 The
Problems of Philosophy
Bertrand Russell
CHAPTER XIII
KNOWLEDGE, ERROR, AND PROBABLE OPINION
THE question as to what we mean by truth and falsehood,
which we considered in the preceding chapter, is of much
less interest than the question as to how we can know what
is true and what is false. This question will occupy us
in the present chapter. There can be no doubt that some
of our beliefs are erroneous; thus we are led to inquire
what certainty we can ever have that such and such a belief
is not erroneous. In other words, can we ever know
anything at all, or do we merely sometimes by good luck
believe what is true? Before we can attack this question,
we must, however, first decide what we mean by 'knowing',
and this question is not so easy as might be supposed.
At first sight we might imagine that knowledge could be
defined as 'true belief'. When what we believe is true,
it might be supposed that we had achieved a knowledge of
what we believe. But this would not accord with the way
in which the word is commonly used. To take a very trivial
instance: If a man believes that the late Prime Minister's
last name began with a B, he believes what is true, since
the late Prime Minister was Sir Henry Campbell Bannerman.
But if he believes that Mr. Balfour was the late Prime Minister,
he will still believe that the late Prime Minister's last
name began with a B, yet this belief, though true, would
not be thought to constitute knowledge. If a newspaper,
by an intelligent anticipation, announces the result of
a battle before any telegram giving the result has been
received, it may by good fortune announce what afterwards
turns out to be the right result, and it may produce belief
in some of its less experienced readers. But in spite of
the truth of their belief, they cannot be said to have knowledge.
Thus it is clear that a true belief is not knowledge when
it is deduced from a false belief.
In like manner, a true belief cannot be called knowledge
when it is deduced by a fallacious process of reasoning,
even if the premisses from which it is deduced are true.
If I know that all Greeks are men and that Socrates was
a man, and I infer that Socrates was a Greek, I cannot be
said to know that Socrates was a Greek, because,
although my premisses and my conclusion are true, the conclusion
does not follow from the premisses.
But are we to say that nothing is knowledge except what
is validly deduced from true premisses? Obviously we cannot
say this. Such a definition is at once too wide and too
narrow. In the first place, it is too wide, because it is
not enough that our premisses should be true, they
must also be known. The man who believes that Mr.
Balfour was the late Prime Minister may proceed to draw
valid deductions from the true premiss that the late Prime
Minister's name began with a B, but he cannot be said to
know the conclusions reached by these deductions.
Thus we shall have to amend our definition by saying that
knowledge is what is validly deduced from known
premisses. This, however, is a circular definition: it assumes
that we already know what is meant by 'known premisses'.
It can, therefore, at best define one sort of knowledge,
the sort we call derivative, as opposed to intuitive knowledge.
We may say: 'Derivative knowledge is what is validly
deduced from premisses known intuitively'. In this statement
there is no formal defect, but it leaves the definition
of intuitive knowledge still to seek.
Leaving on one side, for the moment, the question of intuitive
knowledge, let us consider the above suggested definition
of derivative knowledge. The chief objection to it is that
it unduly limits knowledge. It constantly happens that people
entertain a true belief, which has grown up in them because
of some piece of intuitive knowledge from which it is capable
of being validly inferred, but from which it has not, as
a matter of fact, been inferred by any logical process.
Take, for example, the beliefs produced by reading. If
the newspapers announce the death of the King, we are fairly
well justified in believing that the King is dead, since
this is the sort of announcement which would not be made
if it were false. And we are quite amply justified in believing
that the newspaper asserts that the King is dead. But here
the intuitive knowledge upon which our belief is based is
knowledge of the existence of sense-data derived from looking
at the print which gives the news. This knowledge scarcely
rises into consciousness, except in a person who cannot
read easily. A child may be aware of the shapes of the letters,
and pass gradually and painfully to a realization of their
meaning. But anybody accustomed to reading passes at once
to what the letters mean, and is not aware, except on reflection,
that he has derived this knowledge from the sense-data called
seeing the printed letters. Thus although a valid inference
from the letters to their meaning is possible, and could
be performed by the reader, it s not in fact performed,
since he does not in fact perform any operation which can
be called logical inference. Yet it would be absurd to say
that the reader does not know that the newspaper
announces the King's death.
We must, therefore, admit as derivative knowledge whatever
is the result of intuitive knowledge even if by mere association,
provided there is a valid logical connexion, and
the person in question could become aware of this connexion
by reflection. There are in fact many ways, besides logical
inference, by which we pass from one belief to another:
the passage from the print to its meaning illustrates these
ways. These ways may be called 'psychological inference'.
We shall, then, admit such psychological inference as a
means of obtaining derivative knowledge, provided there
is a discoverable logical inference which runs parallel
to the psychological inference. This renders our definition
of derivative knowledge less precise than we could wish,
since the word 'discoverable' is vague: it does not tell
us how much reflection may be needed in order to make the
discovery. But in fact 'knowledge' is not a precise conception:
it merges into 'probable opinion', as we shall see more
fully in the course of the present chapter. A very precise
definition, therefore, should not be sought, since any such
definition must be more or less misleading.
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.
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