The definition of truth and falsehood, which is our topic to-day, lies
strictly outside our general subject, namely the analysis of mind. From
the psychological standpoint, there may be different kinds of belief,
and different degrees of certainty, but there cannot be any purely
psychological means of distinguishing between true and false beliefs.
A belief is rendered true or false by relation to a fact, which may lie
outside the experience of the person entertaining the belief. Truth and
falsehood, except in the case of beliefs about our own minds, depend
upon the relations of mental occurrences to outside things, and thus
take us beyond the analysis of mental occurrences as they are in
themselves. Nevertheless, we can hardly avoid the consideration of truth
and falsehood. We wish to believe that our beliefs, sometimes at least,
yield KNOWLEDGE, and a belief does not yield knowledge unless it is
true. The question whether our minds are instruments of knowledge, and,
if so, in what sense, is so vital that any suggested analysis of mind
must be examined in relation to this question. To ignore this question
would be like describing a chronometer without regard to its accuracy
as a time-keeper, or a thermometer without mentioning the fact that it
measures temperature.
Many difficult questions arise in connection with knowledge. It is
difficult to define knowledge, difficult to decide whether we have any
knowledge, and difficult, even if it is conceded that we sometimes have
knowledge to discover whether we can ever know that we have knowledge
in this or that particular case. I shall divide the discussion into four
parts:
I. We may regard knowledge, from a behaviourist standpoint, as exhibited
in a certain kind of response to the environment. This response must
have some characteristics which it shares with those of scientific
instruments, but must also have others that are peculiar to knowledge.
We shall find that this point of view is important, but not exhaustive
of the nature of knowledge.
II. We may hold that the beliefs that constitute knowledge are
distinguished from such as are erroneous or uncertain by properties
which are intrinsic either to single beliefs or to systems of beliefs,
being in either case discoverable without reference to outside fact.
Views of this kind have been widely held among philosophers, but we
shall find no reason to accept them.
III. We believe that some beliefs are true, and some false. This raises
the problem of VERIFIABILITY: are there any circumstances which can
justifiably give us an unusual degree of certainty that such and such a
belief is true? It is obvious that there are circumstances which in fact
cause a certainty of this sort, and we wish to learn what we can from
examining these circumstances.
IV. Finally, there is the formal problem of defining truth and
falsehood, and deriving the objective reference of a proposition from
the meanings of its component words.
We will consider these four problems in succession.
I. We may regard a human being as an instrument, which makes various
responses to various stimuli. If we observe these responses from
outside, we shall regard them as showing knowledge when they display
two characteristics, ACCURACY and APPROPRIATENESS. These two are quite
distinct, and even sometimes incompatible. If I am being pursued by
a tiger, accuracy is furthered by turning round to look at him, but
appropriateness by running away without making any search for
further knowledge of the beast. I shall return to the question of
appropriateness later; for the present it is accuracy that I wish to
consider.
When we are viewing a man from the outside, it is not his beliefs,
but his bodily movements, that we can observe. His knowledge must be
inferred from his bodily movements, and especially from what he says
and writes. For the present we may ignore beliefs, and regard a man's
knowledge as actually consisting in what he says and does. That is to
say, we will construct, as far as possible, a purely behaviouristic
account of truth and falsehood.
If you ask a boy "What is twice two?" and the boy says "four," you take
that as prima facie evidence that the boy knows what twice two is. But
if you go on to ask what is twice three, twice four, twice five, and so
on, and the boy always answers "four," you come to the conclusion that
he knows nothing about it. Exactly similar remarks apply to scientific
instruments. I know a certain weather-cock which has the pessimistic
habit of always pointing to the north-east. If you were to see it first
on a cold March day, you would think it an excellent weather-cock; but
with the first warm day of spring your confidence would be shaken. The
boy and the weather-cock have the same defect: they do not vary their
response when the stimulus is varied. A good instrument, or a person
with much knowledge, will give different responses to stimuli which
differ in relevant ways. This is the first point in defining accuracy of
response.
We will now assume another boy, who also, when you first question him,
asserts that twice two is four. But with this boy, instead of asking him
different questions, you make a practice of asking him the same question
every day at breakfast. You find that he says five, or six, or seven, or
any other number at random, and you conclude that he also does not know
what twice two is, though by good luck he answered right the first time.
This boy is like a weather-cock which, instead of being stuck fast, is
always going round and round, changing without any change of wind. This
boy and weather-cock have the opposite defect to that of the previous
pair: they give different responses to stimuli which do not differ in
any relevant way.
In connection with vagueness in memory, we already had occasion to
consider the definition of accuracy. Omitting some of the niceties of
our previous discussion, we may say that an instrument is ACCURATE when
it avoids the defects of the two boys and weather-cocks, that is to say,
when--
(a) It gives different responses to stimuli which differ in relevant
ways;
(b) It gives the same response to stimuli which do not differ in
relevant ways.
What are relevant ways depends upon the nature and purpose of the
instrument. In the case of a weather-cock, the direction of the wind is
relevant, but not its strength; in the case of the boy, the meaning of
the words of your question is relevant, but not the loudness of your
voice, or whether you are his father or his schoolmaster If, however,
you were a boy of his own age, that would be relevant, and the
appropriate response would be different.
It is clear that knowledge is displayed by accuracy of response to
certain kinds of stimuli, e.g. examinations. Can we say, conversely,
that it consists wholly of such accuracy of response? I do not think
we can; but we can go a certain distance in this direction. For this
purpose we must define more carefully the kind of accuracy and the kind
of response that may be expected where there is knowledge.
From our present point of view, it is difficult to exclude perception
from knowledge; at any rate, knowledge is displayed by actions based
upon perception. A bird flying among trees avoids bumping into their
branches; its avoidance is a response to visual sensations. This
response has the characteristic of accuracy, in the main, and leads
us to say that the bird "knows," by sight, what objects are in its
neighbourhood. For a behaviourist, this must certainly count as
knowledge, however it may be viewed by analytic psychology. In this
case, what is known, roughly, is the stimulus; but in more advanced
knowledge the stimulus and what is known become different. For example,
you look in your calendar and find that Easter will be early next year.
Here the stimulus is the calendar, whereas the response concerns the
future. Even this can be paralleled among instruments: the behaviour of
the barometer has a present stimulus but foretells the future, so that
the barometer might be said, in a sense, to know the future. However
that may be, the point I am emphasizing as regards knowledge is that
what is known may be quite different from the stimulus, and no part of
the cause of the knowledge-response. It is only in sense-knowledge that
the stimulus and what is known are, with qualifications, identifiable.
In knowledge of the future, it is obvious that they are totally
distinct, since otherwise the response would precede the stimulus. In
abstract knowledge also they are distinct, since abstract facts have no
date. In knowledge of the past there are complications, which we must
briefly examine.
Every form of memory will be, from our present point of view, in one
sense a delayed response. But this phrase does not quite clearly
express what is meant. If you light a fuse and connect it with a heap of
dynamite, the explosion of the dynamite may be spoken of, in a sense,
as a delayed response to your lighting of the fuse. But that only means
that it is a somewhat late portion of a continuous process of which the
earlier parts have less emotional interest. This is not the case
with habit. A display of habit has two sorts of causes: (a) the past
occurrences which generated the habit, (b) the present occurrence which
brings it into play. When you drop a weight on your toe, and say what
you do say, the habit has been caused by imitation of your undesirable
associates, whereas it is brought into play by the dropping of the
weight. The great bulk of our knowledge is a habit in this sense:
whenever I am asked when I was born, I reply correctly by mere habit. It
would hardly be correct to say that getting born was the stimulus, and
that my reply is a delayed response But in cases of memory this way
of speaking would have an element of truth. In an habitual memory, the
event remembered was clearly an essential part of the stimulus to the
formation of the habit. The present stimulus which brings the habit into
play produces a different response from that which it would produce if
the habit did not exist. Therefore the habit enters into the causation
of the response, and so do, at one remove, the causes of the habit. It
follows that an event remembered is an essential part of the causes of
our remembering.
In spite, however, of the fact that what is known is SOMETIMES an
indispensable part of the cause of the knowledge, this circumstance is,
I think, irrelevant to the general question with which we are concerned,
namely What sort of response to what sort of stimulus can be regarded
as displaying knowledge? There is one characteristic which the response
must have, namely, it must consist of voluntary movements. The need
of this characteristic is connected with the characteristic of
APPROPRIATENESS, which I do not wish to consider as yet. For the present
I wish only to obtain a clearer idea of the sort of ACCURACY that a
knowledge-response must have. It is clear from many instances that
accuracy, in other cases, may be purely mechanical. The most complete
form of accuracy consists in giving correct answers to questions, an
achievement in which calculating machines far surpass human beings. In
asking a question of a calculating machine, you must use its language:
you must not address it in English, any more than you would address
an Englishman in Chinese. But if you address it in the language it
understands, it will tell you what is 34521 times 19987, without a
moment's hesitation or a hint of inaccuracy. We do not say the machine
KNOWS the answer, because it has no purpose of its own in giving the
answer: it does not wish to impress you with its cleverness, or feel
proud of being such a good machine. But as far as mere accuracy goes,
the machine leaves nothing to be desired.
Accuracy of response is a perfectly clear notion in the case of answers
to questions, but in other cases it is much more obscure. We may say
generally that an object whether animate or inanimate, is "sensitive" to
a certain feature of the environment if it behaves differently according
to the presence or absence of that feature. Thus iron is sensitive to
anything magnetic. But sensitiveness does not constitute knowledge, and
knowledge of a fact which is not sensible is not sensitiveness to
that fact, as we have seen in distinguishing the fact known from the
stimulus. As soon as we pass beyond the simple case of question and
answer, the definition of knowledge by means of behaviour demands the
consideration of purpose. A carrier pigeon flies home, and so we say
it "knows" the way. But if it merely flew to some place at random, we
should not say that it "knew" the way to that place, any more than a
stone rolling down hill knows the way to the valley.
On the features which distinguish knowledge from accuracy of response in
general, not much can be said from a behaviourist point of view without
referring to purpose. But the necessity of SOMETHING besides accuracy of
response may be brought out by the following consideration: Suppose
two persons, of whom one believed whatever the other disbelieved,
and disbelieved whatever the other believed. So far as accuracy and
sensitiveness of response alone are concerned, there would be nothing to
choose between these two persons. A thermometer which went down for warm
weather and up for cold might be just as accurate as the usual kind; and
a person who always believes falsely is just as sensitive an instrument
as a person who always believes truly. The observable and practical
difference between them would be that the one who always believed
falsely would quickly come to a bad end. This illustrates once more that
accuracy of response to stimulus does not alone show knowledge, but must
be reinforced by appropriateness, i.e. suitability for realizing one's
purpose. This applies even in the apparently simple case of answering
questions: if the purpose of the answers is to deceive, their falsehood,
not their truth, will be evidence of knowledge. The proportion of
the combination of appropriateness with accuracy in the definition
of knowledge is difficult; it seems that both enter in, but that
appropriateness is only required as regards the general type of
response, not as regards each individual instance.
II. I have so far assumed as unquestionable the view that the truth or
falsehood of a belief consists in a relation to a certain fact,
namely the objective of the belief. This view has, however, been often
questioned. Philosophers have sought some intrinsic criterion by which
true and false beliefs could be distinguished.* I am afraid their chief
reason for this search has been the wish to feel more certainty than
seems otherwise possible as to what is true and what is false. If
we could discover the truth of a belief by examining its intrinsic
characteristics, or those of some collection of beliefs of which it
forms part, the pursuit of truth, it is thought, would be a less arduous
business than it otherwise appears to be. But the attempts which
have been made in this direction are not encouraging. I will take two
criteria which have been suggested, namely, (1) self-evidence, (2)
mutual coherence. If we can show that these are inadequate, we may
feel fairly certain that no intrinsic criterion hitherto suggested will
suffice to distinguish true from false beliefs.
* The view that such a criterion exists is generally held by
those whose views are in any degree derived from Hegel. It
may be illustrated by the following passage from Lossky,
"The Intuitive Basis of Knowledge" (Macmillan, 1919), p.
268: "Strictly speaking, a false judgment is not a judgment
at all. The predicate does not follow from the subject S
alone, but from the subject plus a certain addition C, WHICH
IN NO SENSE BELONGS TO THE CONTENT OF THE JUDGMENT. What
takes place may be a process of association of ideas, of
imagining, or the like, but is not a process of judging. An
experienced psychologist will be able by careful observation
to detect that in this process there is wanting just the
specific element of the objective dependence of the
predicate upon the subject which is characteristic of a
judgment. It must be admitted, however, that an exceptional
power of observation is needed in order to distinguish, by
means of introspection, mere combination of ideas from
judgments."
(1) Self-evidence.--Some of our beliefs seem to be peculiarly
indubitable. One might instance the belief that two and two are four,
that two things cannot be in the same place at the same time, nor one
thing in two places, or that a particular buttercup that we are seeing
is yellow. The suggestion we are to examine is that such: beliefs have
some recognizable quality which secures their truth, and the truth of
whatever is deduced from them according to self-evident principles of
inference. This theory is set forth, for example, by Meinong in his
book, "Ueber die Erfahrungsgrundlagen unseres Wissens."
If this theory is to be logically tenable, self-evidence must not
consist merely in the fact that we believe a proposition. We believe
that our beliefs are sometimes erroneous, and we wish to be able to
select a certain class of beliefs which are never erroneous. If we
are to do this, it must be by some mark which belongs only to certain
beliefs, not to all; and among those to which it belongs there must be
none that are mutually inconsistent. If, for example, two propositions
p and q were self-evident, and it were also self-evident that p and q
could not both be true, that would condemn self-evidence as a guarantee
of truth. Again, self-evidence must not be the same thing as the absence
of doubt or the presence of complete certainty. If we are completely
certain of a proposition, we do not seek a ground to support our belief.
If self-evidence is alleged as a ground of belief, that implies that
doubt has crept in, and that our self-evident proposition has not
wholly resisted the assaults of scepticism. To say that any given person
believes some things so firmly that he cannot be made to doubt them is
no doubt true. Such beliefs he will be willing to use as premisses in
reasoning, and to him personally they will seem to have as much evidence
as any belief can need. But among the propositions which one man finds
indubitable there will be some that another man finds it quite possible
to doubt. It used to seem self-evident that there could not be men at
the Antipodes, because they would fall off, or at best grow giddy from
standing on their heads. But New Zealanders find the falsehood of this
proposition self-evident. Therefore, if self-evidence is a guarantee of
truth, our ancestors must have been mistaken in thinking their beliefs
about the Antipodes self-evident. Meinong meets this difficulty by
saying that some beliefs are falsely thought to be self-evident, but in
the case of others it is self-evident that they are self-evident, and
these are wholly reliable. Even this, however, does not remove the
practical risk of error, since we may mistakenly believe it self-evident
that a certain belief is self-evident. To remove all risk of error, we
shall need an endless series of more and more complicated self-evident
beliefs, which cannot possibly be realized in practice. It would seem,
therefore, that self-evidence is useless as a practical criterion for
insuring truth.
The same result follows from examining instances. If we take the four
instances mentioned at the beginning of this discussion, we shall
find that three of them are logical, while the fourth is a judgment of
perception. The proposition that two and two are four follows by purely
logical deduction from definitions: that means that its truth results,
not from the properties of objects, but from the meanings of symbols.
Now symbols, in mathematics, mean what we choose; thus the feeling of
self-evidence, in this case, seems explicable by the fact that the whole
matter is within our control. I do not wish to assert that this is
the whole truth about mathematical propositions, for the question is
complicated, and I do not know what the whole truth is. But I do wish to
suggest that the feeling of self-evidence in mathematical propositions
has to do with the fact that they are concerned with the meanings of
symbols, not with properties of the world such as external observation
might reveal.
Similar considerations apply to the impossibility of a thing being in
two places at once, or of two things being in one place at the same
time. These impossibilities result logically, if I am not mistaken, from
the definitions of one thing and one place. That is to say, they are not
laws of physics, but only part of the intellectual apparatus which we
have manufactured for manipulating physics. Their self-evidence, if this
is so, lies merely in the fact that they represent our decision as to
the use of words, not a property of physical objects.
Judgments of perception, such as "this buttercup is yellow," are in
a quite different position from judgments of logic, and their
self-evidence must have a different explanation. In order to arrive at
the nucleus of such a judgment, we will eliminate, as far as possible,
the use of words which take us beyond the present fact, such as
"buttercup" and "yellow." The simplest kind of judgment underlying the
perception that a buttercup is yellow would seem to be the perception of
similarity in two colours seen simultaneously. Suppose we are seeing
two buttercups, and we perceive that their colours are similar. This
similarity is a physical fact, not a matter of symbols or words; and it
certainly seems to be indubitable in a way that many judgments are not.
The first thing to observe, in regard to such judgments, is that as they
stand they are vague. The word "similar" is a vague word, since there
are degrees of similarity, and no one can say where similarity ends
and dissimilarity begins. It is unlikely that our two buttercups have
EXACTLY the same colour, and if we judged that they had we should have
passed altogether outside the region of self-evidence. To make our
proposition more precise, let us suppose that we are also seeing a
red rose at the same time. Then we may judge that the colours of the
buttercups are more similar to each other than to the colour of the
rose. This judgment seems more complicated, but has certainly gained
in precision. Even now, however, it falls short of complete precision,
since similarity is not prima facie measurable, and it would require
much discussion to decide what we mean by greater or less similarity. To
this process of the pursuit of precision there is strictly no limit.
The next thing to observe (although I do not personally doubt that most
of our judgments of perception are true) is that it is very difficult to
define any class of such judgments which can be known, by its intrinsic
quality, to be always exempt from error. Most of our judgments of
perception involve correlations, as when we judge that a certain noise
is that of a passing cart. Such judgments are all obviously liable to
error, since there is no correlation of which we have a right to be
certain that it is invariable. Other judgments of perception are derived
from recognition, as when we say "this is a buttercup," or even merely
"this is yellow." All such judgments entail some risk of error,
though sometimes perhaps a very small one; some flowers that look like
buttercups are marigolds, and colours that some would call yellow others
might call orange. Our subjective certainty is usually a result of
habit, and may lead us astray in circumstances which are unusual in ways
of which we are unaware.
For such reasons, no form of self-evidence seems to afford an absolute
criterion of truth. Nevertheless, it is perhaps true that judgments
having a high degree of subjective certainty are more apt to be true
than other judgments. But if this be the case, it is a result to be
demonstrated, not a premiss from which to start in defining truth and
falsehood. As an initial guarantee, therefore, neither self-evidence nor
subjective certainty can be accepted as adequate.
(2) Coherence.--Coherence as the definition of truth is advocated by
idealists, particularly by those who in the main follow Hegel. It is set
forth ably in Mr. Joachim's book, "The Nature of Truth" (Oxford, 1906).
According to this view, any set of propositions other than the whole
of truth can be condemned on purely logical grounds, as internally
inconsistent; a single proposition, if it is what we should ordinarily
call false, contradicts itself irremediably, while if it is what we
should ordinarily call true, it has implications which compel us to
admit other propositions, which in turn lead to others, and so on, until
we find ourselves committed to the whole of truth. One might illustrate
by a very simple example: if I say "so-and-so is a married man," that
is not a self-subsistent proposition. We cannot logically conceive of a
universe in which this proposition constituted the whole of truth. There
must be also someone who is a married woman, and who is married to
the particular man in question. The view we are considering regards
everything that can be said about any one object as relative in the same
sort of way as "so-and-so is a married man." But everything, according
to this view, is relative, not to one or two other things, but to all
other things, so that from one bit of truth the whole can be inferred.
The fundamental objection to this view is logical, and consists in a
criticism of its doctrine as to relations. I shall omit this line of
argument, which I have developed elsewhere.* For the moment I will
content myself with saying that the powers of logic seem to me very
much less than this theory supposes. If it were taken seriously, its
advocates ought to profess that any one truth is logically inferable
from any other, and that, for example, the fact that Caesar conquered
Gaul, if adequately considered, would enable us to discover what the
weather will be to-morrow. No such claim is put forward in practice, and
the necessity of empirical observation is not denied; but according to
the theory it ought to be.
* In the article on "The Monistic Theory of Truth" in
"Philosophical Essays" (Longmans, 1910), reprinted from the
"Proceedings of the Aristotelian Society," 1906-7.
Another objection is that no endeavour is made to show that we cannot
form a consistent whole composed partly or wholly of false propositions,
as in a novel. Leibniz's conception of many possible worlds seems to
accord much better with modern logic and with the practical empiricism
which is now universal. The attempt to deduce the world by pure thought
is attractive, and in former times was largely supposed capable of
success. But nowadays most men admit that beliefs must be tested by
observation, and not merely by the fact that they harmonize with other
beliefs. A consistent fairy-tale is a different thing from truth,
however elaborate it may be. But to pursue this topic would lead us
into difficult technicalities; I shall therefore assume, without further
argument, that coherence is not sufficient as a definition of truth.
III. Many difficult problems arise as regards the verifiability of
beliefs. We believe various things, and while we believe them we think
we know them. But it sometimes turns out that we were mistaken, or at
any rate we come to think we were. We must be mistaken either in our
previous opinion or in our subsequent recantation; therefore our beliefs
are not all correct, and there are cases of belief which are not cases
of knowledge. The question of verifiability is in essence this: can we
discover any set of beliefs which are never mistaken or any test which,
when applicable, will always enable us to discriminate between true
and false beliefs? Put thus broadly and abstractly, the answer must be
negative. There is no way hitherto discovered of wholly eliminating the
risk of error, and no infallible criterion. If we believe we have found
a criterion, this belief itself may be mistaken; we should be begging
the question if we tried to test the criterion by applying the criterion
to itself.
But although the notion of an absolute criterion is chimerical, there
may be relative criteria, which increase the probability of truth.
Common sense and science hold that there are. Let us see what they have
to say.
One of the plainest cases of verification, perhaps ultimately the only
case, consists in the happening of something expected. You go to the
station believing that there will be a train at a certain time; you
find the train, you get into it, and it starts at the expected time This
constitutes verification, and is a perfectly definite experience. It is,
in a sense, the converse of memory instead of having first sensations
and then images accompanied by belief, we have first images accompanied
by belief and then sensations. Apart from differences as to the
time-order and the accompanying feelings, the relation between image and
sensation is closely similar in the two cases of memory and expectation;
it is a relation of similarity, with difference as to causal
efficacy--broadly, the image has the psychological but not the physical
effects that the sensation would have. When an image accompanied by
an expectation-belief is thus succeeded by a sensation which is the
"meaning" of the image, we say that the expectation-belief has been
verified. The experience of verification in this sense is exceedingly
familiar; it happens every time that accustomed activities have results
that are not surprising, in eating and walking and talking and all our
daily pursuits.
But although the experience in question is common, it is not wholly easy
to give a theoretical account of it. How do we know that the sensation
resembles the previous image? Does the image persist in presence of the
sensation, so that we can compare the two? And even if SOME image does
persist, how do we know that it is the previous image unchanged? It does
not seem as if this line of inquiry offered much hope of a successful
issue. It is better, I think, to take a more external and causal view of
the relation of expectation to expected occurrence. If the occurrence,
when it comes, gives us the feeling of expectedness, and if the
expectation, beforehand, enabled us to act in a way which proves
appropriate to the occurrence, that must be held to constitute the
maximum of verification. We have first an expectation, then a sensation
with the feeling of expectedness related to memory of the expectation.
This whole experience, when it occurs, may be defined as verification,
and as constituting the truth of the expectation. Appropriate action,
during the period of expectation, may be regarded as additional
verification, but is not essential. The whole process may be illustrated
by looking up a familiar quotation, finding it in the expected words,
and in the expected part of the book. In this case we can strengthen
the verification by writing down beforehand the words which we expect to
find.
I think all verification is ultimately of the above sort. We verify a
scientific hypothesis indirectly, by deducing consequences as to the
future, which subsequent experience confirms. If somebody were to doubt
whether Caesar had crossed the Rubicon, verification could only be
obtained from the future. We could proceed to display manuscripts to our
historical sceptic, in which it was said that Caesar had behaved in this
way. We could advance arguments, verifiable by future experience, to
prove the antiquity of the manuscript from its texture, colour, etc. We
could find inscriptions agreeing with the historian on other points,
and tending to show his general accuracy. The causal laws which our
arguments would assume could be verified by the future occurrence of
events inferred by means of them. The existence and persistence of
causal laws, it is true, must be regarded as a fortunate accident, and
how long it will continue we cannot tell. Meanwhile verification remains
often practically possible. And since it is sometimes possible, we
can gradually discover what kinds of beliefs tend to be verified by
experience, and what kinds tend to be falsified; to the former kinds
we give an increased degree of assent, to the latter kinds a diminished
degree. The process is not absolute or infallible, but it has been
found capable of sifting beliefs and building up science. It affords
no theoretical refutation of the sceptic, whose position must remain
logically unassailable; but if complete scepticism is rejected, it gives
the practical method by which the system of our beliefs grows gradually
towards the unattainable ideal of impeccable knowledge.
IV. I come now to the purely formal definition of the truth or falsehood
of a belief. For this definition it is necessary first of all to
consider the derivation of the objective reference of a proposition from
the meanings of its component words or images.
Just as a word has meaning, so a proposition has an objective reference.
The objective reference of a proposition is a function (in the
mathematical sense) of the meanings of its component words. But the
objective reference differs from the meaning of a word through the
duality of truth and falsehood. You may believe the proposition "to-day
is Tuesday" both when, in fact, to-day is Tuesday, and when to-day is
not Tuesday. If to-day is not Tuesday, this fact is the objective of
your belief that to-day is Tuesday. But obviously the relation of your
belief to the fact is different in this case from what it is in the case
when to-day is Tuesday. We may say, metaphorically, that when to-day is
Tuesday, your belief that it is Tuesday points TOWARDS the fact, whereas
when to-day is not Tuesday your belief points AWAY FROM the fact. Thus
the objective reference of a belief is not determined by the fact alone,
but by the direction of the belief towards or away from the fact.* If,
on a Tuesday, one man believes that it is Tuesday while another believes
that it is not Tuesday, their beliefs have the same objective, namely
the fact that it is Tuesday but the true belief points towards the fact
while the false one points away from it. Thus, in order to define the
reference of a proposition we have to take account not only of the
objective, but also of the direction of pointing, towards the objective
in the case of a true proposition and away from it in the case of a
false one.
* I owe this way of looking at the matter to my friend
Ludwig Wittgenstein.
This mode of stating the nature of the objective reference of a
proposition is necessitated by the circumstance that there are true and
false propositions, but not true and false facts. If to-day is Tuesday,
there is not a false objective "to-day is not Tuesday," which could be
the objective of the false belief "to-day is not Tuesday." This is the
reason why two beliefs which are each other's contradictories have the
same objective. There is, however, a practical inconvenience, namely
that we cannot determine the objective reference of a proposition,
according to this definition, unless we know whether the proposition
is true or false. To avoid this inconvenience, it is better to adopt
a slightly different phraseology, and say: The "meaning" of the
proposition "to-day is Tuesday" consists in pointing to the fact "to-day
is Tuesday" if that is a fact, or away from the fact "to-day is not
Tuesday" if that is a fact. The "meaning" of the proposition "to-day is
not Tuesday" will be exactly the opposite. By this hypothetical form
we are able to speak of the meaning of a proposition without knowing
whether it is true or false. According to this definition, we know the
meaning of a proposition when we know what would make it true and what
would make it false, even if we do not know whether it is in fact true
or false.
The meaning of a proposition is derivative from the meanings of its
constituent words. Propositions occur in pairs, distinguished (in
simple cases) by the absence or presence of the word "not." Two such
propositions have the same objective, but opposite meanings: when one is
true, the other is false, and when one is false, the other is true.
The purely formal definition of truth and falsehood offers little
difficulty. What is required is a formal expression of the fact that a
proposition is true when it points towards its objective, and false when
it points away from it, In very simple cases we can give a very simple
account of this: we can say that true propositions actually resemble
their objectives in a way in which false propositions do not. But for
this purpose it is necessary to revert to image-propositions instead of
word-propositions. Let us take again the illustration of a memory-image
of a familiar room, and let us suppose that in the image the window is
to the left of the door. If in fact the window is to the left of the
door, there is a correspondence between the image and the objective;
there is the same relation between the window and the door as between
the images of them. The image-memory consists of the image of the window
to the left of the image of the door. When this is true, the very same
relation relates the terms of the objective (namely the window and
the door) as relates the images which mean them. In this case the
correspondence which constitutes truth is very simple.
In the case we have just been considering the objective consists of
two parts with a certain relation (that of left-to-right), and the
proposition consists of images of these parts with the very same
relation. The same proposition, if it were false, would have a less
simple formal relation to its objective. If the image-proposition
consists of an image of the window to the left of an image of the door,
while in fact the window is not to the left of the door, the proposition
does not result from the objective by the mere substitution of images
for their prototypes. Thus in this unusually simple case we can say that
a true proposition "corresponds" to its objective in a formal sense in
which a false proposition does not. Perhaps it may be possible to modify
this notion of formal correspondence in such a way as to be more widely
applicable, but if so, the modifications required will be by no means
slight. The reasons for this must now be considered.
To begin with, the simple type of correspondence we have been exhibiting
can hardly occur when words are substituted for images, because, in
word-propositions, relations are usually expressed by words, which are
not themselves relations. Take such a proposition as "Socrates
precedes Plato." Here the word "precedes" is just as solid as the words
"Socrates" and "Plato"; it MEANS a relation, but is not a relation. Thus
the objective which makes our proposition true consists of TWO terms
with a relation between them, whereas our proposition consists of THREE
terms with a relation of order between them. Of course, it would be
perfectly possible, theoretically, to indicate a few chosen relations,
not by words, but by relations between the other words. "Socrates-Plato"
might be used to mean "Socrates precedes Plato"; "Plato-Socrates" might
be used to mean "Plato was born before Socrates and died after him"; and
so on. But the possibilities of such a method would be very limited. For
aught I know, there may be languages that use it, but they are not among
the languages with which I am acquainted. And in any case, in view of
the multiplicity of relations that we wish to express, no language could
advance far without words for relations. But as soon as we have words
for relations, word-propositions have necessarily more terms than the
facts to which they refer, and cannot therefore correspond so simply
with their objectives as some image-propositions can.
The consideration of negative propositions and negative facts introduces
further complications. An image-proposition is necessarily positive:
we can image the window to the left of the door, or to the right of the
door, but we can form no image of the bare negative "the window not to
the left of the door." We can DISBELIEVE the image-proposition expressed
by "the window to the left of the door," and our disbelief will be true
if the window is not to the left of the door. But we can form no image
of the fact that the window is not to the left of the door. Attempts
have often been made to deny such negative facts, but, for reasons which
I have given elsewhere,* I believe these attempts to be mistaken, and I
shall assume that there are negative facts.
* "Monist," January, 1919, p. 42 ff.
Word-propositions, like image-propositions, are always positive facts.
The fact that Socrates precedes Plato is symbolized in English by the
fact that the word "precedes" occurs between the words "Socrates" and
"Plato." But we cannot symbolize the fact that Plato does not precede
Socrates by not putting the word "precedes" between "Plato" and
"Socrates." A negative fact is not sensible, and language, being
intended for communication, has to be sensible. Therefore we symbolize
the fact that Plato does not precede Socrates by putting the words "does
not precede" between "Plato" and "Socrates." We thus obtain a series of
words which is just as positive a fact as the series "Socrates precedes
Plato." The propositions asserting negative facts are themselves
positive facts; they are merely different positive facts from those
asserting positive facts.
We have thus, as regards the opposition of positive and negative, three
different sorts of duality, according as we are dealing with facts,
image-propositions, or word-propositions. We have, namely:
(1) Positive and negative facts;
(2) Image-propositions, which may be believed or disbelieved, but do
not allow any duality of content corresponding to positive and negative
facts;
(3) Word-propositions, which are always positive facts, but are of two
kinds: one verified by a positive objective, the other by a negative
objective.
Owing to these complications, the simplest type of correspondence is
impossible when either negative facts or negative propositions are
involved.
Even when we confine ourselves to relations between two terms which are
both imaged, it may be impossible to form an image-proposition in which
the relation of the terms is represented by the same relation of the
images. Suppose we say "Caesar was 2,000 years before Foch," we express
a certain temporal relation between Caesar and Foch; but we cannot allow
2,000 years to elapse between our image of Caesar and our image of Foch.
This is perhaps not a fair example, since "2,000 years before" is not a
direct relation. But take a case where the relation is direct, say, "the
sun is brighter than the moon." We can form visual images of sunshine
and moonshine, and it may happen that our image of the sunshine is
the brighter of the two, but this is by no means either necessary or
sufficient. The act of comparison, implied in our judgment, is something
more than the mere coexistence of two images, one of which is in fact
brighter than the other. It would take us too far from our main topic if
we were to go into the question what actually occurs when we make this
judgment. Enough has been said to show that the correspondence between
the belief and its objective is more complicated in this case than in
that of the window to the left of the door, and this was all that had to
be proved.
In spite of these complications, the general nature of the formal
correspondence which makes truth is clear from our instances. In the
case of the simpler kind of propositions, namely those that I call
"atomic" propositions, where there is only one word expressing a
relation, the objective which would verify our proposition, assuming
that the word "not" is absent, is obtained by replacing each word
by what it means, the word meaning a relation being replaced by this
relation among the meanings of the other words. For example, if the
proposition is "Socrates precedes Plato," the objective which verifies
it results from replacing the word "Socrates" by Socrates, the word
"Plato" by Plato, and the word "precedes" by the relation of preceding
between Socrates and Plato. If the result of this process is a fact,
the proposition is true; if not, it is false. When our proposition is
"Socrates does not precede Plato," the conditions of truth and falsehood
are exactly reversed. More complicated propositions can be dealt with on
the same lines. In fact, the purely formal question, which has occupied
us in this last section, offers no very formidable difficulties.
I do not believe that the above formal theory is untrue, but I do
believe that it is inadequate. It does not, for example, throw any
light upon our preference for true beliefs rather than false ones. This
preference is only explicable by taking account of the causal efficacy
of beliefs, and of the greater appropriateness of the responses
resulting from true beliefs. But appropriateness depends upon purpose,
and purpose thus becomes a vital part of theory of knowledge.