_ CHAPTER XIV - THE LIMITS OF PHILOSOPHICAL KNOWLEDGE
In all that we have said hitherto concerning philosophy, we have
scarcely touched on many matters that occupy a great space in the
writings of most philosophers. Most philosophers--or, at any rate,
very many--profess to be able to prove, by _a priori_ metaphysical
reasoning, such things as the fundamental dogmas of religion, the
essential rationality of the universe, the illusoriness of matter, the
unreality of all evil, and so on. There can be no doubt that the hope
of finding reason to believe such theses as these has been the chief
inspiration of many life-long students of philosophy. This hope, I
believe, is vain. It would seem that knowledge concerning the
universe as a whole is not to be obtained by metaphysics, and that the
proposed proofs that, in virtue of the laws of logic such and such
things _must_ exist and such and such others cannot, are not capable
of surviving a critical scrutiny. In this chapter we shall briefly
consider the kind of way in which such reasoning is attempted, with a
view to discovering whether we can hope that it may be valid.
The great representative, in modern times, of the kind of view which
we wish to examine, was Hegel (1770-1831). Hegel's philosophy is very
difficult, and commentators differ as to the true interpretation of
it. According to the interpretation I shall adopt, which is that of
many, if not most, of the commentators and has the merit of giving an
interesting and important type of philosophy, his main thesis is that
everything short of the Whole is obviously fragmentary, and obviously
incapable of existing without the complement supplied by the rest of
the world. Just as a comparative anatomist, from a single bone, sees
what kind of animal the whole must have been, so the metaphysician,
according to Hegel, sees, from any one piece of reality, what the
whole of reality must be--at least in its large outlines. Every
apparently separate piece of reality has, as it were, hooks which
grapple it to the next piece; the next piece, in turn, has fresh
hooks, and so on, until the whole universe is reconstructed. This
essential incompleteness appears, according to Hegel, equally in the
world of thought and in the world of things. In the world of thought,
if we take any idea which is abstract or incomplete, we find, on
examination, that if we forget its incompleteness, we become involved
in contradictions; these contradictions turn the idea in question into
its opposite, or antithesis; and in order to escape, we have to find a
new, less incomplete idea, which is the synthesis of our original idea
and its antithesis. This new idea, though less incomplete than the
idea we started with, will be found, nevertheless, to be still not
wholly complete, but to pass into its antithesis, with which it must
be combined in a new synthesis. In this way Hegel advances until he
reaches the 'Absolute Idea', which, according to him, has no
incompleteness, no opposite, and no need of further development. The
Absolute Idea, therefore, is adequate to describe Absolute Reality;
but all lower ideas only describe reality as it appears to a partial
view, not as it is to one who simultaneously surveys the Whole. Thus
Hegel reaches the conclusion that Absolute Reality forms one single
harmonious system, not in space or time, not in any degree evil,
wholly rational, and wholly spiritual. Any appearance to the
contrary, in the world we know, can be proved logically--so he
believes--to be entirely due to our fragmentary piecemeal view of the
universe. If we saw the universe whole, as we may suppose God sees
it, space and time and matter and evil and all striving and struggling
would disappear, and we should see instead an eternal perfect
unchanging spiritual unity.
In this conception, there is undeniably something sublime, something
to which we could wish to yield assent. Nevertheless, when the
arguments in support of it are carefully examined, they appear to
involve much confusion and many unwarrantable assumptions. The
fundamental tenet upon which the system is built up is that what is
incomplete must be not self-subsistent, but must need the support of
other things before it can exist. It is held that whatever has
relations to things outside itself must contain some reference to
those outside things in its own nature, and could not, therefore, be
what it is if those outside things did not exist. A man's nature, for
example, is constituted by his memories and the rest of his knowledge,
by his loves and hatreds, and so on; thus, but for the objects which
he knows or loves or hates, he could not be what he is. He is
essentially and obviously a fragment: taken as the sum-total of
reality he would be self-contradictory.
This whole point of view, however, turns upon the notion of the
'nature' of a thing, which seems to mean 'all the truths about the
thing'. It is of course the case that a truth which connects one
thing with another thing could not subsist if the other thing did not
subsist. But a truth about a thing is not part of the thing itself,
although it must, according to the above usage, be part of the
'nature' of the thing. If we mean by a thing's 'nature' all the
truths about the thing, then plainly we cannot know a thing's 'nature'
unless we know all the thing's relations to all the other things in
the universe. But if the word 'nature' is used in this sense, we
shall have to hold that the thing may be known when its 'nature' is
not known, or at any rate is not known completely. There is a
confusion, when this use of the word 'nature' is employed, between
knowledge of things and knowledge of truths. We may have knowledge of
a thing by acquaintance even if we know very few propositions about
it--theoretically we need not know any propositions about it. Thus,
acquaintance with a thing does not involve knowledge of its 'nature'
in the above sense. And although acquaintance with a thing is
involved in our knowing any one proposition about a thing, knowledge
of its 'nature', in the above sense, is not involved. Hence, (1)
acquaintance with a thing does not logically involve a knowledge of
its relations, and (2) a knowledge of some of its relations does not
involve a knowledge of all of its relations nor a knowledge of its
'nature' in the above sense. I may be acquainted, for example, with
my toothache, and this knowledge may be as complete as knowledge by
acquaintance ever can be, without knowing all that the dentist (who is
not acquainted with it) can tell me about its cause, and without
therefore knowing its 'nature' in the above sense. Thus the fact that
a thing has relations does not prove that its relations are logically
necessary. That is to say, from the mere fact that it is the thing it
is we cannot deduce that it must have the various relations which in
fact it has. This only _seems_ to follow because we know it already.
It follows that we cannot prove that the universe as a whole forms a
single harmonious system such as Hegel believes that it forms. And if
we cannot prove this, we also cannot prove the unreality of space and
time and matter and evil, for this is deduced by Hegel from the
fragmentary and relational character of these things. Thus we are
left to the piecemeal investigation of the world, and are unable to
know the characters of those parts of the universe that are remote
from our experience. This result, disappointing as it is to those
whose hopes have been raised by the systems of philosophers, is in
harmony with the inductive and scientific temper of our age, and is
borne out by the whole examination of human knowledge which has
occupied our previous chapters.
Most of the great ambitious attempts of metaphysicians have proceeded
by the attempt to prove that such and such apparent features of the
actual world were self-contradictory, and therefore could not be real.
The whole tendency of modern thought, however, is more and more in the
direction of showing that the supposed contradictions were illusory,
and that very little can be proved _a priori_ from considerations of
what _must_ be. A good illustration of this is afforded by space and
time. Space and time appear to be infinite in extent, and infinitely
divisible. If we travel along a straight line in either direction, it
is difficult to believe that we shall finally reach a last point,
beyond which there is nothing, not even empty space. Similarly, if in
imagination we travel backwards or forwards in time, it is difficult
to believe that we shall reach a first or last time, with not even
empty time beyond it. Thus space and time appear to be infinite in
extent.
Again, if we take any two points on a line, it seems evident that
there must be other points between them however small the distance
between them may be: every distance can be halved, and the halves can
be halved again, and so on _ad infinitum_. In time, similarly,
however little time may elapse between two moments, it seems evident
that there will be other moments between them. Thus space and time
appear to be infinitely divisible. But as against these apparent
facts--infinite extent and infinite divisibility--philosophers have
advanced arguments tending to show that there could be no infinite
collections of things, and that therefore the number of points in
space, or of instants in time, must be finite. Thus a contradiction
emerged between the apparent nature of space and time and the supposed
impossibility of infinite collections.
Kant, who first emphasized this contradiction, deduced the
impossibility of space and time, which he declared to be merely
subjective; and since his time very many philosophers have believed
that space and time are mere appearance, not characteristic of the
world as it really is. Now, however, owing to the labours of the
mathematicians, notably Georg Cantor, it has appeared that the
impossibility of infinite collections was a mistake. They are not in
fact self-contradictory, but only contradictory of certain rather
obstinate mental prejudices. Hence the reasons for regarding space
and time as unreal have become inoperative, and one of the great
sources of metaphysical constructions is dried up.
The mathematicians, however, have not been content with showing that
space as it is commonly supposed to be is possible; they have shown
also that many other forms of space are equally possible, so far as
logic can show. Some of Euclid's axioms, which appear to common sense
to be necessary, and were formerly supposed to be necessary by
philosophers, are now known to derive their appearance of necessity
from our mere familiarity with actual space, and not from any _a
priori_ logical foundation. By imagining worlds in which these axioms
are false, the mathematicians have used logic to loosen the prejudices
of common sense, and to show the possibility of spaces differing--some
more, some less--from that in which we live. And some of these spaces
differ so little from Euclidean space, where distances such as we can
measure are concerned, that it is impossible to discover by
observation whether our actual space is strictly Euclidean or of one
of these other kinds. Thus the position is completely reversed.
Formerly it appeared that experience left only one kind of space to
logic, and logic showed this one kind to be impossible. Now, logic
presents many kinds of space as possible apart from experience, and
experience only partially decides between them. Thus, while our
knowledge of what is has become less than it was formerly supposed to
be, our knowledge of what may be is enormously increased. Instead of
being shut in within narrow walls, of which every nook and cranny
could be explored, we find ourselves in an open world of free
possibilities, where much remains unknown because there is so much to
know.
What has happened in the case of space and time has happened, to some
extent, in other directions as well. The attempt to prescribe to the
universe by means of _a priori_ principles has broken down; logic,
instead of being, as formerly, the bar to possibilities, has become
the great liberator of the imagination, presenting innumerable
alternatives which are closed to unreflective common sense, and
leaving to experience the task of deciding, where decision is
possible, between the many worlds which logic offers for our choice.
Thus knowledge as to what exists becomes limited to what we can learn
from experience--not to what we can actually experience, for, as we
have seen, there is much knowledge by description concerning things of
which we have no direct experience. But in all cases of knowledge by
description, we need some connexion of universals, enabling us, from
such and such a datum, to infer an object of a certain sort as implied
by our datum. Thus in regard to physical objects, for example, the
principle that sense-data are signs of physical objects is itself a
connexion of universals; and it is only in virtue of this principle
that experience enables us to acquire knowledge concerning physical
objects. The same applies to the law of causality, or, to descend to
what is less general, to such principles as the law of gravitation.
Principles such as the law of gravitation are proved, or rather are
rendered highly probable, by a combination of experience with some
wholly _a priori_ principle, such as the principle of induction. Thus
our intuitive knowledge, which is the source of all our other
knowledge of truths, is of two sorts: pure empirical knowledge, which
tells us of the existence and some of the properties of particular
things with which we are acquainted, and pure _a priori_ knowledge,
which gives us connexions between universals, and enables us to draw
inferences from the particular facts given in empirical knowledge.
Our derivative knowledge always depends upon some pure _a priori_
knowledge and usually also depends upon some pure empirical knowledge.
Philosophical knowledge, if what has been said above is true, does not
differ essentially from scientific knowledge; there is no special
source of wisdom which is open to philosophy but not to science, and
the results obtained by philosophy are not radically different from
those obtained from science. The essential characteristic of
philosophy, which makes it a study distinct from science, is
criticism. It examines critically the principles employed in science
and in daily life; it searches out any inconsistencies there may be in
these principles, and it only accepts them when, as the result of a
critical inquiry, no reason for rejecting them has appeared. If, as
many philosophers have believed, the principles underlying the
sciences were capable, when disengaged from irrelevant detail, of
giving us knowledge concerning the universe as a whole, such knowledge
would have the same claim on our belief as scientific knowledge has;
but our inquiry has not revealed any such knowledge, and therefore, as
regards the special doctrines of the bolder metaphysicians, has had a
mainly negative result. But as regards what would be commonly
accepted as knowledge, our result is in the main positive: we have
seldom found reason to reject such knowledge as the result of our
criticism, and we have seen no reason to suppose man incapable of the
kind of knowledge which he is generally believed to possess.
When, however, we speak of philosophy as a _criticism_ of knowledge,
it is necessary to impose a certain limitation. If we adopt the
attitude of the complete sceptic, placing ourselves wholly outside all
knowledge, and asking, from this outside position, to be compelled to
return within the circle of knowledge, we are demanding what is
impossible, and our scepticism can never be refuted. For all
refutation must begin with some piece of knowledge which the
disputants share; from blank doubt, no argument can begin. Hence the
criticism of knowledge which philosophy employs must not be of this
destructive kind, if any result is to be achieved. Against this
absolute scepticism, no _logical_ argument can be advanced. But it is
not difficult to see that scepticism of this kind is unreasonable.
Descartes' 'methodical doubt', with which modern philosophy began, is
not of this kind, but is rather the kind of criticism which we are
asserting to be the essence of philosophy. His 'methodical doubt'
consisted in doubting whatever seemed doubtful; in pausing, with each
apparent piece of knowledge, to ask himself whether, on reflection, he
could feel certain that he really knew it. This is the kind of
criticism which constitutes philosophy. Some knowledge, such as
knowledge of the existence of our sense-data, appears quite
indubitable, however calmly and thoroughly we reflect upon it. In
regard to such knowledge, philosophical criticism does not require
that we should abstain from belief. But there are beliefs--such, for
example, as the belief that physical objects exactly resemble our
sense-data--which are entertained until we begin to reflect, but are
found to melt away when subjected to a close inquiry. Such beliefs
philosophy will bid us reject, unless some new line of argument is
found to support them. But to reject the beliefs which do not appear
open to any objections, however closely we examine them, is not
reasonable, and is not what philosophy advocates.
The criticism aimed at, in a word, is not that which, without reason,
determines to reject, but that which considers each piece of apparent
knowledge on its merits, and retains whatever still appears to be
knowledge when this consideration is completed. That some risk of
error remains must be admitted, since human beings are fallible.
Philosophy may claim justly that it diminishes the risk of error, and
that in some cases it renders the risk so small as to be practically
negligible. To do more than this is not possible in a world where
mistakes must occur; and more than this no prudent advocate of
philosophy would claim to have performed.
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End of CHAPTER XIV - THE LIMITS OF PHILOSOPHICAL KNOWLEDGE
[Bertrand Russell's essay: The Problems of Philosophy] _