philosophy, is not a matter of great practical importance to animals, or
to savages, or even to most civilised men. It is hardly to be supposed,
therefore, that the rapid, rough and ready methods of instinct or
intuition will find in this field a favourable ground for their
application. It is the older kinds of activity, which bring out our
kinship with remote generations of animal and semi-human ancestors, that
show intuition at its best. In such matters as self-preservation and
love, intuition will act sometimes (though not always) with a swiftness
and precision which are astonishing to the critical intellect. But
philosophy is not one of the pursuits which illustrate our affinity with
the past: it is a highly refined, highly civilised pursuit, demanding,
for its success, a certain liberation from the life of instinct, and
even, at times, a certain aloofness from all mundane hopes and fears. It
is not in philosophy, therefore, that we can hope to see intuition at
its best. On the contrary, since the true objects of philosophy, and the
habits of thought demanded for their apprehension, are strange, unusual,
and remote, it is here, more almost than anywhere else, that intellect
proves superior to intuition, and that quick unanalysed convictions are
least deserving of uncritical acceptance.
Before embarking upon the somewhat difficult and abstract discussions
which lie before us, it will be well to take a survey of the hopes we
may retain and the hopes we must abandon. The hope of satisfaction to
our more human desires--the hope of demonstrating that the world has
this or that desirable ethical characteristic--is not one which, so far
as I can see, philosophy can do anything whatever to satisfy. The
difference between a good world and a bad one is a difference in the
particular characteristics of the particular things that exist in these
worlds: it is not a sufficiently abstract difference to come within the
province of philosophy. Love and hate, for example, are ethical
opposites, but to philosophy they are closely analogous attitudes
towards objects. The general form and structure of those attitudes
towards objects which constitute mental phenomena is a problem for
philosophy; but the difference between love and hate is not a difference
of form or structure, and therefore belongs rather to the special
science of psychology than to philosophy. Thus the ethical interests
which have often inspired philosophers must remain in the background:
some kind of ethical interest may inspire the whole study, but none must
obtrude in the detail or be expected in the special results which are
sought.
If this view seems at first sight disappointing, we may remind ourselves
that a similar change has been found necessary in all the other
sciences. The physicist or chemist is not now required to prove the
ethical importance of his ions or atoms; the biologist is not expected
to prove the utility of the plants or animals which he dissects. In
pre-scientific ages this was not the case. Astronomy, for example, was
studied because men believed in astrology: it was thought that the
movements of the planets had the most direct and important bearing upon
the lives of human beings. Presumably, when this belief decayed and the
disinterested study of astronomy began, many who had found astrology
absorbingly interesting decided that astronomy had too little human
interest to be worthy of study. Physics, as it appears in Plato's
_Timaeus_ for example, is full of ethical notions: it is an essential
part of its purpose to show that the earth is worthy of admiration. The
modern physicist, on the contrary, though he has no wish to deny that
the earth is admirable, is not concerned, as physicist, with its ethical
attributes: he is merely concerned to find out facts, not to consider
whether they are good or bad. In psychology, the scientific attitude is
even more recent and more difficult than in the physical sciences: it is
natural to consider that human nature is either good or bad, and to
suppose that the difference between good and bad, so all-important in
practice, must be important in theory also. It is only during the last
century that an ethically neutral science of psychology has grown up;
and here too ethical neutrality has been essential to scientific
success.
In philosophy, hitherto, ethical neutrality has been seldom sought and
hardly ever achieved. Men have remembered their wishes, and have judged
philosophies in relation to their wishes. Driven from the particular
sciences, the belief that the notions of good and evil must afford a key
to the understanding of the world has sought a refuge in philosophy. But
even from this last refuge, if philosophy is not to remain a set of
pleasing dreams, this belief must be driven forth. It is a commonplace
that happiness is not best achieved by those who seek it directly; and
it would seem that the same is true of the good. In thought, at any
rate, those who forget good and evil and seek only to know the facts are
more likely to achieve good than those who view the world through the
distorting medium of their own desires.
The immense extension of our knowledge of facts in recent times has had,
as it had in the Renaissance, two effects upon the general intellectual
outlook. On the one hand, it has made men distrustful of the truth of
wide, ambitious systems: theories come and go swiftly, each serving, for
a moment, to classify known facts and promote the search for new ones,
but each in turn proving inadequate to deal with the new facts when they
have been found. Even those who invent the theories do not, in science,
regard them as anything but a temporary makeshift. The ideal of an
all-embracing synthesis, such as the Middle Ages believed themselves to
have attained, recedes further and further beyond the limits of what
seems feasible. In such a world, as in the world of Montaigne, nothing
seems worth while except the discovery of more and more facts, each in
turn the deathblow to some cherished theory; the ordering intellect
grows weary, and becomes slovenly through despair.
On the other hand, the new facts have brought new powers; man's physical
control over natural forces has been increasing with unexampled
rapidity, and promises to increase in the future beyond all easily
assignable limits. Thus alongside of despair as regards ultimate theory
there is an immense optimism as regards practice: what man can _do_
seems almost boundless. The old fixed limits of human power, such as
death, or the dependence of the race on an equilibrium of cosmic forces,
are forgotten, and no hard facts are allowed to break in upon the dream
of omnipotence. No philosophy is tolerated which sets bounds to man's
capacity of gratifying his wishes; and thus the very despair of theory
is invoked to silence every whisper of doubt as regards the
possibilities of practical achievement.
In the welcoming of new fact, and in the suspicion of dogmatism as
regards the universe at large, the modern spirit should, I think, be
accepted as wholly an advance. But both in its practical pretensions and
in its theoretical despair it seems to me to go too far. Most of what is
greatest in man is called forth in response to the thwarting of his
hopes by immutable natural obstacles; by the pretence of omnipotence, he
becomes trivial and a little absurd. And on the theoretical side,
ultimate metaphysical truth, though less all-embracing and harder of
attainment than it appeared to some philosophers in the past, can, I
believe, be discovered by those who are willing to combine the
hopefulness, patience, and open-mindedness of science with something of
the Greek feeling for beauty in the abstract world of logic and for the
ultimate intrinsic value in the contemplation of truth.
The philosophy, therefore, which is to be genuinely inspired by the
scientific spirit, must deal with somewhat dry and abstract matters, and
must not hope to find an answer to the practical problems of life. To
those who wish to understand much of what has in the past been most
difficult and obscure in the constitution of the universe, it has great
rewards to offer--triumphs as noteworthy as those of Newton and Darwin,
and as important in the long run, for the moulding of our mental habits.
And it brings with it--as a new and powerful method of investigation
always does--a sense of power and a hope of progress more reliable and
better grounded than any that rests on hasty and fallacious
generalisation as to the nature of the universe at large. Many hopes
which inspired philosophers in the past it cannot claim to fulfil; but
other hopes, more purely intellectual, it can satisfy more fully than
former ages could have deemed possible for human minds.
LECTURE II
LOGIC AS THE ESSENCE OF PHILOSOPHY
The topics we discussed in our first lecture, and the topics we shall
discuss later, all reduce themselves, in so far as they are genuinely
philosophical, to problems of logic. This is not due to any accident,
but to the fact that every philosophical problem, when it is subjected
to the necessary analysis and purification, is found either to be not
really philosophical at all, or else to be, in the sense in which we are
using the word, logical. But as the word "logic" is never used in the
same sense by two different philosophers, some explanation of what I
mean by the word is indispensable at the outset.
Logic, in the Middle Ages, and down to the present day in teaching,
meant no more than a scholastic collection of technical terms and rules
of syllogistic inference. Aristotle had spoken, and it was the part of
humbler men merely to repeat the lesson after him. The trivial nonsense
embodied in this tradition is still set in examinations, and defended by
eminent authorities as an excellent "propaedeutic," _i.e._ a training in
those habits of solemn humbug which are so great a help in later life.
But it is not this that I mean to praise in saying that all philosophy
is logic. Ever since the beginning of the seventeenth century, all
vigorous minds that have concerned themselves with inference have
abandoned the mediaeval tradition, and in one way or other have widened
the scope of logic.
The first extension was the introduction of the inductive method by
Bacon and Galileo--by the former in a theoretical and largely mistaken
form, by the latter in actual use in establishing the foundations of
modern physics and astronomy. This is probably the only extension of the
old logic which has become familiar to the general educated public. But
induction, important as it is when regarded as a method of
investigation, does not seem to remain when its work is done: in the
final form of a perfected science, it would seem that everything ought
to be deductive. If induction remains at all, which is a difficult
question, it will remain merely as one of the principles according to
which deductions are effected. Thus the ultimate result of the
introduction of the inductive method seems not the creation of a new
kind of non-deductive reasoning, but rather the widening of the scope of
deduction by pointing out a way of deducing which is certainly not
syllogistic, and does not fit into the mediaeval scheme.
The question of the scope and validity of induction is of great
difficulty, and of great importance to our knowledge. Take such a
question as, "Will the sun rise to-morrow?" Our first instinctive
feeling is that we have abundant reason for saying that it will, because
it has risen on so many previous mornings. Now, I do not myself know
whether this does afford a ground or not, but I am willing to suppose
that it does. The question which then arises is: What is the principle
of inference by which we pass from past sunrises to future ones? The
answer given by Mill is that the inference depends upon the law of
causation. Let us suppose this to be true; then what is the reason for
believing in the law of causation? There are broadly three possible
answers: (1) that it is itself known _a priori_; (2) that it is a
postulate; (3) that it is an empirical generalisation from past
instances in which it has been found to hold. The theory that causation
is known _a priori_ cannot be definitely refuted, but it can be rendered
very unplausible by the mere process of formulating the law exactly, and
thereby showing that it is immensely more complicated and less obvious
than is generally supposed. The theory that causation is a postulate,
_i.e._ that it is something which we choose to assert although we know
that it is very likely false, is also incapable of refutation; but it is
plainly also incapable of justifying any use of the law in inference. We
are thus brought to the theory that the law is an empirical
generalisation, which is the view held by Mill.
But if so, how are empirical generalisations to be justified? The
evidence in their favour cannot be empirical, since we wish to argue
from what has been observed to what has not been observed, which can
only be done by means of some known relation of the observed and the
unobserved; but the unobserved, by definition, is not known empirically,
and therefore its relation to the observed, if known at all, must be
known independently of empirical evidence. Let us see what Mill says on
this subject.
According to Mill, the law of causation is proved by an admittedly
fallible process called "induction by simple enumeration." This process,
he says, "consists in ascribing the nature of general truths to all
propositions which are true in every instance that we happen to know
of."[8] As regards its fallibility, he asserts that "the precariousness
of the method of simple enumeration is in an inverse ratio to the
largeness of the generalisation. The process is delusive and
insufficient, exactly in proportion as the subject-matter of the
observation is special and limited in extent. As the sphere widens, this
unscientific method becomes less and less liable to mislead; and the
most universal class of truths, the law of causation for instance, and
the principles of number and of geometry, are duly and satisfactorily
proved by that method alone, nor are they susceptible of any other
proof."[9]
[8] _Logic_, book iii., chapter iii., Sec. 2.
[9] Book iii., chapter xxi., Sec. 3.
In the above statement, there are two obvious lacunae: (1) How is the
method of simple enumeration itself justified? (2) What logical
principle, if any, covers the same ground as this method, without being
liable to its failures? Let us take the second question first.
A method of proof which, when used as directed, gives sometimes truth
and sometimes falsehood--as the method of simple enumeration does--is
obviously not a valid method, for validity demands invariable truth.
Thus, if simple enumeration is to be rendered valid, it must not be
stated as Mill states it. We shall have to say, at most, that the data
render the result _probable_. Causation holds, we shall say, in every
instance we have been able to test; therefore it _probably_ holds in
untested instances. There are terrible difficulties in the notion of
probability, but we may ignore them at present. We thus have what at
least _may_ be a logical principle, since it is without exception. If a
proposition is true in every instance that we happen to know of, and if
the instances are very numerous, then, we shall say, it becomes very
probable, on the data, that it will be true in any further instance.
This is not refuted by the fact that what we declare to be probable does
not always happen, for an event may be probable on the data and yet not
occur. It is, however, obviously capable of further analysis, and of
more exact statement. We shall have to say something like this: that
every instance of a proposition[10] being true increases the probability
of its being true in a fresh instance, and that a sufficient number of
favourable instances will, in the absence of instances to the contrary,
make the probability of the truth of a fresh instance approach
indefinitely near to certainty. Some such principle as this is required
if the method of simple enumeration is to be valid.
[10] Or rather a propositional function.
But this brings us to our other question, namely, how is our principle
known to be true? Obviously, since it is required to justify induction,
it cannot be proved by induction; since it goes beyond the empirical
data, it cannot be proved by them alone; since it is required to justify
all inferences from empirical data to what goes beyond them, it cannot
itself be even rendered in any degree probable by such data. Hence, _if_
it is known, it is not known by experience, but independently of
experience. I do not say that any such principle is known: I only say
that it is required to justify the inferences from experience which
empiricists allow, and that it cannot itself be justified
empirically.[11]
[11] The subject of causality and induction will be discussed again in
Lecture VIII.
A similar conclusion can be proved by similar arguments concerning any
other logical principle. Thus logical knowledge is not derivable from
experience alone, and the empiricist's philosophy can therefore not be
accepted in its entirety, in spite of its excellence in many matters
which lie outside logic.
Hegel and his followers widened the scope of logic in quite a different
way--a way which I believe to be fallacious, but which requires
discussion if only to show how their conception of logic differs from
the conception which I wish to advocate. In their writings, logic is
practically identical with metaphysics. In broad outline, the way this
came about is as follows. Hegel believed that, by means of _a priori_
reasoning, it could be shown that the world _must_ have various
important and interesting characteristics, since any world without these
characteristics would be impossible and self-contradictory. Thus what he
calls "logic" is an investigation of the nature of the universe, in so
far as this can be inferred merely from the principle that the universe
must be logically self-consistent. I do not myself believe that from
this principle alone anything of importance can be inferred as regards
the existing universe. But, however that may be, I should not regard
Hegel's reasoning, even if it were valid, as properly belonging to
logic: it would rather be an application of logic to the actual world.
Logic itself would be concerned rather with such questions as what
self-consistency is, which Hegel, so far as I know, does not discuss.
And though he criticises the traditional logic, and professes to replace
it by an improved logic of his own, there is some sense in which the
traditional logic, with all its faults, is uncritically and
unconsciously assumed throughout his reasoning. It is not in the
direction advocated by him, it seems to me, that the reform of logic is
to be sought, but by a more fundamental, more patient, and less
ambitious investigation into the presuppositions which his system shares
with those of most other philosophers.
The way in which, as it seems to me, Hegel's system assumes the ordinary
logic which it subsequently criticises, is exemplified by the general
conception of "categories" with which he operates throughout. This
conception is, I think, essentially a product of logical confusion, but
it seems in some way to stand for the conception of "qualities of
Reality as a whole." Mr Bradley has worked out a theory according to
which, in all judgment, we are ascribing a predicate to Reality as a
whole; and this theory is derived from Hegel. Now the traditional logic
holds that every proposition ascribes a predicate to a subject, and from
this it easily follows that there can be only one subject, the Absolute,
for if there were two, the proposition that there were two would not
ascribe a predicate to either. Thus Hegel's doctrine, that philosophical
propositions must be of the form, "the Absolute is such-and-such,"
depends upon the traditional belief in the universality of the
subject-predicate form. This belief, being traditional, scarcely
self-conscious, and not supposed to be important, operates underground,
and is assumed in arguments which, like the refutation of relations,
appear at first sight such as to establish its truth. This is the most
important respect in which Hegel uncritically assumes the traditional
logic. Other less important respects--though important enough to be the
source of such essentially Hegelian conceptions as the "concrete
universal" and the "union of identity in difference"--will be found
where he explicitly deals with formal logic.[12]
[12] See the translation by H. S. Macran, _Hegel's Doctrine of Formal
Logic_, Oxford, 1912. Hegel's argument in this portion of his "Logic"
depends throughout upon confusing the "is" of predication, as in
"Socrates is mortal," with the "is" of identity, as in "Socrates is
the philosopher who drank the hemlock." Owing to this confusion, he
thinks that "Socrates" and "mortal" must be identical. Seeing that
they are different, he does not infer, as others would, that there is
a mistake somewhere, but that they exhibit "identity in difference."
Again, Socrates is particular, "mortal" is universal. Therefore, he
says, since Socrates is mortal, it follows that the particular is the
universal--taking the "is" to be throughout expressive of identity.
But to say "the particular is the universal" is self-contradictory.
Again Hegel does not suspect a mistake but proceeds to synthesise
particular and universal in the individual, or concrete universal.
This is an example of how, for want of care at the start, vast and
imposing systems of philosophy are built upon stupid and trivial
confusions, which, but for the almost incredible fact that they are
unintentional, one would be tempted to characterise as puns.
There is quite another direction in which a large technical development
of logic has taken place: I mean the direction of what is called
logistic or mathematical logic. This kind of logic is mathematical in
two different senses: it is itself a branch of mathematics, and it is
the logic which is specially applicable to other more traditional
branches of mathematics. Historically, it began as _merely_ a branch of
mathematics: its special applicability to other branches is a more
recent development. In both respects, it is the fulfilment of a hope
which Leibniz cherished throughout his life, and pursued with all the
ardour of his amazing intellectual energy. Much of his work on this
subject has been published recently, since his discoveries have been
remade by others; but none was published by him, because his results
persisted in contradicting certain points in the traditional doctrine of
the syllogism. We now know that on these points the traditional doctrine
is wrong, but respect for Aristotle prevented Leibniz from realising
that this was possible.[13]
[13] _Cf._ Couturat, _La Logique de Leibniz_, pp. 361, 386.
The modern development of mathematical logic dates from Boole's _Laws of
Thought_ (1854). But in him and his successors, before Peano and Frege,
the only thing really achieved, apart from certain details, was the
invention of a mathematical symbolism for deducing consequences from the
premisses which the newer methods shared with those of Aristotle. This
subject has considerable interest as an independent branch of
mathematics, but it has very little to do with real logic. The first
serious advance in real logic since the time of the Greeks was made
independently by Peano and Frege--both mathematicians. They both arrived
at their logical results by an analysis of mathematics. Traditional
logic regarded the two propositions, "Socrates is mortal" and "All men
are mortal," as being of the same form;[14] Peano and Frege showed that
they are utterly different in form. The philosophical importance of
logic may be illustrated by the fact that this confusion--which is still
committed by most writers--obscured not only the whole study of the
forms of judgment and inference, but also the relations of things to
their qualities, of concrete existence to abstract concepts, and of the
world of sense to the world of Platonic ideas. Peano and Frege, who
pointed out the error, did so for technical reasons, and applied their
logic mainly to technical developments; but the philosophical importance
of the advance which they made is impossible to exaggerate.
[14] It was often recognised that there was _some_ difference between
them, but it was not recognised that the difference is fundamental,
and of very great importance.