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.
Footnote 2:
See the _Definitions_ at the end of the book.
V
IDEALS AND TESTS