upon them. If I have told you that if it rains I shall bring my
umbrella, and if you see that there is a steady downpour, you can infer
that I shall bring my umbrella. There can be no inference except where
propositions are connected in some such way, so that from the truth or
falsehood of the one something follows as to the truth or falsehood of
the other. It seems to be the case that we can sometimes know molecular
propositions, as in the above instance of the umbrella, when we do not
know whether the component atomic propositions are true or false. The
_practical_ utility of inference rests upon this fact.
The next kind of propositions we have to consider are _general_
propositions, such as "all men are mortal," "all equilateral triangles
are equiangular." And with these belong propositions in which the word
"some" occurs, such as "some men are philosophers" or "some philosophers
are not wise." These are the denials of general propositions, namely (in
the above instances), of "all men are non-philosophers" and "all
philosophers are wise." We will call propositions containing the word
"some" _negative_ general propositions, and those containing the word
"all" _positive_ general propositions. These propositions, it will be
seen, begin to have the appearance of the propositions in logical
text-books. But their peculiarity and complexity are not known to the
text-books, and the problems which they raise are only discussed in the
most superficial manner.
When we were discussing atomic facts, we saw that we should be able,
theoretically, to infer all other truths by logic if we knew all atomic
facts and also knew that there were no other atomic facts besides those
we knew. The knowledge that there are no other atomic facts is positive
general knowledge; it is the knowledge that "all atomic facts are known
to me," or at least "all atomic facts are in this collection"--however
the collection may be given. It is easy to see that general
propositions, such as "all men are mortal," cannot be known by inference
from atomic facts alone. If we could know each individual man, and know
that he was mortal, that would not enable us to know that all men are
mortal, unless we _knew_ that those were all the men there are, which is
a general proposition. If we knew every other existing thing throughout
the universe, and knew that each separate thing was not an immortal man,
that would not give us our result unless we _knew_ that we had explored
the whole universe, _i.e._ unless we knew "all things belong to this
collection of things I have examined." Thus general truths cannot be
inferred from particular truths alone, but must, if they are to be
known, be either self-evident, or inferred from premisses of which at
least one is a general truth. But all _empirical_ evidence is of
_particular_ truths. Hence, if there is any knowledge of general truths
at all, there must be _some_ knowledge of general truths which is
independent of empirical evidence, _i.e._ does not depend upon the data
of sense.
The above conclusion, of which we had an instance in the case of the
inductive principle, is important, since it affords a refutation of the
older empiricists. They believed that all our knowledge is derived from
the senses and dependent upon them. We see that, if this view is to be
maintained, we must refuse to admit that we know any general
propositions. It is perfectly possible logically that this should be the
case, but it does not appear to be so in fact, and indeed no one would
dream of maintaining such a view except a theorist at the last
extremity. We must therefore admit that there is general knowledge not
derived from sense, and that some of this knowledge is not obtained by
inference but is primitive.
Such general knowledge is to be found in logic. Whether there is any
such knowledge not derived from logic, I do not know; but in logic, at
any rate, we have such knowledge. It will be remembered that we excluded
from pure logic such propositions as, "Socrates is a man, all men are
mortal, therefore Socrates is mortal," because Socrates and _man_ and
_mortal_ are empirical terms, only to be understood through particular
experience. The corresponding proposition in pure logic is: "If anything
has a certain property, and whatever has this property has a certain
other property, then the thing in question has the other property." This
proposition is absolutely general: it applies to all things and all
properties. And it is quite self-evident. Thus in such propositions of
pure logic we have the self-evident general propositions of which we
were in search.
A proposition such as, "If Socrates is a man, and all men are mortal,
then Socrates is mortal," is true in virtue of its _form_ alone. Its
truth, in this hypothetical form, does not depend upon whether Socrates
actually is a man, nor upon whether in fact all men are mortal; thus it
is equally true when we substitute other terms for Socrates and _man_
and _mortal_. The general truth of which it is an instance is purely
formal, and belongs to logic. Since it does not mention any particular
thing, or even any particular quality or relation, it is wholly
independent of the accidental facts of the existent world, and can be
known, theoretically, without any experience of particular things or
their qualities and relations.
Logic, we may say, consists of two parts. The first part investigates
what propositions are and what forms they may have; this part enumerates
the different kinds of atomic propositions, of molecular propositions,
of general propositions, and so on. The second part consists of certain
supremely general propositions, which assert the truth of all
propositions of certain forms. This second part merges into pure
mathematics, whose propositions all turn out, on analysis, to be such
general formal truths. The first part, which merely enumerates forms, is
the more difficult, and philosophically the more important; and it is
the recent progress in this first part, more than anything else, that
has rendered a truly scientific discussion of many philosophical
problems possible.
The problem of the nature of judgment or belief may be taken as an
example of a problem whose solution depends upon an adequate inventory
of logical forms. We have already seen how the supposed universality of
the subject-predicate form made it impossible to give a right analysis
of serial order, and therefore made space and time unintelligible. But
in this case it was only necessary to admit relations of two terms. The
case of judgment demands the admission of more complicated forms. If all
judgments were true, we might suppose that a judgment consisted in
apprehension of a _fact_, and that the apprehension was a relation of a
mind to the fact. From poverty in the logical inventory, this view has
often been held. But it leads to absolutely insoluble difficulties in
the case of error. Suppose I believe that Charles I. died in his bed.
There is no objective fact "Charles I.'s death in his bed" to which I
can have a relation of apprehension. Charles I. and death and his bed
are objective, but they are not, except in my thought, put together as
my false belief supposes. It is therefore necessary, in analysing a
belief, to look for some other logical form than a two-term relation.
Failure to realise this necessity has, in my opinion, vitiated almost
everything that has hitherto been written on the theory of knowledge,
making the problem of error insoluble and the difference between belief
and perception inexplicable.
Modern logic, as I hope is now evident, has the effect of enlarging our
abstract imagination, and providing an infinite number of possible
hypotheses to be applied in the analysis of any complex fact. In this
respect it is the exact opposite of the logic practised by the classical
tradition. In that logic, hypotheses which seem _prima facie_ possible
are professedly proved impossible, and it is decreed in advance that
reality must have a certain special character. In modern logic, on the
contrary, while the _prima facie_ hypotheses as a rule remain
admissible, others, which only logic would have suggested, are added to
our stock, and are very often found to be indispensable if a right
analysis of the facts is to be obtained. The old logic put thought in
fetters, while the new logic gives it wings. It has, in my opinion,
introduced the same kind of advance into philosophy as Galileo
introduced into physics, making it possible at last to see what kinds of
problems may be capable of solution, and what kinds must be abandoned as
beyond human powers. And where a solution appears possible, the new
logic provides a method which enables us to obtain results that do not
merely embody personal idiosyncrasies, but must command the assent of
all who are competent to form an opinion.
LECTURE III
ON OUR KNOWLEDGE OF THE EXTERNAL WORLD
Philosophy may be approached by many roads, but one of the oldest and
most travelled is the road which leads through doubt as to the reality
of the world of sense. In Indian mysticism, in Greek and modern monistic
philosophy from Parmenides onward, in Berkeley, in modern physics, we
find sensible appearance criticised and condemned for a bewildering
variety of motives. The mystic condemns it on the ground of immediate
knowledge of a more real and significant world behind the veil;
Parmenides and Plato condemn it because its continual flux is thought
inconsistent with the unchanging nature of the abstract entities
revealed by logical analysis; Berkeley brings several weapons, but his
chief is the subjectivity of sense-data, their dependence upon the
organisation and point of view of the spectator; while modern physics,
on the basis of sensible evidence itself, maintains a mad dance of
electrons which has, superficially at least, very little resemblance to
the immediate objects of sight or touch.
Every one of these lines of attack raises vital and interesting
problems.
The mystic, so long as he merely reports a positive revelation, cannot
be refuted; but when he _denies_ reality to objects of sense, he may be
questioned as to what he means by "reality," and may be asked how their
unreality follows from the supposed reality of his super-sensible world.
In answering these questions, he is led to a logic which merges into
that of Parmenides and Plato and the idealist tradition.
The logic of the idealist tradition has gradually grown very complex and
very abstruse, as may be seen from the Bradleian sample considered in
our first lecture. If we attempted to deal fully with this logic, we
should not have time to reach any other aspect of our subject; we will
therefore, while acknowledging that it deserves a long discussion, pass
by its central doctrines with only such occasional criticism as may
serve to exemplify other topics, and concentrate our attention on such
matters as its objections to the continuity of motion and the infinity
of space and time--objections which have been fully answered by modern
mathematicians in a manner constituting an abiding triumph for the
method of logical analysis in philosophy. These objections and the
modern answers to them will occupy our fifth, sixth, and seventh
lectures.
Berkeley's attack, as reinforced by the physiology of the sense-organs
and nerves and brain, is very powerful. I think it must be admitted as
probable that the immediate objects of sense depend for their existence
upon physiological conditions in ourselves, and that, for example, the
coloured surfaces which we see cease to exist when we shut our eyes. But
it would be a mistake to infer that they are dependent upon mind, not
real while we see them, or not the sole basis for our knowledge of the
external world. This line of argument will be developed in the present
lecture.
The discrepancy between the world of physics and the world of sense,
which we shall consider in our fourth lecture, will be found to be more
apparent than real, and it will be shown that whatever there is reason
to believe in physics can probably be interpreted in terms of sense.
The instrument of discovery throughout is modern logic, a very different
science from the logic of the text-books and also from the logic of
idealism. Our second lecture has given a short account of modern logic
and of its points of divergence from the various traditional kinds of
logic.
In our last lecture, after a discussion of causality and free will, we
shall try to reach a general account of the logical-analytic method of
scientific philosophy, and a tentative estimate of the hopes of
philosophical progress which it allows us to entertain.
In this lecture, I wish to apply the logical-analytic method to one of
the oldest problems of philosophy, namely, the problem of our knowledge
of the external world. What I have to say on this problem does not
amount to an answer of a definite and dogmatic kind; it amounts only to
an analysis and statement of the questions involved, with an indication
of the directions in which evidence may be sought. But although not yet
a definite solution, what can be said at present seems to me to throw a
completely new light on the problem, and to be indispensable, not only
in seeking the answer, but also in the preliminary question as to what
parts of our problem may possibly have an ascertainable answer.
In every philosophical problem, our investigation starts from what may
be called "data," by which I mean matters of common knowledge, vague,
complex, inexact, as common knowledge always is, but yet somehow
commanding our assent as on the whole and in some interpretation pretty
certainly true. In the case of our present problem, the common knowledge
involved is of various kinds. There is first our acquaintance with
particular objects of daily life--furniture, houses, towns, other
people, and so on. Then there is the extension of such particular
knowledge to particular things outside our personal experience, through
history and geography, newspapers, etc. And lastly, there is the
systematisation of all this knowledge of particulars by means of
physical science, which derives immense persuasive force from its
astonishing power of foretelling the future. We are quite willing to
admit that there may be errors of detail in this knowledge, but we
believe them to be discoverable and corrigible by the methods which have
given rise to our beliefs, and we do not, as practical men, entertain
for a moment the hypothesis that the whole edifice may be built on
insecure foundations. In the main, therefore, and without absolute
dogmatism as to this or that special portion, we may accept this mass of
common knowledge as affording data for our philosophical analysis.
It may be said--and this is an objection which must be met at the
outset--that it is the duty of the philosopher to call in question the
admittedly fallible beliefs of daily life, and to replace them by
something more solid and irrefragable. In a sense this is true, and in a
sense it is effected in the course of analysis. But in another sense,
and a very important one, it is quite impossible. While admitting that
doubt is possible with regard to all our common knowledge, we must
nevertheless accept that knowledge in the main if philosophy is to be
possible at all. There is not any superfine brand of knowledge,
obtainable by the philosopher, which can give us a standpoint from which
to criticise the whole of the knowledge of daily life. The most that can
be done is to examine and purify our common knowledge by an internal
scrutiny, assuming the canons by which it has been obtained, and
applying them with more care and with more precision. Philosophy cannot
boast of having achieved such a degree of certainty that it can have
authority to condemn the facts of experience and the laws of science.
The philosophic scrutiny, therefore, though sceptical in regard to every
detail, is not sceptical as regards the whole. That is to say, its
criticism of details will only be based upon their relation to other
details, not upon some external criterion which can be applied to all
the details equally. The reason for this abstention from a universal
criticism is not any dogmatic confidence, but its exact opposite; it is
not that common knowledge _must_ be true, but that we possess no
radically different kind of knowledge derived from some other source.
Universal scepticism, though logically irrefutable, is practically
barren; it can only, therefore, give a certain flavour of hesitancy to
our beliefs, and cannot be used to substitute other beliefs for them.
Although data can only be criticised by other data, not by an outside
standard, yet we may distinguish different grades of certainty in the
different kinds of common knowledge which we enumerated just now. What
does not go beyond our own personal sensible acquaintance must be for us
the most certain: the "evidence of the senses" is proverbially the least
open to question. What depends on testimony, like the facts of history
and geography which are learnt from books, has varying degrees of
certainty according to the nature and extent of the testimony. Doubts as
to the existence of Napoleon can only be maintained for a joke, whereas
the historicity of Agamemnon is a legitimate subject of debate. In
science, again, we find all grades of certainty short of the highest.
The law of gravitation, at least as an approximate truth, has acquired
by this time the same kind of certainty as the existence of Napoleon,
whereas the latest speculations concerning the constitution of matter
would be universally acknowledged to have as yet only a rather slight
probability in their favour. These varying degrees of certainty
attaching to different data may be regarded as themselves forming part
of our data; they, along with the other data, lie within the vague,
complex, inexact body of knowledge which it is the business of the
philosopher to analyse.
The first thing that appears when we begin to analyse our common
knowledge is that some of it is derivative, while some is primitive;
that is to say, there is some that we only believe because of something
else from which it has been inferred in some sense, though not
necessarily in a strict logical sense, while other parts are believed on
their own account, without the support of any outside evidence. It is
obvious that the senses give knowledge of the latter kind: the immediate
facts perceived by sight or touch or hearing do not need to be proved by
argument, but are completely self-evident. Psychologists, however, have
made us aware that what is actually given in sense is much less than
most people would naturally suppose, and that much of what at first
sight seems to be given is really inferred. This applies especially in
regard to our space-perceptions. For instance, we instinctively infer
the "real" size and shape of a visible object from its apparent size and
shape, according to its distance and our point of view. When we hear a
person speaking, our actual sensations usually miss a great deal of what
he says, and we supply its place by unconscious inference; in a foreign
language, where this process is more difficult, we find ourselves
apparently grown deaf, requiring, for example, to be much nearer the
stage at a theatre than would be necessary in our own country. Thus the
first step in the analysis of data, namely, the discovery of what is
really given in sense, is full of difficulty. We will, however, not
linger on this point; so long as its existence is realised, the exact
outcome does not make any very great difference in our main problem.
The next step in our analysis must be the consideration of how the
derivative parts of our common knowledge arise. Here we become involved
in a somewhat puzzling entanglement of logic and psychology.
Psychologically, a belief may be called derivative whenever it is caused
by one or more other beliefs, or by some fact of sense which is not
simply what the belief asserts. Derivative beliefs in this sense
constantly arise without any process of logical inference, merely by
association of ideas or some equally extra-logical process. From the
expression of a man's face we judge as to what he is feeling: we say we
_see_ that he is angry, when in fact we only see a frown. We do not
judge as to his state of mind by any logical process: the judgment grows
up, often without our being able to say what physical mark of emotion we
actually saw. In such a case, the knowledge is derivative
psychologically; but logically it is in a sense primitive, since it is
not the result of any logical deduction. There may or may not be a
possible deduction leading to the same result, but whether there is or
not, we certainly do not employ it. If we call a belief "logically
primitive" when it is not actually arrived at by a logical inference,
then innumerable beliefs are logically primitive which psychologically
are derivative. The separation of these two kinds of primitiveness is
vitally important to our present discussion.
When we reflect upon the beliefs which are logically but not
psychologically primitive, we find that, unless they can on reflection
be deduced by a logical process from beliefs which are also
psychologically primitive, our confidence in their truth tends to
diminish the more we think about them. We naturally believe, for
example, that tables and chairs, trees and mountains, are still there
when we turn our backs upon them. I do not wish for a moment to maintain
that this is certainly not the case, but I do maintain that the question
whether it is the case is not to be settled off-hand on any supposed
ground of obviousness. The belief that they persist is, in all men
except a few philosophers, logically primitive, but it is not
psychologically primitive; psychologically, it arises only through our
having seen those tables and chairs, trees and mountains. As soon as the
question is seriously raised whether, because we have seen them, we have
a right to suppose that they are there still, we feel that some kind of
argument must be produced, and that if none is forthcoming, our belief
can be no more than a pious opinion. We do not feel this as regards the
immediate objects of sense: there they are, and as far as their
momentary existence is concerned, no further argument is required. There
is accordingly more need of justifying our psychologically derivative
beliefs than of justifying those that are primitive.
We are thus led to a somewhat vague distinction between what we may call
"hard" data and "soft" data. This distinction is a matter of degree, and
must not be pressed; but if not taken too seriously it may help to make
the situation clear. I mean by "hard" data those which resist the
solvent influence of critical reflection, and by "soft" data those
which, under the operation of this process, become to our minds more or
less doubtful. The hardest of hard data are of two sorts: the particular
facts of sense, and the general truths of logic. The more we reflect
upon these, the more we realise exactly what they are, and exactly what
a doubt concerning them really means, the more luminously certain do
they become. _Verbal_ doubt concerning even these is possible, but
verbal doubt may occur when what is nominally being doubted is not
really in our thoughts, and only words are actually present to our
minds. Real doubt, in these two cases, would, I think, be pathological.
At any rate, to me they seem quite certain, and I shall assume that you
agree with me in this. Without this assumption, we are in danger of
falling into that universal scepticism which, as we saw, is as barren as
it is irrefutable. If we are to continue philosophising, we must make
our bow to the sceptical hypothesis, and, while admitting the elegant
terseness of its philosophy, proceed to the consideration of other
hypotheses which, though perhaps not certain, have at least as good a
right to our respect as the hypothesis of the sceptic.