 The
Problems of Philosophy
Bertrand Russell
CHAPTER XII
TRUTH AND FALSEHOOD
OUR knowledge of truths, unlike our knowledge of things,
has an opposite, namely error. So far as things
are concerned, we may know them or not know them, but there
is no positive state of mind which can be described as erroneous
knowledge of things, so long, at any rate, as we confine
ourselves to knowledge by acquaintance. Whatever we are
acquainted with must be something; we may draw wrong inferences
from our acquaintance, but the acquaintance itself cannot
be deceptive. Thus there is no dualism as regards acquaintance.
But as regards knowledge of truths, there is a dualism.
We may believe what is false as well as what is true. We
know that on very many subjects different people hold different
and incompatible opinions: hence some beliefs must be erroneous.
Since erroneous beliefs are often held just as strongly
as true beliefs, it becomes a difficult question how they
are to be distinguished from true beliefs. How are we to
know, in a given case, that our belief is not erroneous?
This is a question of the very greatest difficulty, to which
no completely satisfactory answer is possible. There is,
however, a preliminary question which is rather less difficult,
and that is: What do we mean by truth and falsehood?
It is this preliminary question which is to be considered
in this chapter.
In this chapter we are not asking how we can know whether
a belief is true or false: we are asking what is meant by
the question whether a belief is true or false. It is to
be hoped that a clear answer to this question may help us
to obtain an answer to the question what beliefs are true,
but for the present we ask only 'What is truth?' and 'What
is falsehood?' not 'What beliefs are true?' and 'What beliefs
are false?' It is very important to keep these different
questions entirely separate, since any confusion between
them is sure to produce an answer which is not really applicable
to either.
There are three points to observe in the attempt to discover
the nature of truth, three requisites which any theory must
fulfil.
(1) Our theory of truth must be such as to admit of its
opposite, falsehood. A good many philosophers have failed
adequately to satisfy this condition: they have constructed
theories according to which all our thinking ought to have
been true, and have then had the greatest difficulty in
finding a place for falsehood. In this respect our theory
of belief must differ from our theory of acquaintance, since
in the case of acquaintance it was not necessary to take
account of any opposite.
(2) It seems fairly evident that if there were no beliefs
there could be no falsehood, and no truth either, in the
sense in which truth is correlative to falsehood. If we
imagine a world of mere matter, there would be no room for
falsehood in such a world, and although it would contain
what may be called 'facts', it would not contain any truths,
in the sense in which truths are thins of the same kind
as falsehoods. In fact, truth and falsehood are properties
of beliefs and statements: hence a world of mere matter,
since it would contain no beliefs or statements, would also
contain no truth or falsehood.
(3) But, as against what we have just said, it is to be
observed that the truth or falsehood of a belief always
depends upon something which lies outside the belief itself.
If I believe that Charles I died on the scaffold, I believe
truly, not because of any intrinsic quality of my belief,
which could be discovered by merely examining the belief,
but because of an historical event which happened two and
a half centuries ago. If I believe that Charles I died in
his bed, I believe falsely: no degree of vividness in my
belief, or of care in arriving at it, prevents it from being
false, again because of what happened long ago, and not
because of any intrinsic property of my belief. Hence, although
truth and falsehood are properties of beliefs, they are
properties dependent upon the relations of the beliefs to
other things, not upon any internal quality of the beliefs.
The third of the above requisites leads us to adopt the
view -- which has on the whole been commonest among philosophers
-- that truth consists in some form of correspondence between
belief and fact. It is, however, by no means an easy matter
to discover a form of correspondence to which there are
no irrefutable objections. By this partly -- and partly
by the feeling that, if truth consists in a correspondence
of thought with something outside thought, thought can never
know when truth has been attained -- many philosophers have
been led to try to find some definition of truth which shall
not consist in relation to something wholly outside belief.
The most important attempt at a definition of this sort
is the theory that truth consists in coherence.
It is said that the mark of falsehood is failure to cohere
in the body of our beliefs, and that it is the essence of
a truth to form part of the completely rounded system which
is The Truth.
There is, however, a great difficulty in this view, or
rather two great difficulties. The first is that there is
no reason to suppose that only one coherent body
of beliefs is possible. It may be that, with sufficient
imagination, a novelist might invent a past for the world
that would perfectly fit on to what we know, and yet be
quite different from the real past. In more scientific matters,
it is certain that there are often two or more hypotheses
which account for all the known facts on some subject, and
although, in such cases, men of science endeavour to find
facts which will rule out all the hypotheses except one,
there is no reason why they should always succeed.
In philosophy, again, it seems not uncommon for two rival
hypotheses to be both able to account for all the facts.
Thus, for example, it is possible that life is one long
dream, and that the outer world has only that degree of
reality that the objects of dreams have; but although such
a view does not seem inconsistent with known facts, there
is no reason to prefer it to the common-sense view, according
to which other people and things do really exist. Thus coherence
as the definition of truth fails because there is no proof
that there can be only one coherent system.
The other objection to this definition of truth is that
it assumes the meaning of 'coherence' known, whereas, in
fact, 'coherence' presupposes the truth of the laws of logic.
Two propositions are coherent when both may be true, and
are incoherent when one at least must be false. Now in order
to know whether two propositions can both be true, we must
know such truths as the law of contradiction. For example,
the two propositions, 'this tree is a beech' and 'this tree
is not a beech', are not coherent, because of the law of
contradiction. But if the law of contradiction itself were
subjected to the test of coherence, we should find that,
if we choose to suppose it false, nothing will any longer
be incoherent with anything else. Thus the laws of logic
supply the skeleton or framework within which the test of
coherence applies, and they themselves cannot be established
by this test.
For the above two reasons, coherence cannot be accepted
as giving the meaning of truth, though it is often
a most important test of truth after a certain
amount of truth has become known.
Hence we are driven back to correspondence with fact
as constituting the nature of truth. It remains to define
precisely what we mean by 'fact', and what is the nature
of the correspondence which must subsist between belief
and fact, in order that belief may be true.
In accordance with our three requisites, we have to seek
a theory of truth which (1) allows truth to have an opposite,
namely falsehood, (2) makes truth a property of beliefs,
but (3) makes it a property wholly dependent upon the relation
of the beliefs to outside things.
The necessity of allowing for falsehood makes it impossible
to regard belief as a relation of the mind to a single object,
which could be said to be what is believed. If belief were
so regarded, we should find that, like acquaintance, it
would not admit of the opposition of truth and falsehood,
but would have to be always true. This may be made clear
by examples. Othello believes falsely that Desdemona loves
Cassio. We cannot say that this belief consists in a relation
to a single object, 'Desdemona's love for Cassio', for if
there were such an object, the belief would be true. There
is in fact no such object, and therefore Othello cannot
have any relation to such an object. Hence his belief cannot
possibly consist in a relation to this object.
It might be said that his belief is a relation to a different
object, namely 'that Desdemona loves Cassio'; but it is
almost as difficult to suppose that there is such an object
as this, when Desdemona does not love Cassio, as it was
to suppose that there is 'Desdemona's love for Cassio'.
Hence it will be better to seek for a theory of belief which
does not make it consist in a relation of the mind to a
single object.
It is common to think of relations as though they always
held between two terms, but in fact this is not
always the case. Some relations demand three terms, some
four, and so on. Take, for instance, the relation 'between'.
So long as only two terms come in, the relation 'between'
is impossible: three terms are the smallest number that
render it possible. York is between London and Edinburgh;
but if London and Edinburgh were the only places in the
world, there could be nothing which was between one place
and another. Similarly jealousy requires three
people: there can be no such relation that does not involve
three at least. Such a proposition as 'A wishes B to promote
C's marriage with D' involves a relation of four terms;
that is to say, A and B and C and D all come in, and the
relation involved cannot be expressed otherwise than in
a form involving all four. Instances might be multiplied
indefinitely, but enough has been said to show that there
are relations which require more than two terms before they
can occur.
The relation involved in judging or believing
must, if falsehood is to be duly allowed for, be taken to
be a relation between several terms, not between two. When
Othello believes that Desdemona loves Cassio, he must not
have before his mind a single object, 'Desdemona's love
for Cassio', or 'that Desdemona loves Cassio', for that
would require that there should be objective falsehoods,
which subsist independently of any minds; and this, though
not logically refutable, is a theory to be avoided if possible.
Thus it is easier to account for falsehood if we take judgement
to be a relation in which the mind and the various objects
concerned all occur severally; that is to say, Desdemona
and loving and Cassio must all be terms in the relation
which subsists when Othello believes that Desdemona loves
Cassio. This relation, therefore, is a relation of four
terms, since Othello also is one of the terms of the relation.
When we say that it is a relation of four terms, we do not
mean that Othello has a certain relation to Desdemona, and
has the same relation to loving and also to Cassio. This
may be true of some other relation than believing; but believing,
plainly, is not a relation which Othello has to each
of the three terms concerned, but to all of them
together: there is only one example of the relation of believing
involved, but this one example knits together four terms.
Thus the actual occurrence, at the moment when Othello is
entertaining his belief, is that the relation called 'believing'
is knitting together into one complex whole the four terms
Othello, Desdemona, loving, and Cassio. What is called belief
or judgement is nothing but this relation of believing or
judging, which relates a mind to several things other than
itself. An act of belief or of judgement is the
occurrence between certain terms at some particular time,
of the relation of believing or judging.
We are now in a position to understand what it is that
distinguishes a true judgement from a false one. For this
purpose we will adopt certain definitions. In every act
of judgement there is a mind which judges, and there are
terms concerning which it judges. We will call the mind
the subject in the judgement, and the remaining
terms the objects. Thus, when Othello judges that
Desdemona loves Cassio, Othello is the subject, while the
objects are Desdemona and loving and Cassio. The subject
and the objects together are called the constituents
of the judgement. It will be observed that the elation of
judging has what is called a 'sense' or 'direction'. We
may say, metaphorically, that it puts its objects in a certain
order, which we may indicate by means of the order
of the words in the sentence. (In an inflected language,
the same thing will be indicated by inflections, e.g. by
the difference between nominative and accusative.) Othello's
judgement that Cassio loves Desdemona differs from his judgement
that Desdemona loves Cassio, in spite of the fact that it
consists of the same constituents, because the relation
of judging places the constituents in a different order
in the two cases. Similarly, if Cassio judges that Desdemona
loves Othello, the constituents of the judgement are still
the same, but their order is different. This property of
having a 'sense' or 'direction' is one which the relation
of judging shares with all other relations. The 'sense'
of relations is the ultimate source of order and series
and a host of mathematical concepts; but we need not concern
ourselves further with this aspect.
We spoke of the relation called 'judging' or 'believing'
as knitting together into one complex whole the subject
and the objects. In this respect, judging is exactly like
every other relation. Whenever a relation holds between
two or more terms, it unites the terms into a complex whole.
If Othello loves Desdemona, there is such a complex whole
as 'Othello's love for Desdemona'. The terms united by the
relation may be themselves complex, or may be simple, but
the whole which results from their being united must be
complex. Wherever there is a relation which relates certain
terms, there is a complex object formed of the union of
those terms; and conversely, wherever there is a complex
object, there is a relation which relates its constituents.
When an act of believing occurs, there is a complex, in
which 'believing' is the uniting relation, and subject and
objects are arranged in a certain order by the 'sense' of
the relation of believing. Among the objects, as we saw
in considering 'Othello believes that Desdemona loves Cassio',
one must be a relation -- in this instance, the relation
'loving'. But this relation, as it occurs in the act of
believing, is not the relation which creates the unity of
the complex whole consisting of the subject and the objects.
The relation 'loving', as it occurs in the act of believing,
is one of the objects -- it is a brick in the structure,
not the cement. The cement is the relation 'believing'.
When the belief is true, there is another complex
unity, in which the relation which was one of the objects
of the belief relates the other objects. Thus, e.g., if
Othello believes truly that Desdemona loves Cassio,
then there is a complex unity, 'Desdemona's love for Cassio',
which is composed exclusively of the objects of
the belief, in the same order as they had in the belief,
with the relation which was one of the objects occurring
now as the cement that binds together the other objects
of the belief. On the other hand, when a belief is false,
there is no such complex unity composed only of the objects
of the belief. If Othello believes falsely that
Desdemona loves Cassio, then there is no such complex unity
as 'Desdemona's love for Cassio'.
Thus a belief is true when it corresponds
to a certain associated complex, and false when
it does not. Assuming, for the sake of definiteness, that
the objects of the belief are two terms and a relation,
the terms being put in a certain order by the 'sense' of
the believing, then if the two terms in that order are united
by the relation into a complex, the belief is true; if not,
it is false. This constitutes the definition of truth and
falsehood that we were in search of. Judging or believing
is a certain complex unity of which a mind is a constituent;
if the remaining constituents, taken in the order which
they have in the belief, form a complex unity, then the
belief is true; if not, it is false.
Thus although truth and falsehood are properties of beliefs,
yet they are in a sense extrinsic properties, for the condition
of the truth of a belief is something not involving beliefs,
or (in general) any mind at all, but only the objects
of the belief. A mind, which believes, believes truly when
there is a corresponding complex not involving
the mind, but only its objects. This correspondence ensures
truth, and its absence entails falsehood. Hence we account
simultaneously for the two facts that beliefs (a)
depend on minds for their existence, (b)
do not depend on minds for their truth.
We may restate our theory as follows: If we take such a
belief as 'Othello believes that Desdemona loves Cassio',
we will call Desdemona and Cassio the object-terms,
and loving the object-relation. If there is a complex
unity 'Desdemona's love for Cassio', consisting of the object-terms
related by the object-relation in the same order as they
have in the belief, then this complex unity is called the
fact corresponding to the belief. Thus a belief
is true when there is a corresponding fact, and is false
when there is no corresponding fact.
It will be seen that minds do not create truth or falsehood.
They create beliefs, but when once the beliefs are created,
the mind cannot make them true or false, except in the special
case where they concern future things which are within the
power of the person believing, such as catching trains.
What makes a belief true is a fact, and this fact
does not (except in exceptional cases) in any way involve
the mind of the person who has the belief.
Having now decided what we mean by truth and falsehood,
we have next to consider what ways there are of knowing
whether this or that belief is true or false. This consideration
will occupy the next chapter.
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