← catalogue

Our Knowledge of the External World as a Field for Scientific Method in Philosophy

by Bertrand Russell · English · Gutenberg #37090 · 439,982 chars · public domain (US)

The Project Gutenberg eBook of Our Knowledge of the External World as a Field for Scientific Method in Philosophy
    
This eBook is for the use of anyone anywhere in the United States and
most other parts of the world at no cost and with almost no restrictions
whatsoever. You may copy it, give it away or re-use it under the terms
of the Project Gutenberg License included with this eBook or online
at www.gutenberg.org. If you are not located in the United States,
you will have to check the laws of the country where you are located
before using this eBook.

Title: Our Knowledge of the External World as a Field for Scientific Method in Philosophy

Author: Bertrand Russell


        
Release date: August 15, 2011 [eBook #37090]
                Most recently updated: January 8, 2021

Language: English

Other information and formats: www.gutenberg.org/ebooks/37090

Credits: Produced by Jana Srna and the Online Distributed
        Proofreading Team at https://www.pgdp.net


*** START OF THE PROJECT GUTENBERG EBOOK OUR KNOWLEDGE OF THE EXTERNAL WORLD AS A FIELD FOR SCIENTIFIC METHOD IN PHILOSOPHY ***




Produced by Jana Srna and the Online Distributed
Proofreading Team at https://www.pgdp.net






  [ Transcriber's Notes:

    Every effort has been made to replicate this text as faithfully
    as possible, including inconsistencies in spelling and hyphenation.
    Some corrections of spelling and punctuation have been made. They
    are listed at the end of the text.

    Italic text has been marked with _underscores_.
    Greek text has been transliterated and marked with ~tildes~.
  ]




  OUR KNOWLEDGE OF THE
  EXTERNAL WORLD

  AS A FIELD FOR SCIENTIFIC METHOD
  IN PHILOSOPHY




BY THE SAME AUTHOR


  INTRODUCTION TO MATHEMATICAL PHILOSOPHY
  Second Edition.
  Demy 8vo, 12s. 6d. net.

  THE ANALYSIS OF MIND
  Demy 8vo, 16s. net.

  PRINCIPLES OF SOCIAL RECONSTRUCTION
  Seventh Impression.
  Cr. 8vo, 5s. net; Limp, 3s. 6d. net.

  ROADS TO FREEDOM: SOCIALISM, ANARCHISM AND SYNDICALISM
  Fourth Impression.
  Cr. 8vo, 5s. net; Limp, 3s. 6d. net.

  THE PRACTICE AND THEORY OF BOLSHEVISM
  Second Impression.
  Cr. 8vo, 6s. net.




  OUR KNOWLEDGE OF
  THE EXTERNAL WORLD
  AS A FIELD FOR SCIENTIFIC METHOD
  IN PHILOSOPHY

  BY
  BERTRAND RUSSELL, F.R.S

  LONDON: GEORGE ALLEN & UNWIN LTD
  RUSKIN HOUSE, 40 MUSEUM STREET, W.C. 1


  First published in 1914 by
  The Open Court Publishing Company

  Reissued by George Allen & Unwin Ltd.
  1922




PREFACE


The following lectures[1] are an attempt to show, by means of examples,
the nature, capacity, and limitations of the logical-analytic method in
philosophy. This method, of which the first complete example is to be
found in the writings of Frege, has gradually, in the course of actual
research, increasingly forced itself upon me as something perfectly
definite, capable of embodiment in maxims, and adequate, in all branches
of philosophy, to yield whatever objective scientific knowledge it is
possible to obtain. Most of the methods hitherto practised have
professed to lead to more ambitious results than any that logical
analysis can claim to reach, but unfortunately these results have always
been such as many competent philosophers considered inadmissible.
Regarded merely as hypotheses and as aids to imagination, the great
systems of the past serve a very useful purpose, and are abundantly
worthy of study. But something different is required if philosophy is to
become a science, and to aim at results independent of the tastes and
temperament of the philosopher who advocates them. In what follows, I
have endeavoured to show, however imperfectly, the way by which I
believe that this _desideratum_ is to be found.

  [1] Delivered as Lowell Lectures in Boston, in March and April 1914.

The central problem by which I have sought to illustrate method is the
problem of the relation between the crude data of sense and the space,
time, and matter of mathematical physics. I have been made aware of the
importance of this problem by my friend and collaborator Dr Whitehead,
to whom are due almost all the differences between the views advocated
here and those suggested in _The Problems of Philosophy_.[2] I owe to
him the definition of points, the suggestion for the treatment of
instants and "things," and the whole conception of the world of physics
as a _construction_ rather than an _inference_. What is said on these
topics here is, in fact, a rough preliminary account of the more precise
results which he is giving in the fourth volume of our _Principia
Mathematica_.[3] It will be seen that if his way of dealing with these
topics is capable of being successfully carried through, a wholly new
light is thrown on the time-honoured controversies of realists and
idealists, and a method is obtained of solving all that is soluble in
their problem.

  [2] London and New York, 1912 ("Home University Library").

  [3] The first volume was published at Cambridge in 1910, the second in
  1912, and the third in 1913.

The speculations of the past as to the reality or unreality of the world
of physics were baffled, at the outset, by the absence of any
satisfactory theory of the mathematical infinite. This difficulty has
been removed by the work of Georg Cantor. But the positive and detailed
solution of the problem by means of mathematical constructions based
upon sensible objects as data has only been rendered possible by the
growth of mathematical logic, without which it is practically impossible
to manipulate ideas of the requisite abstractness and complexity. This
aspect, which is somewhat obscured in a merely popular outline such as
is contained in the following lectures, will become plain as soon as Dr
Whitehead's work is published. In pure logic, which, however, will be
very briefly discussed in these lectures, I have had the benefit of
vitally important discoveries, not yet published, by my friend Mr Ludwig
Wittgenstein.

Since my purpose was to illustrate method, I have included much that is
tentative and incomplete, for it is not by the study of finished
structures alone that the manner of construction can be learnt. Except
in regard to such matters as Cantor's theory of infinity, no finality is
claimed for the theories suggested; but I believe that where they are
found to require modification, this will be discovered by substantially
the same method as that which at present makes them appear probable, and
it is on this ground that I ask the reader to be tolerant of their
incompleteness.

  Cambridge,
    June 1914.




CONTENTS


  LECTURE                                                     PAGE

       I. Current Tendencies                                     3

      II. Logic as the Essence of Philosophy                    33

     III. On our Knowledge of the External World                63

      IV. The World of Physics and the World of Sense          101

       V. The Theory of Continuity                             129

      VI. The Problem of Infinity considered Historically      155

     VII. The Positive Theory of Infinity                      185

    VIII. On the Notion of Cause, with Applications to
             the Free-will Problem                             211

          Index                                                243




LECTURE I

CURRENT TENDENCIES


Philosophy, from the earliest times, has made greater claims, and
achieved fewer results, than any other branch of learning. Ever since
Thales said that all is water, philosophers have been ready with glib
assertions about the sum-total of things; and equally glib denials have
come from other philosophers ever since Thales was contradicted by
Anaximander. I believe that the time has now arrived when this
unsatisfactory state of things can be brought to an end. In the
following course of lectures I shall try, chiefly by taking certain
special problems as examples, to indicate wherein the claims of
philosophers have been excessive, and why their achievements have not
been greater. The problems and the method of philosophy have, I believe,
been misconceived by all schools, many of its traditional problems being
insoluble with our means of knowledge, while other more neglected but
not less important problems can, by a more patient and more adequate
method, be solved with all the precision and certainty to which the most
advanced sciences have attained.

Among present-day philosophies, we may distinguish three principal
types, often combined in varying proportions by a single philosopher,
but in essence and tendency distinct. The first of these, which I shall
call the classical tradition, descends in the main from Kant and Hegel;
it represents the attempt to adapt to present needs the methods and
results of the great constructive philosophers from Plato downwards. The
second type, which may be called evolutionism, derived its predominance
from Darwin, and must be reckoned as having had Herbert Spencer for its
first philosophical representative; but in recent times it has become,
chiefly through William James and M. Bergson, far bolder and far more
searching in its innovations than it was in the hands of Herbert
Spencer. The third type, which may be called "logical atomism" for want
of a better name, has gradually crept into philosophy through the
critical scrutiny of mathematics. This type of philosophy, which is the
one that I wish to advocate, has not as yet many whole-hearted
adherents, but the "new realism" which owes its inception to Harvard is
very largely impregnated with its spirit. It represents, I believe, the
same kind of advance as was introduced into physics by Galileo: the
substitution of piecemeal, detailed, and verifiable results for large
untested generalities recommended only by a certain appeal to
imagination. But before we can understand the changes advocated by this
new philosophy, we must briefly examine and criticise the other two
types with which it has to contend.


A. The Classical Tradition

Twenty years ago, the classical tradition, having vanquished the
opposing tradition of the English empiricists, held almost unquestioned
sway in all Anglo-Saxon universities. At the present day, though it is
losing ground, many of the most prominent teachers still adhere to it.
In academic France, in spite of M. Bergson, it is far stronger than all
its opponents combined; and in Germany it has many vigorous advocates.
Nevertheless, it represents on the whole a decaying force, and it has
failed to adapt itself to the temper of the age. Its advocates are, in
the main, those whose extra-philosophical knowledge is literary, rather
than those who have felt the inspiration of science. There are, apart
from reasoned arguments, certain general intellectual forces against
it--the same general forces which are breaking down the other great
syntheses of the past, and making our age one of bewildered groping
where our ancestors walked in the clear daylight of unquestioning
certainty.

The original impulse out of which the classical tradition developed was
the naive faith of the Greek philosophers in the omnipotence of
reasoning. The discovery of geometry had intoxicated them, and its _a
priori_ deductive method appeared capable of universal application. They
would prove, for instance, that all reality is one, that there is no
such thing as change, that the world of sense is a world of mere
illusion; and the strangeness of their results gave them no qualms
because they believed in the correctness of their reasoning. Thus it
came to be thought that by mere thinking the most surprising and
important truths concerning the whole of reality could be established
with a certainty which no contrary observations could shake. As the
vital impulse of the early philosophers died away, its place was taken
by authority and tradition, reinforced, in the Middle Ages and almost to
our own day, by systematic theology. Modern philosophy, from Descartes
onwards, though not bound by authority like that of the Middle Ages,
still accepted more or less uncritically the Aristotelian logic.
Moreover, it still believed, except in Great Britain, that _a priori_
reasoning could reveal otherwise undiscoverable secrets about the
universe, and could prove reality to be quite different from what, to
direct observation, it appears to be. It is this belief, rather than any
particular tenets resulting from it, that I regard as the distinguishing
characteristic of the classical tradition, and as hitherto the main
obstacle to a scientific attitude in philosophy.

The nature of the philosophy embodied in the classical tradition may be
made clearer by taking a particular exponent as an illustration. For
this purpose, let us consider for a moment the doctrines of Mr Bradley,
who is probably the most distinguished living representative of this
school. Mr Bradley's _Appearance and Reality_ is a book consisting of
two parts, the first called _Appearance_, the second _Reality_. The
first part examines and condemns almost all that makes up our everyday
world: things and qualities, relations, space and time, change,
causation, activity, the self. All these, though in some sense facts
which qualify reality, are not real as they appear. What is real is one
single, indivisible, timeless whole, called the Absolute, which is in
some sense spiritual, but does not consist of souls, or of thought and
will as we know them. And all this is established by abstract logical
reasoning professing to find self-contradictions in the categories
condemned as mere appearance, and to leave no tenable alternative to the
kind of Absolute which is finally affirmed to be real.

One brief example may suffice to illustrate Mr Bradley's method. The
world appears to be full of many things with various relations to each
other--right and left, before and after, father and son, and so on. But
relations, according to Mr Bradley, are found on examination to be
self-contradictory and therefore impossible. He first argues that, if
there are relations, there must be qualities between which they hold.
This part of his argument need not detain us. He then proceeds:

"But how the relation can stand to the qualities is, on the other side,
unintelligible. If it is nothing to the qualities, then they are not
related at all; and, if so, as we saw, they have ceased to be qualities,
and their relation is a nonentity. But if it is to be something to them,
then clearly we shall require a _new_ connecting relation. For the
relation hardly can be the mere adjective of one or both of its terms;
or, at least, as such it seems indefensible. And, being something
itself, if it does not itself bear a relation to the terms, in what
intelligible way will it succeed in being anything to them? But here
again we are hurried off into the eddy of a hopeless process, since we
are forced to go on finding new relations without end. The links are
united by a link, and this bond of union is a link which also has two
ends; and these require each a fresh link to connect them with the old.
The problem is to find how the relation can stand to its qualities, and
this problem is insoluble."[4]

  [4] _Appearance and Reality_, pp. 32-33.

I do not propose to examine this argument in detail, or to show the
exact points where, in my opinion, it is fallacious. I have quoted it
only as an example of method. Most people will admit, I think, that it
is calculated to produce bewilderment rather than conviction, because
there is more likelihood of error in a very subtle, abstract, and
difficult argument than in so patent a fact as the interrelatedness of
the things in the world. To the early Greeks, to whom geometry was
practically the only known science, it was possible to follow reasoning
with assent even when it led to the strangest conclusions. But to us,
with our methods of experiment and observation, our knowledge of the
long history of _a priori_ errors refuted by empirical science, it has
become natural to suspect a fallacy in any deduction of which the
conclusion appears to contradict patent facts. It is easy to carry such
suspicion too far, and it is very desirable, if possible, actually to
discover the exact nature of the error when it exists. But there is no
doubt that what we may call the empirical outlook has become part of
most educated people's habit of mind; and it is this, rather than any
definite argument, that has diminished the hold of the classical
tradition upon students of philosophy and the instructed public
generally.

The function of logic in philosophy, as I shall try to show at a later
stage, is all-important; but I do not think its function is that which
it has in the classical tradition. In that tradition, logic becomes
constructive through negation. Where a number of alternatives seem, at
first sight, to be equally possible, logic is made to condemn all of
them except one, and that one is then pronounced to be realised in the
actual world. Thus the world is constructed by means of logic, with
little or no appeal to concrete experience. The true function of logic
is, in my opinion, exactly the opposite of this. As applied to matters
of experience, it is analytic rather than constructive; taken _a
priori_, it shows the possibility of hitherto unsuspected alternatives
more often than the impossibility of alternatives which seemed _prima
facie_ possible. Thus, while it liberates imagination as to what the
world _may_ be, it refuses to legislate as to what the world _is_. This
change, which has been brought about by an internal revolution in logic,
has swept away the ambitious constructions of traditional metaphysics,
even for those whose faith in logic is greatest; while to the many who
regard logic as a chimera the paradoxical systems to which it has given
rise do not seem worthy even of refutation. Thus on all sides these
systems have ceased to attract, and even the philosophical world tends
more and more to pass them by.

One or two of the favourite doctrines of the school we are considering
may be mentioned to illustrate the nature of its claims. The universe,
it tells us, is an "organic unity," like an animal or a perfect work of
art. By this it means, roughly speaking, that all the different parts
fit together and co-operate, and are what they are because of their
place in the whole. This belief is sometimes advanced dogmatically,
while at other times it is defended by certain logical arguments. If it
is true, every part of the universe is a microcosm, a miniature
reflection of the whole. If we knew ourselves thoroughly, according to
this doctrine, we should know everything. Common sense would naturally
object that there are people--say in China--with whom our relations are
so indirect and trivial that we cannot infer anything important as to
them from any fact about ourselves. If there are living beings in Mars
or in more distant parts of the universe, the same argument becomes even
stronger. But further, perhaps the whole contents of the space and time
in which we live form only one of many universes, each seeming to itself
complete. And thus the conception of the necessary unity of all that is
resolves itself into the poverty of imagination, and a freer logic
emancipates us from the strait-waistcoated benevolent institution which
idealism palms off as the totality of being.

Another very important doctrine held by most, though not all, of the
school we are examining is the doctrine that all reality is what is
called "mental" or "spiritual," or that, at any rate, all reality is
dependent for its existence upon what is mental. This view is often
particularised into the form which states that the relation of knower
and known is fundamental, and that nothing can exist unless it either
knows or is known. Here again the same legislative function is ascribed
to _a priori_ argumentation: it is thought that there are contradictions
in an unknown reality. Again, if I am not mistaken, the argument is
fallacious, and a better logic will show that no limits can be set to
the extent and nature of the unknown. And when I speak of the unknown, I
do not mean merely what we personally do not know, but what is not known
to any mind. Here as elsewhere, while the older logic shut out
possibilities and imprisoned imagination within the walls of the
familiar, the newer logic shows rather what may happen, and refuses to
decide as to what _must_ happen.

The classical tradition in philosophy is the last surviving child of two
very diverse parents: the Greek belief in reason, and the mediaeval
belief in the tidiness of the universe. To the schoolmen, who lived amid
wars, massacres, and pestilences, nothing appeared so delightful as
safety and order. In their idealising dreams, it was safety and order
that they sought: the universe of Thomas Aquinas or Dante is as small
and neat as a Dutch interior. To us, to whom safety has become monotony,
to whom the primeval savageries of nature are so remote as to become a
mere pleasing condiment to our ordered routine, the world of dreams is
very different from what it was amid the wars of Guelf and Ghibelline.
Hence William James's protest against what he calls the "block universe"
of the classical tradition; hence Nietzsche's worship of force; hence
the verbal bloodthirstiness of many quiet literary men. The barbaric
substratum of human nature, unsatisfied in action, finds an outlet in
imagination. In philosophy, as elsewhere, this tendency is visible; and
it is this, rather than formal argument, that has thrust aside the
classical tradition for a philosophy which fancies itself more virile
and more vital.


B. Evolutionism

Evolutionism, in one form or another, is the prevailing creed of our
time. It dominates our politics, our literature, and not least our
philosophy. Nietzsche, pragmatism, Bergson, are phases in its
philosophic development, and their popularity far beyond the circles of
professional philosophers shows its consonance with the spirit of the
age. It believes itself firmly based on science, a liberator of hopes,
an inspirer of an invigorating faith in human power, a sure antidote to
the ratiocinative authority of the Greeks and the dogmatic authority of
mediaeval systems. Against so fashionable and so agreeable a creed it may
seem useless to raise a protest; and with much of its spirit every
modern man must be in sympathy. But I think that, in the intoxication of
a quick success, much that is important and vital to a true
understanding of the universe has been forgotten. Something of Hellenism
must be combined with the new spirit before it can emerge from the
ardour of youth into the wisdom of manhood. And it is time to remember
that biology is neither the only science, nor yet the model to which all
other sciences must adapt themselves. Evolutionism, as I shall try to
show, is not a truly scientific philosophy, either in its method or in
the problems which it considers. The true scientific philosophy is
something more arduous and more aloof, appealing to less mundane hopes,
and requiring a severer discipline for its successful practice.

Darwin's _Origin of Species_ persuaded the world that the difference
between different species of animals and plants is not the fixed,
immutable difference that it appears to be. The doctrine of natural
kinds, which had rendered classification easy and definite, which was
enshrined in the Aristotelian tradition, and protected by its supposed
necessity for orthodox dogma, was suddenly swept away for ever out of
the biological world. The difference between man and the lower animals,
which to our human conceit appears enormous, was shown to be a gradual
achievement, involving intermediate beings who could not with certainty
be placed either within or without the human family. The sun and planets
had already been shown by Laplace to be very probably derived from a
primitive more or less undifferentiated nebula. Thus the old fixed
landmarks became wavering and indistinct, and all sharp outlines were
blurred. Things and species lost their boundaries, and none could say
where they began or where they ended.

But if human conceit was staggered for a moment by its kinship with the
ape, it soon found a way to reassert itself, and that way is the
"philosophy" of evolution. A process which led from the amoeba to man
appeared to the philosophers to be obviously a progress--though whether
the amoeba would agree with this opinion is not known. Hence the cycle
of changes which science had shown to be the probable history of the
past was welcomed as revealing a law of development towards good in the
universe--an evolution or unfolding of an ideal slowly embodying itself
in the actual. But such a view, though it might satisfy Spencer and
those whom we may call Hegelian evolutionists, could not be accepted as
adequate by the more whole-hearted votaries of change. An ideal to which
the world continuously approaches is, to these minds, too dead and
static to be inspiring. Not only the aspirations, but the ideal too,
must change and develop with the course of evolution; there must be no
fixed goal, but a continual fashioning of fresh needs by the impulse
which is life and which alone gives unity to the process.

Ever since the seventeenth century, those whom William James described
as the "tender-minded" have been engaged in a desperate struggle with
the mechanical view of the course of nature which physical science seems
to impose. A great part of the attractiveness of the classical tradition
was due to the partial escape from mechanism which it provided. But now,
with the influence of biology, the "tender-minded" believe that a more
radical escape is possible, sweeping aside not merely the laws of
physics, but the whole apparently immutable apparatus of logic, with its
fixed concepts, its general principles, and its reasonings which seem
able to compel even the most unwilling assent. The older kind of
teleology, therefore, which regarded the End as a fixed goal, already
partially visible, towards which we were gradually approaching, is
rejected by M. Bergson as not allowing enough for the absolute dominion
of change. After explaining why he does not accept mechanism, he
proceeds:[5]

"But radical finalism is quite as unacceptable, and for the same reason.
The doctrine of teleology, in its extreme form, as we find it in Leibniz
for example, implies that things and beings merely realise a programme
previously arranged. But if there is nothing unforeseen, no invention or
creation in the universe, time is useless again. As in the mechanistic
hypothesis, here again it is supposed that _all is given_. Finalism thus
understood is only inverted mechanism. It springs from the same
postulate, with this sole difference, that in the movement of our finite
intellects along successive things, whose successiveness is reduced to a
mere appearance, it holds in front of us the light with which it claims
to guide us, instead of putting it behind. It substitutes the attraction
of the future for the impulsion of the past. But succession remains none
the less a mere appearance, as indeed does movement itself. In the
doctrine of Leibniz, time is reduced to a confused perception, relative
to the human standpoint, a perception which would vanish, like a rising
mist, for a mind seated at the centre of things.

"Yet finalism is not, like mechanism, a doctrine with fixed rigid
outlines. It admits of as many inflections as we like. The mechanistic
philosophy is to be taken or left: it must be left if the least grain of
dust, by straying from the path foreseen by mechanics, should show the
slightest trace of spontaneity. The doctrine of final causes, on the
contrary, will never be definitively refuted. If one form of it be put
aside, it will take another. Its principle, which is essentially
psychological, is very flexible. It is so extensible, and thereby so
comprehensive, that one accepts something of it as soon as one rejects
pure mechanism. The theory we shall put forward in this book will
therefore necessarily partake of finalism to a certain extent."

  [5] _Creative Evolution_, English translation, p. 41.

M. Bergson's form of finalism depends upon his conception of life. Life,
in his philosophy, is a continuous stream, in which all divisions are
artificial and unreal. Separate things, beginnings and endings, are mere
convenient fictions: there is only smooth, unbroken transition. The
beliefs of to-day may count as true to-day, if they carry us along the
stream; but to-morrow they will be false, and must be replaced by new
beliefs to meet the new situation. All our thinking consists of
convenient fictions, imaginary congealings of the stream: reality flows
on in spite of all our fictions, and though it can be lived, it cannot
be conceived in thought. Somehow, without explicit statement, the
assurance is slipped in that the future, though we cannot foresee it,
will be better than the past or the present: the reader is like the
child who expects a sweet because it has been told to open its mouth and
shut its eyes. Logic, mathematics, physics disappear in this philosophy,
because they are too "static"; what is real is an impulse and movement
towards a goal which, like the rainbow, recedes as we advance, and makes
every place different when we reach it from what it appeared to be at a
distance.

Now I do not propose at present to enter upon a technical examination of
this philosophy. At present I wish to make only two criticisms of
it--first, that its truth does not follow from what science has rendered
probable concerning the facts of evolution, and secondly, that the
motives and interests which inspire it are so exclusively practical, and
the problems with which it deals are so special, that it can hardly be
regarded as really touching any of the questions that to my mind
constitute genuine philosophy.

(1) What biology has rendered probable is that the diverse species arose
by adaptation from a less differentiated ancestry. This fact is in
itself exceedingly interesting, but it is not the kind of fact from
which philosophical consequences follow. Philosophy is general, and
takes an impartial interest in all that exists. The changes suffered by
minute portions of matter on the earth's surface are very important to
us as active sentient beings; but to us as philosophers they have no
greater interest than other changes in portions of matter elsewhere. And
if the changes on the earth's surface during the last few millions of
years appear to our present ethical notions to be in the nature of a
progress, that gives no ground for believing that progress is a general
law of the universe. Except under the influence of desire, no one would
admit for a moment so crude a generalisation from such a tiny selection
of facts. What does result, not specially from biology, but from all the
sciences which deal with what exists, is that we cannot understand the
world unless we can understand change and continuity. This is even more
evident in physics than it is in biology. But the analysis of change and
continuity is not a problem upon which either physics or biology throws
any light: it is a problem of a new kind, belonging to a different kind
of study. The question whether evolutionism offers a true or a false
answer to this problem is not, therefore, a question to be solved by
appeals to particular facts, such as biology and physics reveal. In
assuming dogmatically a certain answer to this question, evolutionism
ceases to be scientific, yet it is only in touching on this question
that evolutionism reaches the subject-matter of philosophy. Evolutionism
thus consists of two parts: one not philosophical, but only a hasty
generalisation of the kind which the special sciences might hereafter
confirm or confute; the other not scientific, but a mere unsupported
dogma, belonging to philosophy by its subject-matter, but in no way
deducible from the facts upon which evolution relies.

(2) The predominant interest of evolutionism is in the question of human
destiny, or at least of the destiny of Life. It is more interested in
morality and happiness than in knowledge for its own sake. It must be
admitted that the same may be said of many other philosophies, and that
a desire for the kind of knowledge which philosophy really can give is
very rare. But if philosophy is to become scientific--and it is our
object to discover how this can be achieved--it is necessary first and
foremost that philosophers should acquire the disinterested intellectual
curiosity which characterises the genuine man of science. Knowledge
concerning the future--which is the kind of knowledge that must be
sought if we are to know about human destiny--is possible within certain
narrow limits. It is impossible to say how much the limits may be
enlarged with the progress of science. But what is evident is that any
proposition about the future belongs by its subject-matter to some
particular science, and is to be ascertained, if at all, by the methods
of that science. Philosophy is not a short cut to the same kind of
results as those of the other sciences: if it is to be a genuine study,
it must have a province of its own, and aim at results which the other
sciences can neither prove nor disprove.

The consideration that philosophy, if there is such a study, must
consist of propositions which could not occur in the other sciences, is
one which has very far-reaching consequences. All the questions which
have what is called a human interest--such, for example, as the question
of a future life--belong, at least in theory, to special sciences, and
are capable, at least in theory, of being decided by empirical evidence.
Philosophers have too often, in the past, permitted themselves to
pronounce on empirical questions, and found themselves, as a result, in
disastrous conflict with well-attested facts. We must, therefore,
renounce the hope that philosophy can promise satisfaction to our
mundane desires. What it can do, when it is purified from all practical
taint, is to help us to understand the general aspects of the world and
the logical analysis of familiar but complex things. Through this
achievement, by the suggestion of fruitful hypotheses, it may be
indirectly useful in other sciences, notably mathematics, physics, and
psychology. But a genuinely scientific philosophy cannot hope to appeal
to any except those who have the wish to understand, to escape from
intellectual bewilderment. It offers, in its own domain, the kind of
satisfaction which the other sciences offer. But it does not offer, or
attempt to offer, a solution of the problem of human destiny, or of the
destiny of the universe.

Evolutionism, if what has been said is true, is to be regarded as a
hasty generalisation from certain rather special facts, accompanied by a
dogmatic rejection of all attempts at analysis, and inspired by
interests which are practical rather than theoretical. In spite,
therefore, of its appeal to detailed results in various sciences, it
cannot be regarded as any more genuinely scientific than the classical
tradition which it has replaced. How philosophy is to be rendered
scientific, and what is the true subject-matter of philosophy, I shall
try to show first by examples of certain achieved results, and then more
generally. We will begin with the problem of the physical conceptions of
space and time and matter, which, as we have seen, are challenged by the
contentions of the evolutionists. That these conceptions stand in need
of reconstruction will be admitted, and is indeed increasingly urged by
physicists themselves. It will also be admitted that the reconstruction
must take more account of change and the universal flux than is done in
the older mechanics with its fundamental conception of an indestructible
matter. But I do not think the reconstruction required is on Bergsonian
lines, nor do I think that his rejection of logic can be anything but
harmful. I shall not, however, adopt the method of explicit controversy,
but rather the method of independent inquiry, starting from what, in a
pre-philosophic stage, appear to be facts, and keeping always as close
to these initial data as the requirements of consistency will permit.

Although explicit controversy is almost always fruitless in philosophy,
owing to the fact that no two philosophers ever understand one another,
yet it seems necessary to say something at the outset in justification
of the scientific as against the mystical attitude. Metaphysics, from
the first, has been developed by the union or the conflict of these two
attitudes. Among the earliest Greek philosophers, the Ionians were more
scientific and the Sicilians more mystical.[6] But among the latter,
Pythagoras, for example, was in himself a curious mixture of the two
tendencies: the scientific attitude led him to his proposition on
right-angled triangles, while his mystic insight showed him that it is
wicked to eat beans. Naturally enough, his followers divided into two
sects, the lovers of right-angled triangles and the abhorrers of beans;
but the former sect died out, leaving, however, a haunting flavour of
mysticism over much Greek mathematical speculation, and in particular
over Plato's views on mathematics. Plato, of course, embodies both the
scientific and the mystical attitudes in a higher form than his
predecessors, but the mystical attitude is distinctly the stronger of
the two, and secures ultimate victory whenever the conflict is sharp.
Plato, moreover, adopted from the Eleatics the device of using logic to
defeat common sense, and thus to leave the field clear for mysticism--a
device still employed in our own day by the adherents of the classical
tradition.

  [6] _Cf._ Burnet, _Early Greek Philosophy_, pp. 85 ff.

The logic used in defence of mysticism seems to me faulty as logic, and
in a later lecture I shall criticise it on this ground. But the more
thorough-going mystics do not employ logic, which they despise: they
appeal instead directly to the immediate deliverance of their insight.
Now, although fully developed mysticism is rare in the West, some
tincture of it colours the thoughts of many people, particularly as
regards matters on which they have strong convictions not based on
evidence. In all who seek passionately for the fugitive and difficult
goods, the conviction is almost irresistible that there is in the world
something deeper, more significant, than the multiplicity of little
facts chronicled and classified by science. Behind the veil of these
mundane things, they feel, something quite different obscurely shimmers,
shining forth clearly in the great moments of illumination, which alone
give anything worthy to be called real knowledge of truth. To seek such
moments, therefore, is to them the way of wisdom, rather than, like the
man of science, to observe coolly, to analyse without emotion, and to
accept without question the equal reality of the trivial and the
important.

Of the reality or unreality of the mystic's world I know nothing. I have
no wish to deny it, nor even to declare that the insight which reveals
it is not a genuine insight. What I do wish to maintain--and it is here
that the scientific attitude becomes imperative--is that insight,
untested and unsupported, is an insufficient guarantee of truth, in
spite of the fact that much of the most important truth is first
suggested by its means. It is common to speak of an opposition between
instinct and reason; in the eighteenth century, the opposition was drawn
in favour of reason, but under the influence of Rousseau and the
romantic movement instinct was given the preference, first by those who
rebelled against artificial forms of government and thought, and then,
as the purely rationalistic defence of traditional theology became
increasingly difficult, by all who felt in science a menace to creeds
which they associated with a spiritual outlook on life and the world.
Bergson, under the name of "intuition," has raised instinct to the
position of sole arbiter of metaphysical truth. But in fact the
opposition of instinct and reason is mainly illusory. Instinct,
intuition, or insight is what first leads to the beliefs which
subsequent reason confirms or confutes; but the confirmation, where it
is possible, consists, in the last analysis, of agreement with other
beliefs no less instinctive. Reason is a harmonising, controlling force
rather than a creative one. Even in the most purely logical realms, it
is insight that first arrives at what is new.

Where instinct and reason do sometimes conflict is in regard to single
beliefs, held instinctively, and held with such determination that no
degree of inconsistency with other beliefs leads to their abandonment.
Instinct, like all human faculties, is liable to error. Those in whom
reason is weak are often unwilling to admit this as regards themselves,
though all admit it in regard to others. Where instinct is least liable
to error is in practical matters as to which right judgment is a help to
survival; friendship and hostility in others, for instance, are often
felt with extraordinary discrimination through very careful disguises.
But even in such matters a wrong impression may be given by reserve or
flattery; and in matters less directly practical, such as philosophy
deals with, very strong instinctive beliefs may be wholly mistaken, as
we may come to know through their perceived inconsistency with other
equally strong beliefs. It is such considerations that necessitate the
harmonising mediation of reason, which tests our beliefs by their mutual
compatibility, and examines, in doubtful cases, the possible sources of
error on the one side and on the other. In this there is no opposition
to instinct as a whole, but only to blind reliance upon some one
interesting aspect of instinct to the exclusion of other more
commonplace but not less trustworthy aspects. It is such onesidedness,
not instinct itself, that reason aims at correcting.

These more or less trite maxims may be illustrated by application to
Bergson's advocacy of "intuition" as against "intellect." There are, he
says, "two profoundly different ways of knowing a thing. The first
implies that we move round the object; the second that we enter into it.
The first depends on the point of view at which we are placed and on the
symbols by which we express ourselves. The second neither depends on a
point of view nor relies on any symbol. The first kind of knowledge may
be said to stop at the _relative_; the second, in those cases where it
is possible, to attain the _absolute_."[7] The second of these, which is
intuition, is, he says, "the kind of intellectual _sympathy_ by which
one places oneself within an object in order to coincide with what is
unique in it and therefore inexpressible" (p. 6). In illustration, he
mentions self-knowledge: "there is one reality, at least, which we all
seize from within, by intuition and not by simple analysis. It is our
own personality in its flowing through time--our self which endures"
(p. 8). The rest of Bergson's philosophy consists in reporting, through
the imperfect medium of words, the knowledge gained by intuition, and
the consequent complete condemnation of all the pretended knowledge
derived from science and common sense.

  [7] _Introduction to Metaphysics_, p. 1.

This procedure, since it takes sides in a conflict of instinctive
beliefs, stands in need of justification by proving the greater
trustworthiness of the beliefs on one side than of those on the other.
Bergson attempts this justification in two ways--first, by explaining
that intellect is a purely practical faculty designed to secure
biological success; secondly, by mentioning remarkable feats of instinct
in animals, and by pointing out characteristics of the world which,
though intuition can apprehend them, are baffling to intellect as he
interprets it.

Of Bergson's theory that intellect is a purely practical faculty
developed in the struggle for survival, and not a source of true
beliefs, we may say, first, that it is only through intellect that we
know of the struggle for survival and of the biological ancestry of man:
if the intellect is misleading, the whole of this merely inferred
history is presumably untrue. If, on the other hand, we agree with M.
Bergson in thinking that evolution took place as Darwin believed, then
it is not only intellect, but all our faculties, that have been
developed under the stress of practical utility. Intuition is seen at
its best where it is directly useful--for example, in regard to other
people's characters and dispositions. Bergson apparently holds that
capacity for this kind of knowledge is less explicable by the struggle
for existence than, for example, capacity for pure mathematics. Yet the
savage deceived by false friendship is likely to pay for his mistake
with his life; whereas even in the most civilised societies men are not
put to death for mathematical incompetence. All the most striking of his
instances of intuition in animals have a very direct survival value. The
fact is, of course, that both intuition and intellect have been
developed because they are useful, and that, speaking broadly, they are
useful when they give truth and become harmful when they give falsehood.
Intellect, in civilised man, like artistic capacity, has occasionally
been developed beyond the point where it is useful to the individual;
intuition, on the other hand, seems on the whole to diminish as
civilisation increases. Speaking broadly, it is greater in children than
in adults, in the uneducated than in the educated. Probably in dogs it
exceeds anything to be found in human beings. But those who find in
these facts a recommendation of intuition ought to return to running
wild in the woods, dyeing themselves with woad and living on hips and
haws.

Let us next examine whether intuition possesses any such infallibility
as Bergson claims for it. The best instance of it, according to him, is
our acquaintance with ourselves; yet self-knowledge is proverbially rare
and difficult. Most men, for example, have in their nature meannesses,
vanities, and envies of which they are quite unconscious, though even
their best friends can perceive them without any difficulty. It is true
that intuition has a convincingness which is lacking to intellect: while
it is present, it is almost impossible to doubt its truth. But if it
should appear, on examination, to be at least as fallible as intellect,
its greater subjective certainty becomes a demerit, making it only the
more irresistibly deceptive. Apart from self-knowledge, one of the most
notable examples of intuition is the knowledge people believe themselves
to possess of those with whom they are in love: the wall between
different personalities seems to become transparent, and people think
they see into another soul as into their own. Yet deception in such
cases is constantly practised with success; and even where there is no
intentional deception, experience gradually proves, as a rule, that the
supposed insight was illusory, and that the slower, more groping methods
of the intellect are in the long run more reliable.

Bergson maintains that intellect can only deal with things in so far as
they resemble what has been experienced in the past, while intuition has
the power of apprehending the uniqueness and novelty that always belong
to each fresh moment. That there is something unique and new at every
moment, is certainly true; it is also true that this cannot be fully
expressed by means of intellectual concepts. Only direct acquaintance
can give knowledge of what is unique and new. But direct acquaintance of
this kind is given fully in sensation, and does not require, so far as I
can see, any special faculty of intuition for its apprehension. It is
neither intellect nor intuition, but sensation, that supplies new data;
but when the data are new in any remarkable manner, intellect is much
more capable of dealing with them than intuition would be. The hen with
a brood of ducklings no doubt has intuitions which seem to place her
inside them, and not merely to know them analytically; but when the
ducklings take to the water, the whole apparent intuition is seen to be
illusory, and the hen is left helpless on the shore. Intuition, in fact,
is an aspect and development of instinct, and, like all instinct, is
admirable in those customary surroundings which have moulded the habits
of the animal in question, but totally incompetent as soon as the
surroundings are changed in a way which demands some non-habitual mode
of action.

The theoretical understanding of the world, which is the aim of
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.

Mathematical logic, even in its most modern form, is not _directly_ of
philosophical importance except in its beginnings. After the beginnings,
it belongs rather to mathematics than to philosophy. Of its beginnings,
which are the only part of it that can properly be called
_philosophical_ logic, I shall speak shortly. But even the later
developments, though not directly philosophical, will be found of great
indirect use in philosophising. They enable us to deal easily with more
abstract conceptions than merely verbal reasoning can enumerate; they
suggest fruitful hypotheses which otherwise could hardly be thought of;
and they enable us to see quickly what is the smallest store of
materials with which a given logical or scientific edifice can be
constructed. Not only Frege's theory of number, which we shall deal with
in Lecture VII., but the whole theory of physical concepts which will be
outlined in our next two lectures, is inspired by mathematical logic,
and could never have been imagined without it.

In both these cases, and in many others, we shall appeal to a certain
principle called "the principle of abstraction." This principle, which
might equally well be called "the principle which dispenses with
abstraction," and is one which clears away incredible accumulations of
metaphysical lumber, was directly suggested by mathematical logic, and
could hardly have been proved or practically used without its help. The
principle will be explained in our fourth lecture, but its use may be
briefly indicated in advance. When a group of objects have that kind of
similarity which we are inclined to attribute to possession of a common
quality, the principle in question shows that membership of the group
will serve all the purposes of the supposed common quality, and that
therefore, unless some common quality is actually known, the group or
class of similar objects may be used to replace the common quality,
which need not be assumed to exist. In this and other ways, the indirect
uses of even the later parts of mathematical logic are very great; but
it is now time to turn our attention to its philosophical foundations.

In every proposition and in every inference there is, besides the
particular subject-matter concerned, a certain _form_, a way in which
the constituents of the proposition or inference are put together. If I
say, "Socrates is mortal," "Jones is angry," "The sun is hot," there is
something in common in these three cases, something indicated by the
word "is." What is in common is the _form_ of the proposition, not an
actual constituent. If I say a number of things about Socrates--that he
was an Athenian, that he married Xantippe, that he drank the
hemlock--there is a common constituent, namely Socrates, in all the
propositions I enunciate, but they have diverse forms. If, on the other
hand, I take any one of these propositions and replace its constituents,
one at a time, by other constituents, the form remains constant, but no
constituent remains. Take (say) the series of propositions, "Socrates
drank the hemlock," "Coleridge drank the hemlock," "Coleridge drank
opium," "Coleridge ate opium." The form remains unchanged throughout
this series, but all the constituents are altered. Thus form is not
another constituent, but is the way the constituents are put together.
It is forms, in this sense, that are the proper object of philosophical
logic.

It is obvious that the knowledge of logical forms is something quite
different from knowledge of existing things. The form of "Socrates drank
the hemlock" is not an existing thing like Socrates or the hemlock, nor
does it even have that close relation to existing things that drinking
has. It is something altogether more abstract and remote. We might
understand all the separate words of a sentence without understanding
the sentence: if a sentence is long and complicated, this is apt to
happen. In such a case we have knowledge of the constituents, but not of
the form. We may also have knowledge of the form without having
knowledge of the constituents. If I say, "Rorarius drank the hemlock,"
those among you who have never heard of Rorarius (supposing there are
any) will understand the form, without having knowledge of all the
constituents. In order to understand a sentence, it is necessary to have
knowledge both of the constituents and of the particular instance of the
form. It is in this way that a sentence conveys information, since it
tells us that certain known objects are related according to a certain
known form. Thus some kind of knowledge of logical forms, though with
most people it is not explicit, is involved in all understanding of
discourse. It is the business of philosophical logic to extract this
knowledge from its concrete integuments, and to render it explicit and
pure.

In all inference, form alone is essential: the particular subject-matter
is irrelevant except as securing the truth of the premisses. This is one
reason for the great importance of logical form. When I say, "Socrates
was a man, all men are mortal, therefore Socrates was mortal," the
connection of premisses and conclusion does not in any way depend upon
its being Socrates and man and mortality that I am mentioning. The
general form of the inference may be expressed in some such words as,
"If a thing has a certain property, and whatever has this property has a
certain other property, then the thing in question also has that other
property." Here no particular things or properties are mentioned: the
proposition is absolutely general. All inferences, when stated fully,
are instances of propositions having this kind of generality. If they
seem to depend upon the subject-matter otherwise than as regards the
truth of the premisses, that is because the premisses have not been all
explicitly stated. In logic, it is a waste of time to deal with
inferences concerning particular cases: we deal throughout with
completely general and purely formal implications, leaving it to other
sciences to discover when the hypotheses are verified and when they are
not.

But the forms of propositions giving rise to inferences are not the
simplest forms: they are always hypothetical, stating that if one
proposition is true, then so is another. Before considering inference,
therefore, logic must consider those simpler forms which inference
presupposes. Here the traditional logic failed completely: it believed
that there was only one form of simple proposition (_i.e._ of
proposition not stating a relation between two or more other
propositions), namely, the form which ascribes a predicate to a subject.
This is the appropriate form in assigning the qualities of a given
thing--we may say "this thing is round, and red, and so on." Grammar
favours this form, but philosophically it is so far from universal that
it is not even very common. If we say "this thing is bigger than that,"
we are not assigning a mere quality of "this," but a relation of "this"
and "that." We might express the same fact by saying "that thing is
smaller than this," where grammatically the subject is changed. Thus
propositions stating that two things have a certain relation have a
different form from subject-predicate propositions, and the failure to
perceive this difference or to allow for it has been the source of many
errors in traditional metaphysics.

The belief or unconscious conviction that all propositions are of the
subject-predicate form--in other words, that every fact consists in some
thing having some quality--has rendered most philosophers incapable of
giving any account of the world of science and daily life. If they had
been honestly anxious to give such an account, they would probably have
discovered their error very quickly; but most of them were less anxious
to understand the world of science and daily life, than to convict it of
unreality in the interests of a super-sensible "real" world. Belief in
the unreality of the world of sense arises with irresistible force in
certain moods--moods which, I imagine, have some simple physiological
basis, but are none the less powerfully persuasive. The conviction born
of these moods is the source of most mysticism and of most metaphysics.
When the emotional intensity of such a mood subsides, a man who is in
the habit of reasoning will search for logical reasons in favour of the
belief which he finds in himself. But since the belief already exists,
he will be very hospitable to any reason that suggests itself. The
paradoxes apparently proved by his logic are really the paradoxes of
mysticism, and are the goal which he feels his logic must reach if it is
to be in accordance with insight. It is in this way that logic has been
pursued by those of the great philosophers who were mystics--notably
Plato, Spinoza, and Hegel. But since they usually took for granted the
supposed insight of the mystic emotion, their logical doctrines were
presented with a certain dryness, and were believed by their disciples
to be quite independent of the sudden illumination from which they
sprang. Nevertheless their origin clung to them, and they remained--to
borrow a useful word from Mr Santayana--"malicious" in regard to the
world of science and common sense. It is only so that we can account for
the complacency with which philosophers have accepted the inconsistency
of their doctrines with all the common and scientific facts which seem
best established and most worthy of belief.

The logic of mysticism shows, as is natural, the defects which are
inherent in anything malicious. While the mystic mood is dominant, the
need of logic is not felt; as the mood fades, the impulse to logic
reasserts itself, but with a desire to retain the vanishing insight, or
at least to prove that it _was_ insight, and that what seems to
contradict it is illusion. The logic which thus arises is not quite
disinterested or candid, and is inspired by a certain hatred of the
daily world to which it is to be applied. Such an attitude naturally
does not tend to the best results. Everyone knows that to read an author
simply in order to refute him is not the way to understand him; and to
read the book of Nature with a conviction that it is all illusion is
just as unlikely to lead to understanding. If our logic is to find the
common world intelligible, it must not be hostile, but must be inspired
by a genuine acceptance such as is not usually to be found among
metaphysicians.

Traditional logic, since it holds that all propositions have the
subject-predicate form, is unable to admit the reality of relations: all
relations, it maintains, must be reduced to properties of the apparently
related terms. There are many ways of refuting this opinion; one of the
easiest is derived from the consideration of what are called
"asymmetrical" relations. In order to explain this, I will first explain
two independent ways of classifying relations.

Some relations, when they hold between A and B, also hold between B and
A. Such, for example, is the relation "brother or sister." If A is a
brother or sister of B, then B is a brother or sister of A. Such again
is any kind of similarity, say similarity of colour. Any kind of
dissimilarity is also of this kind: if the colour of A is unlike the
colour of B, then the colour of B is unlike the colour of A. Relations
of this sort are called _symmetrical_. Thus a relation is symmetrical
if, whenever it holds between A and B, it also holds between B and A.

All relations that are not symmetrical are called _non-symmetrical_.
Thus "brother" is non-symmetrical, because, if A is a brother of B, it
may happen that B is a _sister_ of A.

A relation is called _asymmetrical_ when, if it holds between A and B,
it _never_ holds between B and A. Thus husband, father, grandfather,
etc., are asymmetrical relations. So are _before_, _after_, _greater_,
_above_, _to the right of_, etc. All the relations that give rise to
series are of this kind.

Classification into symmetrical, asymmetrical, and merely
non-symmetrical relations is the first of the two classifications we had
to consider. The second is into transitive, intransitive, and merely
non-transitive relations, which are defined as follows.

A relation is said to be _transitive_, if, whenever it holds between A
and B and also between B and C, it holds between A and C. Thus _before_,
_after_, _greater_, _above_ are transitive. All relations giving rise to
series are transitive, but so are many others. The transitive relations
just mentioned were asymmetrical, but many transitive relations are
symmetrical--for instance, equality in any respect, exact identity of
colour, being equally numerous (as applied to collections), and so on.

A relation is said to be _non-transitive_ whenever it is not transitive.
Thus "brother" is non-transitive, because a brother of one's brother may
be oneself. All kinds of dissimilarity are non-transitive.

A relation is said to be _intransitive_ when, if A has the relation to
B, and B to C, A never has it to C. Thus "father" is intransitive. So is
such a relation as "one inch taller" or "one year later."

Let us now, in the light of this classification, return to the question
whether all relations can be reduced to predications.

In the case of symmetrical relations--_i.e._ relations which, if they
hold between A and B, also hold between B and A--some kind of
plausibility can be given to this doctrine. A symmetrical relation which
is transitive, such as equality, can be regarded as expressing
possession of some common property, while one which is not transitive,
such as inequality, can be regarded as expressing possession of
different properties. But when we come to asymmetrical relations, such
as before and after, greater and less, etc., the attempt to reduce them
to properties becomes obviously impossible. When, for example, two
things are merely known to be unequal, without our knowing which is
greater, we may say that the inequality results from their having
different magnitudes, because inequality is a symmetrical relation; but
to say that when one thing is _greater_ than another, and not merely
unequal to it, that means that they have different magnitudes, is
formally incapable of explaining the facts. For if the other thing had
been greater than the one, the magnitudes would also have been
different, though the fact to be explained would not have been the same.
Thus mere _difference_ of magnitude is not _all_ that is involved,
since, if it were, there would be no difference between one thing being
greater than another, and the other being greater than the one. We shall
have to say that the one magnitude is _greater_ than the other, and thus
we shall have failed to get rid of the relation "greater." In short,
both possession of the same property and possession of different
properties are _symmetrical_ relations, and therefore cannot account for
the existence of _asymmetrical_ relations.

Asymmetrical relations are involved in all series--in space and time,
greater and less, whole and part, and many others of the most important
characteristics of the actual world. All these aspects, therefore, the
logic which reduces everything to subjects and predicates is compelled
to condemn as error and mere appearance. To those whose logic is not
malicious, such a wholesale condemnation appears impossible. And in fact
there is no reason except prejudice, so far as I can discover, for
denying the reality of relations. When once their reality is admitted,
all _logical_ grounds for supposing the world of sense to be illusory
disappear. If this is to be supposed, it must be frankly and simply on
the ground of mystic insight unsupported by argument. It is impossible
to argue against what professes to be insight, so long as it does not
argue in its own favour. As logicians, therefore, we may admit the
possibility of the mystic's world, while yet, so long as we do not have
his insight, we must continue to study the everyday world with which we
are familiar. But when he contends that our world is impossible, then
our logic is ready to repel his attack. And the first step in creating
the logic which is to perform this service is the recognition of the
reality of relations.

Relations which have two terms are only one kind of relations. A
relation may have three terms, or four, or any number. Relations of two
terms, being the simplest, have received more attention than the others,
and have generally been alone considered by philosophers, both those who
accepted and those who denied the reality of relations. But other
relations have their importance, and are indispensable in the solution
of certain problems. Jealousy, for example, is a relation between three
people. Professor Royce mentions the relation "giving": when A gives B
to C, that is a relation of three terms.[15] When a man says to his
wife: "My dear, I wish you could induce Angelina to accept Edwin," his
wish constitutes a relation between four people, himself, his wife,
Angelina, and Edwin. Thus such relations are by no means recondite or
rare. But in order to explain exactly how they differ from relations of
two terms, we must embark upon a classification of the logical forms of
facts, which is the first business of logic, and the business in which
the traditional logic has been most deficient.

  [15] _Encyclopaedia of the Philosophical Sciences_, vol. i. p. 97.

The existing world consists of many things with many qualities and
relations. A complete description of the existing world would require
not only a catalogue of the things, but also a mention of all their
qualities and relations. We should have to know not only this, that, and
the other thing, but also which was red, which yellow, which was earlier
than which, which was between which two others, and so on. When I speak
of a "fact," I do not mean one of the simple things in the world; I mean
that a certain thing has a certain quality, or that certain things have
a certain relation. Thus, for example, I should not call Napoleon a
fact, but I should call it a fact that he was ambitious, or that he
married Josephine. Now a fact, in this sense, is never simple, but
always has two or more constituents. When it simply assigns a quality to
a thing, it has only two constituents, the thing and the quality. When
it consists of a relation between two things, it has three constituents,
the things and the relation. When it consists of a relation between
three things, it has four constituents, and so on. The constituents of
facts, in the sense in which we are using the word "fact," are not other
facts, but are things and qualities or relations. When we say that there
are relations of more than two terms, we mean that there are single
facts consisting of a single relation and more than two things. I do not
mean that one relation of two terms may hold between A and B, and also
between A and C, as, for example, a man is the son of his father and
also the son of his mother. This constitutes two distinct facts: if we
choose to treat it as one fact, it is a fact which has facts for its
constituents. But the facts I am speaking of have no facts among their
constituents, but only things and relations. For example, when A is
jealous of B on account of C, there is only one fact, involving three
people; there are not two instances of jealousy, but only one. It is in
such cases that I speak of a relation of three terms, where the simplest
possible fact in which the relation occurs is one involving three things
in addition to the relation. And the same applies to relations of four
terms or five or any other number. All such relations must be admitted
in our inventory of the logical forms of facts: two facts involving the
same number of things have the same form, and two which involve
different numbers of things have different forms.

Given any fact, there is an assertion which expresses the fact. The fact
itself is objective, and independent of our thought or opinion about it;
but the assertion is something which involves thought, and may be either
true or false. An assertion may be positive or negative: we may assert
that Charles I. was executed, or that he did _not_ die in his bed. A
negative assertion may be said to be a _denial_. Given a form of words
which must be either true or false, such as "Charles I. died in his
bed," we may either assert or deny this form of words: in the one case
we have a positive assertion, in the other a negative one. A form of
words which must be either true or false I shall call a _proposition_.
Thus a proposition is the same as what may be significantly asserted or
denied. A proposition which expresses what we have called a fact, _i.e._
which, when asserted, asserts that a certain thing has a certain
quality, or that certain things have a certain relation, will be called
an atomic proposition, because, as we shall see immediately, there are
other propositions into which atomic propositions enter in a way
analogous to that in which atoms enter into molecules. Atomic
propositions, although, like facts, they may have any one of an infinite
number of forms, are only one kind of propositions. All other kinds are
more complicated. In order to preserve the parallelism in language as
regards facts and propositions, we shall give the name "atomic facts" to
the facts we have hitherto been considering. Thus atomic facts are what
determine whether atomic propositions are to be asserted or denied.

Whether an atomic proposition, such as "this is red," or "this is before
that," is to be asserted or denied can only be known empirically.
Perhaps one atomic fact may sometimes be capable of being inferred from
another, though this seems very doubtful; but in any case it cannot be
inferred from premisses no one of which is an atomic fact. It follows
that, if atomic facts are to be known at all, some at least must be
known without inference. The atomic facts which we come to know in this
way are the facts of sense-perception; at any rate, the facts of
sense-perception are those which we most obviously and certainly come to
know in this way. If we knew all atomic facts, and also knew that there
were none except those we knew, we should, theoretically, be able to
infer all truths of whatever form.[16] Thus logic would then supply us
with the whole of the apparatus required. But in the first acquisition
of knowledge concerning atomic facts, logic is useless. In pure logic,
no atomic fact is ever mentioned: we confine ourselves wholly to forms,
without asking ourselves what objects can fill the forms. Thus pure
logic is independent of atomic facts; but conversely, they are, in a
sense, independent of logic. Pure logic and atomic facts are the two
poles, the wholly _a priori_ and the wholly empirical. But between the
two lies a vast intermediate region, which we must now briefly explore.

  [16] This perhaps requires modification in order to include such facts
  as beliefs and wishes, since such facts apparently contain
  propositions as components. Such facts, though not strictly atomic,
  must be supposed included if the statement in the text is to be true.

"Molecular" propositions are such as contain conjunctions--_if_, _or_,
_and_, _unless_, etc.--and such words are the marks of a molecular
proposition. Consider such an assertion as, "If it rains, I shall bring
my umbrella." This assertion is just as capable of truth or falsehood as
the assertion of an atomic proposition, but it is obvious that either
the corresponding fact, or the nature of the correspondence with fact,
must be quite different from what it is in the case of an atomic
proposition. Whether it rains, and whether I bring my umbrella, are each
severally matters of atomic fact, ascertainable by observation. But the
connection of the two involved in saying that _if_ the one happens,
_then_ the other will happen, is something radically different from
either of the two separately. It does not require for its truth that it
should actually rain, or that I should actually bring my umbrella; even
if the weather is cloudless, it may still be true that I should have
brought my umbrella if the weather had been different. Thus we have here
a connection of two propositions, which does not depend upon whether
they are to be asserted or denied, but only upon the second being
inferable from the first. Such propositions, therefore, have a form
which is different from that of any atomic proposition.

Such propositions are important to logic, because all inference depends
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.

Applying our distinction of "hard" and "soft" data to psychologically
derivative but logically primitive beliefs, we shall find that most, if
not all, are to be classed as soft data. They may be found, on
reflection, to be capable of logical proof, and they then again become
believed, but no longer as data. As data, though entitled to a certain
limited respect, they cannot be placed on a level with the facts of
sense or the laws of logic. The kind of respect which they deserve seems
to me such as to warrant us in hoping, though not too confidently, that
the hard data may prove them to be at least probable. Also, if the hard
data are found to throw no light whatever upon their truth or falsehood,
we are justified, I think, in giving rather more weight to the
hypothesis of their truth than to the hypothesis of their falsehood. For
the present, however, let us confine ourselves to the hard data, with a
view to discovering what sort of world can be constructed by their means
alone.

Our data now are primarily the facts of sense (_i.e._ of _our own_
sense-data) and the laws of logic. But even the severest scrutiny will
allow some additions to this slender stock. Some facts of
memory--especially of recent memory--seem to have the highest degree of
certainty. Some introspective facts are as certain as any facts of
sense. And facts of sense themselves must, for our present purposes, be
interpreted with a certain latitude. Spatial and temporal relations must
sometimes be included, for example in the case of a swift motion falling
wholly within the specious present. And some facts of comparison, such
as the likeness or unlikeness of two shades of colour, are certainly to
be included among hard data. Also we must remember that the distinction
of hard and soft data is psychological and subjective, so that, if there
are other minds than our own--which at our present stage must be held
doubtful--the catalogue of hard data may be different for them from what
it is for us.

Certain common beliefs are undoubtedly excluded from hard data. Such is
the belief which led us to introduce the distinction, namely, that
sensible objects in general persist when we are not perceiving them.
Such also is the belief in other people's minds: this belief is
obviously derivative from our perception of their bodies, and is felt to
demand logical justification as soon as we become aware of its
derivativeness. Belief in what is reported by the testimony of others,
including all that we learn from books, is of course involved in the
doubt as to whether other people have minds at all. Thus the world from
which our reconstruction is to begin is very fragmentary. The best we
can say for it is that it is slightly more extensive than the world at
which Descartes arrived by a similar process, since that world contained
nothing except himself and his thoughts.

We are now in a position to understand and state the problem of our
knowledge of the external world, and to remove various misunderstandings
which have obscured the meaning of the problem. The problem really is:
Can the existence of anything other than our own hard data be inferred
from the existence of those data? But before considering this problem,
let us briefly consider what the problem is _not_.

When we speak of the "external" world in this discussion, we must not
mean "spatially external," unless "space" is interpreted in a peculiar
and recondite manner. The immediate objects of sight, the coloured
surfaces which make up the visible world, are spatially external in the
natural meaning of this phrase. We feel them to be "there" as opposed to
"here"; without making any assumption of an existence other than hard
data, we can more or less estimate the distance of a coloured surface.
It seems probable that distances, provided they are not too great, are
actually given more or less roughly in sight; but whether this is the
case or not, ordinary distances can certainly be estimated approximately
by means of the data of sense alone. The immediately given world is
spatial, and is further not wholly contained within our own bodies. Thus
our knowledge of what is external in this sense is not open to doubt.

Another form in which the question is often put is: "Can we know of the
existence of any reality which is independent of ourselves?" This form
of the question suffers from the ambiguity of the two words
"independent" and "self." To take the Self first: the question as to
what is to be reckoned part of the Self and what is not, is a very
difficult one. Among many other things which we may mean by the Self,
two may be selected as specially important, namely, (1) the bare subject
which thinks and is aware of objects, (2) the whole assemblage of things
that would necessarily cease to exist if our lives came to an end. The
bare subject, if it exists at all, is an inference, and is not part of
the data; therefore this meaning of Self may be ignored in our present
inquiry. The second meaning is difficult to make precise, since we
hardly know what things depend upon our lives for their existence. And
in this form, the definition of Self introduces the word "depend," which
raises the same questions as are raised by the word "independent." Let
us therefore take up the word "independent," and return to the Self
later.

When we say that one thing is "independent" of another, we may mean
either that it is logically possible for the one to exist without the
other, or that there is no causal relation between the two such that the
one only occurs as the effect of the other. The only way, so far as I
know, in which one thing can be _logically_ dependent upon another is
when the other is _part_ of the one. The existence of a book, for
example, is logically dependent upon that of its pages: without the
pages there would be no book. Thus in this sense the question, "Can we
know of the existence of any reality which is independent of ourselves?"
reduces to the question, "Can we know of the existence of any reality of
which our Self is not part?" In this form, the question brings us back
to the problem of defining the Self; but I think, however the Self may
be defined, even when it is taken as the bare subject, it cannot be
supposed to be part of the immediate object of sense; thus in this form
of the question we must admit that we can know of the existence of
realities independent of ourselves.

The question of causal dependence is much more difficult. To know that
one kind of thing is causally independent of another, we must know that
it actually occurs without the other. Now it is fairly obvious that,
whatever legitimate meaning we give to the Self, our thoughts and
feelings are causally dependent upon ourselves, _i.e._ do not occur when
there is no Self for them to belong to. But in the case of objects of
sense this is not obvious; indeed, as we saw, the common-sense view is
that such objects persist in the absence of any percipient. If this is
the case, then they are causally independent of ourselves; if not, not.
Thus in this form the question reduces to the question whether we can
know that objects of sense, or any other objects not our own thoughts
and feelings, exist at times when we are not perceiving them. This form,
in which the difficult word "independent" no longer occurs, is the form
in which we stated the problem a minute ago.

Our question in the above form raises two distinct problems, which it is
important to keep separate. First, can we know that objects of sense, or
very similar objects, exist at times when we are not perceiving them?
Secondly, if this cannot be known, can we know that other objects,
inferable from objects of sense but not necessarily resembling them,
exist either when we are perceiving the objects of sense or at any other
time? This latter problem arises in philosophy as the problem of the
"thing in itself," and in science as the problem of matter as assumed in
physics. We will consider this latter problem first.

Owing to the fact that we feel passive in sensation, we naturally
suppose that our sensations have outside causes. Now it is necessary
here first of all to distinguish between (1) our sensation, which is a
mental event consisting in our being aware of a sensible object, and (2)
the sensible object of which we are aware in sensation. When I speak of
the sensible object, it must be understood that I do not mean such a
thing as a table, which is both visible and tangible, can be seen by
many people at once, and is more or less permanent. What I mean is just
that patch of colour which is momentarily seen when we look at the
table, or just that particular hardness which is felt when we press it,
or just that particular sound which is heard when we rap it. Each of
these I call a sensible object, and our awareness of it I call a
sensation. Now our sense of passivity, if it really afforded any
argument, would only tend to show that the _sensation_ has an outside
cause; this cause we should naturally seek in the sensible object. Thus
there is no good reason, so far, for supposing that sensible objects
must have outside causes. But both the thing-in-itself of philosophy and
the matter of physics present themselves as outside causes of the
sensible object as much as of the sensation. What are the grounds for
this common opinion?

In each case, I think, the opinion has resulted from the combination of
a belief that _something_ which can persist independently of our
consciousness makes itself known in sensation, with the fact that our
sensations often change in ways which seem to depend upon us rather than
upon anything which would be supposed to persist independently of us. At
first, we believe unreflectingly that everything is as it seems to be,
and that, if we shut our eyes, the objects we had been seeing remain as
they were though we no longer see them. But there are arguments against
this view, which have generally been thought conclusive. It is
extraordinarily difficult to see just what the arguments prove; but if
we are to make any progress with the problem of the external world, we
must try to make up our minds as to these arguments.

A table viewed from one place presents a different appearance from that
which it presents from another place. This is the language of common
sense, but this language already assumes that there is a real table of
which we see the appearances. Let us try to state what is known in terms
of sensible objects alone, without any element of hypothesis. We find
that as we walk round the table, we perceive a series of gradually
changing visible objects. But in speaking of "walking round the table,"
we have still retained the hypothesis that there is a single table
connected with all the appearances. What we ought to say is that, while
we have those muscular and other sensations which make us say we are
walking, our visual sensations change in a continuous way, so that, for
example, a striking patch of colour is not suddenly replaced by
something wholly different, but is replaced by an insensible gradation
of slightly different colours with slightly different shapes. This is
what we really know by experience, when we have freed our minds from the
assumption of permanent "things" with changing appearances. What is
really known is a correlation of muscular and other bodily sensations
with changes in visual sensations.

But walking round the table is not the only way of altering its
appearance. We can shut one eye, or put on blue spectacles, or look
through a microscope. All these operations, in various ways, alter the
visual appearance which we call that of the table. More distant objects
will also alter their appearance if (as we say) the state of the
atmosphere changes--if there is fog or rain or sunshine. Physiological
changes also alter the appearances of things. If we assume the world of
common sense, all these changes, including those attributed to
physiological causes, are changes in the intervening medium. It is not
quite so easy as in the former case to reduce this set of facts to a
form in which nothing is assumed beyond sensible objects. Anything
intervening between ourselves and what we see must be invisible: our
view in every direction is bounded by the nearest visible object. It
might be objected that a dirty pane of glass, for example, is visible
although we can see things through it. But in this case we really see a
spotted patchwork: the dirtier specks in the glass are visible, while
the cleaner parts are invisible and allow us to see what is beyond. Thus
the discovery that the intervening medium affects the appearances of
things cannot be made by means of the sense of sight alone.

Let us take the case of the blue spectacles, which is the simplest, but
may serve as a type for the others. The frame of the spectacles is of
course visible, but the blue glass, if it is clean, is not visible. The
blueness, which we say is in the glass, appears as being in the objects
seen through the glass. The glass itself is known by means of the sense
of touch. In order to know that it is between us and the objects seen
through it, we must know how to correlate the space of touch with the
space of sight. This correlation itself, when stated in terms of the
data of sense alone, is by no means a simple matter. But it presents no
difficulties of principle, and may therefore be supposed accomplished.
When it has been accomplished, it becomes possible to attach a meaning
to the statement that the blue glass, which we can touch, is between us
and the object seen, as we say, "through" it.

But we have still not reduced our statement completely to what is
actually given in sense. We have fallen into the assumption that the
object of which we are conscious when we touch the blue spectacles still
exists after we have ceased to touch them. So long as we are touching
them, nothing except our finger can be seen through the part touched,
which is the only part where we immediately know that there is
something. If we are to account for the blue appearance of objects other
than the spectacles, when seen through them, it might seem as if we must
assume that the spectacles still exist when we are not touching them;
and if this assumption really is necessary, our main problem is
answered: we have means of knowing of the present existence of objects
not given in sense, though of the same kind as objects formerly given in
sense.

It may be questioned, however, whether this assumption is actually
unavoidable, though it is unquestionably the most natural one to make.
We may say that the object of which we become aware when we touch the
spectacles continues to have effects afterwards, though perhaps it no
longer exists. In this view, the supposed continued existence of
sensible objects after they have ceased to be sensible will be a
fallacious inference from the fact that they still have effects. It is
often supposed that nothing which has ceased to exist can continue to
have effects, but this is a mere prejudice, due to a wrong conception of
causality. We cannot, therefore, dismiss our present hypothesis on the
ground of _a priori_ impossibility, but must examine further whether it
can really account for the facts.

It may be said that our hypothesis is useless in the case when the blue
glass is never touched at all. How, in that case, are we to account for
the blue appearance of objects? And more generally, what are we to make
of the hypothetical sensations of touch which we associate with
untouched visible objects, which we know would be verified if we chose,
though in fact we do not verify them? Must not these be attributed to
permanent possession, by the objects, of the properties which touch
would reveal?

Let us consider the more general question first. Experience has taught
us that where we see certain kinds of coloured surfaces we can, by
touch, obtain certain expected sensations of hardness or softness,
tactile shape, and so on. This leads us to believe that what is seen is
usually tangible, and that it has, whether we touch it or not, the
hardness or softness which we should expect to feel if we touched it.
But the mere fact that we are able to infer what our tactile sensations
would be shows that it is not logically necessary to assume tactile
qualities before they are felt. All that is really known is that the
visual appearance in question, together with touch, will lead to certain
sensations, which can necessarily be determined in terms of the visual
appearance, since otherwise they could not be inferred from it.

We can now give a statement of the experienced facts concerning the blue
spectacles, which will supply an interpretation of common-sense beliefs
without assuming anything beyond the existence of sensible objects at
the times when they are sensible. By experience of the correlation of
touch and sight sensations, we become able to associate a certain place
in touch-space with a certain corresponding place in sight-space.
Sometimes, namely in the case of transparent things, we find that there
is a tangible object in a touch-place without there being any visible
object in the corresponding sight-place. But in such a case as that of
the blue spectacles, we find that whatever object is visible beyond the
empty sight-place in the same line of sight has a different colour from
what it has when there is no tangible object in the intervening
touch-place; and as we move the tangible object in touch-space, the blue
patch moves in sight-space. If now we find a blue patch moving in this
way in sight-space, when we have no sensible experience of an
intervening tangible object, we nevertheless infer that, if we put our
hand at a certain place in touch-space, we should experience a certain
touch-sensation. If we are to avoid non-sensible objects, this must be
taken as the whole of our meaning when we say that the blue spectacles
are in a certain place, though we have not touched them, and have only
seen other things rendered blue by their interposition.

I think it may be laid down quite generally that, _in so far_ as physics
or common sense is verifiable, it must be capable of interpretation in
terms of actual sense-data alone. The reason for this is simple.
Verification consists always in the occurrence of an expected
sense-datum. Astronomers tell us there will be an eclipse of the moon:
we look at the moon, and find the earth's shadow biting into it, that is
to say, we see an appearance quite different from that of the usual full
moon. Now if an expected sense-datum constitutes a verification, what
was asserted must have been about sense-data; or, at any rate, if part
of what was asserted was not about sense-data, then only the other part
has been verified. There is in fact a certain regularity or conformity
to law about the occurrence of sense-data, but the sense-data that occur
at one time are often causally connected with those that occur at quite
other times, and not, or at least not very closely, with those that
occur at neighbouring times. If I look at the moon and immediately
afterwards hear a train coming, there is no very close causal connection
between my two sense-data; but if I look at the moon on two nights a
week apart, there is a very close causal connection between the two
sense-data. The simplest, or at least the easiest, statement of the
connection is obtained by imagining a "real" moon which goes on whether
I look at it or not, providing a series of _possible_ sense-data of
which only those are actual which belong to moments when I choose to
look at the moon.

But the degree of verification obtainable in this way is very small. It
must be remembered that, at our present level of doubt, we are not at
liberty to accept testimony. When we hear certain noises, which are
those we should utter if we wished to express a certain thought, we
assume that that thought, or one very like it, has been in another mind,
and has given rise to the expression which we hear. If at the same time
we see a body resembling our own, moving its lips as we move ours when
we speak, we cannot resist the belief that it is alive, and that the
feelings inside it continue when we are not looking at it. When we see
our friend drop a weight upon his toe, and hear him say--what we should
say in similar circumstances, the phenomena _can_ no doubt be explained
without assuming that he is anything but a series of shapes and noises
seen and heard by us, but practically no man is so infected with
philosophy as not to be quite certain that his friend has felt the same
kind of pain as he himself would feel. We will consider the legitimacy
of this belief presently; for the moment, I only wish to point out that
it needs the same kind of justification as our belief that the moon
exists when we do not see it, and that, without it, testimony heard or
read is reduced to noises and shapes, and cannot be regarded as evidence
of the facts which it reports. The verification of physics which is
possible at our present level is, therefore, only that degree of
verification which is possible by one man's unaided observations, which
will not carry us very far towards the establishment of a whole science.

Before proceeding further, let us summarise the argument so far as it
has gone. The problem is: "Can the existence of anything other than our
own hard data be inferred from these data?" It is a mistake to state the
problem in the form: "Can we know of the existence of anything other
than ourselves and our states?" or: "Can we know of the existence of
anything independent of ourselves?" because of the extreme difficulty of
defining "self" and "independent" precisely. The felt passivity of
sensation is irrelevant, since, even if it proved anything, it could
only prove that sensations are caused by sensible objects. The natural
_naive_ belief is that things seen persist, when unseen, exactly or
approximately as they appeared when seen; but this belief tends to be
dispelled by the fact that what common sense regards as the appearance
of one object changes with what common sense regards as changes in the
point of view and in the intervening medium, including in the latter our
own sense-organs and nerves and brain. This fact, as just stated,
assumes, however, the common-sense world of stable objects which it
professes to call in question; hence, before we can discover its precise
bearing on our problem, we must find a way of stating it which does not
involve any of the assumptions which it is designed to render doubtful.
What we then find, as the bare outcome of experience, is that gradual
changes in certain sense-data are correlated with gradual changes in
certain others, or (in the case of bodily motions) with the other
sense-data themselves.

The assumption that sensible objects persist after they have ceased to
be sensible--for example, that the hardness of a visible body, which has
been discovered by touch, continues when the body is no longer
touched--may be replaced by the statement that the _effects_ of sensible
objects persist, _i.e._ that what happens now can only be accounted for,
in many cases, by taking account of what happened at an earlier time.
Everything that one man, by his own personal experience, can verify in
the account of the world given by common sense and physics, will be
explicable by some such means, since verification consists merely in the
occurrence of an expected sense-datum. But what depends upon testimony,
whether heard or read, cannot be explained in this way, since testimony
depends upon the existence of minds other than our own, and thus
requires a knowledge of something not given in sense. But before
examining the question of our knowledge of other minds, let us return to
the question of the thing-in-itself, namely, to the theory that what
exists at times when we are not perceiving a given sensible object is
something quite unlike that object, something which, together with us
and our sense-organs, causes our sensations, but is never itself given
in sensation.

The thing-in-itself, when we start from common-sense assumptions, is a
fairly natural outcome of the difficulties due to the changing
appearances of what is supposed to be one object. It is supposed that
the table (for example) causes our sense-data of sight and touch, but
must, since these are altered by the point of view and the intervening
medium, be quite different from the sense-data to which it gives rise.
There is, in this theory, a tendency to a confusion from which it
derives some of its plausibility, namely, the confusion between a
sensation as a psychical occurrence and its object. A patch of colour,
even if it only exists when it is seen, is still something quite
different from the seeing of it: the seeing of it is mental, but the
patch of colour is not. This confusion, however, can be avoided without
our necessarily abandoning the theory we are examining. The objection to
it, I think, lies in its failure to realise the radical nature of the
reconstruction demanded by the difficulties to which it points. We
cannot speak legitimately of changes in the point of view and the
intervening medium until we have already constructed some world more
stable than that of momentary sensation. Our discussion of the blue
spectacles and the walk round the table has, I hope, made this clear.
But what remains far from clear is the nature of the reconstruction
required.

Although we cannot rest content with the above theory, in the terms in
which it is stated, we must nevertheless treat it with a certain
respect, for it is in outline the theory upon which physical science and
physiology are built, and it must, therefore, be susceptible of a true
interpretation. Let us see how this is to be done.

The first thing to realise is that there are no such things as
"illusions of sense." Objects of sense, even when they occur in dreams,
are the most indubitably real objects known to us. What, then, makes us
call them unreal in dreams? Merely the unusual nature of their
connection with other objects of sense. I dream that I am in America,
but I wake up and find myself in England without those intervening days
on the Atlantic which, alas! are inseparably connected with a "real"
visit to America. Objects of sense are called "real" when they have the
kind of connection with other objects of sense which experience has led
us to regard as normal; when they fail in this, they are called
"illusions." But what is illusory is only the inferences to which they
give rise; in themselves, they are every bit as real as the objects of
waking life. And conversely, the sensible objects of waking life must
not be expected to have any more intrinsic reality than those of dreams.
Dreams and waking life, in our first efforts at construction, must be
treated with equal respect; it is only by some reality not _merely_
sensible that dreams can be condemned.

Accepting the indubitable momentary reality of objects of sense, the
next thing to notice is the confusion underlying objections derived from
their changeableness. As we walk round the table, its aspect changes;
but it is thought impossible to maintain either that the table changes,
or that its various aspects can all "really" exist in the same place. If
we press one eyeball, we shall see two tables; but it is thought
preposterous to maintain that there are "really" two tables. Such
arguments, however, seem to involve the assumption that there can be
something more real than objects of sense. If we see two tables, then
there _are_ two visual tables. It is perfectly true that, at the same
moment, we may discover by touch that there is only one tactile table.
This makes us declare the two visual tables an illusion, because usually
one visual object corresponds to one tactile object. But all that we are
warranted in saying is that, in this case, the manner of correlation of
touch and sight is unusual. Again, when the aspect of the table changes
as we walk round it, and we are told there cannot be so many different
aspects in the same place, the answer is simple: what does the critic of
the table mean by "the same place"? The use of such a phrase presupposes
that all our difficulties have been solved; as yet, we have no right to
speak of a "place" except with reference to one given set of momentary
sense-data. When all are changed by a bodily movement, no place remains
the same as it was. Thus the difficulty, if it exists, has at least not
been rightly stated.

We will now make a new start, adopting a different method. Instead of
inquiring what is the minimum of assumption by which we can explain the
world of sense, we will, in order to have a model hypothesis as a help
for the imagination, construct one possible (not necessary) explanation
of the facts. It may perhaps then be possible to pare away what is
superfluous in our hypothesis, leaving a residue which may be regarded
as the abstract answer to our problem.

Let us imagine that each mind looks out upon the world, as in Leibniz's
monadology, from a point of view peculiar to itself; and for the sake of
simplicity let us confine ourselves to the sense of sight, ignoring
minds which are devoid of this sense. Each mind sees at each moment an
immensely complex three-dimensional world; but there is absolutely
nothing which is seen by two minds simultaneously. When we say that two
people see the same thing, we always find that, owing to difference of
point of view, there are differences, however slight, between their
immediate sensible objects. (I am here assuming the validity of
testimony, but as we are only constructing a _possible_ theory, that is
a legitimate assumption.) The three-dimensional world seen by one mind
therefore contains no place in common with that seen by another, for
places can only be constituted by the things in or around them. Hence we
may suppose, in spite of the differences between the different worlds,
that each exists entire exactly as it is perceived, and might be exactly
as it is even if it were not perceived. We may further suppose that
there are an infinite number of such worlds which are in fact
unperceived. If two men are sitting in a room, two somewhat similar
worlds are perceived by them; if a third man enters and sits between
them, a third world, intermediate between the two previous worlds,
begins to be perceived. It is true that we cannot reasonably suppose
just this world to have existed before, because it is conditioned by the
sense-organs, nerves, and brain of the newly arrived man; but we can
reasonably suppose that _some_ aspect of the universe existed from that
point of view, though no one was perceiving it. The system consisting of
all views of the universe perceived and unperceived, I shall call the
system of "perspectives"; I shall confine the expression "private
worlds" to such views of the universe as are actually perceived. Thus a
"private world" is a perceived "perspective"; but there may be any
number of unperceived perspectives.

Two men are sometimes found to perceive very similar perspectives, so
similar that they can use the same words to describe them. They say they
see the same table, because the differences between the two tables they
see are slight and not practically important. Thus it is possible,
sometimes, to establish a correlation by similarity between a great many
of the things of one perspective, and a great many of the things of
another. In case the similarity is very great, we say the points of view
of the two perspectives are near together in space; but this space in
which they are near together is totally different from the spaces inside
the two perspectives. It is a relation between the perspectives, and is
not in either of them; no one can perceive it, and if it is to be known
it can be only by inference. Between two perceived perspectives which
are similar, we can imagine a whole series of other perspectives, some
at least unperceived, and such that between any two, however similar,
there are others still more similar. In this way the space which
consists of relations between perspectives can be rendered continuous,
and (if we choose) three-dimensional.

We can now define the momentary common-sense "thing," as opposed to its
momentary appearances. By the similarity of neighbouring perspectives,
many objects in the one can be correlated with objects in the other,
namely, with the similar objects. Given an object in one perspective,
form the system of all the objects correlated with it in all the
perspectives; that system may be identified with the momentary
common-sense "thing." Thus an aspect of a "thing" is a member of the
system of aspects which _is_ the "thing" at that moment. (The
correlation of the times of different perspectives raises certain
complications, of the kind considered in the theory of relativity; but
we may ignore these at present.) All the aspects of a thing are real,
whereas the thing is a mere logical construction. It has, however, the
merit of being neutral as between different points of view, and of being
visible to more than one person, in the only sense in which it can ever
be visible, namely, in the sense that each sees one of its aspects.

It will be observed that, while each perspective contains its own space,
there is only one space in which the perspectives themselves are the
elements. There are as many private spaces as there are perspectives;
there are therefore at least as many as there are percipients, and there
may be any number of others which have a merely material existence and
are not seen by anyone. But there is only one perspective-space, whose
elements are single perspectives, each with its own private space. We
have now to explain how the private space of a single perspective is
correlated with part of the one all-embracing perspective space.

Perspective space is the system of "points of view" of private spaces
(perspectives), or, since "points of view" have not been defined, we may
say it is the system of the private spaces themselves. These private
spaces will each count as one point, or at any rate as one element, in
perspective space. They are ordered by means of their similarities.
Suppose, for example, that we start from one which contains the
appearance of a circular disc, such as would be called a penny, and
suppose this appearance, in the perspective in question, is circular,
not elliptic. We can then form a whole series of perspectives containing
a graduated series of circular aspects of varying sizes: for this
purpose we only have to move (as we say) towards the penny or away from
it. The perspectives in which the penny looks circular will be said to
lie on a straight line in perspective space, and their order on this
line will be that of the sizes of the circular aspects. Moreover--though
this statement must be noticed and subsequently examined--the
perspectives in which the penny looks big will be said to be nearer to
the penny than those in which it looks small. It is to be remarked also
that any other "thing" than our penny might have been chosen to define
the relations of our perspectives in perspective space, and that
experience shows that the same spatial order of perspectives would have
resulted.

In order to explain the correlation of private spaces with perspective
space, we have first to explain what is meant by "the place (in
perspective space) where a thing is." For this purpose, let us again
consider the penny which appears in many perspectives. We formed a
straight line of perspectives in which the penny looked circular, and we
agreed that those in which it looked larger were to be considered as
nearer to the penny. We can form another straight line of perspectives
in which the penny is seen end-on and looks like a straight line of a
certain thickness. These two lines will meet in a certain place in
perspective space, _i.e._ in a certain perspective, which may be defined
as "the place (in perspective space) where the penny is." It is true
that, in order to prolong our lines until they reach this place, we
shall have to make use of other things besides the penny, because, so
far as experience goes, the penny ceases to present any appearance after
we have come so near to it that it touches the eye. But this raises no
real difficulty, because the spatial order of perspectives is found
empirically to be independent of the particular "things" chosen for
defining the order. We can, for example, remove our penny and prolong
each of our two straight lines up to their intersection by placing other
pennies further off in such a way that the aspects of the one are
circular where those of our original penny were circular, and the
aspects of the other are straight where those of our original penny were
straight. There will then be just one perspective in which one of the
new pennies looks circular and the other straight. This will be, by
definition, the place where the original penny was in perspective space.

The above is, of course, only a first rough sketch of the way in which
our definition is to be reached. It neglects the size of the penny, and
it assumes that we can remove the penny without being disturbed by any
simultaneous changes in the positions of other things. But it is plain
that such niceties cannot affect the principle, and can only introduce
complications in its application.

Having now defined the perspective which is the place where a given
thing is, we can understand what is meant by saying that the
perspectives in which a thing looks large are nearer to the thing than
those in which it looks small: they are, in fact, nearer to the
perspective which is the place where the thing is.

We can now also explain the correlation between a private space and
parts of perspective space. If there is an aspect of a given thing in a
certain private space, then we correlate the place where this aspect is
in the private space with the place where the thing is in perspective
space.

We may define "here" as the place, in perspective space, which is
occupied by our private world. Thus we can now understand what is meant
by speaking of a thing as near to or far from "here." A thing is near to
"here" if the place where it is is near to my private world. We can also
understand what is meant by saying that our private world is inside our
head; for our private world is a place in perspective space, and may be
part of the place where our head is.

It will be observed that _two_ places in perspective space are
associated with every aspect of a thing: namely, the place where the
thing is, and the place which is the perspective of which the aspect in
question forms part. Every aspect of a thing is a member of two
different classes of aspects, namely: (1) the various aspects of the
thing, of which at most one appears in any given perspective; (2) the
perspective of which the given aspect is a member, _i.e._ that in which
the thing has the given aspect. The physicist naturally classifies
aspects in the first way, the psychologist in the second. The two places
associated with a single aspect correspond to the two ways of
classifying it. We may distinguish the two places as that _at_ which,
and that _from_ which, the aspect appears. The "place at which" is the
place of the thing to which the aspect belongs; the "place from which"
is the place of the perspective to which the aspect belongs.

Let us now endeavour to state the fact that the aspect which a thing
presents at a given place is affected by the intervening medium. The
aspects of a thing in different perspectives are to be conceived as
spreading outwards from the place where the thing is, and undergoing
various changes as they get further away from this place. The laws
according to which they change cannot be stated if we only take account
of the aspects that are near the thing, but require that we should also
take account of the things that are at the places from which these
aspects appear. This empirical fact can, therefore, be interpreted in
terms of our construction.

We have now constructed a largely hypothetical picture of the world,
which contains and places the experienced facts, including those derived
from testimony. The world we have constructed can, with a certain amount
of trouble, be used to interpret the crude facts of sense, the facts of
physics, and the facts of physiology. It is therefore a world which
_may_ be actual. It fits the facts, and there is no empirical evidence
against it; it also is free from logical impossibilities. But have we
any good reason to suppose that it is real? This brings us back to our
original problem, as to the grounds for believing in the existence of
anything outside my private world. What we have derived from our
hypothetical construction is that there are no grounds _against_ the
truth of this belief, but we have not derived any positive grounds in
its favour. We will resume this inquiry by taking up again the question
of testimony and the evidence for the existence of other minds.

It must be conceded to begin with that the argument in favour of the
existence of other people's minds cannot be conclusive. A phantasm of
our dreams will appear to have a mind--a mind to be annoying, as a rule.
It will give unexpected answers, refuse to conform to our desires, and
show all those other signs of intelligence to which we are accustomed in
the acquaintances of our waking hours. And yet, when we are awake, we do
not believe that the phantasm was, like the appearances of people in
waking life, representative of a private world to which we have no
direct access. If we are to believe this of the people we meet when we
are awake, it must be on some ground short of demonstration, since it is
obviously possible that what we call waking life may be only an
unusually persistent and recurrent nightmare. It may be that our
imagination brings forth all that other people seem to say to us, all
that we read in books, all the daily, weekly, monthly, and quarterly
journals that distract our thoughts, all the advertisements of soap and
all the speeches of politicians. This _may_ be true, since it cannot be
shown to be false, yet no one can really believe it. Is there any
_logical_ ground for regarding this possibility as improbable? Or is
there nothing beyond habit and prejudice?

The minds of other people are among our data, in the very wide sense in
which we used the word at first. That is to say, when we first begin to
reflect, we find ourselves already believing in them, not because of any
argument, but because the belief is natural to us. It is, however, a
psychologically derivative belief, since it results from observation of
people's bodies; and along with other such beliefs, it does not belong
to the hardest of hard data, but becomes, under the influence of
philosophic reflection, just sufficiently questionable to make us desire
some argument connecting it with the facts of sense.

The obvious argument is, of course, derived from analogy. Other people's
bodies behave as ours do when we have certain thoughts and feelings;
hence, by analogy, it is natural to suppose that such behaviour is
connected with thoughts and feelings like our own. Someone says, "Look
out!" and we find we are on the point of being killed by a motor-car; we
therefore attribute the words we heard to the person in question having
seen the motor-car first, in which case there are existing things of
which we are not directly conscious. But this whole scene, with our
inference, may occur in a dream, in which case the inference is
generally considered to be mistaken. Is there anything to make the
argument from analogy more cogent when we are (as we think) awake?

The analogy in waking life is only to be preferred to that in dreams on
the ground of its greater extent and consistency. If a man were to dream
every night about a set of people whom he never met by day, who had
consistent characters and grew older with the lapse of years, he might,
like the man in Calderon's play, find it difficult to decide which was
the dream-world and which was the so-called "real" world. It is only the
failure of our dreams to form a consistent whole either with each other
or with waking life that makes us condemn them. Certain uniformities are
observed in waking life, while dreams seem quite erratic. The natural
hypothesis would be that demons and the spirits of the dead visit us
while we sleep; but the modern mind, as a rule, refuses to entertain
this view, though it is hard to see what could be said against it. On
the other hand, the mystic, in moments of illumination, seems to awaken
from a sleep which has filled all his mundane life: the whole world of
sense becomes phantasmal, and he sees, with the clarity and
convincingness that belongs to our morning realisation after dreams, a
world utterly different from that of our daily cares and troubles. Who
shall condemn him? Who shall justify him? Or who shall justify the
seeming solidity of the common objects among which we suppose ourselves
to live?

The hypothesis that other people have minds must, I think, be allowed to
be not susceptible of any very strong support from the analogical
argument. At the same time, it is a hypothesis which systematises a vast
body of facts and never leads to any consequences which there is reason
to think false. There is therefore nothing to be said against its truth,
and good reason to use it as a working hypothesis. When once it is
admitted, it enables us to extend our knowledge of the sensible world by
testimony, and thus leads to the system of private worlds which we
assumed in our hypothetical construction. In actual fact, whatever we
may try to think as philosophers, we cannot help believing in the minds
of other people, so that the question whether our belief is justified
has a merely speculative interest. And if it is justified, then there is
no further difficulty of principle in that vast extension of our
knowledge, beyond our own private data, which we find in science and
common sense.

This somewhat meagre conclusion must not be regarded as the whole
outcome of our long discussion. The problem of the connection of sense
with objective reality has commonly been dealt with from a standpoint
which did not carry initial doubt so far as we have carried it; most
writers, consciously or unconsciously, have assumed that the testimony
of others is to be admitted, and therefore (at least by implication)
that others have minds. Their difficulties have arisen after this
admission, from the differences in the appearance which one physical
object presents to two people at the same time, or to one person at two
times between which it cannot be supposed to have changed. Such
difficulties have made people doubtful how far objective reality could
be known by sense at all, and have made them suppose that there were
positive arguments against the view that it can be so known. Our
hypothetical construction meets these arguments, and shows that the
account of the world given by common sense and physical science can be
interpreted in a way which is logically unobjectionable, and finds a
place for all the data, both hard and soft. It is this hypothetical
construction, with its reconciliation of psychology and physics, which
is the chief outcome of our discussion. Probably the construction is
only in part necessary as an initial assumption, and can be obtained
from more slender materials by the logical methods of which we shall
have an example in the definitions of points, instants, and particles;
but I do not yet know to what lengths this diminution in our initial
assumptions can be carried.




LECTURE IV

THE WORLD OF PHYSICS AND THE WORLD OF SENSE


Among the objections to the reality of objects of sense, there is one
which is derived from the apparent difference between matter as it
appears in physics and things as they appear in sensation. Men of
science, for the most part, are willing to condemn immediate data as
"merely subjective," while yet maintaining the truth of the physics
inferred from those data. But such an attitude, though it may be
_capable_ of justification, obviously stands in need of it; and the only
justification possible must be one which exhibits matter as a logical
construction from sense-data--unless, indeed, there were some wholly _a
priori_ principle by which unknown entities could be inferred from such
as are known. It is therefore necessary to find some way of bridging the
gulf between the world of physics and the world of sense, and it is this
problem which will occupy us in the present lecture. Physicists appear
to be unconscious of the gulf, while psychologists, who are conscious of
it, have not the mathematical knowledge required for spanning it. The
problem is difficult, and I do not know its solution in detail. All that
I can hope to do is to make the problem felt, and to indicate the kind
of methods by which a solution is to be sought.

Let us begin by a brief description of the two contrasted worlds. We
will take first the world of physics, for, though the other world is
given while the physical world is inferred, to us now the world of
physics is the more familiar, the world of pure sense having become
strange and difficult to rediscover. Physics started from the
common-sense belief in fairly permanent and fairly rigid bodies--tables
and chairs, stones, mountains, the earth and moon and sun. This
common-sense belief, it should be noticed, is a piece of audacious
metaphysical theorising; objects are not continually present to
sensation, and it may be doubted whether they are there when they are
not seen or felt. This problem, which has been acute since the time of
Berkeley, is ignored by common sense, and has therefore hitherto been
ignored by physicists. We have thus here a first departure from the
immediate data of sensation, though it is a departure merely by way of
extension, and was probably made by our savage ancestors in some very
remote prehistoric epoch.

But tables and chairs, stones and mountains, are not _quite_ permanent
or _quite_ rigid. Tables and chairs lose their legs, stones are split by
frost, and mountains are cleft by earthquakes and eruptions. Then there
are other things, which seem material, and yet present almost no
permanence or rigidity. Breath, smoke, clouds, are examples of such
things--so, in a lesser degree, are ice and snow; and rivers and seas,
though fairly permanent, are not in any degree rigid. Breath, smoke,
clouds, and generally things that can be seen but not touched, were
thought to be hardly real; to this day the usual mark of a ghost is that
it can be seen but not touched. Such objects were peculiar in the fact
that they seemed to disappear completely, not merely to be transformed
into something else. Ice and snow, when they disappear, are replaced by
water; and it required no great theoretical effort to invent the
hypothesis that the water was the same thing as the ice and snow, but in
a new form. Solid bodies, when they break, break into parts which are
practically the same in shape and size as they were before. A stone can
be hammered into a powder, but the powder consists of grains which
retain the character they had before the pounding. Thus the ideal of
absolutely rigid and absolutely permanent bodies, which early physicists
pursued throughout the changing appearances, seemed attainable by
supposing ordinary bodies to be composed of a vast number of tiny atoms.
This billiard-ball view of matter dominated the imagination of
physicists until quite modern times, until, in fact, it was replaced by
the electromagnetic theory, which in its turn is developing into a new
atomism. Apart from the special form of the atomic theory which was
invented for the needs of chemistry, some kind of atomism dominated the
whole of traditional dynamics, and was implied in every statement of its
laws and axioms.

The pictorial accounts which physicists give of the material world as
they conceive it undergo violent changes under the influence of
modifications in theory which are much slighter than the layman might
suppose from the alterations of the description. Certain features,
however, have remained fairly stable. It is always assumed that there is
_something_ indestructible which is capable of motion in space; what is
indestructible is always very small, but does not always occupy a mere
point in space. There is supposed to be one all-embracing space in which
the motion takes place, and until lately we might have assumed one
all-embracing time also. But the principle of relativity has given
prominence to the conception of "local time," and has somewhat
diminished men's confidence in the one even-flowing stream of time.
Without dogmatising as to the ultimate outcome of the principle of
relativity, however, we may safely say, I think, that it does not
destroy the possibility of correlating different local times, and does
not therefore have such far-reaching philosophical consequences as is
sometimes supposed. In fact, in spite of difficulties as to measurement,
the one all-embracing time still, I think, underlies all that physics
has to say about motion. We thus have still in physics, as we had in
Newton's time, a set of indestructible entities which may be called
particles, moving relatively to each other in a single space and a
single time.

The world of immediate data is quite different from this. Nothing is
permanent; even the things that we think are fairly permanent, such as
mountains, only become data when we see them, and are not immediately
given as existing at other moments. So far from one all-embracing space
being given, there are several spaces for each person, according to the
different senses which give relations that may be called spatial.
Experience teaches us to obtain one space from these by correlation, and
experience, together with instinctive theorising, teaches us to
correlate our spaces with those which we believe to exist in the
sensible worlds of other people. The construction of a single time
offers less difficulty so long as we confine ourselves to one person's
private world, but the correlation of one private time with another is a
matter of great difficulty. Thus, apart from any of the fluctuating
hypotheses of physics, three main problems arise in connecting the world
of physics with the world of sense, namely (1) the construction of
permanent "things," (2) the construction of a single space, and (3) the
construction of a single time. We will consider these three problems in
succession.

(1) The belief in indestructible "things" very early took the form of
atomism. The underlying motive in atomism was not, I think, any
empirical success in interpreting phenomena, but rather an instinctive
belief that beneath all the changes of the sensible world there must be
something permanent and unchanging. This belief was, no doubt, fostered
and nourished by its practical successes, culminating in the
conservation of mass; but it was not produced by these successes. On the
contrary, they were produced by it. Philosophical writers on physics
sometimes speak as though the conservation of something or other were
essential to the possibility of science, but this, I believe, is an
entirely erroneous opinion. If the _a priori_ belief in permanence had
not existed, the same laws which are now formulated in terms of this
belief might just as well have been formulated without it. Why should we
suppose that, when ice melts, the water which replaces it is the same
thing in a new form? Merely because this supposition enables us to state
the phenomena in a way which is consonant with our prejudices. What we
really know is that, under certain conditions of temperature, the
appearance we call ice is replaced by the appearance we call water. We
can give laws according to which the one appearance will be succeeded by
the other, but there is no reason except prejudice for regarding both as
appearances of the same substance.

One task, if what has just been said is correct, which confronts us in
trying to connect the world of sense with the world of physics, is the
task of reconstructing the conception of matter without the _a priori_
beliefs which historically gave rise to it. In spite of the
revolutionary results of modern physics, the empirical successes of the
conception of matter show that there must be some legitimate conception
which fulfils roughly the same functions. The time has hardly come when
we can state precisely what this legitimate conception is, but we can
see in a general way what it must be like. For this purpose, it is only
necessary to take our ordinary common-sense statements and reword them
without the assumption of permanent substance. We say, for example, that
things change gradually--sometimes very quickly, but not without passing
through a continuous series of intermediate states. What this means is
that, given any sensible appearance, there will usually be, _if we
watch_, a continuous series of appearances connected with the given one,
leading on by imperceptible gradations to the new appearances which
common-sense regards as those of the same thing. Thus a thing may be
defined as a certain series of appearances, connected with each other by
continuity and by certain causal laws. In the case of slowly changing
things, this is easily seen. Consider, say, a wall-paper which fades in
the course of years. It is an effort not to conceive of it as one
"thing" whose colour is slightly different at one time from what it is
at another. But what do we really _know_ about it? We know that under
suitable circumstances--_i.e._ when we are, as is said, "in the
room"--we perceive certain colours in a certain pattern: not always
precisely the same colours, but sufficiently similar to feel familiar.
If we can state the laws according to which the colour varies, we can
state all that is empirically verifiable; the assumption that there is a
constant entity, the wall-paper, which "has" these various colours at
various times, is a piece of gratuitous metaphysics. We may, if we like,
_define_ the wall-paper as the series of its aspects. These are
collected together by the same motives which led us to regard the
wall-paper as one thing, namely a combination of sensible continuity and
causal connection. More generally, a "thing" will be defined as a
certain series of aspects, namely those which would commonly be said to
be _of_ the thing. To say that a certain aspect is an aspect _of_ a
certain thing will merely mean that it is one of those which, taken
serially, _are_ the thing. Everything will then proceed as before:
whatever was verifiable is unchanged, but our language is so interpreted
as to avoid an unnecessary metaphysical assumption of permanence.

The above extrusion of permanent things affords an example of the maxim
which inspires all scientific philosophising, namely "Occam's razor":
_Entities are not to be multiplied without necessity._ In other words,
in dealing with any subject-matter, find out what entities are
undeniably involved, and state everything in terms of these entities.
Very often the resulting statement is more complicated and difficult
than one which, like common sense and most philosophy, assumes
hypothetical entities whose existence there is no good reason to believe
in. We find it easier to imagine a wall-paper with changing colours than
to think merely of the series of colours; but it is a mistake to suppose
that what is easy and natural in thought is what is most free from
unwarrantable assumptions, as the case of "things" very aptly
illustrates.

The above summary account of the genesis of "things," though it may be
correct in outline, has omitted some serious difficulties which it is
necessary briefly to consider. Starting from a world of helter-skelter
sense-data, we wish to collect them into series, each of which can be
regarded as consisting of the successive appearances of one "thing."
There is, to begin with, some conflict between what common sense regards
as one thing, and what physics regards an unchanging collection of
particles. To common sense, a human body is one thing, but to science
the matter composing it is continually changing. This conflict, however,
is not very serious, and may, for our rough preliminary purpose, be
largely ignored. The problem is: by what principles shall we select
certain data from the chaos, and call them all appearances of the same
thing?

A rough and approximate answer to this question is not very difficult.
There are certain fairly stable collections of appearances, such as
landscapes, the furniture of rooms, the faces of acquaintances. In these
cases, we have little hesitation in regarding them on successive
occasions as appearances of one thing or collection of things. But, as
the _Comedy of Errors_ illustrates, we may be led astray if we judge by
mere resemblance. This shows that something more is involved, for two
different things may have any degree of likeness up to exact similarity.

Another insufficient criterion of one thing is _continuity_. As we have
already seen, if we watch what we regard as one changing thing, we
usually find its changes to be continuous so far as our senses can
perceive. We are thus led to assume that, if we see two finitely
different appearances at two different times, and if we have reason to
regard them as belonging to the same thing, then there was a continuous
series of intermediate states of that thing during the time when we were
not observing it. And so it comes to be thought that continuity of
change is necessary and sufficient to constitute one thing. But in fact
it is neither. It is not _necessary_, because the unobserved states, in
the case where our attention has not been concentrated on the thing
throughout, are purely hypothetical, and cannot possibly be our ground
for supposing the earlier and later appearances to belong to the same
thing; on the contrary, it is because we suppose this that we assume
intermediate unobserved states. Continuity is also not sufficient, since
we can, for example, pass by sensibly continuous gradations from any one
drop of the sea to any other drop. The utmost we can say is that
discontinuity during uninterrupted observation is as a rule a mark of
difference between things, though even this cannot be said in such cases
as sudden explosions.

The assumption of continuity is, however, successfully made in physics.
This proves something, though not anything of very obvious utility to
our present problem: it proves that nothing in the known world is
inconsistent with the hypothesis that all changes are really continuous,
though from too great rapidity or from our lack of observation they may
not always appear continuous. In this hypothetical sense, continuity may
be allowed to be a _necessary_ condition if two appearances are to be
classed as appearances of the same thing. But it is not a _sufficient_
condition, as appears from the instance of the drops in the sea. Thus
something more must be sought before we can give even the roughest
definition of a "thing."

What is wanted further seems to be something in the nature of fulfilment
of causal laws. This statement, as it stands, is very vague, but we will
endeavour to give it precision. When I speak of "causal laws," I mean
any laws which connect events at different times, or even, as a limiting
case, events at the same time provided the connection is not logically
demonstrable. In this very general sense, the laws of dynamics are
causal laws, and so are the laws correlating the simultaneous
appearances of one "thing" to different senses. The question is: How do
such laws help in the definition of a "thing"?

To answer this question, we must consider what it is that is proved by
the empirical success of physics. What is proved is that its hypotheses,
though unverifiable where they go beyond sense-data, are at no point in
contradiction with sense-data, but, on the contrary, are ideally such as
to render all sense-data calculable from a sufficient collection of data
all belonging to a given period of time. Now physics has found it
empirically possible to collect sense-data into series, each series
being regarded as belonging to one "thing," and behaving, with regard to
the laws of physics, in a way in which series not belonging to one thing
would in general not behave. If it is to be unambiguous whether two
appearances belong to the same thing or not, there must be only one way
of grouping appearances so that the resulting things obey the laws of
physics. It would be very difficult to prove that this is the case, but
for our present purposes we may let this point pass, and assume that
there is only one way. We must include in our definition of a "thing"
those of its aspects, if any, which are not observed. Thus we may lay
down the following definition: _Things are those series of aspects which
obey the laws of physics._ That such series exist is an empirical fact,
which constitutes the verifiability of physics.

It may still be objected that the "matter" of physics is something other
than series of sense-data. Sense-data, it may be said, belong to
psychology and are, at any rate in some sense, subjective, whereas
physics is quite independent of psychological considerations, and does
not assume that its matter only exists when it is perceived.

To this objection there are two answers, both of some importance.

(a) We have been considering, in the above account, the question of the
_verifiability_ of physics. Now verifiability is by no means the same
thing as truth; it is, in fact, something far more subjective and
psychological. For a proposition to be verifiable, it is not enough that
it should be true, but it must also be such as we can _discover_ to be
true. Thus verifiability depends upon our capacity for acquiring
knowledge, and not only upon the objective truth. In physics, as
ordinarily set forth, there is much that is unverifiable: there are
hypotheses as to (A) how things would appear to a spectator in a place
where, as it happens, there is no spectator; (B) how things would appear
at times when, in fact, they are not appearing to anyone; (C) things
which never appear at all. All these are introduced to simplify the
statement of the causal laws, but none of them form an integral part of
what is _known_ to be true in physics. This brings us to our second
answer.

(b) If physics is to consist wholly of propositions known to be true, or
at least capable of being proved or disproved, the three kinds of
hypothetical entities we have just enumerated must all be capable of
being exhibited as logical functions of sense-data. In order to show how
this might possibly be done, let us recall the hypothetical Leibnizian
universe of Lecture III. In that universe, we had a number of
perspectives, two of which never had any entity in common, but often
contained entities which could be sufficiently correlated to be regarded
as belonging to the same thing. We will call one of these an "actual"
private world when there is an actual spectator to which it appears, and
"ideal" when it is merely constructed on principles of continuity. A
physical thing consists, at each instant, of the whole set of its
aspects at that instant, in all the different worlds; thus a momentary
state of a thing is a whole set of aspects. An "ideal" appearance will
be an aspect merely calculated, but not actually perceived by any
spectator. An "ideal" state of a thing will be a state at a moment when
all its appearances are ideal. An ideal thing will be one whose states
at all times are ideal. Ideal appearances, states, and things, since
they are calculated, must be functions of actual appearances, states,
and things; in fact, ultimately, they must be functions of actual
appearances. Thus it is unnecessary, for the enunciation of the laws of
physics, to assign any reality to ideal elements: it is enough to accept
them as logical constructions, provided we have means of knowing how to
determine when they become actual. This, in fact, we have with some
degree of approximation; the starry heaven, for instance, becomes actual
whenever we choose to look at it. It is open to us to believe that the
ideal elements exist, and there can be no reason for _dis_believing
this; but unless in virtue of some _a priori_ law we cannot _know_ it,
for empirical knowledge is confined to what we actually observe.

(2) The three main conceptions of physics are space, time, and matter.
Some of the problems raised by the conception of matter have been
indicated in the above discussion of "things." But space and time also
raise difficult problems of much the same kind, namely, difficulties in
reducing the haphazard untidy world of immediate sensation to the smooth
orderly world of geometry and kinematics. Let us begin with the
consideration of space.

People who have never read any psychology seldom realise how much mental
labour has gone into the construction of the one all-embracing space
into which all sensible objects are supposed to fit. Kant, who was
unusually ignorant of psychology, described space as "an infinite given
whole," whereas a moment's psychological reflection shows that a space
which is infinite is not given, while a space which can be called given
is not infinite. What the nature of "given" space really is, is a
difficult question, upon which psychologists are by no means agreed. But
some general remarks may be made, which will suffice to show the
problems, without taking sides on any psychological issue still in
debate.

The first thing to notice is that different senses have different
spaces. The space of sight is quite different from the space of touch:
it is only by experience in infancy that we learn to correlate them. In
later life, when we see an object within reach, we know how to touch it,
and more or less what it will feel like; if we touch an object with our
eyes shut, we know where we should have to look for it, and more or less
what it would look like. But this knowledge is derived from early
experience of the correlation of certain kinds of touch-sensations with
certain kinds of sight-sensations. The one space into which both kinds
of sensations fit is an intellectual construction, not a datum. And
besides touch and sight, there are other kinds of sensation which give
other, though less important spaces: these also have to be fitted into
the one space by means of experienced correlations. And as in the case
of things, so here: the one all-embracing space, though convenient as a
way of speaking, need not be supposed really to exist. All that
experience makes certain is the several spaces of the several senses,
correlated by empirically discovered laws. The one space may turn out to
be valid as a logical construction, compounded of the several spaces,
but there is no good reason to assume its independent metaphysical
reality.

Another respect in which the spaces of immediate experience differ from
the space of geometry and physics is in regard to _points_. The space of
geometry and physics consists of an infinite number of points, but no
one has ever seen or touched a point. If there are points in a sensible
space, they must be an inference. It is not easy to see any way in
which, as independent entities, they could be validly inferred from the
data; thus here again, we shall have, if possible, to find some logical
construction, some complex assemblage of immediately given objects,
which will have the geometrical properties required of points. It is
customary to think of points as simple and infinitely small, but
geometry in no way demands that we should think of them in this way. All
that is necessary for geometry is that they should have mutual relations
possessing certain enumerated abstract properties, and it may be that an
assemblage of data of sensation will serve this purpose. Exactly how
this is to be done, I do not yet know, but it seems fairly certain that
it can be done.

The following illustrative method, simplified so as to be easily
manipulated, has been invented by Dr Whitehead for the purpose of
showing how points might be manufactured from sense-data. We have first
of all to observe that there are no infinitesimal sense-data: any
surface we can see, for example, must be of some finite extent. But what
at first appears as one undivided whole is often found, under the
influence of attention, to split up into parts contained within the
whole. Thus one spatial object may be contained within another, and
entirely enclosed by the other. This relation of enclosure, by the help
of some very natural hypotheses, will enable us to define a "point" as a
certain class of spatial objects, namely all those (as it will turn out
in the end) which would naturally be said to contain the point. In order
to obtain a definition of a "point" in this way, we proceed as follows:

Given any set of volumes or surfaces, they will not in general converge
into one point. But if they get smaller and smaller, while of any two of
the set there is always one that encloses the other, then we begin to
have the kind of conditions which would enable us to treat them as
having a point for their limit. The hypotheses required for the relation
of enclosure are that (1) it must be transitive; (2) of two _different_
spatial objects, it is impossible for each to enclose the other, but a
single spatial object always encloses itself; (3) any set of spatial
objects such that there is at least one spatial object enclosed by them
all has a lower limit or minimum, _i.e._ an object enclosed by all of
them and enclosing all objects which are enclosed by all of them; (4) to
prevent trivial exceptions, we must add that there are to be instances
of enclosure, _i.e._ there are really to be objects of which one
encloses the other. When an enclosure-relation has these properties, we
will call it a "point-producer." Given any relation of enclosure, we
will call a set of objects an "enclosure-series" if, of any two of them,
one is contained in the other. We require a condition which shall secure
that an enclosure-series converges to a point, and this is obtained as
follows: Let our enclosure-series be such that, given any other
enclosure-series of which there are members enclosed in any arbitrarily
chosen member of our first series, then there are members of our first
series enclosed in any arbitrarily chosen member of our second series.
In this case, our first enclosure-series may be called a "punctual
enclosure-series." Then a "point" is all the objects which enclose
members of a given punctual enclosure-series. In order to ensure
infinite divisibility, we require one further property to be added to
those defining point-producers, namely that any object which encloses
itself also encloses an object other than itself. The "points" generated
by point-producers with this property will be found to be such as
geometry requires.

(3) The question of time, so long as we confine ourselves to one private
world, is rather less complicated than that of space, and we can see
pretty clearly how it might be dealt with by such methods as we have
been considering. Events of which we are conscious do not last merely
for a mathematical instant, but always for some finite time, however
short. Even if there be a physical world such as the mathematical theory
of motion supposes, impressions on our sense-organs produce sensations
which are not merely and strictly instantaneous, and therefore the
objects of sense of which we are immediately conscious are not strictly
instantaneous. Instants, therefore, are not among the data of
experience, and, if legitimate, must be either inferred or constructed.
It is difficult to see how they can be validly inferred; thus we are
left with the alternative that they must be constructed. How is this to
be done?

Immediate experience provides us with two time-relations among events:
they may be simultaneous, or one may be earlier and the other later.
These two are both part of the crude data; it is not the case that only
the events are given, and their time-order is added by our subjective
activity. The time-order, within certain limits, is as much given as the
events. In any story of adventure you will find such passages as the
following: "With a cynical smile he pointed the revolver at the breast
of the dauntless youth. 'At the word _three_ I shall fire,' he said. The
words one and two had already been spoken with a cool and deliberate
distinctness. The word _three_ was forming on his lips. At this moment a
blinding flash of lightning rent the air." Here we have
simultaneity--not due, as Kant would have us believe, to the subjective
mental apparatus of the dauntless youth, but given as objectively as the
revolver and the lightning. And it is equally given in immediate
experience that the words _one_ and _two_ come earlier than the flash.
These time-relations hold between events which are not strictly
instantaneous. Thus one event may begin sooner than another, and
therefore be before it, but may continue after the other has begun, and
therefore be also simultaneous with it. If it persists after the other
is over, it will also be later than the other. Earlier, simultaneous,
and later, are not inconsistent with each other when we are concerned
with events which last for a finite time, however short; they only
become inconsistent when we are dealing with something instantaneous.

It is to be observed that we cannot give what may be called _absolute_
dates, but only dates determined by events. We cannot point to a time
itself, but only to some event occurring at that time. There is
therefore no reason in experience to suppose that there are times as
opposed to events: the events, ordered by the relations of simultaneity
and succession, are all that experience provides. Hence, unless we are

Showing first 200,000 characters. Full text: gutenberg.org/ebooks/37090