute truth into statements that are not absolutely true. The angles at the base of your chalk isosceles triangle are not exactly equal, if you measure them with sufficient accuracy. In a word the whole of Geometry is an appeal to the Imagination in which the geometer says to us, “I know that my propositions are not exactly true except with respect to invisible, ideal, and imaginary figures, planes, and solids. These ideas, therefore, you must endeavour to imagine. In order to relieve the strain on your imagination, I will place before you material and visible figures about which my reasoning will be approximately true. From these I must ask you to try to rise upward to the imagination of their archetypes, the immaterial realities.”

What shall we reply to our overbearing mathematician who in this abrupt and audacious manner introduces the non-existent and imaginary creatures of his brain as being “realities”? Shall we deride him, and the arithmetician likewise? Shall we bid the latter exchange his calculations in abstract numbers for manifestly useful sums about sacks of wheat and casks of beer? Shall we bid the mathematician descend from his high geometrical theories to the practical measurements of agriculture? Pouring scorn on his avowal that the objects of his reasoning are “invisible, ideal, and imaginary,” shall we decline to study a science that is confessedly—so we can word it—visionary and illusive? If we do, he will not be without a reply, somewhat after this fashion: “My practical friends, it will be the worse for you if you despise these invisible, ideal and imaginary objects. I say nothing about the mental training and development to be derived from the study of these things; for to this argument you do not appear to me to be at present accessible: but I will take your own line—the practical. Do you then want to measure your fields with ease and to make accurate maps and charts; to construct houses that shall stand longer, ships that shall sail faster, cannon that shall shoot further, engines that shall pull harder, than any known before; do you want to utilize electricity for lighting, gas for motion, water for pressure; in a word do you wish to make yourselves lords over the material world and to have all the forces of Nature at your beck and call? If you do, you must not despise the non-existent numbers of my arithmetical brother, nor my immaterial and imaginary lines. Give me leave to repeat, in spite of your indignation, that though they are (in this present visible world of ours) non-existent, yet these lines and numbers are ‘realities.’ That they are realities, and that our conclusions about them are real and true, is proved by the one test of truth: our conclusions work. Our discoveries are in harmony with the universe. A perfect circle you never saw and never will see: yet it is as real as a beefsteak and a pint of porter. I believe in a perfect circle by Faith; I accept it with reverence as an impression, if I may so dare to speak, on the Mind of the Universe, which He has communicated to me. What is more, I believe that He intended us to study this and other immaterial realities that our minds might approximate to His. Take a cone, my practical friends. What do you see in it? Nothing, I fear, except a shape that reminds you of an extinguisher or a fool’s cap. Yet this little solid contains within itself the suggestions of all the mysteries of motion in heaven and earth. Slice your cone parallel to the base: there you have the perfect circle. Slice it again, parallel to one of the sides: there you have the parabola, the curve of terrestrial motion. Slice it once more, midway between these two sections: there you have the ellipse, the curve of celestial motion for which all the astronomers were seeking in vain through something like a score of centuries. Seriously now, my half-educated friends, in spite of the sense you may for the most part entertain of your own importance, do you not in your more modest moods sometimes feel inclined to say that, ‘A circle is, after all, a reality, perhaps more real than I am myself’?”

What do you think of all this? For my part, I am inclined to think the Mathematician has the best of it. A good deal will turn upon the meaning of that dangerous word “reality,” about which I will give you my notions, perhaps, hereafter.^[2] But even if you dispute his assertions about the reality of his “ideas,” you cannot, I am sure, deny the immense practical importance, as well as the universal acceptance, of his conclusions and discoveries; and you will do well to remember that this immensely important, this undisputed and indisputable knowledge, could never have been attained if we had not called in the Imagination to create for us ideas that never will be, and never can be, realised in this present material world.

Let us pass now from knowledge about things to knowledge about persons, i.e. about actions and motives.

Our knowledge about actions depends on (1) personal observation; (2) testimony; (3) circumstantial evidence or any combination of these three.

The knowledge that we derive of actions from our own observation is of course independent of Faith, so far as concerns the past; but it is very limited, and entirely useless and unpractical, except as a basis for knowledge about the present and future; for which knowledge (as we have seen) Faith in the permanence of Nature is absolutely necessary.

The knowledge of actions that comes to us from evidence, direct and circumstantial, is largely dependent on Faith. “Julius CÆsar invaded Britain”—how certain we all feel of that! Yet how slight the testimony! Simply a few pages of narrative, written by the supposed invader himself, and some casual remarks by one or two contemporary letter-writers about CÆsar’s doings in Britain and the Senate’s reception of the news. Why should we believe on so apparently flimsy a basis? Why should not CÆsar have sent one of his lieutenants to invade the island, and afterwards have taken the credit of it himself? Or there might have been no invasion at all, nothing but a reconnaissance grossly exaggerated and intermixed with facts derived from travellers. Yet we believe in the invasion without the slightest hesitation. CÆsar, we say, would not have told the lie; or, if he had, it would have been quickly exposed by his enemies. In other words, we believe in the truth of the narrative, because a belief in its falsehood does not “work,” that is to say, does not suit with what we know (or, more properly, with what others know) of CÆsar’s character and CÆsar’s times. Of precisely the same kind is almost all our knowledge about history: it is based upon evidence, but it is belief; and the only test of its truth is, does it “work,” i.e. does it fit in with other knowledge which we regard as established truth?

But you see that, even in dealing with a simple action of CÆsar’s, we have already drifted into a reference to CÆsar’s motives: and obviously knowledge about “motives” is an important and indeed a paramount element in knowledge about persons. “My father,” says the child, “has his brows knit; his face looks dark; he speaks very loud; his eyes look brighter than usual:”—this is knowledge about actions derived from personal observation, but, so far, perfectly useless, until something is added to it. “Whenever my father has looked and spoken like this before, he has been angry and has punished somebody: therefore he is angry and will punish somebody now”—this is not knowledge, it is only belief; but it is belief not about actions simply, but about motives as well as actions, and it may be of the greatest use.

How do we gain knowledge about motives, the moving powers of the human machine? Since we cannot take this machinery to pieces, or experiment with it freely, we must derive our knowledge largely from the consciousness of our own motives. Tickling produces laughter in us, and pricking, a cry; affection, and the command of those whom we love, produce in us obedience; desire of a result or reward produces effort; fear of pain or penalty produces avoidance of certain actions, performance of others. Hence we infer that, in others also, similar effects have been produced, or will be produced, by similar causes. In either case, our inference is based partly upon our observation that these causes have preceded these effects in other persons, and partly upon our faith that other people’s machinery is like our own.

But we have not yet touched one of the most powerful of motives, that power within us which we call Conscience (“joint-knowledge”); as though there were in us an Assessor sitting in judgment by the side of the mysterious “I,” the two together pronouncing sentence of “Right” or “Wrong” upon the several propositions and intentions which are, as it were, called up before their tribunal. The development of Conscience and our sensibility to its dictation appears to me largely due to the Imagination. If a philosopher tells me that when Conscience appears to us to say “Right” it really says “Expedient for society and ultimately for yourself,” or “Calculated to gain esteem for yourself,” or “Conducive to your own peace of mind,” I am obliged, with all deference to him, but with greater deference to truth, to assure him that (however correct he may be as to the origin of this feeling in my own infant mind or in the matured mind of my primÆval ancestors) he is mistaken, at all events in my own case, as to the action of Conscience now. I may possibly have been long ago guided to my idea of “Right” by my observation of what is expedient: but, to me, now, the sense of “right” is as different from the sense of “expedient,” as the eye is different from some sensitive protuberance which may ultimately be developed into an eye, but is at present responsive only to the touch.

How then do we gain this knowledge of right and wrong? For of course it is not enough to reply that we gain it by the voice of Conscience: such an answer only makes us repeat our question in a different shape: “In the very young, Conscience, though it may be existent, is certainly latent; when and whence does it begin to work?” I should reply that the first idea of good and evil is communicated to the very young through the habit of obedience to their parents or those who stand to them in the parental position. A child is so created as to be in constant dependence on the favour and good-will of his mother. When he is obedient to her he finds himself at peace and happy, and he welcomes on her face that sunshine which indicates that she is pleased with him. When he is disobedient, harsh sounds follow, a lowering darkness on the countenance close to his, obstacles to his freedom, restrictions of his pleasures, perhaps sharper pains or penalties: and he is now out of harmony with his little Universe. All this strange and subtle evil inside him and outside him he has brought on himself by disobeying the maternal will; and hence there gradually springs up in his mind an Imagination of some unnameable thing, which is his first idea of right. But as he grows older and widens his sphere of observation he finds—if he is placed in anything like those favourable circumstances which Nature has appointed for most of us—that this parental will is in harmony with the widening world around him. The parents say, “Do not play with fire;” Nature says the same, and punishes him if he transgresses. The parents say, “Do not touch that knife;” again Nature confirms their authority by inflicting a penalty on disobedience. Thus, if the parents have anything of parental forethought, the child gradually associates them with the governing powers of his growing Universe, and begins to feel that the parental will is also the will, or order, of Nature. They are as God to him: and the confirmed habit of obedience to them deepens in his heart the conviction—but still a conviction rather springing from Imagination than from Reason—that the power which thus induces him to obey is a great and grand Power, orderly, not to be resisted; wise and justified by results, but to be obeyed without thinking about results; it ought to be obeyed; it is Right.

Now he steps out into the world of other human beings; and here he learns to widen his idea of Right. Perhaps he also learns to alter it. If he was born and reared among thieves, his conscience may have been altogether perverted so that he actually thought it honourable to steal. But in any case, even though he may come from the best of homes, he often learns that the parental will is not always in harmony with the highest and best will; and gradually he forms a different standard of “Right” from that which he held before. It was once the will of his parents, now it is often the will of Society. Conforming himself to the will of Society he is free from pains and penalties; he is at peace with those around him, and he is generally at peace with himself. I say generally, not always: for by this time he has begun to think for himself and to see that Conscience ought to speak in the interests not merely of his parents, nor of a select circle of his own friends or companions, but of all mankind. His Imagination pictures for him an ideal Order such as he has never actually experienced. He feels that he “ought” to be at peace and in harmony with this imaginary Order, and not with some distorted and narrowed conception of it conveyed to him by his “set,” his class, his city, his nation, or his church. In his conscience, he hears the voice of this Moral Order of humanity. Hence it is that men have been sometimes impelled to thoughts beyond, or even against, the conscience of their contemporaries; to protest, for example, against unjust wars, against war of any kind, against slavery, against duelling, against legalized oppression. In every case the impelling power has been the same, a sense of discord between the man’s imaginary ideal and the actual environment in which these evils and disorders have existed. Others, his commonplace companions, have been content to go with the world around them—to be kind slave-holders, honourable duellists, moderate oppressors—and they have felt no pangs of conscience. But by a few, a chosen few, there has been acquired a keener sense of the ideal of moral harmony, a keener eye for detecting moral disorder, and an abhorrence of it which will not permit them to live in peace amid such evils: they must either die or mend them.

They often do die in mending them; but while in the process of dying, or preparing for death—with all deference to the clergyman who lately maintained that “if there is no hereafter, and if the only reward of self-sacrifice and the only punishment of crime are those which happen in the present life, it would have been far better to have been FouchÉ than Paul”—they have at least a peace of mind which they could not have attained by conformity with the world. The grosser conscience that “worked” well enough in their companions would not have “worked” in them. Even, therefore, though they appear to be exceptions to the rule that tests truth by its “working,” they are not really exceptional. They have been in discord with the world but in concord with themselves. Often they prove to others the truth of their conceptions by raising up the world to their level, and by pointing to the moral order which has issued from the fulfilment of their ideas. But in any case, though they may fail for a time or (apparently) for all time, they have had in themselves a sufficient test of the truth of their ideas: they have followed their conscience and they have found that this course “worked”—that is to say, suited and developed their nature—as no other course could have worked for them. But in order thus to hear and obey the voice of conscience and to discern its highest truths, how much of faith, how much of imagination has been needed!

But this digression about Conscience has led me a little astray from my subject, which was “the knowledge of persons:” I must return to it in my next letter.