Bertrand Russell: The Problems of Philosophy
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
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
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
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
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
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.