Books: The Problems of Philosophy
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Bertrand Russell >> The Problems of Philosophy
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The chief difficulty in regard to knowledge, however, does not arise
over derivative knowledge, but over intuitive knowledge. So long as
we are dealing with derivative knowledge, we have the test of
intuitive knowledge to fall back upon. But in regard to intuitive
beliefs, it is by no means easy to discover any criterion by which to
distinguish some as true and others as erroneous. In this question it
is scarcely possible to reach any very precise result: all our
knowledge of truths is infected with some degree of doubt, and a
theory which ignored this fact would be plainly wrong. Something may
be done, however, to mitigate the difficulties of the question.
Our theory of truth, to begin with, supplies the possibility of
distinguishing certain truths as _self-evident_ in a sense which
ensures infallibility. When a belief is true, we said, there is a
corresponding fact, in which the several objects of the belief form a
single complex. The belief is said to constitute _knowledge_ of this
fact, provided it fulfils those further somewhat vague conditions
which we have been considering in the present chapter. But in regard
to any fact, besides the knowledge constituted by belief, we may also
have the kind of knowledge constituted by _perception_ (taking this
word in its widest possible sense). For example, if you know the hour
of the sunset, you can at that hour know the fact that the sun is
setting: this is knowledge of the fact by way of knowledge of
_truths_; but you can also, if the weather is fine, look to the west
and actually see the setting sun: you then know the same fact by the
way of knowledge of _things_.
Thus in regard to any complex fact, there are, theoretically, two ways
in which it may be known: (1) by means of a judgement, in which its
several parts are judged to be related as they are in fact related;
(2) by means of _acquaintance_ with the complex fact itself, which may
(in a large sense) be called perception, though it is by no means
confined to objects of the senses. Now it will be observed that the
second way of knowing a complex fact, the way of acquaintance, is only
possible when there really is such a fact, while the first way, like
all judgement, is liable to error. The second way gives us the
complex whole, and is therefore only possible when its parts do
actually have that relation which makes them combine to form such a
complex. The first way, on the contrary, gives us the parts and the
relation severally, and demands only the reality of the parts and the
relation: the relation may not relate those parts in that way, and yet
the judgement may occur.
It will be remembered that at the end of Chapter XI we suggested that
there might be two kinds of self-evidence, one giving an absolute
guarantee of truth, the other only a partial guarantee. These two
kinds can now be distinguished.
We may say that a truth is self-evident, in the first and most
absolute sense, when we have acquaintance with the fact which
corresponds to the truth. When Othello believes that Desdemona loves
Cassio, the corresponding fact, if his belief were true, would be
'Desdemona's love for Cassio'. This would be a fact with which no one
could have acquaintance except Desdemona; hence in the sense of
self-evidence that we are considering, the truth that Desdemona loves
Cassio (if it were a truth) could only be self-evident to Desdemona.
All mental facts, and all facts concerning sense-data, have this same
privacy: there is only one person to whom they can be self-evident in
our present sense, since there is only one person who can be
acquainted with the mental things or the sense-data concerned. Thus
no fact about any particular existing thing can be self-evident to
more than one person. On the other hand, facts about universals do
not have this privacy. Many minds may be acquainted with the same
universals; hence a relation between universals may be known by
acquaintance to many different people. In all cases where we know by
acquaintance a complex fact consisting of certain terms in a certain
relation, we say that the truth that these terms are so related has
the first or absolute kind of self-evidence, and in these cases the
judgement that the terms are so related _must_ be true. Thus this
sort of self-evidence is an absolute guarantee of truth.
But although this sort of self-evidence is an absolute guarantee of
truth, it does not enable us to be _absolutely_ certain, in the case
of any given judgement, that the judgement in question is true.
Suppose we first perceive the sun shining, which is a complex fact,
and thence proceed to make the judgement 'the sun is shining'. In
passing from the perception to the judgement, it is necessary to
analyse the given complex fact: we have to separate out 'the sun' and
'shining' as constituents of the fact. In this process it is possible
to commit an error; hence even where a _fact_ has the first or
absolute kind of self-evidence, a judgement believed to correspond to
the fact is not absolutely infallible, because it may not really
correspond to the fact. But if it does correspond (in the sense
explained in the preceding chapter), then it _must_ be true.
The second sort of self-evidence will be that which belongs to
judgements in the first instance, and is not derived from direct
perception of a fact as a single complex whole. This second kind of
self-evidence will have degrees, from the very highest degree down to
a bare inclination in favour of the belief. Take, for example, the
case of a horse trotting away from us along a hard road. At first our
certainty that we hear the hoofs is complete; gradually, if we listen
intently, there comes a moment when we think perhaps it was
imagination or the blind upstairs or our own heartbeats; at last we
become doubtful whether there was any noise at all; then we _think_ we
no longer hear anything, and at last we _know_ we no longer hear
anything. In this process, there is a continual gradation of
self-evidence, from the highest degree to the least, not in the
sense-data themselves, but in the judgements based on them.
Or again: Suppose we are comparing two shades of colour, one blue and
one green. We can be quite sure they are different shades of colour;
but if the green colour is gradually altered to be more and more like
the blue, becoming first a blue-green, then a greeny-blue, then blue,
there will come a moment when we are doubtful whether we can see any
difference, and then a moment when we know that we cannot see any
difference. The same thing happens in tuning a musical instrument, or
in any other case where there is a continuous gradation. Thus
self-evidence of this sort is a matter of degree; and it seems plain
that the higher degrees are more to be trusted than the lower degrees.
In derivative knowledge our ultimate premisses must have some degree
of self-evidence, and so must their connexion with the conclusions
deduced from them. Take for example a piece of reasoning in geometry.
It is not enough that the axioms from which we start should be
self-evident: it is necessary also that, at each step in the
reasoning, the connexion of premiss and conclusion should be
self-evident. In difficult reasoning, this connexion has often only a
very small degree of self-evidence; hence errors of reasoning are not
improbable where the difficulty is great.
From what has been said it is evident that, both as regards intuitive
knowledge and as regards derivative knowledge, if we assume that
intuitive knowledge is trustworthy in proportion to the degree of its
self-evidence, there will be a gradation in trustworthiness, from the
existence of noteworthy sense-data and the simpler truths of logic and
arithmetic, which may be taken as quite certain, down to judgements
which seem only just more probable than their opposites. What we
firmly believe, if it is true, is called _knowledge_, provided it is
either intuitive or inferred (logically or psychologically) from
intuitive knowledge from which it follows logically. What we firmly
believe, if it is not true, is called _error_. What we firmly
believe, if it is neither knowledge nor error, and also what we
believe hesitatingly, because it is, or is derived from, something
which has not the highest degree of self-evidence, may be called
_probable opinion_. Thus the greater part of what would commonly pass
as knowledge is more or less probable opinion.
In regard to probable opinion, we can derive great assistance from
_coherence_, which we rejected as the _definition_ of truth, but may
often use as a _criterion_. A body of individually probable opinions,
if they are mutually coherent, become more probable than any one of
them would be individually. It is in this way that many scientific
hypotheses acquire their probability. They fit into a coherent system
of probable opinions, and thus become more probable than they would be
in isolation. The same thing applies to general philosophical
hypotheses. Often in a single case such hypotheses may seem highly
doubtful, while yet, when we consider the order and coherence which
they introduce into a mass of probable opinion, they become pretty
nearly certain. This applies, in particular, to such matters as the
distinction between dreams and waking life. If our dreams, night
after night, were as coherent one with another as our days, we should
hardly know whether to believe the dreams or the waking life. As it
is, the test of coherence condemns the dreams and confirms the waking
life. But this test, though it increases probability where it is
successful, never gives absolute certainty, unless there is certainty
already at some point in the coherent system. Thus the mere
organization of probable opinion will never, by itself, transform it
into indubitable knowledge.
CHAPTER XIV
THE LIMITS OF PHILOSOPHICAL KNOWLEDGE
In all that we have said hitherto concerning philosophy, we have
scarcely touched on many matters that occupy a great space in the
writings of most philosophers. Most philosophers--or, at any rate,
very many--profess to be able to prove, by _a priori_ metaphysical
reasoning, such things as the fundamental dogmas of religion, the
essential rationality of the universe, the illusoriness of matter, the
unreality of all evil, and so on. There can be no doubt that the hope
of finding reason to believe such theses as these has been the chief
inspiration of many life-long students of philosophy. This hope, I
believe, is vain. It would seem that knowledge concerning the
universe as a whole is not to be obtained by metaphysics, and that the
proposed proofs that, in virtue of the laws of logic such and such
things _must_ exist and such and such others cannot, are not capable
of surviving a critical scrutiny. In this chapter we shall briefly
consider the kind of way in which such reasoning is attempted, with a
view to discovering whether we can hope that it may be valid.
The great representative, in modern times, of the kind of view which
we wish to examine, was Hegel (1770-1831). Hegel's philosophy is very
difficult, and commentators differ as to the true interpretation of
it. According to the interpretation I shall adopt, which is that of
many, if not most, of the commentators and has the merit of giving an
interesting and important type of philosophy, his main thesis is that
everything short of the Whole is obviously fragmentary, and obviously
incapable of existing without the complement supplied by the rest of
the world. Just as a comparative anatomist, from a single bone, sees
what kind of animal the whole must have been, so the metaphysician,
according to Hegel, sees, from any one piece of reality, what the
whole of reality must be--at least in its large outlines. Every
apparently separate piece of reality has, as it were, hooks which
grapple it to the next piece; the next piece, in turn, has fresh
hooks, and so on, until the whole universe is reconstructed. This
essential incompleteness appears, according to Hegel, equally in the
world of thought and in the world of things. In the world of thought,
if we take any idea which is abstract or incomplete, we find, on
examination, that if we forget its incompleteness, we become involved
in contradictions; these contradictions turn the idea in question into
its opposite, or antithesis; and in order to escape, we have to find a
new, less incomplete idea, which is the synthesis of our original idea
and its antithesis. This new idea, though less incomplete than the
idea we started with, will be found, nevertheless, to be still not
wholly complete, but to pass into its antithesis, with which it must
be combined in a new synthesis. In this way Hegel advances until he
reaches the 'Absolute Idea', which, according to him, has no
incompleteness, no opposite, and no need of further development. The
Absolute Idea, therefore, is adequate to describe Absolute Reality;
but all lower ideas only describe reality as it appears to a partial
view, not as it is to one who simultaneously surveys the Whole. Thus
Hegel reaches the conclusion that Absolute Reality forms one single
harmonious system, not in space or time, not in any degree evil,
wholly rational, and wholly spiritual. Any appearance to the
contrary, in the world we know, can be proved logically--so he
believes--to be entirely due to our fragmentary piecemeal view of the
universe. If we saw the universe whole, as we may suppose God sees
it, space and time and matter and evil and all striving and struggling
would disappear, and we should see instead an eternal perfect
unchanging spiritual unity.
In this conception, there is undeniably something sublime, something
to which we could wish to yield assent. Nevertheless, when the
arguments in support of it are carefully examined, they appear to
involve much confusion and many unwarrantable assumptions. The
fundamental tenet upon which the system is built up is that what is
incomplete must be not self-subsistent, but must need the support of
other things before it can exist. It is held that whatever has
relations to things outside itself must contain some reference to
those outside things in its own nature, and could not, therefore, be
what it is if those outside things did not exist. A man's nature, for
example, is constituted by his memories and the rest of his knowledge,
by his loves and hatreds, and so on; thus, but for the objects which
he knows or loves or hates, he could not be what he is. He is
essentially and obviously a fragment: taken as the sum-total of
reality he would be self-contradictory.
This whole point of view, however, turns upon the notion of the
'nature' of a thing, which seems to mean 'all the truths about the
thing'. It is of course the case that a truth which connects one
thing with another thing could not subsist if the other thing did not
subsist. But a truth about a thing is not part of the thing itself,
although it must, according to the above usage, be part of the
'nature' of the thing. If we mean by a thing's 'nature' all the
truths about the thing, then plainly we cannot know a thing's 'nature'
unless we know all the thing's relations to all the other things in
the universe. But if the word 'nature' is used in this sense, we
shall have to hold that the thing may be known when its 'nature' is
not known, or at any rate is not known completely. There is a
confusion, when this use of the word 'nature' is employed, between
knowledge of things and knowledge of truths. We may have knowledge of
a thing by acquaintance even if we know very few propositions about
it--theoretically we need not know any propositions about it. Thus,
acquaintance with a thing does not involve knowledge of its 'nature'
in the above sense. And although acquaintance with a thing is
involved in our knowing any one proposition about a thing, knowledge
of its 'nature', in the above sense, is not involved. Hence, (1)
acquaintance with a thing does not logically involve a knowledge of
its relations, and (2) a knowledge of some of its relations does not
involve a knowledge of all of its relations nor a knowledge of its
'nature' in the above sense. I may be acquainted, for example, with
my toothache, and this knowledge may be as complete as knowledge by
acquaintance ever can be, without knowing all that the dentist (who is
not acquainted with it) can tell me about its cause, and without
therefore knowing its 'nature' in the above sense. Thus the fact that
a thing has relations does not prove that its relations are logically
necessary. That is to say, from the mere fact that it is the thing it
is we cannot deduce that it must have the various relations which in
fact it has. This only _seems_ to follow because we know it already.
It follows that we cannot prove that the universe as a whole forms a
single harmonious system such as Hegel believes that it forms. And if
we cannot prove this, we also cannot prove the unreality of space and
time and matter and evil, for this is deduced by Hegel from the
fragmentary and relational character of these things. Thus we are
left to the piecemeal investigation of the world, and are unable to
know the characters of those parts of the universe that are remote
from our experience. This result, disappointing as it is to those
whose hopes have been raised by the systems of philosophers, is in
harmony with the inductive and scientific temper of our age, and is
borne out by the whole examination of human knowledge which has
occupied our previous chapters.
Most of the great ambitious attempts of metaphysicians have proceeded
by the attempt to prove that such and such apparent features of the
actual world were self-contradictory, and therefore could not be real.
The whole tendency of modern thought, however, is more and more in the
direction of showing that the supposed contradictions were illusory,
and that very little can be proved _a priori_ from considerations of
what _must_ be. A good illustration of this is afforded by space and
time. Space and time appear to be infinite in extent, and infinitely
divisible. If we travel along a straight line in either direction, it
is difficult to believe that we shall finally reach a last point,
beyond which there is nothing, not even empty space. Similarly, if in
imagination we travel backwards or forwards in time, it is difficult
to believe that we shall reach a first or last time, with not even
empty time beyond it. Thus space and time appear to be infinite in
extent.
Again, if we take any two points on a line, it seems evident that
there must be other points between them however small the distance
between them may be: every distance can be halved, and the halves can
be halved again, and so on _ad infinitum_. In time, similarly,
however little time may elapse between two moments, it seems evident
that there will be other moments between them. Thus space and time
appear to be infinitely divisible. But as against these apparent
facts--infinite extent and infinite divisibility--philosophers have
advanced arguments tending to show that there could be no infinite
collections of things, and that therefore the number of points in
space, or of instants in time, must be finite. Thus a contradiction
emerged between the apparent nature of space and time and the supposed
impossibility of infinite collections.
Kant, who first emphasized this contradiction, deduced the
impossibility of space and time, which he declared to be merely
subjective; and since his time very many philosophers have believed
that space and time are mere appearance, not characteristic of the
world as it really is. Now, however, owing to the labours of the
mathematicians, notably Georg Cantor, it has appeared that the
impossibility of infinite collections was a mistake. They are not in
fact self-contradictory, but only contradictory of certain rather
obstinate mental prejudices. Hence the reasons for regarding space
and time as unreal have become inoperative, and one of the great
sources of metaphysical constructions is dried up.
The mathematicians, however, have not been content with showing that
space as it is commonly supposed to be is possible; they have shown
also that many other forms of space are equally possible, so far as
logic can show. Some of Euclid's axioms, which appear to common sense
to be necessary, and were formerly supposed to be necessary by
philosophers, are now known to derive their appearance of necessity
from our mere familiarity with actual space, and not from any _a
priori_ logical foundation. By imagining worlds in which these axioms
are false, the mathematicians have used logic to loosen the prejudices
of common sense, and to show the possibility of spaces differing--some
more, some less--from that in which we live. And some of these spaces
differ so little from Euclidean space, where distances such as we can
measure are concerned, that it is impossible to discover by
observation whether our actual space is strictly Euclidean or of one
of these other kinds. Thus the position is completely reversed.
Formerly it appeared that experience left only one kind of space to
logic, and logic showed this one kind to be impossible. Now, logic
presents many kinds of space as possible apart from experience, and
experience only partially decides between them. Thus, while our
knowledge of what is has become less than it was formerly supposed to
be, our knowledge of what may be is enormously increased. Instead of
being shut in within narrow walls, of which every nook and cranny
could be explored, we find ourselves in an open world of free
possibilities, where much remains unknown because there is so much to
know.
What has happened in the case of space and time has happened, to some
extent, in other directions as well. The attempt to prescribe to the
universe by means of _a priori_ principles has broken down; logic,
instead of being, as formerly, the bar to possibilities, has become
the great liberator of the imagination, presenting innumerable
alternatives which are closed to unreflective common sense, and
leaving to experience the task of deciding, where decision is
possible, between the many worlds which logic offers for our choice.
Thus knowledge as to what exists becomes limited to what we can learn
from experience--not to what we can actually experience, for, as we
have seen, there is much knowledge by description concerning things of
which we have no direct experience. But in all cases of knowledge by
description, we need some connexion of universals, enabling us, from
such and such a datum, to infer an object of a certain sort as implied
by our datum. Thus in regard to physical objects, for example, the
principle that sense-data are signs of physical objects is itself a
connexion of universals; and it is only in virtue of this principle
that experience enables us to acquire knowledge concerning physical
objects. The same applies to the law of causality, or, to descend to
what is less general, to such principles as the law of gravitation.
Principles such as the law of gravitation are proved, or rather are
rendered highly probable, by a combination of experience with some
wholly _a priori_ principle, such as the principle of induction. Thus
our intuitive knowledge, which is the source of all our other
knowledge of truths, is of two sorts: pure empirical knowledge, which
tells us of the existence and some of the properties of particular
things with which we are acquainted, and pure _a priori_ knowledge,
which gives us connexions between universals, and enables us to draw
inferences from the particular facts given in empirical knowledge.
Our derivative knowledge always depends upon some pure _a priori_
knowledge and usually also depends upon some pure empirical knowledge.
Philosophical knowledge, if what has been said above is true, does not
differ essentially from scientific knowledge; there is no special
source of wisdom which is open to philosophy but not to science, and
the results obtained by philosophy are not radically different from
those obtained from science. The essential characteristic of
philosophy, which makes it a study distinct from science, is
criticism. It examines critically the principles employed in science
and in daily life; it searches out any inconsistencies there may be in
these principles, and it only accepts them when, as the result of a
critical inquiry, no reason for rejecting them has appeared. If, as
many philosophers have believed, the principles underlying the
sciences were capable, when disengaged from irrelevant detail, of
giving us knowledge concerning the universe as a whole, such knowledge
would have the same claim on our belief as scientific knowledge has;
but our inquiry has not revealed any such knowledge, and therefore, as
regards the special doctrines of the bolder metaphysicians, has had a
mainly negative result. But as regards what would be commonly
accepted as knowledge, our result is in the main positive: we have
seldom found reason to reject such knowledge as the result of our
criticism, and we have seen no reason to suppose man incapable of the
kind of knowledge which he is generally believed to possess.
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