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 is 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.
