Concerning other and more complex kinds of knowledge what need is there to say a word? For if such simple propositions as “a stone is hard,” are shown to depend upon Imagination for suggesting, and Faith for retaining, a conviction of the uniformity of Nature, much more must these influences be presupposed if the child is to attain knowledge about matters avowedly future, e.g. “the sun will rise to-morrow.” In reality all knowledge of any practical value has to do with a future, immediate or remote; and therefore I do not think I shall be exaggerating in saying that for all knowledge about things outside us we depend largely upon Imagination and Faith.
But I pass now to consider a child’s knowledge about himself. Take for example such a proposition as this, “I like sugar.” Is Faith or Imagination required to enable a child to arrive at the knowledge of this proposition about himself? I think so. The very use of the word “I,” if used intelligently, appears to need some imaginative effort. Of course I do not deny that this subtle metaphysical idea may have been suggested to us originally by our faculty of touch, and especially the faculty of self-pinching or self-touching. I dare say you have read how men have sometimes caught hold of their own benumbed hand by night, and awakened a household by shouting that they had caught a robber: has it ever occurred to you that, if you never had the power of distinguishing your own hand from anybody else’s hand by the sense of touch, you might have gone through life with no sense, or with a very tardily acquired sense, of your own identity? If the monkey who boiled his own tail in the caldron had felt no pain, might he not have been excused for doubting sometimes whether the tail belonged to him? And if his head were equally painless or joyless when he thumped it or scratched it, ought he to be condemned for disowning his own head? And if a monkey, or even a child, could not lay claim to its own head, it seems to me doubtful whether he could ever claim such a separation from the outside world as would necessitate his using the word “I.” But, as it is, having this self-pinching faculty, the child soon finds that to pinch a ball, or a bladder, or a sister, is an entirely different thing from pinching himself: and this self-touching faculty confirms the evidence suggested by the bumps and thumps of the external world; all of which lead him to the belief that he has a bodily frame of his own, liable to pain and to pleasure, and largely dependent for pain and pleasure on his own motions, which motions he dimly perceives dependent upon something that appears to be inside himself.
But neither this nor any other explanation of the manner in which the sensations prepare the way for the construction of the idea of the “I,” ought to prevent us from recognizing that the idea itself is the work of the Imagination, and not of the unaided sensations, nor of the unaided reason. Self-pinching and contact with the rough external world might convince the child that he was different from his environment at the time when he made his last experiments and underwent his last experiences; but they could not convince him that he is different now, or that he will be different in the next instant; and for this conviction he depends upon faith. Again, the imagination of the “I” seems closely bound up with two other nearly simultaneous imaginations, those of Force and Cause. First he feels a desire to touch the inkstand, then he feels himself moving towards the inkstand, then he feels the inkstand touched. These sequences of desire, action, result, he can repeat as often as he likes. By their frequency therefore, as well as by their vividness, they impress him more powerfully than sequences of phenomena not dependent on himself; and it is from these probably that he first imagines the idea of “must,” or “necessity,” or “cause and effect.” If he feels a desire to move a limb, the motion of the limb immediately follows; it always obeys him; it must obey him. He pushes a brick; what caused the brick to fall? He feels that it was his own force that caused it; he no longer looks upon the push and the fall as if the former merely preceded the latter; he imagines a connection of necessity between the push and the fall, the cause and the effect, and gradually comes to imagine himself as the causer of the cause. But all these imaginations are mere imaginations, not proofs. To gather together all the sensations of which he retains the memory, the sensations of which he is at present conscious, and the sensations to which he looks forward, and to put an “I” behind or below all these, as the foundation of them all, and partial causer of them all—what an audacious assumption is this! Not Plato and Aristotle combined could prove to a child, or to the most consummate of philosophers, that he has a right to call himself “I,” or that he is any other than a machine and a part of the universal machinery. How can I prove and vindicate my independence, my right to an “I”? By saying that I will do, or not do, and by then doing, or not doing, any conceivable thing at any conceivable time? Such an attempt is futile. The retort is unanswerable: “In the great machine which you call the universe, that small part which you call ‘I’ was so constructed and wound up that it could no more help saying and doing what it did and said, than a clock could help pointing and striking.”
What then is the real proof that we are right in using the word “I” and in distinguishing ourselves from other objects which we call external? There is no proof at all except that, first, we are led to this way of looking at things by Nature and Imagination, and secondly, this way of looking at things works best. The “I-view” is better fitted than the “machine-view” to develop in us the faculties of judgment and self-control, to give us a sense of responsibility and a capability of amendment, and to make us ultimately more hopeful and more active. So too, the belief in “cause and effect” works better than a mere mental record of past antecedents and sequences, accompanied by a blank and strictly logical neutrality of mind as to what will happen in the future. Faith in “cause and effect” is the foundation of all stable life and all regular progress alike in the individual and in the state. The unfaithful unbeliever in causality is the Esau, both in the moral and in the intellectual world, the happy-go-lucky hunter who depends on stray venison and refuses to resort to system in order to make a sure provision for the needs of the future; the believer is the quiet plodding Jacob who has his goats in the fold where he knows he can find them when wanted. The unbeliever is the unimaginative savage who has not faith enough to see the harvest in the seed; the believer is the man of civilisation who can trust Nature through six long months of waiting and can say to her, not in the language of hope, “do ut des,” but in the language of conviction, “do daturae.” Nevertheless, convenient as these ideas may be for our comfort, nay, though they may be even necessary for our existence, we are bound to recollect that they are merely ideas. Like the ideas of force, cause, effect, necessity, so the idea of “I,”—though produced with the aid of experience and tested by appeal to experience and reason—appears to be nothing but a child of the Imagination, and a foster-child of Faith.
Perhaps your conclusion from all this is that I am proving that we can know nothing? Not in the least. What I am saying does not prove that we know less or more than we profess to know at present. I am merely showing that our knowledge comes to us from sources other than those which are ordinarily assumed.
IV
IDEALS
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.”