of view. In what sense, then, was he different from the pigs?"
I much fear that the evolutionists too often resemble the Grand Augur
and the pigs.
The ethical element which has been prominent in many of the most
famous systems of philosophy is, in my opinion, one of the most
serious obstacles to the victory of scientific method in the
investigation of philosophical questions. Human ethical notions, as
Chuang Tz[)u] perceived, are essentially anthropocentric, and involve,
when used in metaphysics, an attempt, however veiled, to legislate for
the universe on the basis of the present desires of men. In this way
they interfere with that receptivity to fact which is the essence of
the scientific attitude towards the world. To regard ethical notions
as a key to the understanding of the world is essentially
pre-Copernican. It is to make man, with the hopes and ideals which he
happens to have at the present moment, the centre of the universe and
the interpreter of its supposed aims and purposes. Ethical metaphysics
is fundamentally an attempt, however disguised, to give legislative
force to our own wishes. This may, of course, be questioned, but I
think that it is confirmed by a consideration of the way in which
ethical notions arise. Ethics is essentially a product of the
gregarious instinct, that is to say, of the instinct to co-operate
with those who are to form our own group against those who belong to
other groups. Those who belong to our own group are good; those who
belong to hostile groups are wicked. The ends which are pursued by our
own group are desirable ends, the ends pursued by hostile groups are
nefarious. The subjectivity of this situation is not apparent to the
gregarious animal, which feels that the general principles of justice
are on the side of its own herd. When the animal has arrived at the
dignity of the metaphysician, it invents ethics as the embodiment of
its belief in the justice of its own herd. So the Grand Augur invokes
ethics as the justification of Augurs in their conflicts with pigs.
But, it may be said, this view of ethics takes no account of such
truly ethical notions as that of self-sacrifice. This, however, would
be a mistake. The success of gregarious animals in the struggle for
existence depends upon co-operation within the herd, and co-operation
requires sacrifice, to some extent, of what would otherwise be the
interest of the individual. Hence arises a conflict of desires and
instincts, since both self-preservation and the preservation of the
herd are biological ends to the individual. Ethics is in origin the
art of recommending to others the sacrifices required for co-operation
with oneself. Hence, by reflexion, it comes, through the operation of
social justice, to recommend sacrifices by oneself, but all ethics,
however refined, remains more or less subjective. Even vegetarians do
not hesitate, for example, to save the life of a man in a fever,
although in doing so they destroy the lives of many millions of
microbes. The view of the world taken by the philosophy derived from
ethical notions is thus never impartial and therefore never fully
scientific. As compared with science, it fails to achieve the
imaginative liberation from self which is necessary to such
understanding of the world as man can hope to achieve, and the
philosophy which it inspires is always more or less parochial, more or
less infected with the prejudices of a time and a place.
I do not deny the importance or value, within its own sphere, of the
kind of philosophy which is inspired by ethical notions. The ethical
work of Spinoza, for example, appears to me of the very highest
significance, but what is valuable in such work is not any
metaphysical theory as to the nature of the world to which it may give
rise, nor indeed anything which can be proved or disproved by
argument. What is valuable is the indication of some new way of
feeling towards life and the world, some way of feeling by which our
own existence can acquire more of the characteristics which we must
deeply desire. The value of such work, however immeasurable it is,
belongs with practice and not with theory. Such theoretic importance
as it may possess is only in relation to human nature, not in relation
to the world at large. The scientific philosophy, therefore, which
aims only at understanding the world and not directly at any other
improvement of human life, cannot take account of ethical notions
without being turned aside from that submission to fact which is the
essence of the scientific temper.
II
If the notion of the universe and the notion of good and evil are
extruded from scientific philosophy, it may be asked what specific
problems remain for the philosopher as opposed to the man of science?
It would be difficult to give a precise answer to this question, but
certain characteristics may be noted as distinguishing the province of
philosophy from that of the special sciences.
In the first place a philosophical proposition must be general. It
must not deal specially with things on the surface of the earth, or
with the solar system, or with any other portion of space and time. It
is this need of generality which has led to the belief that philosophy
deals with the universe as a whole. I do not believe that this belief
is justified, but I do believe that a philosophical proposition must
be applicable to everything that exists or may exist. It might be
supposed that this admission would be scarcely distinguishable from
the view which I wish to reject. This, however, would be an error, and
an important one. The traditional view would make the universe itself
the subject of various predicates which could not be applied to any
particular thing in the universe, and the ascription of such peculiar
predicates to the universe would be the special business of
philosophy. I maintain, on the contrary, that there are no
propositions of which the "universe" is the subject; in other words,
that there is no such thing as the "universe." What I do maintain is
that there are general propositions which may be asserted of each
individual thing, such as the propositions of logic. This does not
involve that all the things there are form a whole which could be
regarded as another thing and be made the subject of predicates. It
involves only the assertion that there are properties which belong to
each separate thing, not that there are properties belonging to the
whole of things collectively. The philosophy which I wish to advocate
may be called logical atomism or absolute pluralism, because, while
maintaining that there are many things, it denies that there is a
whole composed of those things. We shall see, therefore, that
philosophical propositions, instead of being concerned with the whole
of things collectively, are concerned with all things distributively;
and not only must they be concerned with all things, but they must be
concerned with such properties of all things as do not depend upon the
accidental nature of the things that there happen to be, but are true
of any possible world, independently of such facts as can only be
discovered by our senses.
This brings us to a second characteristic of philosophical
propositions, namely, that they must be _a priori_. A philosophical
proposition must be such as can be neither proved nor disproved by
empirical evidence. Too often we find in philosophical books arguments
based upon the course of history, or the convolutions of the brain, or
the eyes of shell-fish. Special and accidental facts of this kind are
irrelevant to philosophy, which must make only such assertions as
would be equally true however the actual world were constituted.
We may sum up these two characteristics of philosophical propositions
by saying that _philosophy is the science of the possible_. But this
statement unexplained is liable to be misleading, since it may be
thought that the possible is something other than the general, whereas
in fact the two are indistinguishable.
Philosophy, if what has been said is correct, becomes
indistinguishable from logic as that word has now come to be used.
The study of logic consists, broadly speaking, of two not very sharply
distinguished portions. On the one hand it is concerned with those
general statements which can be made concerning everything without
mentioning any one thing or predicate or relation, such for example as
"if _x_ is a member of the class [alpha] and every member of [alpha]
is a member of [beta], then _x_ is a member of the class [beta],
whatever _x_, [alpha], and [beta] may be." On the other hand, it is
concerned with the analysis and enumeration of logical _forms_, i.e.
with the kinds of propositions that may occur, with the various types
of facts, and with the classification of the constituents of facts. In
this way logic provides an inventory of possibilities, a repertory of
abstractly tenable hypotheses.
It might be thought that such a study would be too vague and too
general to be of any very great importance, and that, if its problems
became at any point sufficiently definite, they would be merged in the
problems of some special science. It appears, however, that this is
not the case. In some problems, for example, the analysis of space and
time, the nature of perception, or the theory of judgment, the
discovery of the logical form of the facts involved is the hardest
part of the work and the part whose performance has been most lacking
hitherto. It is chiefly for want of the right logical hypothesis that
such problems have hitherto been treated in such an unsatisfactory
manner, and have given rise to those contradictions or antinomies in
which the enemies of reason among philosophers have at all times
delighted.
By concentrating attention upon the investigation of logical forms, it
becomes possible at last for philosophy to deal with its problems
piecemeal, and to obtain, as the sciences do, such partial and
probably not wholly correct results as subsequent investigation can
utilise even while it supplements and improves them. Most
philosophies hitherto have been constructed all in one block, in such
a way that, if they were not wholly correct, they were wholly
incorrect, and could not be used as a basis for further
investigations. It is chiefly owing to this fact that philosophy,
unlike science, has hitherto been unprogressive, because each original
philosopher has had to begin the work again from the beginning,
without being able to accept anything definite from the work of his
predecessors. A scientific philosophy such as I wish to recommend will
be piecemeal and tentative like other sciences; above all, it will be
able to invent hypotheses which, even if they are not wholly true,
will yet remain fruitful after the necessary corrections have been
made. This possibility of successive approximations to the truth is,
more than anything else, the source of the triumphs of science, and to
transfer this possibility to philosophy is to ensure a progress in
method whose importance it would be almost impossible to exaggerate.
The essence of philosophy as thus conceived is analysis, not
synthesis. To build up systems of the world, like Heine's German
professor who knit together fragments of life and made an intelligible
system out of them, is not, I believe, any more feasible than the
discovery of the philosopher's stone. What is feasible is the
understanding of general forms, and the division of traditional
problems into a number of separate and less baffling questions.
"Divide and conquer" is the maxim of success here as elsewhere.
Let us illustrate these somewhat general maxims by examining their
application to the philosophy of space, for it is only in application
that the meaning or importance of a method can be understood. Suppose
we are confronted with the problem of space as presented in Kant's
Transcendental Æsthetic, and suppose we wish to discover what are the
elements of the problem and what hope there is of obtaining a solution
of them. It will soon appear that three entirely distinct problems,
belonging to different studies, and requiring different methods for
their solution, have been confusedly combined in the supposed single
problem with which Kant is concerned. There is a problem of logic, a
problem of physics, and a problem of theory of knowledge. Of these
three, the problem of logic can be solved exactly and perfectly; the
problem of physics can probably be solved with as great a degree of
certainty and as great an approach to exactness as can be hoped in an
empirical region; the problem of theory of knowledge, however, remains
very obscure and very difficult to deal with. Let us see how these
three problems arise.
(1) The logical problem has arisen through the suggestions of
non-Euclidean geometry. Given a body of geometrical propositions, it
is not difficult to find a minimum statement of the axioms from which
this body of propositions can be deduced. It is also not difficult, by
dropping or altering some of these axioms, to obtain a more general or
a different geometry, having, from the point of view of pure
mathematics, the same logical coherence and the same title to respect
as the more familiar Euclidean geometry. The Euclidean geometry itself
is true perhaps of actual space (though this is doubtful), but
certainly of an infinite number of purely arithmetical systems, each
of which, from the point of view of abstract logic, has an equal and
indefeasible right to be called a Euclidean space. Thus space as an
object of logical or mathematical study loses its uniqueness; not only
are there many kinds of spaces, but there are an infinity of examples
of each kind, though it is difficult to find any kind of which the
space of physics may be an example, and it is impossible to find any
kind of which the space of physics is certainly an example. As an
illustration of one possible logical system of geometry we may
consider all relations of three terms which are analogous in certain
formal respects to the relation "between" as it appears to be in
actual space. A space is then defined by means of one such three-term
relation. The points of the space are all the terms which have this
relation to something or other, and their order in the space in
question is determined by this relation. The points of one space are
necessarily also points of other spaces, since there are necessarily
other three-term relations having those same points for their field.
The space in fact is not determined by the class of its points, but by
the ordering three-term relation. When enough abstract logical
properties of such relations have been enumerated to determine the
resulting kind of geometry, say, for example, Euclidean geometry, it
becomes unnecessary for the pure geometer in his abstract capacity to
distinguish between the various relations which have all these
properties. He considers the whole class of such relations, not any
single one among them. Thus in studying a given kind of geometry the
pure mathematician is studying a certain class of relations defined by
means of certain abstract logical properties which take the place of
what used to be called axioms. The nature of geometrical _reasoning_
therefore is purely deductive and purely logical; if any special
epistemological peculiarities are to be found in geometry, it must not
be in the reasoning, but in our knowledge concerning the axioms in
some given space.
(2) The physical problem of space is both more interesting and more
difficult than the logical problem. The physical problem may be
stated as follows: to find in the physical world, or to construct from
physical materials, a space of one of the kinds enumerated by the
logical treatment of geometry. This problem derives its difficulty
from the attempt to accommodate to the roughness and vagueness of the
real world some system possessing the logical clearness and exactitude
of pure mathematics. That this can be done with a certain degree of
approximation is fairly evident If I see three people _A_, _B_, and
_C_ sitting in a row, I become aware of the fact which may be
expressed by saying that _B_ is between _A_ and _C_ rather than that
_A_ is between _B_ and _C_, or _C_ is between _A_ and _B_. This
relation of "between" which is thus perceived to hold has some of the
abstract logical properties of those three-term relations which, we
saw, give rise to a geometry, but its properties fail to be exact, and
are not, as empirically given, amenable to the kind of treatment at
which geometry aims. In abstract geometry we deal with points,
straight lines, and planes; but the three people _A_, _B_, and _C_
whom I see sitting in a row are not exactly points, nor is the row
exactly a straight line. Nevertheless physics, which formally assumes
a space containing points, straight lines, and planes, is found
empirically to give results applicable to the sensible world. It must
therefore be possible to find an interpretation of the points,
straight lines, and planes of physics in terms of physical data, or at
any rate in terms of data together with such hypothetical additions as
seem least open to question. Since all data suffer from a lack of
mathematical precision through being of a certain size and somewhat
vague in outline, it is plain that if such a notion as that of a point
is to find any application to empirical material, the point must be
neither a datum nor a hypothetical addition to data, but a
_construction_ by means of data with their hypothetical additions. It
is obvious that any hypothetical filling out of data is less dubious
and unsatisfactory when the additions are closely analogous to data
than when they are of a radically different sort. To assume, for
example, that objects which we see continue, after we have turned away
our eyes, to be more or less analogous to what they were while we were
looking, is a less violent assumption than to assume that such objects
are composed of an infinite number of mathematical points. Hence in
the physical study of the geometry of physical space, points must not
be assumed _ab initio_ as they are in the logical treatment of
geometry, but must be constructed as systems composed of data and
hypothetical analogues of data. We are thus led naturally to define a
physical point as a certain class of those objects which are the
ultimate constituents of the physical world. It will be the class of
all those objects which, as one would naturally say, _contain_ the
point. To secure a definition giving this result, without previously
assuming that physical objects are composed of points, is an agreeable
problem in mathematical logic. The solution of this problem and the
perception of its importance are due to my friend Dr. Whitehead. The
oddity of regarding a point as a class of physical entities wears off
with familiarity, and ought in any case not to be felt by those who
maintain, as practically every one does, that points are mathematical
fictions. The word "fiction" is used glibly in such connexions by many
men who seem not to feel the necessity of explaining how it can come
about that a fiction can be so useful in the study of the actual world
as the points of mathematical physics have been found to be. By our
definition, which regards a point as a class of physical objects, it
is explained both how the use of points can lead to important
physical results, and how we can nevertheless avoid the assumption
that points are themselves entities in the physical world.
Many of the mathematically convenient properties of abstract logical
spaces cannot be either known to belong or known not to belong to the
space of physics. Such are all the properties connected with continuity.
For to know that actual space has these properties would require an
infinite exactness of sense-perception. If actual space is continuous,
there are nevertheless many possible non-continuous spaces which will be
empirically indistinguishable from it; and, conversely, actual space may
be non-continuous and yet empirically indistinguishable from a possible
continuous space. Continuity, therefore, though obtainable in the _a
priori_ region of arithmetic, is not with certainty obtainable in the
space or time of the physical world: whether these are continuous or not
would seem to be a question not only unanswered but for ever
unanswerable. From the point of view of philosophy, however, the
discovery that a question is unanswerable is as complete an answer as
any that could possibly be obtained. And from the point of view of
physics, where no empirical means of distinction can be found, there can
be no empirical objection to the mathematically simplest assumption,
which is that of continuity.
The subject of the physical theory of space is a very large one,
hitherto little explored. It is associated with a similar theory of
time, and both have been forced upon the attention of philosophically
minded physicists by the discussions which have raged concerning the
theory of relativity.