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.