_INTELLECTUAL VALUES_
LECTURE V
INTRODUCTION TO PART III
I
In the preceding lectures I have given reasons for thinking that in two
great departments of human interest—Æsthetics and Ethics—the highest
beliefs and emotions cannot claim to have any survival value. They
must be treated as by-products of the evolutionary process; and are,
therefore, on the naturalistic hypothesis, doubly accidental. They are
accidental in the larger sense of being the product of the undesigned
collocation and interplay of material entities—molecular atoms,
sub-atoms, and ether—which preceded, and will presumably outlast,
that fraction of time during which organic life will have appeared,
developed, and perished. They are also accidental in the narrower sense
of being only accidentally associated with that process of selective
elimination, which, if Darwinism be true, has so happily imitated
contrivance in the adaptation of organisms to their environment. They
are the accidents of an accident.
I disagreed with this conclusion, but I did not attempt to refute it. I
contented myself with pointing out that it was destructive of values;
and that, the greater the values, the more destructive it became.
The difficulty, indeed, on which I have so far insisted is not a
logical one. We have not been concerned with premises and conclusions.
Neither our æsthetic emotions nor our moral sentiments are the product
of ratiocination; nor is it by ratiocination that they are likely
to suffer essential wrong. If you would damage them beyond repair,
yoke them to a theory of the universe which robs them of all general
significance. Then, at the very moment when they aspire to transcendent
authority, their own history will rise up in judgment against them,
impugning their pretensions, and testifying to their imposture.
II
The inquiry on which I now propose to enter will follow a more or less
parallel course, and will reach a more or less similar conclusion.
Yet some characteristic differences it must necessarily exhibit.
In the higher regions of æsthetics and ethics, emotions and beliefs
are inextricably intertwined. They are what naturalists describe as
“symbiotic.” Though essentially different, they are mutually dependent.
If one be destroyed, the other withers away.
But Knowledge—the department of human interest to which I now turn—is
differently placed. The values with which we shall be concerned are
mainly rational; and intellectual curiosity is the only emotion
with which they are associated. Yet here also two questions arise
corresponding to those which we have already dealt with in a different
connection: (1) what are the causes of our knowledge, or of that part
of our knowledge which concerns the world of common sense and of
science? (2) does the naturalistic account of these causes affect the
rational value—in other words the validity—of their results?
We are, perhaps, more sensitive about the pedigree of our intellectual
creed than we are about the pedigree of our tastes or our sentiments.
We like to think that beliefs which claim to be rational are the
product of a purely rational process; and though, where others are
concerned, we complacently admit the intrusion of non-rational links
in the causal chain, we have higher ambitions for ourselves.
Yet surely, on the naturalistic theory of the world, all such ambitions
are vain. It is abundantly evident that, however important be the part
which reason plays among the immediate antecedents of our beliefs,
there are no beliefs which do not trace back their origin to causes
which are wholly irrational. Proximately, these beliefs may take rank
as logical conclusions. Ultimately, they are without exception rooted
in matter and motion. The rational order is but a graft upon the causal
order; and, if Naturalism be true, the causal order is blind.
III
Before I further develop this line of speculation it may help you to
understand what I am driving at if I venture upon an autobiographical
parenthesis. The point I have just endeavoured to make I have made
before in these lectures, and I have made it elsewhere. It is one
of a number of considerations which have led me to question the
prevalent account of the theoretical ground-work of our accepted
beliefs. Taken by itself, its tendency is sceptical; and, since it
has been associated with arguments in favour of a spiritual view
of the universe, I have been charged (and not always by unfriendly
commentators) with the desire to force doubt into the service of
orthodoxy by recommending mankind to believe what they wish, since all
beliefs alike are destitute of proof. As we cannot extricate ourselves
from the labyrinth of illusion, let us at least see to it that our
illusions are agreeable.
This, however, is not what I have ever wanted to say, nor is it what I
want to say now. If I have given just occasion for such a travesty of
my opinions, it must have been an indirect consequence of my early, and
no doubt emphatically expressed, contempt for the complacent dogmatism
of the empirical philosophy, which in Great Britain reigned supreme
through the third quarter of the nineteenth century. But was this
contempt altogether unreasonable?
I went to Cambridge in the middle sixties with a very small equipment
of either philosophy or science, but a very keen desire to discover
_what_ I ought to think of the world, and _why_. For the history
of speculation I cared not a jot. Dead systems seemed to me of no
more interest than abandoned fashions. My business was with the
ground-work of living beliefs; in particular, with the ground-work of
that scientific knowledge whose recent developments had so profoundly
moved mankind. And surely there was nothing perverse in asking modern
philosophers to provide us with a theory of modern science!
I was referred to Mill; and the shock of disillusionment remains with
me to the present hour. Mill possessed at that time an authority in
the English Universities, and, for anything I know to the contrary,
in the Scotch Universities also, comparable to that wielded forty
years earlier by Hegel in Germany and in the Middle Ages by Aristotle.
Precisely the kind of questions which I wished to put, his Logic was
deemed qualified to answer. He was supposed to have done for scientific
inference what Bacon tried to do, and failed. He had provided science
with a philosophy.
I could have forgiven the claims then made for him by his admirers;
I could have forgiven, though young and intolerant, what seemed to
me the futility of his philosophic system, if he had ever displayed
any serious misgiving as to the scope and validity of his empirical
methods. If he had admitted, for example, that, when all had been done
that could be done to systematise our ordinary modes of experimental
inference, the underlying problem of knowledge still remained unsolved.
But he seemed to hold, in common with the whole empirical school
of which, in English-speaking countries, he was the head, that the
fundamental difficulties of knowledge do not begin till the frontier is
crossed which divides physics from metaphysics, the natural from the
supernatural, the world of “phenomena” from the world of “noumena,”
“positive” experiences from religious dreams. It may be urged that, if
these be errors, they are errors shared by ninety-nine out of every
hundred persons educated in the atmosphere of Western civilisation,
whatever be their theological views: and I admit that it has sunk deep
into our ordinary habits of thought. Apologetics are saturated with
it, not less than agnosticism or infidelity. But, for my own part, I
feel now, as I felt in the early days of which I am speaking, that
the problem of knowledge cannot properly be sundered in this fashion.
Its difficulties begin with the convictions of common sense, not with
remote, or subtle, or otherworldly speculations; and if we could
solve the problem in respect of the beliefs which, roughly speaking,
everybody shares, we might see our way more clearly in respect of the
beliefs on which many people are profoundly divided.
That Mill’s reasoning should have satisfied himself and his immediate
disciples is strange. But that the wider public of thinking men, whom
he so powerfully influenced, should on the strength of this flimsy
philosophy adopt an attitude of dogmatic assurance both as to what can
be known and what cannot, is surely stranger still. Thus, at least, I
thought nearly half a century ago, and thus I think still.
Consider, for example, a typical form of the ordinary agnostic
position: that presented by Leslie Stephen. The best work of this
excellent writer was biographical and literary; but he was always
deeply interested in speculation; and his own creed seems early to have
taken its final shape under the philosophical influences of the British
empiricists. He regarded the “appeal to experience” as the fundamental
dogma of agnosticism, and by the “appeal to experience” he meant what
Mill meant by it. He sincerely supposed that this gave you indisputable
knowledge of “phenomena,” and that if you went beyond “phenomena” you
were dreaming, or you were inventing.
This is a possible creed; and it is, in fact, the creed held
implicitly, or explicitly, by many thousands of quite sensible people.
But why should those who hold it suppose that it must always satisfy
impartial inquirers? Why should they assume that those who reject it
are sacrificing their reason to their prejudices or their fancies? It
may represent the best we can do, but is it, after all, so obviously
reasonable? On this subject the empirical agnostic has no doubts. He
holds, with unshaken confidence, that nothing deserves to be believed
but that which in the last resort is proved by “experience”; that the
strength of our beliefs should be exactly proportioned to the evidence
which “experience” can supply, and that every one knows or can discover
exactly what this evidence amounts to. Leslie Stephen refers to a
well-known aphorism of Locke, who declared that “there is one unerring
mark by which a man may know whether he is a lover of truth in earnest,
viz. the not entertaining any proposition with greater assurance than
the proofs it is built on will warrant.” Upon which Leslie Stephen
observes that the sentiment is a platitude, but, in view of the
weakness of human nature, a useful platitude.
Is it a platitude? Did Locke act up to it? Did Hume act up to it, or
any other of Leslie Stephen’s philosophic progenitors? Does anybody
act up to it? Does anybody sincerely try to act up to it?
Read through the relevant chapters in Locke’s Essay, and observe
his ineffectual struggles, self-imprisoned in the circle of his own
sensations and ideas, to reach the external world in which he believed
with a far “greater assurance” than was warranted by any proofs which
_he_, at all events, was able to supply. Read Hume’s criticism of our
grounds for believing in a real world without, or a real self within,
and compare it with his admission that scepticism on these subjects is
a practical impossibility.
But we need not go beyond the first chapter of “An Agnostic’s Apology”
to find an illustration of my argument. Leslie Stephen there absolves
himself from giving heed to the conclusions of philosophers, because
there are none on which all philosophers are agreed, none on which
there is even a clear preponderance of opinion. On the other hand,
he is ready to agree with astronomers, because astronomers, “from
Galileo to Adams and Leverrier,” substantially agree with each other.
Agreement among experts is, in his opinion, a guarantee of truth, and
disagreement a proof of error.
But then he forgets that these distressing differences among
philosophers do not touch merely such entities as God and the soul, or
the other subjects with which agnostics conceive man’s faculties are
incapable of dealing. They are concerned (among other things) with the
presuppositions on which our knowledge of “phenomena”—including, of
course “astronomy from Galileo to Adams and Leverrier,” is entirely
constructed. What, in these circumstances, is Locke’s “sincere lover
of truth” to do? How is he to avoid “entertaining propositions with
greater assurance than the proofs they are built on will warrant”?
Where will he find a refuge from the “pure scepticism” which is, in
Leslie Stephen’s opinion, the natural result of divided opinions? How
is he to get on while he is making up his mind whether any theory of
the world within his reach will satisfy unbiased reason?
The fact is that the adherents of this philosophic school apply,
quite unconsciously, very different canons of intellectual probity to
themselves and to their opponents. “Why,” asks Mr. Stephen, “should
a lad who has just run the gauntlet of examination and escaped to a
country parsonage be dogmatic?” If to be dogmatic is to hold opinions
with a conviction in excess of any reason that can be assigned for
them, there seems to be no escape for the poor fellow. The common lot
of man is not going to be reversed for him. Though he abandon his
parsonage and renounce his Church, though he scrupulously purify his
creed from every taint of the “metempirical,” though he rigidly confine
himself to themes which his critics declare to be within the range of
his intellectual vision, fate will pursue him still. He may argue much
or argue little; he may believe much or believe little; but, however
much he argues and however little he believes, his beliefs will always
transcend his arguments, and to faith, in his own despite, he must
still appeal.
Those who accept Leslie Stephen’s philosophy suppose that for this
young man, as for all others, a way of escape may be found by appealing
to experience. But surely none are so sanguine as to suppose that,
by appealing to experience, they are going to avoid what Mr. Stephen
describes as “endless and hopeless controversies.” Alas, this is not
so! The field of experience is no well-defined and protected region
under whose clear skies useful knowledge flourishes unchallenged, while
the mist-enshrouded territories of its metaphysical neighbours are
devastated by unending disputations. On the contrary, it is the very
battlefield of philosophy, the cockpit of metaphysics, strewn with
abandoned arguments, where every strategic position has been taken
and retaken, to which every school lays formal claim, which every
contending system pretends to hold in effective occupation. Indeed, by
a singular irony, the thinkers who, at this particular moment, talk
most about experience are those metaphysicians of the Absolute in
whose speculations Mr. Stephen saw no beginning of interest, except
that of being (as he supposed) at once the refuge and the ruin of
traditional religion. But these philosophers have no monopoly. All men
nowadays speak well of experience. They begin to differ only when they
attempt to say what experience is, to define its character, explain its
credentials, and expound its message. But, unhappily, when this stage
is reached their differences are endless.
IV
I am, of course, not concerned with Mr. Stephen except as a brilliant
representative of a mode of thought to which I most vehemently object.
I do not object to it merely because it is in my judgment insufficient
and erroneous, still less because I dislike its conclusion. I object
to it because it talks loudly of experience, yet never faces facts;
and boasts its rationality, yet rarely reasons home. These are far
graver crimes against the spirit of truth than any condemned in Locke’s
pretentious aphorism, and they lead to far more serious consequences.
If you ask me what I have in mind when I say that agnostic empiricism
never faces facts, I reply that it never really takes account of that
natural history of knowledge, of that complex of causes, rational and
non-rational, which have brought our accepted stock of beliefs into
being. And if you ask me what I have in mind when I say that though it
reasons, it rarely reasons home, I reply that, when it is resolved not
to part with a conclusion, anything will serve it for an argument; only
when it is incredulous does it know how to be critical.
This is not an error into which I propose to fall. But I hope that
I shall not on that account be deemed indifferent to the claims of
reason, or inclined to treat lightly our beliefs either about the
material world or the immaterial. On the contrary, my object, and my
only object, is to bring reason and belief into the closest harmony
that at present seems practicable. And if you thereupon reply that such
a statement is by itself enough to prove that I am no ardent lover of
reason; if you tell me that it implies, if not permanent contentment,
at least temporary acquiescence in a creed imperfectly rationalised,
I altogether deny the charge. So far as I am concerned, there is no
acquiescence. Let him that thinks otherwise show me a better way. Let
him produce a body of beliefs which shall be at once living, logical,
and sufficient;—not forgetting that it cannot be sufficient unless it
includes within the circuit of its doctrines some account of itself
regarded as a product of natural causes, nor logical unless it provides
a rational explanation of the good fortune which has made causes which
are not reasons, mixed, it may be, with causes which are not _good_
reasons, issue in what is, by hypothesis, a perfectly rational system.
He who is fortunate enough to achieve all this may trample as he
likes upon less successful inquirers. But I doubt whether, when this
discoverer appears, he will be found to have reached his goal by the
beaten road of empirical agnosticism. This, though it be fashionably
frequented, is but a blind alley after all.
In the meanwhile we must, I fear, suffer under a system of beliefs
which is far short of rational perfection. But we need not acquiesce,
and we should not be contented. Whether this state of affairs will ever
be cured by the sudden flash of some great philosophic discovery is
another matter. My present aim, at all events, is far more modest. But
they, at least, should make no complaint who hold that common-sense
beliefs, and science which is a development of common-sense beliefs,
are, if not true, at least on the way to truth. For this conviction
I share. I profess it; I desire to act upon it. And surely I cannot
act upon it better than by endeavouring, so far as I can, to place it
in the setting which shall most effectually preserve its intellectual
value. This, at all events, is the object to which the four lectures
that immediately follow are designed to contribute.
LECTURE VI
PERCEPTION, COMMON SENSE, AND SCIENCE
I
Nothing would seem easier, at first sight, than to give a general
description of the ordinary beliefs of ordinary people about our
familiar world of things and persons. It is the world in which we live;
it is for all men _a_ real world; it is for many men _the_ real world;
it is the world of common sense, the world where the plain man feels at
home, and where the practical man seeks refuge from the vain subtleties
of metaphysics. Our stock of beliefs about it may perhaps be difficult
to justify, but it seems strange that they should be difficult to
describe; yet difficult, I think, they are.
Some statements about it may, however, be made with confidence. It is
in space and time; i.e. the material things of which it is composed,
including living bodies, are extended, have mutual position, and
possess at least some measure of duration.
Things are not changed by a mere change of place, but a change of place
relative to an observer always changes their appearance _for him_.
Common sense is, therefore, compelled in this, as in countless other
cases, to distinguish the appearance of a thing from its reality; and
to hold, as an essential article of its working creed, that appearances
may alter, leaving realities unchanged.
Common sense does not, however, draw the inference that our experiences
of material things is other than direct and immediate. It has never
held the opinion—or, if you will, the heresy—that what we perceive (at
least by sight and touch) are states of our own mind, which somehow
copy or represent external things. Neither has it ever held that the
character or duration of external things in any way depends upon
our observations of them. In perception there is no reaction by the
perceiving mind on the object perceived. Things in their true reality
are not affected by mere observation, still less are they constituted
by it. When material objects are in question, common sense never
supposes that _esse_ and _percipi_ are identical.
But then, what, according to common sense, _are_ things in their true
reality? What are they “in themselves,” when no one is looking at them,
or when only some of their aspects are under observation?
We can, at all events, say what (according to common sense) things
are _not_. They are more than collections of aspects. If we could
simultaneously perceive a “thing” at a thousand different distances,
at a thousand different angles, under a thousand varieties of
illumination, with its interior ideally exposed in a thousand different
sections, common sense, if pressed, would, I suppose, still hold that
these were no more than specimens of the endless variety of ways in
which things may appear, without either changing their nature or
fully revealing what that nature is. But though common sense might
give this answer, it would certainly resent the question being put.
It finds no difficulty in carrying on its work without starting these
disturbing inquiries. It is content to say that, though a thing is
doubtless always more than the sum of those aspects of it to which
we happen to be attending, yet our knowledge _that_ it is and _what_
it is, however imperfect, is, for practical purposes, sufficiently
clear and trustworthy, requiring the support neither of metaphysics
nor psychology.—This, with all its difficulties, is, I believe, an
account, true as far as it goes, of the world of things as common sense
conceives it. This is the sort of world which science sets out to
explain. Let me give an illustration.
We perceive some object—let us say the sun. We perceive it directly
and not symbolically. What we see is not a mental image of the sun,
nor a complex of sensations caused by the sun; but the sun itself.
Moreover, this material external object retains its identity while it
varies in appearance. It is red in the morning; it is white at midday;
it is red once more in the evening; it may be obscured by clouds or
hidden in eclipse; it vanishes and reappears once in every twenty-four
hours; yet, amid all these changes and vanishings, its identity is
unquestioned. Though we perceive it differently at different times, and
though there are times when we do not perceive it at all, we know it
to be the same; nor do we for a moment believe (with Heraclitus) that
when it is lost to view it has, on that account, either altered its
character or ceased to exist.
In the main, therefore, experience is, according to common sense, a
very simple affair. We see something, or we feel something, or, like
Dr. Johnson, we kick something, and “there’s an end on’t.” Experience
is the source of all knowledge, and therefore of all explanation; but,
in itself, it seems scarcely to require to be explained. Common sense
is prepared to leave it where it finds it. No doubt the occurrence
of optical or other illusions may disturb this mood of intellectual
tranquillity. Common sense, when it has to consider the case of
appearances, some of which are held, on extraneous grounds, to be real
and others to be illusory, may feel that there are, after all, problems
raised by perception—by the direct experience of things—which are not
without their difficulties. But the case of illusions is exceptional,
and rarely disturbs the even tenor of our daily round.
II
Now science, as it gladly acknowledges, is but an extension of common
sense. It accepts, among other matters, the common-sense view of
perception. Like common sense, it distinguishes the thing as it is
from the thing as it appears. Like common sense, it regards the things
which are experienced as being themselves unaffected by experience.
But, unlike common sense, it devotes great attention to the way in
which experience is produced by things. Its business is with the causal
series. This, to be sure, is a subject which common sense does not
wholly ignore. It would acknowledge that we perceive a lamp through the
light which it sheds, and recognise a trumpet through the sound which
it emits; but the nature of light or sound, and the manner in which
they produce our experience of bright or sonorous objects, it hands
over to science for further investigation.
And the task is cheerfully undertaken. Science also deems perception to
be the source of all our knowledge of external nature. But it regards
it as something more, and different. For perception is itself a part
of nature, a natural process, the product of antecedent causes, the
cause of subsequent effects. It requires, therefore, like other natural
facts, to be observed and explained; and it is the business of science
to explain it.
Thus we are brought face to face with the contrast on which so much
of the argument of these lectures turns: the contrast between beliefs
considered as members of a cognitive series, and beliefs considered
as members of a causal series. In the cognitive series, beliefs of
perception are at the root of our whole knowledge of natural laws.
In the causal series, they are the effects of natural laws in actual
operation. This is so important an example of this dual state that you
must permit me to consider it in some detail.
We may examine what goes on between the perceiving person and the
thing he perceives from either end; but it is by no means a matter of
indifference with which end we begin. If we examine the relation of the
perceiver to the perceived it does not seem convenient or accurate to
describe that relation as a process. It is an experience, immediate and
intuitive; not indeed infallible, but direct and self-sufficient. If
I look at the sun, it is the sun I see, and not an image of the sun,
nor a sensation which suggests the sun, or symbolises the sun. Still
less do I see ethereal vibrations, or a retinal image, or a nervous
reaction, or a cerebral disturbance. For, in the act of perceiving, no
intermediate entities are themselves perceived.
But now if we, as it were, turn round, and, beginning at the other end,
consider the relation of the perceived to the perceiver, no similar
statements can be made. We find ourselves concerned, not with an
act of intuition, but with a physical process, which is complicated,
which occupies time, which involves many stages. We have left behind
cognition; we are plunged in causation. Experience is no longer the
immediate apprehension of fact; it is the transmission of a message
conveyed from the object to the percipient by relays of material
messengers. As to how the transmission is effected explanations vary
with the growth of science. They have been entirely altered more than
once since the modern era began, and with each alteration they become
more complicated. They depend, not on one branch of science only, but
on many. Newtonian astronomy, solar physics, the theory of radiation,
the optical properties of the atmosphere, the physiology of vision,
the psychology of perception, and I daresay many other branches of
research, have to be drawn upon: and all this to tell us what it is we
see, and how it is we come to see it.
III
Now there is no one who possesses the least smattering of philosophy
who does not know that the views I have just endeavoured to describe
are saturated with difficulties: difficulties connected with the nature
of perception; difficulties connected with the nature of the object as
perceived; difficulties connected with its unperceived physical basis;
difficulties connected with the relation in which these three stand to
each other. For common sense the material object consists of a certain
number of qualities and aspects which are perceived, an inexhaustible
number which might be perceived, but are not, and (perhaps) a vaguely
conceived “somewhat” lying behind both. The medieval Aristotelian,
if I rightly understand him (which very likely I do not), developed
this “somewhat” into the notion of substance—an entity somewhat
loosely connected with the qualities which it supported, and in no
way explaining them. There was “substance” in a piece of gold, and
“substance” in a piece of lead; but there was nothing unreasonable in
the endeavour to associate the qualities of gold with the substance of
lead, and thus for all practical purposes to turn lead into gold.
Modern science teaches a very different lesson. It has, perhaps,
not wholly abandoned the notion of material substance, if this be
defined as the unperceivable support of perceivable qualities; but it
persistently strives to connect the characteristics of matter with
its structure, and, among other characteristics, that of producing, or
helping to produce, in us those immediate perceptions which we describe
as our experience of matter itself.
An important stage in this endeavour was marked by the famous
distinction between the primary and the secondary qualities of matter:
the primary qualities being the attributes of external material things
which were deemed to be independent of the observer (for example,
impenetrability, density, weight, configuration); the secondary
qualities being those which, apart from observers endowed with senses
like our own, would either exist differently, or would not exist at all
(for example, colour and taste). On this view the primary qualities
were among the causes of the secondary qualities, and the secondary
qualities were transferred from the thing perceived to the person
perceiving.
I am not the least concerned to defend this theory. It has been much
derided, and is certainly open to attack. But something like it seems
to be an inevitable stage in the development of modern views of nature.
The whole effort of physical science is to discover the material or
non-psychical facts which shall, among other things, account for
our psychical experiences. It is true that there are men of science,
as well as philosophers, who regard all such constructions as purely
arbitrary—mere labour-saving devices which have nothing to do with
reality. But though I shall have something to say about these theories
in my next course of lectures, for the present I need only observe that
they do not represent ordinary scientific opinion, either as it is,
or as it has ever been. Science thinks, rightly or wrongly, that she
is concerned with a real world, which persists independently of our
experience: she has never assented to the doctrine that the object of
her patient investigations is no more than a well-contrived invention
for enabling us to foretell, and perhaps to modify, the course of our
personal feelings.
But then, if science is right, we are committed to a division between
the contents of immediate experience and its causes, which showed
itself dimly and tentatively in the distinction between the secondary
and the primary qualities of matter, but has become deeper and more
impassable with every advance in physics and physiology. It was
possible to maintain (though, I admit, not very easy) that, while the
secondary qualities of matter are due to the action of the primary
qualities on our organs of perception, the primary qualities themselves
are, nevertheless, the objects of direct experience. The fact, for
example, that colour is no more than a sensation need not preclude us
from perceiving the material qualities which, like shape, or motion, or
mass, are the external and independent causes to which the sensation is
due. I do not say that this view was ever explicitly entertained—nor
does it signify. For, if we accept the teaching of science, it can, I
suppose, be entertained no more. The physical causes of perception are
inferred, but not perceived. The real material world has been driven
by the growth of knowledge further and further into the realm of the
unseen, and now lies completely hidden from direct experience behind
the impenetrable screen of its own effects.
IV
For consider what the causal process of perception really is if we
trace it from the observed to the observer—if we follow the main
strands in the complex lines of communication through which the object
seen reveals itself to the man who sees it.
I revert to my previous example—the sun. We need not consider those
of its attributes which are notoriously arrived at by indirect
methods—which are not perceived but inferred—its magnitude, for
example, or its mass. Confining ourselves to what is directly
perceived, its angular size, its shape (projected on a plane),
its warmth, its brightness, its colour, its (relative) motion,
its separation from the observer in space—how are these immediate
experiences produced?
The answers have varied with the progress of science; nor, for my
present purpose, does it greatly matter which answers we adopt. Let us
take those which are commonly accepted at the present moment. They are
not only the truest, but the fullest; and for that very reason they
put the difficulty with which we are concerned in the highest relief.
We begin our causal series with electrons, or, if you do not accept
the electric theory of matter in any of its forms, then with atoms and
molecules. We start with these, because the sun is a collection of
them, and because it is their movements which set going the whole train
of causes and effects by which the sun produces in us the perception of
itself.
We may take, as the next stage, ethereal vibrations, of various
lengths and various amplitudes, sent travelling into space by the
moving particles. A fraction of these waves reaches our atmosphere, and
of that fraction a fraction reaches our eyes, and of that fraction a
further fraction falls within the narrow limits of length to which our
eyes are sensitive. It is through these that we are able to _see_ the
sun. Still another fraction, not necessarily identical in wave-lengths,
affects the nerves which produce in us the sensation of warmth. It is
through these that we are able to _feel_ the sun.
But, before we either see or feel, there is much still to be
accomplished. The causal series is not nearly completed. Complicated
neural processes, as yet only imperfectly understood; complicated
cerebral processes—as yet understood still less—both involving
physiological changes far more complicated than the electrical
“accelerations” or electro-magnetic disturbances with which we have
hitherto been dealing, bring us to the end of the material sequence of
causes and effects, and lay the message from the object perceived on
the threshold of the perceiving consciousness. So does a postman slip
into your letter-box a message which has been first written, then
carried by hand, then by a mail-cart, then by a train, then by hand
again, till it reaches its destination, and nothing further is required
except that what has been written should be read and understood.
Thus far the material process of transmission. The psychical process
has still to come. Psychology is a science, not less than physiology or
physics; and psychology has much to say on the subject of perception.
It is true that scientific explorers whose point of departure
is introspective; who concern themselves primarily with ideas,
conceptions, sensations, and so forth, rarely succeed in fitting their
conclusions without a break to those of their colleagues who begin
with the “external” causes of perception. The two tunnels, driven from
opposite sides of the mountain, do not always meet under its crest.
Still, we cannot on that account ignore the teaching of psychology on
the genesis of perceptual experience regarded, not as the ground of
knowledge, but as a natural product.
I do not mean to attempt a summary of psychology from this point
of view, any more than I have attempted a summary of physics or
physiology. My argument is really independent, in this case as in the
other, of particular systems. All I ask for is the admission that in
perception there are conditions antecedently supplied by the perceiving
consciousness which profoundly modify every perceptual experience—and
that these conditions (unlike Kant’s forms) are natural growths,
varying, like other natural growths, from individual to individual.
This admission must, I think, be made by every empirical psychologist,
to whatever school he happens to belong.
If this statement seems obscure in its general and abstract form,
consider a particular application of it. Let us assume, with many
psychologists, that Will, in the form of selective attention, lies
at the root of our perceptual activities; that we may therefore be
said, in a sense, voluntarily to create the objects we perceive; that
experience of the present is largely qualified by memories of the
past, and that the perceptual mould into which our sensations are run
is largely a social product—born of the intercourse between human
beings, and, in its turn, rendering that intercourse possible. Is it
not clear that, on assumptions like these, consciousness, so far from
passively receiving the messages conveyed to it through physical and
physiological channels, actively modifies their character?
V
But why, it may be asked, should these considerations involve any
difficulty? And, if there be a difficulty, what is its exact character?
In its most general form the difficulty is this. It is claimed by
science that its conclusions are based upon experience. The experience
spoken of is unquestionably the familiar perception of external things
and their movements as understood by common sense; and, however much
our powers of perception be increased by telescopes, microscopes,
balances, thermometers, electroscopes, and so forth, this common-sense
view suffers no alteration. The perceptions of a man of science are,
in essence, the perceptions of ordinary men in their ordinary moments,
beset with the same difficulties, accepted with the same assurance.
Whatever be the proper way of describing scientific results, the
experimental data on which they rest are sought and obtained in the
spirit of “naïf realism.”
On this foundation science proceeds to build up a theory of nature
by which the foundation itself is shattered. It saws off the branch
on which it is supported. It kicks down the ladder by which it has
climbed. It dissolves the thing perceived into a remote reality which
is neither perceived nor perceivable. It turns the world of common
sense into an illusion, and on this illusion it calmly rests its case.
But this is not the only logical embarrassment in which we are
involved. When science has supplied us with a description of external
things as they “really are,” and we proceed to ask how the physical
reality reveals itself to us in experience, a new difficulty arises,
or, if you like, the old difficulty with a new face. For science
requires us to admit that experience, from this point of view, is
equivalent to perception; and that perception is a remote psychological
effect of a long train of causes, physical and physiological,
originally set in motion by the external thing, but in no way
resembling it. Look carefully at this process from the outside, and
ask yourselves why there should be any such correspondence between the
first of these causes and the last of these effects, as should enable
us to know or infer the one from the other? Why should the long train
of unperceivable intermediaries that connect the perceived with the
perceiver be trusted to speak the truth?
I just now likened these intermediaries to relays of messengers. But
messengers are expected to hand on their message in the form in which
they have received it. The messengers change, but not the message. The
metaphor, therefore, is far too complimentary to the train of physical
causes which reveal the material thing to the perceiving consciousness.
The neural changes which are in immediate causal contiguity with that
psychical effect which we call “the experience of an external object”
have no resemblance whatever either to the thing as it is perceived
or to the thing as it really is. Nor have they any resemblance to the
proximate cause which sets them going, namely, the ethereal vibrations;
nor have these to the accelerated electrons which constitute the
incandescent object which we “experience” as the sun. Nor has the sun,
as experienced, the slightest resemblance to the sun as it really is.
Hume, in his “Dialogues on Natural Religion,” urges the absurdity of
arguing from an effect like the universe to a cause like God, since
the argument from a particular effect to a particular cause, or from
a particular cause to a particular effect, is only legitimate when we
have had some previous experience of that particular class of causal
sequence; and nobody, it is plain, has had the opportunity of observing
Creation. Whatever be the value of this argument in the case of God
and the world, it seems to me conclusive in the case of matter and
man. We cannot argue from purely psychical effects, like perceptions
and sensations, to external causes, like physiological processes or
ethereal vibrations, _unless_ we can experience both sets of facts in
causal relation. And this, if we accept the conclusions of science,
we can never do—partly because the intermediate members of the causal
series are unperceivable; partly because, if they were perceivable,
perception has been reduced by science to a purely psychical
effect—which obviously cannot include its material cause. This last
must for ever remain outside the closed circle of sensible experiences.
Here, of course, we find ourselves face to face with a familiar
objection to those philosophies of perception which deny that we
have any access to external reality, except through ideas which are
its copy. But they are in a better case than science. They need not
explicitly admit a discrepancy between their premises and their
conclusions. They arrive at the subjectivity of perception by methods
of introspection. They interrogate consciousness, and are convinced
that every experience can be analysed into sensations and ideas,
some of which, no doubt, suggest externality, but none of which are
external. If, then, the worst comes to the worst, they can, and often
do, lighten their philosophic ship by pitching the whole material
universe overboard as a bit of superfluous cargo. But physical science
cannot (at least in my opinion) do anything of the kind. Its whole
business is with the material universe. Its premises are experiences
of external things, not of internal sensation and ideas. And if it
has associated its fortunes with a theory of perception which treats
experience as a natural effect of the thing experienced; if it has
thereby wandered within sight of the perilous problems which haunt the
frontier where mind and matter meet, it has not done so in a spirit of
reckless adventure, but in the legitimate pursuit of its own affairs.
This does not necessarily make things easier. We are not here concerned
with questionings about the remoter provinces of knowledge—provinces
unexplored except by specialists, negligible by ordinary men engaged
on ordinary business. On the contrary, the difficulties to which I
have called your attention threaten the unquestioned assumption of
daily life, the presupposition of every scientific experiment, and the
meaning of every scientific generalisation. They cannot be ignored.
On the other hand, threaten as they may, these difficulties can never
modify our attitude either towards practical action or scientific
theory. Beliefs which were inevitable before remain inevitable still.
The supreme act of instinctive faith involved in the perception of
external objects stands quite unshaken. Whatever we may think of
Berkeley, we cannot give up Dr. Johnson. “Seeing,” says the proverb,
“is believing”; and it speaks better than it knows.
VI
Can we, then, adopt a middle course, and, imitating the serene
acquiescence of Hume, accept the position of sceptics in the study and
believers in the market-place? This seems eminently unsatisfactory;
and, since believers on this subject we must perforce remain, it
behoves us to consider how, and on what terms, we can best qualify our
scepticism.
Observe, then, that the particular difficulty which has been occupying
our attention arises in the main from the assumption that our
common-sense beliefs in the reality and character of material things
have no other foundation than the fact that we so perceive them. From
such premises it was impossible, it seemed, to infer that they exist
otherwise than as they are perceived; and still more impossible to
regard the immediate intuition by which we apprehend the object, and
the long-drawn sequence of causes by which the object is revealed, as
being the same process looked at from different ends.
But this difficulty is greatly mitigated if we hold that our belief in
an independent world of material objects, however it may be caused, is
neither a conclusion drawn from this or that particular experience nor
from all our experiences put together, but an irresistible assumption.
Grant the existence of external things, and it becomes possible and
legitimate to attempt explanations of their appearance, to regard
our perceptions of them as a psychical and physiological product
of material realities which do not themselves appear and cannot be
perceived. Refuse, on the other hand, to grant this assumption, and no
inductive legerdemain will enable us to erect our scientific theories
about an enduring world of material things upon the frail foundation
of successive personal perceptions.
If this does not seem clear at first sight it is, I think, because
we do not consider our experiences as a whole. A limited group of
experiences—say Faraday’s experiments with electro-magnets—may guide
us into new knowledge about the external world, including aspects of
that world which are not open to sense perception. But then these
experiences assume that this external world exists, they assume it
to be independent of perception, they assume it to be a cause of
perception. These assumptions once granted, experiment may be, and
is, the source of fresh discoveries. But experiment based on these
assumptions never can establish their truth; and if our theory
of knowledge requires us to hold that “no proposition should be
entertained with greater assurance than the proofs it is built on will
warrant,” our fate is sealed, and we need never hope to extricate
ourselves from the entanglements in which a too credulous empiricism
has involved us. This means that one at least of the inevitable
beliefs enumerated in the first lecture—the belief in an external
world—is a postulate which science is compelled to use but is unable to
demonstrate. How, then, are we to class it? It is not a law of thought
in the accepted meaning of that expression. We are not rationally
required to accept it by the very structure of our thinking faculties.
Many people, indeed, theoretically reject it; none, so far as I know,
regard it as self-evident. On the other hand, it is not an inference
from experience; neither is it an analytic judgment in which the
predicate is involved in the subject. Described in technical language,
it would seem to be _a priori_ without being necessary, and synthetic
without being empirical—qualities which, in combination, scarcely fit
into any familiar philosophic classification.
According to the view which I desire to press in these lectures, this
marks a philosophic omission. I regard the belief in an external world
as one of a class whose importance has been ignored by philosophy,
though all science depends on them. They refuse to be lost in the
common herd of empirical beliefs; though they have no claim to be
treated as axioms. We are inclined to accept them, but not rationally
compelled. The inclination may be so strong as practically to exclude
doubt; and it may diminish from this maximum to a faint feeling of
probability. But, whatever be the strength of these beliefs, and
whatever the nature of their claims, the importance of the part they
play in the development and structure of our current creed cannot
easily be exaggerated.
Before, however, I consider other specimens of this class, I must
interpolate a long parenthesis upon probability. I have just described
these fundamental beliefs as being “probable” in varying degrees.
Gradations of probability are familiar to the mathematical theorist.
Are we, then, here concerned with probability as conceived by the
mathematician? It is evidently essential to settle this question before
proceeding with the main argument; and I propose, therefore, to turn
aside and devote the next lecture to its consideration.
LECTURE VII
PROBABILITY, CALCULABLE AND INTUITIVE
I
I wish I were a mathematician. There is in the history of the
mathematical sciences, as in their substance, something that strangely
stirs the imagination even of the most ignorant. Its younger sister,
Logic, is as abstract, and its claims are yet wider. But it has never
shaken itself free from a certain pretentious futility: it always seems
to be telling us, in language quite unnecessarily technical, what we
understood much better before it was explained. It never helps to
discover, though it may guarantee discovery; it never persuades, though
it may show that persuasion has been legitimate; it never aids the work
of thought, it only acts as its auditor and accountant-general. I am
not referring, of course, to what I see described in recent works as
“modern scientific logic.” Of this I do not presume to speak. Still
less am I referring to so-called Inductive Logic. Of this it is scarce
worth while to speak.[9] I refer to their more famous predecessor, the
formal logic of the schools.
But in what different tones must we speak of mathematics! Mill, if
I remember rightly, said it was as full of mysteries as theology.
But while the value of theology for knowledge is disputed, the value
of mathematics for knowledge is indisputable. Its triumphs can be
appreciated by the most foolish, they appeal to the most material. If
they seem sometimes lost to ordinary view in the realms of abstract
infinities, they do not disdain to serve us in the humbler fields of
practice. They have helped mankind to all the greatest generalisations
about the physical universe: and without them we should still be
fumbling over simple problems of practical mechanics, entangled in a
costly and ineffectual empiricism.
But while we thank the mathematician for his aid in conquering Nature,
we envy him his powers of understanding her. Though he deals, it would
seem, entirely with abstractions, they are abstractions which, at his
persuasion, supply the key to the profoundest secrets of the physical
universe. He holds the clues to mazes where the clearest intellect,
unaided, would wander hopelessly astray. He belongs to a privileged
caste.
I intend no serious qualification of this high praise when I add that,
as regards the immediate subject of this lecture, I mean Probability,
mathematicians do not seem to have given ignorant inquirers like myself
all the aid which perhaps we have a right to ask. They have treated
the subject as a branch of applied mathematics. They have supplied us
with much excellent theory. They have exercised admirable skill in the
solution of problems. But I own that, when we inquire into the rational
basis of all this imposing superstructure, their explanations, from the
lay point of view, leave much to be desired.
“Probability,” says an often-quoted phrase of Butler, “is the guide
of life.” But the Bishop did not define the term; and he wrote
before the theory of probability had attained to all its present
dignities. Neither D’Alembert nor Laplace had discussed it. Quetelet
had not applied it to sociology, nor Maxwell to physics. Jevons had
not described it as the “noblest creation of the intellect.” It is
doubtful whether Butler meant by it exactly what the mathematicians
mean by it, and certain that he did not suspect any lurking ambiguity
in the expression.
Nor, indeed, would the existence of such ambiguity be commonly admitted
by any school of thought. The ordinary view is that the theory of
probabilities is, as Laplace described it, “common sense reduced to
calculation.” That there could be two kinds of probability, only one of
which fitted this description, would be generally regarded as a heresy.
But it is a heresy in which I myself believe; and which, with much
diffidence, I now propose to defend.
II
The well-known paradox of the theory of probabilities is that, to all
seeming, it can extract knowledge from ignorance and certainty from
doubt. The point cannot be better put than by Poincaré in discussing
the physical theory of gases, where the doctrine of probability
finds an important application. Let me give you his view—partly in
paraphrase, partly in translation. “For omniscience,” he says in
substance, “chance would not exist. It is but the measure of our
ignorance. When we describe an event as accidental we mean no more
than that we do not fully comprehend the conditions by which it was
brought about.
“But is this the full truth of the matter? Are not the laws of chance a
source of knowledge? And, stranger still, is it not sometimes easier to
generalise (say) about random movements than about movements which obey
even a simple law—witness the kinetic theory of gases? And, if this be
so, how can chance be the equivalent of ignorance? Ask a physicist to
explain what goes on in a gas. He might, perhaps, express his views in
some such terms as these: ‘You wish me to tell you about these complex
phenomena. If by ill luck I happened to know the laws which govern
them, I should be helpless. I should be lost in endless calculations,
and could never hope to supply you with an answer to your questions.
Fortunately for both of us, I am completely ignorant about the matter;
I can, therefore, supply you with an answer at once. This may seem odd.
But there is something odder still, namely, that my answer will be
right.’”
Now, what are the conditions which make it possible thus to extract
a correct answer from material apparently so unpromising? They
would seem to be a special combination of ignorance and knowledge,
the joint effect of which is to justify us in supposing that the
particular collection of facts or events with which we are concerned
are happening “at random.” If we could calculate the complex causes
which determine the fall of a penny, or the collisions of a molecule,
we might conceivably deal with pennies or molecules individually; and
the calculus of probability might be dispensed with. But we cannot;
ignorance, therefore, real or assumed, is thus one of the conditions
required to provide us with the kind of chaos to which the doctrine of
chances may most fittingly be applied. But there is another condition
not less needful, namely, knowledge—the knowledge that no extraneous
cause or internal tendency is infecting our chaotic group with some
bias or drift whereby its required randomness would be destroyed. Our
penny must be symmetrical, and Maxwell’s demons[10] must not meddle
with the molecules.
The slow disintegration of radium admirably illustrates the behaviour
of a group or collection possessing all the qualities which we require.
The myriad atoms of which the minutest visible fragment is composed are
numerous enough to neutralise eccentricities such as those which, in
the case of a game of chance, we call “runs of luck.” Of these atoms
we have no individual knowledge. What we know of one we know of all;
and we treat them not only as a collection, but as a collection made at
random. Now, physicists tell us that out of any such random collection
a certain proportion will disintegrate in a given time; and always the
same proportion. But whence comes their confidence in the permanence
of this ratio? Why are they so assured of its fixity that these random
explosions are thought to provide us with a better time-keeper than
the astronomical changes which have served mankind in that capacity
through immemorial ages? The reason is that we have here the necessary
ignorance and the necessary knowledge in a very complete form. Nothing
can well exceed our ignorance of the differences between one individual
radium atom and another, though relevant differences there must be.
Nothing, again, seems better assured than our knowledge that no
special bias or drift will make one collection of these atoms behave
differently from another. For the atomic disintegration is due to no
external shock or mutual reaction which might affect not one atom only,
but the whole group. A milligram of radium is not like a magazine of
shells, where if one spontaneously explodes all the rest follow suit.
The disruption of the atom is due to some internal principle of decay
whose effects no known external agent can either hasten or retard.
Although, therefore, the proportion of atoms which will disintegrate
in a given time can only be discovered, like the annual death-rate
among men, by observation, yet once discovered it is discovered for
ever. Our human death-rate not only may change, but does change. The
death-rate of radium atoms changes not. In the one case, causes are in
operation which modify both the organism and the surroundings on which
its life depends. In the other case, it would seem that the average of
successive generations of atoms does not vary, and that, once brought
into existence, they severally run their appointed course unaffected by
each other or by the world outside.
So far we have been concerned with groups or collections or series;
and about these the doctrine of chances and the theory of error
may apparently supply most valuable information. But in practical
affairs—nay, even in many questions of scientific speculation—we are
yet more concerned about individual happenings. We have, therefore,
next to ask how we can infer the probability of a particular event from
our knowledge of some group or series to which it belongs.
There seems at first sight no difficulty in this, provided we have
sufficient knowledge of the group or series of which the particular
event is a member. If we know that a tossed penny will in the long run
give heads and tails equally often, we do not hesitate to declare that
the chances of a particular throw giving “heads” are even. To expect
in any given case heads rather than tails, or tails rather than heads,
is inconsistent with the objective knowledge of the series which by
hypothesis we actually possess.
But what if our information about the group or series is much less
than this? Suppose that, instead of knowing that the two possible
alternatives do in fact occur equally often, we are in the less
advantageous position of knowing no reason why they should _not_ occur
equally often. We ought, I suppose, still to regard the chances of
a particular toss as even; although this estimate, expressed by the
same fraction (½) and held with the same confidence, is apparently
a conclusion based on ignorance, whereas the first conclusion was
apparently based on knowledge.
If, for example, we know that a die is fairly made and fairly thrown,
we can tell how often a particular number will turn up in a long series
of throws, and we can tell what the chances are that it will turn up on
the occasion of a single throw. Moreover, the two conclusions seem to
be logically connected.
But if we know that the die is loaded we can no longer say how the
numbers will be distributed in a series of throws, however long, though
we are sure that the distribution will be very different from what it
would have been had the die been a fair one. Nevertheless, we can still
say (before the event) what the chances are of a particular number
turning up on a single throw; and these chances are exactly the same
whether the die be loaded or whether it be fair—namely, one-sixth. Our
objective knowledge of the group or series has vanished, but, with the
theory of probability to help us, our subjective conviction on this
point apparently remains unchanged.
There is here, surely, a rather awkward transition from the “objective”
to the “subjective” point of view. We were dealing, in the first case,
with groups or series of events about which the doctrine of chances
enabled us to say something positive, something which experience would
always confirm if the groups or series were large enough. A perfect
calculator, endowed with complete knowledge of all the separate group
members, would have no correction to make in our conclusions. His
information would be more complete than our own, but not more accurate.
It is true that for him “averages” would have no interest and “chance”
no meaning. Nevertheless, he would agree that in a long series of
fair throws of a fair die any selected face would turn up one-sixth
times as often as all the others taken together. But in the second
case this is no longer so. Foresight based on complete knowledge would
apparently differ from foresight based on the calculation of chances.
Our calculator would be aware of the exact manner in which the die
was loaded, and of the exact advantage which this gave to certain
numbers. He would, therefore, know that in asserting the chance of any
particular number turning up on the first throw to be one-sixth, we
were wrong. In what sense, then, do we deem ourselves to have been
right?
The answer, I suppose, is that we were right _not_ about a group of
throws made with _this_ loaded die, but about a group of such groups
made with dice loaded at random—a group in which “randomness” was so
happily preserved among its constituent groups that its absence within
each of these groups was immaterial, and no one of the six alternative
numbers was favoured above another.
A similar reply might be given if we suppose our ignorance carried
yet a step further. Instead of knowing that our die was loaded, and
being ignorant only of the manner of its loading, we might be entirely
ignorant whether it was loaded or not. The chances of a particular
number turning up on the first throw would still be one-sixth. But the
series to which this estimate would refer would neither be one composed
of fair throws with a fair die, nor one composed of a series of throws
with dice loaded at random, but one composed of a series of throws with
dice chosen at random from a random collection of dice, loaded and not
loaded!
It seems plain that we have no experimental knowledge of series piled
on series after this fashion. Our conclusions about them are not based
on observation, nor collected from statistics. They are arrived at _a
priori_; and when the character of a series is arrived at _a priori_,
the probability of a particular event belonging to it can be arrived
at independently by the same method. No reference to the series is
required. The reason we estimate the chances against any one of the
six possible throws of a die as five to one under each and all of
the suppositions we have been discussing is that under none of them
have we any ground for thinking any one of the six more probable than
another;—even though we may have ground for thinking that in a series
of throws made with that particular die, some number, to us unknown,
will in fact turn up with exceptional frequency.
The most characteristic examples, therefore, of problems in probability
depend for their solution on a bold use of the “principle of sufficient
reason.” We treat alternatives as equally likely when we cannot see any
ground for supposing that one is more likely than another. This seems
sensible enough; but how far may we carry this process of extracting
knowledge from ignorance? An agnostic declines to offer any opinion
on the being of God because it is a matter about which he professes
to know nothing. But the universe either has a spiritual cause, or it
has not. If the agnostic is as ignorant as he supposes, he cannot have
any reason for preferring the first alternative to the second, or the
second to the first. Must he, therefore, conclude that the chances
of Theism are even? The man who knows this knows much. He knows, or
may know, that God’s existence is slightly more probable than his own
chance of winning a coup at Monte Carlo. He knows, or may know, the
exact fraction by which the two probabilities differ. How, then, can he
call himself an agnostic?
Every one must, I think, feel that such reasoning involves a misuse
of the theory of probability. But is that misuse without some
justification? The theory, unless I misread it, permits, or rather
requires, us to express by the same fraction probabilities based on
what is little less than complete knowledge, and probabilities based
on what is little more than complete ignorance. To arrive at a clear
conclusion, it seems only necessary to apply the “law of sufficient
reason” to defined alternatives; and it is apparently a matter of
perfect indifference whether we apply this law in its affirmative or
its negative shape; whether we say “there is every reason for believing
that such and such alternatives happen equally often,” or whether we
say “there is no reason for thinking that one alternative happens more
often than the other.” I do not criticise this method; still less do
I quarrel with it. On the contrary, I am lost in admiration of this
instrument of investigation, the quality of whose output seems to
depend so little on the sort of raw material with which it is supplied.
III
My object, indeed, is neither to discuss the basis on which rests
the calculus of probabilities—a task for which I own myself totally
unfit—nor yet to show that a certain obscurity hangs over the limits
within which it may properly be employed. I desire rather to suggest
that, wherever those limits are placed, there lies beyond them a kind
of probability yet more fundamental, about which the mathematical
methods can tell us nothing, though it possesses supreme value as a
“guide of life.”