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                      SCIENCE AND THE MODERN WORLD

                         LOWELL LECTURES, 1925

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                                SCIENCE
                          AND THE MODERN WORLD




                         LOWELL LECTURES, 1925




                                   BY
                         ALFRED NORTH WHITEHEAD
          F.R.S., Sc.D. (Cambridge), Hon. D.Sc. (Manchester),
                        Hon. LL.D. (St. Andrews)

        FELLOW OF TRINITY COLLEGE IN THE UNIVERSITY OF CAMBRIDGE
           AND PROFESSOR OF PHILOSOPHY IN HARVARD UNIVERSITY








                           =New York=
                         THE MACMILLAN COMPANY
                                  1925
                         _All rights reserved_

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                            COPYRIGHT, 1925.
                       BY THE MACMILLAN COMPANY.

                                  ---

                          Set up and printed.
                        Published October, 1925.








               PRINTED IN THE UNITED STATES OF AMERICA BY
                      THE FERRIS PRINTING COMPANY

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                                   TO
                             MY COLLEAGUES,
                           PAST AND PRESENT,
                    WHOSE FRIENDSHIP IS INSPIRATION.




                           TABLE OF CONTENTS


    CHAPTER                                                     PAGE

         I. THE ORIGINS OF MODERN SCIENCE                          1

        II. MATHEMATICS AS AN ELEMENT IN THE HISTORY OF           28
            THOUGHT

       III. THE CENTURY OF GENIUS                                 55

        IV. THE EIGHTEENTH CENTURY                                80

         V. THE ROMANTIC REACTION                                105

        VI. THE NINETEENTH CENTURY                               134

       VII. RELATIVITY                                           160

      VIII. THE QUANTUM THEORY                                   181

        IX. SCIENCE AND PHILOSOPHY                               193

         X. ABSTRACTION                                          219

        XI. GOD                                                  242

       XII. RELIGION AND SCIENCE                                 252

      XIII. REQUISITES FOR SOCIAL PROGRESS                       270




                                PREFACE


The present book embodies a study of some aspects of Western culture
during the past three centuries, in so far as it has been influenced by
the development of science. This study has been guided by the conviction
that the mentality of an epoch springs from the view of the world which
is, in fact, dominant in the educated sections of the communities in
question. There may be more than one such scheme, corresponding to
cultural divisions. The various human interests which suggest
cosmologies, and also are influenced by them, are science, aesthetics,
ethics, religion. In every age each of these topics suggests a view of
the world. In so far as the same set of people are swayed by all, or
more than one, of these interests, their effective outlook will be the
joint production from these sources. But each age has it dominant
preoccupation; and, during the three centuries in question, the
cosmology derived from science has been asserting itself at the expense
of older points of view with their origins elsewhere. Men can be
provincial in time, as well as in place. We may ask ourselves whether
the scientific mentality of the modern world in the immediate past is
not a successful example of such provincial limitation.

Philosophy, in one of its functions, is the critic of cosmologies. It is
its function to harmonise, refashion, and justify divergent intuitions
as to the nature of things. It has to insist on the scrutiny of the
ultimate ideas, and on the retention of the whole of the evidence in
shaping our cosmological scheme. Its business is to render explicit,
and—so far as may be—efficient, a process which otherwise is
unconsciously performed without rational tests.

Bearing this in mind, I have avoided the introduction of a variety of
abstruse detail respecting scientific advance. What is wanted, and what
I have striven after, is a sympathetic study of main ideas as seen from
the inside. If my view of the function of philosophy is correct, it is
the most effective of all the intellectual pursuits. It builds
cathedrals before the workmen have moved a stone, and it destroys them
before the elements have worn down their arches. It is the architect of
the buildings of the spirit, and it is also their solvent:—and the
spiritual precedes the material. Philosophy works slowly. Thoughts lie
dormant for ages; and then, almost suddenly as it were, mankind finds
that they have embodied themselves in institutions.

This book in the main consists of a set of eight Lowell Lectures
delivered in the February of 1925. These lectures with some slight
expansion, and the subdivision of one lecture into Chapters VII and
VIII, are here printed as delivered. But some additional matter has
been added, so as to complete the thought of the book on a scale which
could not be included within that lecture course. Of this new matter,
the second chapter—‘Mathematics as an Element in the History of
Thought’—was delivered as a lecture before the Mathematical Society of
Brown University, Providence, R. I.; and the twelfth chapter—‘Religion
and Science’—formed an address delivered in the Phillips Brooks House
at Harvard, and is to be published in the August number of the
_Atlantic Monthly_ of this year (1925). The tenth and eleventh
chapters—‘Abstraction’ and ‘God’—are additions which now appear for
the first time. But the book represents one train of thought, and the
antecedent utilisation of some of its contents is a subsidiary point.

There has been no occasion in the text to make detailed reference to
Lloyd Morgan’s _Emergent Evolution_ or to Alexander’s _Space, Time and
Deity_. It will be obvious to readers that I have found them very
suggestive. I am especially indebted to Alexander’s great work. The wide
scope of the present book makes it impossible to acknowledge in detail
the various sources of information or of ideas. The book is the product
of thought and reading in past years, which were not undertaken with any
anticipation of utilisation for the present purpose. Accordingly it
would now be impossible for me to give reference to my sources for
details, even if it were desirable so to do. But there is no need: the
facts which are relied upon are simple and well known. On the
philosophical side, any consideration of epistemology has been entirely
excluded. It would have been impossible to discuss that topic without
upsetting the whole balance of the work. The key to the book is the
sense of the overwhelming importance of a prevalent philosophy.

My most grateful thanks are due to my colleague Mr. Raphael Demos for
reading the proofs and for the suggestion of many improvements in
expression.

  Harvard University,
    June 29, 1925.

------------------------------------------------------------------------

                         SCIENCE AND THE MODERN
                                 WORLD




                               CHAPTER I

                     THE ORIGINS OF MODERN SCIENCE


The progress of civilisation is not wholly a uniform drift towards
better things. It may perhaps wear this aspect if we map it on a scale
which is large enough. But such broad views obscure the details on which
rest our whole understanding of the process. New epochs emerge with
comparative suddenness, if we have regard to the scores of thousands of
years throughout which the complete history extends. Secluded races
suddenly take their places in the main stream of events: technological
discoveries transform the mechanism of human life: a primitive art
quickly flowers into full satisfaction of some aesthetic craving: great
religions in their crusading youth spread through the nations the peace
of Heaven and the sword of the Lord.

The sixteenth century of our era saw the disruption of Western
Christianity and the rise of modern science. It was an age of ferment.
Nothing was settled, though much was opened—new worlds and new ideas. In
science, Copernicus and Vesalius may be chosen as representative
figures: they typify the new cosmology and the scientific emphasis on
direct observation. Giordano Bruno was the martyr; but the cause for
which he suffered was not that of science, but that of free imaginative
speculation. His death in the year 1600 ushered in the first century of
modern science in the strict sense of the term. In his execution there
was an unconscious symbolism: for the subsequent tone of scientific
thought has contained distrust of his type of general speculativeness.
The Reformation, for all its importance, may be considered as a domestic
affair of the European races. Even the Christianity of the East viewed
it with profound disengagement. Furthermore, such disruptions are no new
phenomena in the history of Christianity or of other religions. When we
project this great revolution upon the whole history of the Christian
Church, we cannot look upon it as introducing a new principle into human
life. For good or for evil, it was a great transformation of religion;
but it was not the coming of religion. It did not itself claim to be so.
Reformers maintained that they were only restoring what had been
forgotten.

It is quite otherwise with the rise of modern science. In every way it
contrasts with the contemporary religious movement. The Reformation was
a popular uprising, and for a century and a half drenched Europe in
blood. The beginnings of the scientific movement were confined to a
minority among the intellectual élite. In a generation which saw the
Thirty Years’ War and remembered Alva in the Netherlands, the worst that
happened to men of science was that Galileo suffered an honourable
detention and a mild reproof, before dying peacefully in his bed. The
way in which the persecution of Galileo has been remembered is a tribute
to the quiet commencement of the most intimate change in outlook which
the human race had yet encountered. Since a babe was born in a manger,
it may be doubted whether so great a thing has happened with so little
stir.

The thesis which these lectures will illustrate is that this quiet
growth of science has practically recoloured our mentality so that modes
of thought which in former times were exceptional, are now broadly
spread through the educated world. This new colouring of ways of thought
had been proceeding slowly for many ages in the European peoples. At
last it issued in the rapid development of science; and has thereby
strengthened itself by its most obvious application. The new mentality
is more important even than the new science and the new technology. It
has altered the metaphysical presuppositions and the imaginative
contents of our minds; so that now the old stimuli provoke a new
response. Perhaps my metaphor of a new colour is too strong. What I mean
is just that slightest change of tone which yet makes all the
difference. This is exactly illustrated by a sentence from a published
letter of that adorable genius, William James. When he was finishing his
great treatise on the _Principles of Psychology_, he wrote to his
brother Henry James, ‘I have to forge every sentence in the teeth of
irreducible and stubborn facts.’

This new tinge to modern minds is a vehement and passionate interest in
the relation of general principles to irreducible and stubborn facts.
All the world over and at all times there have been practical men,
absorbed in ‘irreducible and stubborn facts’: all the world over and at
all times there have been men of philosophic temperament who have been
absorbed in the weaving of general principles. It is this union of
passionate interest in the detailed facts with equal devotion to
abstract generalisation which forms the novelty in our present society.
Previously it had appeared sporadically and as if by chance. This
balance of mind has now become part of the tradition which infects
cultivated thought. It is the salt which keeps life sweet. The main
business of universities is to transmit this tradition as a widespread
inheritance from generation to generation.

Another contrast which singles out science from among the European
movements of the sixteenth and seventeenth centuries, is its
universality. Modern science was born in Europe, but its home is the
whole world. In the last two centuries there has been a long and
confused impact of Western modes upon the civilisation of Asia. The wise
men of the East have been puzzling, and are puzzling, as to what may be
the regulative secret of life which can be passed from West to East
without the wanton destruction of their own inheritance which they so
rightly prize. More and more it is becoming evident that what the West
can most readily give to the East is its science and its scientific
outlook. This is transferable from country to country, and from race to
race, wherever there is a rational society.

In this course of lectures I shall not discuss the details of scientific
discovery. My theme is the energising of a state of mind in the modern
world, its broad generalisations, and its impact upon other spiritual
forces. There are two ways of reading history, forwards and backwards.
In the history of thought, we require both methods. A climate of
opinion—to use the happy phrase of a seventeenth century writer—requires
for its understanding the consideration of its antecedents and its
issues. Accordingly in this lecture I shall consider some of the
antecedents of our modern approach to the investigation of nature.

In the first place, there can be no living science unless there is a
widespread instinctive conviction in the existence of an _Order of
Things_, and, in particular, of an _Order of Nature_. I have used the
word _instinctive_ advisedly. It does not matter what men say in words,
so long as their activities are controlled by settled instincts. The
words may ultimately destroy the instincts. But until this has occurred,
words do not count. This remark is important in respect to the history
of scientific thought. For we shall find that since the time of Hume,
the fashionable scientific philosophy has been such as to deny the
rationality of science. This conclusion lies upon the surface of Hume’s
philosophy. Take, for example, the following passage from Section IV of
his _Inquiry Concerning Human Understanding_:

  “In a word, then, every effect is a distinct event from its cause. It
  could not, therefore, be discovered in the cause; and the first
  invention or conception of it, _à priori_, must be entirely
  arbitrary.”

If the cause in itself discloses no information as to the effect, so
that the first invention of it must be _entirely_ arbitrary, it follows
at once that science is impossible, except in the sense of establishing
_entirely arbitrary_ connections which are not warranted by anything
intrinsic to the natures either of causes or effects. Some variant of
Hume’s philosophy has generally prevailed among men of science. But
scientific faith has risen to the occasion, and has tacitly removed the
philosophic mountain.

In view of this strange contradiction in scientific thought, it is of
the first importance to consider the antecedents of a faith which is
impervious to the demand for a consistent rationality. We have therefore
to trace the rise of the instinctive faith that there is an Order of
Nature which can be traced in every detailed occurrence.

Of course we all share in this faith, and we therefore believe that the
reason for the faith is our apprehension of its truth. But the formation
of a general idea—such as the idea of the Order of Nature—, and the
grasp of its importance, and the observation of its exemplification in a
variety of occasions are by no means the necessary consequences of the
truth of the idea in question. Familiar things happen, and mankind does
not bother about them. It requires a very unusual mind to undertake the
analysis of the obvious. Accordingly I wish to consider the stages in
which this analysis became explicit, and finally became unalterably
impressed upon the educated minds of Western Europe.

Obviously, the main recurrences of life are too insistent to escape the
notice of the least rational of humans; and even before the dawn of
rationality, they have impressed themselves upon the instincts of
animals. It is unnecessary to labour the point, that in broad outline
certain general states of nature recur, and that our very natures have
adapted themselves to such repetitions.

But there is a complementary fact which is equally true and equally
obvious:—nothing ever really recurs in exact detail. No two days are
identical, no two winters. What has gone, has gone forever. Accordingly
the practical philosophy of mankind has been to expect the broad
recurrences, and to accept the details as emanating from the inscrutable
womb of things, beyond the ken of rationality. Men expected the sun to
rise, but the wind bloweth where it listeth.

Certainly from the classical Greek civilisation onwards there have been
men, and indeed groups of men, who have placed themselves beyond this
acceptance of an ultimate irrationality. Such men have endeavoured to
explain all phenomena as the outcome of an order of things which extends
to every detail. Geniuses such as Aristotle, or Archimedes, or Roger
Bacon, must have been endowed with the full scientific mentality, which
instinctively holds that all things great and small are conceivable as
exemplifications of general principles which reign throughout the
natural order.

But until the close of the Middle Ages the general educated public did
not feel that intimate conviction, and that detailed interest, in such
an idea, so as to lead to an unceasing supply of men, with ability and
opportunity adequate to maintain a coordinated search for the discovery
of these hypothetical principles. Either people were doubtful about the
existence of such principles, or were doubtful about any success in
finding them, or took no interest in thinking about them, or were
oblivious to their practical importance when found. For whatever reason,
search was languid, if we have regard to the opportunities of a high
civilisation and the length of time concerned. Why did the pace suddenly
quicken in the sixteenth and seventeenth centuries? At the close of the
Middle Ages a new mentality discloses itself. Invention stimulated
thought, thought quickened physical speculation, Greek manuscripts
disclosed what the ancients had discovered. Finally although in the year
1500 Europe knew less than Archimedes who died in the year 212 B. C.,
yet in the year 1700, Newton’s _Principia_ had been written and the
world was well started on the modern epoch.

There have been great civilisations in which the peculiar balance of
mind required for science has only fitfully appeared and has produced
the feeblest result. For example, the more we know of Chinese art, of
Chinese literature, and of the Chinese philosophy of life, the more we
admire the heights to which that civilization attained. For thousands of
years, there have been in China acute and learned men patiently devoting
their lives to study. Having regard to the span of time, and to the
population concerned, China forms the largest volume of civilisation
which the world has seen. There is no reason to doubt the intrinsic
capacity of individual Chinamen for the pursuit of science. And yet
Chinese science is practically negligible. There is no reason to believe
that China if left to itself would have ever produced any progress in
science. The same may be said of India. Furthermore, if the Persians had
enslaved the Greeks, there is no definite ground for belief that science
would have flourished in Europe. The Romans showed no particular
originality in that line. Even as it was, the Greeks, though they
founded the movement, did not sustain it with the concentrated interest
which modern Europe has shown. I am not alluding to the last few
generations of the European peoples on both sides of the ocean; I mean
the smaller Europe of the Reformation period, distracted as it was with
wars and religious disputes. Consider the world of the eastern
Mediterranean, from Sicily to western Asia, during the period of about
1400 years from the death of Archimedes [in 212 B. C.] to the irruption
of the Tartars. There were wars and revolutions and large changes of
religion: but nothing much worse than the wars of the sixteenth and
seventeenth centuries throughout Europe. There was a great and wealthy
civilisation, Pagan, Christian, Mahometan. In that period a great deal
was added to science. But on the whole the progress was slow and
wavering; and, except in mathematics, the men of the Renaissance
practically started from the position which Archimedes had reached.
There had been some progress in medicine and some progress in astronomy.
But the total advance was very little compared to the marvellous success
of the seventeenth century. For example, compare the progress of
scientific knowledge from the year 1560, just before the births of
Galileo and of Kepler, up to the year 1700, when Newton was in the
height of his fame, with the progress in the ancient period, already
mentioned, exactly ten times as long.

Nevertheless, Greece was the mother of Europe; and it is to Greece that
we must look in order to find the origin of our modern ideas. We all
know that on the eastern shores of the Mediterranean there was a very
flourishing school of Ionian philosophers, deeply interested in theories
concerning nature. Their ideas have been transmitted to us, enriched by
the genius of Plato and Aristotle. But, with the exception of Aristotle,
and it is a large exception, this school of thought had not attained to
the complete scientific mentality. In some ways, it was better. The
Greek genius was philosophical, lucid and logical. The men of this group
were primarily asking philosophical questions. What is the substratum of
nature? Is it fire, or earth, or water, or some combination of any two,
or of all three? Or is it a mere flux, not reducible to some static
material? Mathematics interested them mightily. They invented its
generality, analysed its premises, and made notable discoveries of
theorems by a rigid adherence to deductive reasoning. Their minds were
infected with an eager generality. They demanded clear, bold ideas, and
strict reasoning from them. All this was excellent; it was genius; it
was ideal preparatory work. But it was not science as we understand it.
The patience of minute observation was not nearly so prominent. Their
genius was not so apt for the state of imaginative muddled suspense
which precedes successful inductive generalisation. They were lucid
thinkers and bold reasoners.

Of course there were exceptions, and at the very top: for example,
Aristotle and Archimedes. Also for patient observation, there were the
astronomers. There was a mathematical lucidity about the stars, and a
fascination about the small numerable band of run-a-way planets.

Every philosophy is tinged with the colouring of some secret imaginative
background, which never emerges explicitly into its trains of reasoning.
The Greek view of nature, at least that cosmology transmitted from them
to later ages, was essentially dramatic. It is not necessarily wrong for
this reason: but it was overwhelmingly dramatic. It thus conceived
nature as articulated in the way of a work of dramatic art, for the
exemplification of general ideas converging to an end. Nature was
differentiated so as to provide its proper end for each thing. There was
the centre of the universe as the end of motion for those things which
are heavy, and the celestial spheres as the end of motion for those
things whose natures lead them upwards. The celestial spheres were for
things which are impassible and ingenerable, the lower regions for
things impassible and generable. Nature was a drama in which each thing
played its part.

I do not say that this is a view to which Aristotle would have
subscribed without severe reservations, in fact without the sort of
reservations which we ourselves would make. But it was the view which
subsequent Greek thought extracted from Aristotle and passed on to the
Middle Ages. The effect of such an imaginative setting for nature was to
damp down the historical spirit. For it was the end which seemed
illuminating, so why bother about the beginning? The Reformation and the
scientific movement were two aspects of the historical revolt which was
the dominant intellectual movement of the later Renaissance. The appeal
to the origins of Christianity, and Francis Bacon’s appeal to efficient
causes as against final causes, were two sides of one movement of
thought. Also for this reason Galileo and his adversaries were at
hopeless cross purposes, as can be seen from his _Dialogues on the Two
Systems of the World_.

Galileo keeps harping on how things happen, whereas his adversaries had
a complete theory as to why things happen. Unfortunately the two
theories did not bring out the same results. Galileo insists upon
‘irreducible and stubborn facts,’ and Simplicius, his opponent, brings
forward reasons, completely satisfactory, at least to himself. It is a
great mistake to conceive this historical revolt as an appeal to reason.
On the contrary, it was through and through an anti-intellectualist
movement. It was the return to the contemplation of brute fact; and it
was based on a recoil from the inflexible rationality of medieval
thought. In making this statement I am merely summarising what at the
time the adherents of the old régime themselves asserted. For example,
in the fourth book of Father Paul Sarpi’s _History of the Council of
Trent_, you will find that in the year 1551 the Papal Legates who
presided over the Council ordered: ‘That the Divines ought to confirm
their opinions with the holy Scripture, Traditions of the Apostles,
sacred and approved Councils, and by the Constitutions and Authorities
of the holy Fathers; that they ought to use brevity, and avoid
superfluous and unprofitable questions, and perverse contentions....
This order did not please the Italian Divines; who said it was a novity,
and a condemning of School-Divinity, which, in all difficulties, _useth
reason_, and because it was not lawful [_i.e._, by this decree] to treat
as St. Thomas [Aquinas], St. Bonaventure, and other famous men did.’

It is impossible not to feel sympathy with these Italian divines,
maintaining the lost cause of unbridled rationalism. They were deserted
on all hands. The Protestants were in full revolt against them. The
Papacy failed to support them, and the Bishops of the Council could not
even understand them. For a few sentences below the foregoing quotation,
we read: ‘Though many complained here-of [_i.e._, of the Decree], yet it
prevailed but little, because generally the Fathers [_i.e._, the
Bishops] desired to hear men speak with intelligible terms, not
abstrusely, as in the matter of Justification, and others already
handled.’

Poor belated medievalists! When they used reason they were not even
intelligible to the ruling powers of their epoch. It will take centuries
before stubborn facts are reducible by reason, and meanwhile the
pendulum swings slowly and heavily to the extreme of the historical
method.

Forty-three years after the Italian divines had written this memorial,
Richard Hooker in his famous _Laws of Ecclesiastical Polity_ makes
exactly the same complaint of his Puritan adversaries.[1] Hooker’s
balanced thought—from which the appellation ‘The Judicious Hooker’ is
derived—, and his diffuse style, which is the vehicle of such thought,
make his writings singularly unfit for the process of summarising by a
short, pointed quotation. But, in the section referred to, he reproaches
his opponents with _Their Disparagement of Reason_; and in support of
his own position definitely refers to ‘The greatest amongst the
school-divines,’ by which designation I presume that he refers to St.
Thomas Aquinas.

Footnote 1:

  _Cf._ Book III, Section VIII.

Hooker’s _Ecclesiastical Polity_ was published just before Sarpi’s
_Council of Trent_. Accordingly there was complete independence between
the two works. But both the Italian divines of 1551, and Hooker at the
end of that century testify to the anti-rationalist trend of thought at
that epoch, and in this respect contrast their own age with the epoch of
scholasticism.

This reaction was undoubtedly a very necessary corrective to the
unguarded rationalism of the Middle Ages. But reactions run to extremes.
Accordingly, although one outcome of this reaction was the birth of
modern science, yet we must remember that science thereby inherited the
bias of thought to which it owes its origin.

The effect of Greek dramatic literature was many-sided so far as
concerns the various ways in which it indirectly affected medieval
thought. The pilgrim fathers of the scientific imagination as it exists
today, are the great tragedians of ancient Athens, Aeschylus, Sophocles,
Euripides. Their vision of fate, remorseless and indifferent, urging a
tragic incident to its inevitable issue, is the vision possessed by
science. Fate in Greek Tragedy becomes the order of nature in modern
thought. The absorbing interest in the particular heroic incidents, as
an example and a verification of the workings of fate, reappears in our
epoch as concentration of interest on the crucial experiments. It was my
good fortune to be present at the meeting of the Royal Society in London
when the Astronomer Royal for England announced that the photographic
plates of the famous eclipse, as measured by his colleagues in Greenwich
Observatory, had verified the prediction of Einstein that rays of light
are bent as they pass in the neighbourhood of the sun. The whole
atmosphere of tense interest was exactly that of the Greek drama: we
were the chorus commenting on the decree of destiny as disclosed in the
development of a supreme incident. There was dramatic quality in the
very staging:—the traditional ceremonial, and in the background the
picture of Newton to remind us that the greatest of scientific
generalisations was now, after more than two centuries, to receive its
first modification. Nor was the personal interest wanting: a great
adventure in thought had at length come safe to shore.

Let me here remind you that the essence of dramatic tragedy is not
unhappiness. It resides in the solemnity of the remorseless working of
things. This inevitableness of destiny can only be illustrated in terms
of human life by incidents which in fact involve unhappiness. For it is
only by them that the futility of escape can be made evident in the
drama. This remorseless inevitableness is what pervades scientific
thought. The laws of physics are the decrees of fate.

The conception of the moral order in the Greek plays was certainly not a
discovery of the dramatists. It must have passed into the literary
tradition from the general serious opinion of the times. But in finding
this magnificent expression, it thereby deepened the stream of thought
from which it arose. The spectacle of a moral order was impressed upon
the imagination of classical civilisation.

The time came when that great society decayed, and Europe passed into
the Middle Ages. The direct influence of Greek literature vanished. But
the concept of the moral order and of the order of nature had enshrined
itself in the Stoic philosophy. For example, Lecky in his _History of
European Morals_ tells us ‘Seneca maintains that the Divinity has
determined all things by an inexorable law of destiny, which He has
decreed, but which He Himself obeys.’ But the most effective way in
which the Stoics influenced the mentality of the Middle Ages was by the
diffused sense of order which arose from Roman law. Again to quote
Lecky, ‘The Roman legislation was in a two-fold manner the child of
philosophy. It was in the first place formed upon the philosophical
model, for, instead of being a mere empirical system adjusted to the
existing requirements of society, it laid down abstract principles of
right to which it endeavoured to conform; and, in the next place, these
principles were borrowed directly from Stoicism.’ In spite of the actual
anarchy throughout large regions in Europe after the collapse of the
Empire, the sense of legal order always haunted the racial memories of
the Imperial populations. Also the Western Church was always there as a
living embodiment of the traditions of Imperial rule.

It is important to notice that this legal impress upon medieval
civilisation was not in the form of a few wise precepts which should
permeate conduct. It was the conception of a definite articulated system
which defines the legality of the detailed structure of social organism,
and of the detailed way in which it should function. There was nothing
vague. It was not a question of admirable maxims, but of definite
procedure to put things right and to keep them there. The Middle Ages
formed one long training of the intellect of Western Europe in the sense
of order. There may have been some deficiency in respect to practice.
But the idea never for a moment lost its grip. It was preëminently an
epoch of orderly thought, rationalist through and through. The very
anarchy quickened the sense for coherent system; just as the modern
anarchy of Europe has stimulated the intellectual vision of a League of
Nations.

But for science something more is wanted than a general sense of the
order in things. It needs but a sentence to point out how the habit of
definite exact thought was implanted in the European mind by the long
dominance of scholastic logic and scholastic divinity. The habit
remained after the philosophy had been repudiated, the priceless habit
of looking for an exact point and of sticking to it when found. Galileo
owes more to Aristotle than appears on the surface of his _Dialogues_:
he owes to him his clear head and his analytic mind.

I do not think, however, that I have even yet brought out the greatest
contribution of medievalism to the formation of the scientific movement.
I mean the inexpugnable belief that every detailed occurrence can be
correlated with its antecedents in a perfectly definite manner,
exemplifying general principles. Without this belief the incredible
labours of scientists would be without hope. It is this instinctive
conviction, vividly poised before the imagination, which is the motive
power of research:—that there is a secret, a secret which can be
unveiled. How has this conviction been so vividly implanted on the
European mind?

When we compare this tone of thought in Europe with the attitude of
other civilisations when left to themselves, there seems but one source
for its origin. It must come from the medieval insistence on the
rationality of God, conceived as with the personal energy of Jehovah and
with the rationality of a Greek philosopher. Every detail was supervised
and ordered: the search into nature could only result in the vindication
of the faith in rationality. Remember that I am not talking of the
explicit beliefs of a few individuals. What I mean is the impress on the
European mind arising from the unquestioned faith of centuries. By this
I mean the instinctive tone of thought and not a mere creed of words.

In Asia, the conceptions of God were of a being who was either too
arbitrary or too impersonal for such ideas to have much effect on
instinctive habits of mind. Any definite occurrence might be due to the
fiat of an irrational despot, or might issue from some impersonal,
inscrutable origin of things. There was not the same confidence as in
the intelligible rationality of a personal being. I am not arguing that
the European trust in the scrutability of nature was logically justified
even by its own theology. My only point is to understand how it arose.
My explanation is that the faith in the possibility of science,
generated antecedently to the development of modern scientific theory,
is an unconscious derivative from medieval theology.

But science is not merely the outcome of instinctive faith. It also
requires an active interest in the simple occurrences of life for their
own sake.

This qualification ‘for their own sake’ is important. The first phase of
the Middle Ages was an age of symbolism. It was an age of vast ideas,
and of primitive technique. There was little to be done with nature,
except to coin a hard living from it. But there were realms of thought
to be explored, realms of philosophy and realms of theology. Primitive
art could symbolise those ideas which filled all thoughtful minds. The
first phase of medieval art has a haunting charm beyond compare: its own
intrinsic quality is enhanced by the fact that its message, which
stretched beyond art’s own self-justification of aesthetic achievement,
was the symbolism of things lying behind nature itself. In this symbolic
phase, medieval art energised in nature as its medium, but pointed to
another world.

In order to understand the contrast between these early Middle Ages and
the atmosphere required by the scientific mentality, we should compare
the sixth century in Italy with the sixteenth century. In both centuries
the Italian genius was laying the foundations of a new epoch. The
history of the three centuries preceding the earlier period, despite the
promise for the future introduced by the rise of Christianity, is
overwhelmingly infected by the sense of the decline of civilisation. In
each generation something has been lost. As we read the records, we are
haunted by the shadow of the coming barbarism. There are great men, with
fine achievements in action or in thought. But their total effect is
merely for some short time to arrest the general decline. In the sixth
century we are, so far as Italy is concerned, at the lowest point of the
curve. But in that century every action is laying the foundation for the
tremendous rise of the new European civilisation. In the background the
Byzantine Empire, under Justinian, in three ways determined the
character of the early Middle Ages in Western Europe. In the first
place, its armies, under Belisarius and Narses, cleared Italy from the
Gothic domination. In this way, the stage was freed for the exercise of
the old Italian genius for creating organisations which shall be
protective of ideals of cultural activity. It is impossible not to
sympathise with the Goths: yet there can be no doubt but that a thousand
years of the Papacy were infinitely more valuable for Europe than any
effects derivable from a well-established Gothic kingdom of Italy.

In the second place, the codification of the Roman law established the
ideal of legality which dominated the sociological thought of Europe in
the succeeding centuries. Law is both an engine for government, and a
condition restraining government. The canon law of the Church, and the
civil law of the State, owe to Justinian’s lawyers their influence on
the development of Europe. They established in the Western mind the
ideal that an authority should be at once lawful, and law-enforcing, and
should in itself exhibit a rationally adjusted system of organisation.
The sixth century in Italy gave the initial exhibition of the way in
which the impress of these ideas was fostered by contact with the
Byzantine Empire.

Thirdly, in the non-political spheres of art and learning Constantinople
exhibited a standard of realised achievement which, partly by the
impulse to direct imitation, and partly by the indirect inspiration
arising from the mere knowledge that such things existed, acted as a
perpetual spur to Western culture. The wisdom of the Byzantines, as it
stood in the imagination of the first phase of medieval mentality, and
the wisdom of the Egyptians as it stood in the imagination of the early
Greeks, played analogous rôles. Probably the actual knowledge of these
respective wisdoms was, in either case, about as much as was good for
the recipients. They knew enough to know the sort of standards which are
attainable, and not enough to be fettered by static and traditional ways
of thought. Accordingly, in both cases men went ahead on their own and
did better. No account of the rise of the European scientific mentality
can omit some notice of this influence of the Byzantine civilisation in
the background. In the sixth century there is a crisis in the history of
the relations between the Byzantines and the West; and this crisis is to
be contrasted with the influence of Greek literature on European thought
in the fifteenth and sixteenth centuries. The two outstanding men, who
in the Italy of the sixth century laid the foundations of the future,
were St. Benedict and Gregory the Great. By reference to them, we can at
once see how absolutely in ruins was the approach to the scientific
mentality which had been attained by the Greeks. We are at the zero
point of scientific temperature. But the life-work of Gregory and of
Benedict contributed elements to the reconstruction of Europe which
secured that this reconstruction, when it arrived, should include a more
effective scientific mentality than that of the ancient world. The
Greeks were over-theoretical. For them science was an offshoot of
philosophy. Gregory and Benedict were practical men, with an eye for the
importance of ordinary things; and they combined this practical
temperament with their religious and cultural activities. In particular,
we owe it to St. Benedict that the monasteries were the homes of
practical agriculturalists, as well as of saints and of artists and of
men of learning. The alliance of science with technology, by which
learning is kept in contact with irreducible and stubborn facts, owes
much to the practical bent of the early Benedictines. Modern science
derives from Rome as well as from Greece, and this Roman strain explains
its gain in an energy of thought kept closely in contact with the world
of facts.

But the influence of this contact between the monasteries and the facts
of nature showed itself first in art. The rise of Naturalism in the
later Middle Ages was the entry into the European mind of the final
ingredient necessary for the rise of science. It was the rise of
interest in natural objects, and in natural occurrences, for their own
sakes. The natural foliage of a district was sculptured in
out-of-the-way spots of the later buildings, merely as exhibiting
delight in those familiar objects. The whole atmosphere of every art
exhibited a direct joy in the apprehension of the things which lie
around us. The craftsmen who executed the late medieval decorative
sculpture, Giotto, Chaucer, Wordsworth, Walt Whitman, and, at the
present day, the New England poet Robert Frost, are all akin to each
other in this respect. The simple immediate facts are the topics of
interest, and these reappear in the thought of science as the
‘irreducible stubborn facts.’

The mind of Europe was now prepared for its new venture of thought. It
is unnecessary to tell in detail the various incidents which marked the
rise of science: the growth of wealth and leisure; the expansion of
universities; the invention of printing; the taking of Constantinople;
Copernicus; Vasco da Gama; Columbus; the telescope. The soil, the
climate, the seeds, were there, and the forest grew. Science has never
shaken off the impress of its origin in the historical revolt of the
later Renaissance. It has remained predominantly an anti-rationalistic
movement, based upon a naïve faith. What reasoning it has wanted, has
been borrowed from mathematics which is a surviving relic of Greek
rationalism, following the deductive method. Science repudiates
philosophy. In other words, it has never cared to justify its faith or
to explain its meanings; and has remained blandly indifferent to its
refutation by Hume.

Of course the historical revolt was fully justified. It was wanted. It
was more than wanted: it was an absolute necessity for healthy progress.
The world required centuries of contemplation of irreducible and
stubborn facts. It is difficult for men to do more than one thing at a
time, and that was the sort of thing they had to do after the
rationalistic orgy of the Middle Ages. It was a very sensible reaction;
but it was not a protest on behalf of reason.

There is, however, a Nemesis which waits upon those who deliberately
avoid avenues of knowledge. Oliver Cromwell’s cry echoes down the ages,
‘My brethren, by the bowels of Christ I beseech you, bethink you that
you may be mistaken.’

The progress of science has now reached a turning point. The stable
foundations of physics have broken up: also for the first time
physiology is asserting itself as an effective body of knowledge, as
distinct from a scrap-heap. The old foundations of scientific thought
are becoming unintelligible. Time, space, matter, material, ether,
electricity, mechanism, organism, configuration, structure, pattern,
function, all require reinterpretation. What is the sense of talking
about a mechanical explanation when you do not know what you mean by
mechanics?

The truth is that science started its modern career by taking over ideas
derived from the weakest side of the philosophies of Aristotle’s
successors. In some respects it was a happy choice. It enabled the
knowledge of the seventeenth century to be formularised so far as
physics and chemistry were concerned, with a completeness which has
lasted to the present time. But the progress of biology and psychology
has probably been checked by the uncritical assumption of half-truths.
If science is not to degenerate into a medley of _ad hoc_ hypotheses, it
must become philosophical and must enter upon a thorough criticism of
its own foundations.

In the succeeding lectures of this course, I shall trace the successes
and the failures of the particular conceptions of cosmology with which
the European intellect has clothed itself in the last three centuries.
General climates of opinion persist for periods of about two to three
generations, that is to say, for periods of sixty to a hundred years.
There are also shorter waves of thought, which play on the surface of
the tidal movement. We shall find, therefore, transformations in the
European outlook, slowly modifying the successive centuries. There
persists, however, throughout the whole period the fixed scientific
cosmology which presupposes the ultimate fact of an irreducible brute
matter, or material, spread throughout space in a flux of
configurations. In itself such a material is senseless, valueless,
purposeless. It just does what it does do, following a fixed routine
imposed by external relations which do not spring from the nature of its
being. It is this assumption that I call ‘scientific materialism.’ Also
it is an assumption which I shall challenge as being entirely unsuited
to the scientific situation at which we have now arrived. It is not
wrong, if properly construed. If we confine ourselves to certain types
of facts, abstracted from the complete circumstances in which they
occur, the materialistic assumption expresses these facts to perfection.
But when we pass beyond the abstraction, either by more subtle
employment of our senses, or by the request for meanings and for
coherence of thoughts, the scheme breaks down at once. The narrow
efficiency of the scheme was the very cause of its supreme
methodological success. For it directed attention to just those groups
of facts which, in the state of knowledge then existing, required
investigation.

The success of the scheme has adversely affected the various currents of
European thought. The historical revolt was anti-rationalistic, because
the rationalism of the scholastics required a sharp correction by
contact with brute fact. But the revival of philosophy in the hands of
Descartes and his successors was entirely coloured in its development by
the acceptance of the scientific cosmology at its face value. The
success of their ultimate ideas confirmed scientists in their refusal to
modify them as the result of an enquiry into their rationality. Every
philosophy was bound in some way or other to swallow them whole. Also
the example of science affected other regions of thought. The historical
revolt has thus been exaggerated into the exclusion of philosophy from
its proper rôle of harmonising the various abstractions of
methodological thought. Thought is abstract; and the intolerant use of
abstractions is the major vice of the intellect. This vice is not wholly
corrected by the recurrence to concrete experience. For after all, you
need only attend to those aspects of your concrete experience which lie
within some limited scheme. There are two methods for the purification
of ideas. One of them is dispassionate observation by means of the
bodily senses. But observation is selection. Accordingly, it is
difficult to transcend a scheme of abstraction whose success is
sufficiently wide. The other method is by comparing the various schemes
of abstraction which are well founded in our various types of
experience. This comparison takes the form of satisfying the demands of
the Italian scholastic divines whom Paul Sarpi mentioned. They asked
that _reason_ should be used. Faith in reason is the trust that the
ultimate natures of things lie together in a harmony which excludes mere
arbitrariness. It is the faith that at the base of things we shall not
find mere arbitrary mystery. The faith in the order of nature which has
made possible the growth of science is a particular example of a deeper
faith. This faith cannot be justified by any inductive generalisation.
It springs from direct inspection of the nature of things as disclosed
in our own immediate present experience. There is no parting from your
own shadow. To experience this faith is to know that in being ourselves
we are more than ourselves: to know that our experience, dim and
fragmentary as it is, yet sounds the utmost depths of reality: to know
that detached details merely in order to be themselves demand that they
should find themselves in a system of things: to know that this system
includes the harmony of logical rationality, and the harmony of
aesthetic achievement: to know that, while the harmony of logic lies
upon the universe as an iron necessity, the aesthetic harmony stands
before it as a living ideal moulding the general flux in its broken
progress towards finer, subtler issues.




                               CHAPTER II

                      MATHEMATICS AS AN ELEMENT IN
                         THE HISTORY OF THOUGHT


The science of Pure Mathematics, in its modern developments, may claim
to be the most original creation of the human spirit. Another claimant
for this position is music. But we will put aside all rivals, and
consider the ground on which such a claim can be made for mathematics.
The originality of mathematics consists in the fact that in mathematical
science connections between things are exhibited which, apart from the
agency of human reason, are extremely unobvious. Thus the ideas, now in
the minds of contemporary mathematicians, lie very remote from any
notions which can be immediately derived by perception through the
senses; unless indeed it be perception stimulated and guided by
antecedent mathematical knowledge. This is the thesis which I proceed to
exemplify.

Suppose we project our imaginations backwards through many thousands of
years, and endeavour to realise the simple-mindedness of even the
greatest intellects in those early societies. Abstract ideas which to us
are immediately obvious must have been, for them, matters only of the
most dim apprehension. For example take the question of number. We think
of the number ‘five’ as applying to appropriate groups of any entities
whatsoever—to five fishes, five children, five apples, five days. Thus
in considering the relations of the number ‘five’ to the number ‘three,’
we are thinking of two groups of things, one with five members and the
other with three members. But we are entirely abstracting from any
consideration of any particular entities, or even of any particular
sorts of entities, which go to make up the membership of either of the
two groups. We are merely thinking of those relationships between those
two groups which are entirely independent of the individual essences of
any of the members of either group. This is a very remarkable feat of
abstraction; and it must have taken ages for the human race to rise to
it. During a long period, groups of fishes will have been compared to
each other in respect to their multiplicity, and groups of days to each
other. But the first man who noticed the analogy between a group of
seven fishes and a group of seven days made a notable advance in the
history of thought. He was the first man who entertained a concept
belonging to the science of pure mathematics. At that moment it must
have been impossible for him to divine the complexity and subtlety of
these abstract mathematical ideas which were waiting for discovery. Nor
could he have guessed that these notions would exert a widespread
fascination in each succeeding generation. There is an erroneous
literary tradition which represents the love of mathematics as a
monomania confined to a few eccentrics in each generation. But be this
as it may, it would have been impossible to anticipate the pleasure
derivable from a type of abstract thinking which had no counterpart in
the then-existing society. Thirdly, the tremendous future effect of
mathematical knowledge on the lives of men, on their daily avocations,
on their habitual thoughts, on the organization of society, must have
been even more completely shrouded from the foresight of those early
thinkers. Even now there is a very wavering grasp of the true position
of mathematics as an element in the history of thought. I will not go so
far as to say that to construct a history of thought without profound
study of the mathematical ideas of successive epochs is like omitting
Hamlet from the play which is named after him. That would be claiming
too much. But it is certainly analogous to cutting out the part of
Ophelia. This simile is singularly exact. For Ophelia is quite essential
to the play, she is very charming,—and a little mad. Let us grant that
the pursuit of mathematics is a divine madness of the human spirit, a
refuge from the goading urgency of contingent happenings.

When we think of mathematics, we have in our mind a science devoted to
the exploration of number, quantity, geometry, and in modern times also
including investigation into yet more abstract concepts of order, and
into analogous types of purely logical relations. The point of
mathematics is that in it we have always got rid of the particular
instance, and even of any particular sorts of entities. So that for
example, no mathematical truths apply merely to fish, or merely to
stones, or merely to colours. So long as you are dealing with pure
mathematics, you are in the realm of complete and absolute abstraction.
All you assert is, that reason insists on the admission that, if any
entities whatever have any relations which satisfy such-and-such purely
abstract conditions, then they must have other relations which satisfy
other purely abstract conditions.

Mathematics is thought moving in the sphere of complete abstraction from
any particular instance of what it is talking about. So far is this view
of mathematics from being obvious, that we can easily assure ourselves
that it is not, even now, generally understood. For example, it is
habitually thought that the certainty of mathematics is a reason for the
certainty of our geometrical knowledge of the space of the physical
universe. This is a delusion which has vitiated much philosophy in the
past, and some philosophy in the present. This question of geometry is a
test case of some urgency. There are certain alternative sets of purely
abstract conditions possible for the relationships of groups of
unspecified entities, which I will call _geometrical conditions_. I give
them this name because of their general analogy to those conditions,
which we believe to hold respecting the particular geometrical relations
of things observed by us in our direct perception of nature. So far as
our observations are concerned, we are not quite accurate enough to be
certain of the exact conditions regulating the things we come across in
nature. But we can by a slight stretch of hypothesis identify these
observed conditions with some one set of the purely abstract geometrical
conditions. In doing so, we make a particular determination of the group
of unspecified entities which are the _relata_ in the abstract science.
In the pure mathematics of geometrical relationships, we say that, if
_any_ group of entities enjoy _any_ relationships among its members
satisfying _this_ set of abstract geometrical conditions, then
such-and-such additional abstract conditions must also hold for such
relationships. But when we come to physical space, we say that some
definitely observed group of physical entities enjoys some definitely
observed relationships among its members which do satisfy this
above-mentioned set of abstract geometrical conditions. We thence
conclude that the additional relationships which we concluded to hold in
_any_ such case, must therefore hold in _this particular_ case.

The certainty of mathematics depends upon its complete abstract
generality. But we can have no _à priori_ certainty that we are right in
believing that the observed entities in the concrete universe form a
particular instance of what falls under our general reasoning. To take
another example from arithmetic. It is a general abstract truth of pure
mathematics that any group of forty entities can be subdivided into two
groups of twenty entities. We are therefore justified in concluding that
a particular group of apples which we believe to contain forty members
can be subdivided into two groups of apples of which each contains
twenty members. But there always remains the possibility that we have
miscounted the big group; so that, when we come in practice to subdivide
it, we shall find that one of the two heaps has an apple too few or an
apple too many.

Accordingly, in criticising an argument based upon the application of
mathematics to particular matters of fact, there are always three
processes to be kept perfectly distinct in our minds. We must first scan
the purely mathematical reasoning to make sure that there are no mere
slips in it—no casual illogicalities due to mental failure. Any
mathematician knows from bitter experience that, in first elaborating a
train of reasoning, it is very easy to commit a slight error which yet
makes all the difference. But when a piece of mathematics has been
revised, and has been before the expert world for some time, the chance
of a casual error is almost negligible. The next process is to make
quite certain of all the abstract conditions which have been presupposed
to hold. This is the determination of the abstract premises from which
the mathematical reasoning proceeds. This is a matter of considerable
difficulty. In the past quite remarkable oversights have been made, and
have been accepted by generations of the greatest mathematicians. The
chief danger is that of oversight, namely, tacitly to introduce some
condition, which it is natural for us to presuppose, but which in fact
need not always be holding. There is another opposite oversight in this
connection which does not lead to error, but only to lack of
simplification. It is very easy to think that more postulated conditions
are required than is in fact the case. In other words, we may think that
some abstract postulate is necessary which is in fact capable of being
proved from the other postulates that we have already on hand. The only
effects of this excess of abstract postulates are to diminish our
aesthetic pleasure in the mathematical reasoning, and to give us more
trouble when we come to the third process of criticism.

This third process of criticism is that of verifying that our abstract
postulates hold for the particular case in question. It is in respect to
this process of verification for the particular case that all the
trouble arises. In some simple instances, such as the counting of forty
apples, we can with a little care arrive at practical certainty. But in
general, with more complex instances, complete certainty is
unattainable. Volumes, libraries of volumes, have been written on the
subject. It is the battle ground of rival philosophers. There are two
distinct questions involved. There are particular definite things
observed, and we have to make sure that the relations between these
things really do obey certain definite exact abstract conditions. There
is great room for error here. The exact observational methods of science
are all contrivances for limiting these erroneous conclusions as to
direct matters of fact. But another question arises. The things directly
observed are, almost always, only samples. We want to conclude that the
abstract conditions, which hold for the samples, also hold for all other
entities which, for some reason or other, appear to us to be of the same
sort. This process of reasoning from the sample to the whole species is
Induction. The theory of Induction is the despair of philosophy—and yet
all our activities are based upon it. Anyhow, in criticising a
mathematical conclusion as to a particular matter of fact, the real
difficulties consist in finding out the abstract assumptions involved,
and in estimating the evidence for their applicability to the particular
case in hand.

It often happens, therefore, that in criticising a learned book of
applied mathematics, or a memoir, one’s whole trouble is with the first
chapter, or even with the first page. For it is there, at the very
outset, where the author will probably be found to slip in his
assumptions. Farther, the trouble is not with what the author does say,
but with what he does not say. Also it is not with what he knows he has
assumed, but with what he has unconsciously assumed. We do not doubt the
author’s honesty. It is his perspicacity which we are criticising. Each
generation criticises the unconscious assumptions made by its parents.
It may assent to them, but it brings them out in the open.

The history of the development of language illustrates this point. It is
a history of the progressive analysis of ideas. Latin and Greek were
inflected languages. This means that they express an unanalyzed complex
of ideas by the mere modification of a word; whereas in English, for
example, we use prepositions and auxiliary verbs to drag into the open
the whole bundle of ideas involved. For certain forms of literary
art,—though not always—the compact absorption of auxiliary ideas into
the main word may be an advantage. But in a language such as English
there is the overwhelming gain in explicitness. This increased
explicitness is a more complete exhibition of the various abstractions
involved in the complex idea which is the meaning of the sentence.

By comparison with language, we can now see what is the function in
thought which is performed by pure mathematics. It is a resolute attempt
to go the whole way in the direction of complete analysis, so as to
separate the elements of mere matter of fact from the purely abstract
conditions which they exemplify.

The habit of such analysis enlightens every act of the functioning of
the human mind. It first (by isolating it) emphasizes the direct
aesthetic appreciation of the content of experience. This direct
appreciation means an apprehension of what this experience is in itself
in its own particular essence, including its immediate concrete values.
This is a question of direct experience, dependent upon sensitive
subtlety. There is then the abstraction of the particular entities
involved, viewed in themselves, and as apart from that particular
occasion of experience in which we are then apprehending them. Lastly
there is the further apprehension of the absolutely general conditions
satisfied by the particular relations of those entities as in that
experience. These conditions gain their generality from the fact that
they are expressible without reference to those particular relations or
to those particular relata which occur in that particular occasion of
experience. They are conditions which might hold for an indefinite
variety of other occasions, involving other entities and other relations
between them. Thus these conditions are perfectly general because they
refer to no particular occasion, and to no particular entities (such as
green, or blue, or trees) which enter into a variety of occasions, and
to no particular relationships between such entities.

There is, however, a limitation to be made to the generality of
mathematics; it is a qualification which applies equally to all general
statements. No statement, except one, can be made respecting any remote
occasion which enters into no relationship with the immediate occasion
so as to form a constitutive element of the essence of that immediate
occasion. By the ‘immediate occasion’ I mean that occasion which
involves as an ingredient the individual act of judgment in question.
The one excepted statement is,—If anything out of relationship, then
complete ignorance as to it. Here by ‘ignorance,’ I mean _ignorance_;
accordingly no advice can be given as to how to expect it, or to treat
it, in ‘practice’ or in any other way. Either we know something of the
remote occasion by the cognition which is itself an element of the
immediate occasion, or we know nothing. Accordingly the full universe,
disclosed for every variety of experience, is a universe in which every
detail enters into its proper relationship with the immediate occasion.
The generality of mathematics is the most complete generality consistent
with the community of occasions which constitutes our metaphysical
situation.

It is further to be noticed that the particular entities require these
general conditions for their ingression into any occasions; but the same
general conditions may be required by many types of particular entities.
This fact, that the general conditions transcend any one set of
particular entities, is the ground for the entry into mathematics, and
into mathematical logic, of the notion of the ‘variable.’ It is by the
employment of this notion that general conditions are investigated
without any specification of particular entities. This irrelevance of
the particular entities has not been generally understood: for example,
the shape-iness of shapes, _e.g._, circularity and sphericity and
cubicality as in actual experience, do not enter into the geometrical
reasoning.

The exercise of logical reason is always concerned with these absolutely
general conditions. In its broadest sense, the discovery of mathematics
is the discovery that the totality of these general abstract conditions,
which are concurrently applicable to the relationships among the
entities of any one concrete occasion, are themselves inter-connected in
the manner of a pattern with a key to it. This pattern of relationships
among general abstract conditions is imposed alike on external reality,
and on our abstract representations of it, by the general necessity that
every thing must be just its own individual self, with its own
individual way of differing from everything else. This is nothing else
than the necessity of abstract logic, which is the presupposition
involved in the very fact of interrelated existence as disclosed in each
immediate occasion of experience.

The key to the pattern means this fact:—that from a select set of those
general conditions, exemplified in any one and the same occasion, a
pattern involving an infinite variety of other such conditions, also
exemplified in the same occasion, can be developed by the pure exercise
of abstract logic. Any such select set is called the set of postulates,
or premises, from which the reasoning proceeds. The reasoning is nothing
else than the exhibition of the whole pattern of general conditions
involved in the pattern derived from the selected postulates.

The harmony of the logical reason, which divines the complete pattern as
involved in the postulates, is the most general aesthetic property
arising from the mere fact of concurrent existence in the unity of one
occasion. Wherever there is a unity of occasion there is thereby
established an aesthetic relationship between the general conditions
involved in that occasion. This aesthetic relationship is that which is
divined in the exercise of rationality. Whatever falls within that
relationship is thereby exemplified in that occasion; whatever falls
without that relationship is thereby excluded from exemplification in
that occasion. The complete pattern of general conditions, thus
exemplified, is determined by any one of many select sets of these
conditions. These key sets are sets of equivalent postulates. This
reasonable harmony of being, which is required for the unity of a
complex occasion, together with the completeness of the realisation (in
that occasion) of all that is involved in its logical harmony, is the
primary article of metaphysical doctrine. It means that for things to be
together involves that they are reasonably together. This means that
thought can penetrate into every occasion of fact, so that by
comprehending its key conditions, the whole complex of its pattern of
conditions lies open before it. It comes to this:—provided we know
something which is perfectly general about the elements in any occasion,
we can then know an indefinite number of other equally general concepts
which must also be exemplified in that same occasion. The logical
harmony involved in the unity of an occasion is both exclusive and
inclusive. The occasion must exclude the inharmonious, and it must
include the harmonious.

Pythagoras was the first man who had any grasp of the full sweep of this
general principle. He lived in the sixth century before Christ. Our
knowledge of him is fragmentary. But we know some points which establish
his greatness in the history of thought. He insisted on the importance
of the utmost generality in reasoning, and he divined the importance of
number as an aid to the construction of any representation of the
conditions involved in the order of nature. We know also that he studied
geometry, and discovered the general proof of the remarkable theorem
about right-angled triangles. The formation of the Pythagorean
Brotherhood, and the mysterious rumours as to its rites and its
influence, afford some evidence that Pythagoras divined, however dimly,
the possible importance of mathematics in the formation of science. On
the side of philosophy he started a discussion which has agitated
thinkers ever since. He asked, ‘What is the status of mathematical
entities, such as numbers for example, in the realm of things?’ The
number ‘two,’ for example, is in some sense exempt from the flux of time
and the necessity of position in space. Yet it is involved in the real
world. The same considerations apply to geometrical notions—to circular
shape, for example. Pythagoras is said to have taught that the
mathematical entities, such as numbers and shapes, were the ultimate
stuff out of which the real entities of our perceptual experience are
constructed. As thus boldly stated, the idea seems crude, and indeed
silly. But undoubtedly, he had hit upon a philosophical notion of
considerable importance; a notion which has a long history, and which
has moved the minds of men, and has even entered into Christian
theology. About a thousand years separate the Athanasian Creed from
Pythagoras, and about two thousand four hundred years separate
Pythagoras from Hegel. Yet for all these distances in time, the
importance of definite number in the constitution of the Divine Nature,
and the concept of the real world as exhibiting the evolution of an
idea, can both be traced back to the train of thought set going by
Pythagoras.

The importance of an individual thinker owes something to chance. For it
depends upon the fate of his ideas in the minds of his successors. In
this respect Pythagoras was fortunate. His philosophical speculations
reach us through the mind of Plato. The Platonic world of ideas is the
refined, revised form of the Pythagorean doctrine that number lies at
the base of the real world. Owing to the Greek mode of representing
numbers by patterns of dots, the notions of number and of geometrical
configuration are less separated than with us. Also Pythagoras, without
doubt, included the shape-iness of shape, which is an impure
mathematical entity. So to-day, when Einstein and his followers proclaim
that physical facts, such as gravitation, are to be construed as
exhibitions of local peculiarities of spatio-temporal properties, they
are following the pure Pythagorean tradition. In a sense, Plato and
Pythagoras stand nearer to modern physical science than does Aristotle.
The two former were mathematicians, whereas Aristotle was the son of a
doctor, though of course he was not thereby ignorant of mathematics. The
practical counsel to be derived from Pythagoras, is to measure, and thus
to express quality in terms of numerically determined quantity. But the
biological sciences, then and till our own time, have been
overwhelmingly classificatory. Accordingly, Aristotle by his Logic
throws the emphasis on classification. The popularity of Aristotelian
Logic retarded the advance of physical science throughout the Middle
Ages. If only the schoolmen had measured instead of classifying, how
much they might have learnt!

Classification is a halfway house between the immediate concreteness of
the individual thing and the complete abstraction of mathematical
notions. The species take account of the specific character, and the
genera of the generic character. But in the procedure of relating
mathematical notions to the facts of nature, by counting, by
measurement, and by geometrical relations, and by types of order, the
rational contemplation is lifted from the incomplete abstractions
involved in definite species and genera, to the complete, abstractions
of mathematics. Classification is necessary. But unless you can progress
from classification to mathematics, your reasoning will not take you
very far.

Between the epoch which stretches from Pythagoras to Plato and the epoch
comprised in the seventeenth century of the modern world nearly two
thousand years elapsed. In this long interval mathematics had made
immense strides. Geometry had gained the study of conic sections and
trigonometry; the method of exhaustion had almost anticipated the
integral calculus; and above all the Arabic arithmetical notation and
algebra had been contributed by Asiatic thought. But the progress was on
technical lines. Mathematics, as a formative element in the development
of philosophy, never, during this long period, recovered from its
deposition at the hands of Aristotle. Some of the old ideas derived from
the Pythagorean-Platonic epoch lingered on, and can be traced among the
Platonic influences which shaped the first period of evolution of
Christian theology. But philosophy received no fresh inspiration from
the steady advance of mathematical science. In the seventeenth century
the influence of Aristotle was at its lowest, and mathematics recovered
the importance of its earlier period. It was an age of great physicists
and great philosophers; and the physicists and philosophers were alike
mathematicians. The exception of John Locke should be made; although he
was greatly influenced by the Newtonian circle of the Royal Society. In
the age of Galileo, Descartes, Spinoza, Newton, and Leibniz, mathematics
was an influence of the first magnitude in the formation of philosophic
ideas. But the mathematics, which now emerged into prominence, was a
very different science from the mathematics of the earlier epoch. It had
gained in generality, and had started upon its almost incredible modern
career of piling subtlety of generalization upon subtlety of
generalization; and of finding, with each growth of complexity, some new
application, either to physical science, or to philosophic thought. The
Arabic notation had equipped the science with almost perfect technical
efficiency in the manipulation of numbers. This relief from a struggle
with arithmetical details (as instanced, for example, in the Egyptian
arithmetic of B. C. 1600) gave room for a development which had already
been faintly anticipated in later Greek mathematics. Algebra now came
upon the scene, and algebra is a generalisation of arithmetic. In the
same way as the notion of number abstracted from reference to any one
particular set of entities, so in algebra abstraction is made from the
notion of any particular numbers. Just as the number ‘5’ refers
impartially to any group of five entities, so in algebra the letters are
used to refer impartially to any number, with the proviso that each
letter is to refer to the same number throughout the same context of its
employment.

This usage was first employed in equations, which are methods of asking
complicated arithmetical questions. In this connection, the letters
representing numbers were termed ‘unknowns.’ But equations soon
suggested a new idea, that, namely, of a function of one or more general
symbols, these symbols being letters representing any numbers. In this
employment the algebraic letters are called the ‘arguments’ of the
function, or sometimes they are called the ‘variables.’ Then, for
instance, if an angle is represented by an algebraical letter, as
standing for its numerical measure in terms of a given unit,
Trigonometry is absorbed into this new algebra. Algebra thus develops
into the general science of analysis in which we consider the properties
of various functions of undetermined arguments. Finally the particular
functions, such as the trigonometrical functions, and the logarithmic
functions, and the algebraic functions, are generalised into the idea of
‘any function.’ Too large a generalisation leads to mere barrenness. It
is the large generalisation, limited by a happy particularity, which is
the fruitful conception. For instance the idea of any _continuous_
function, whereby the limitation of continuity is introduced, is the
fruitful idea which has led to most of the important applications. This
rise of algebraic analysis was concurrent with Descartes’ discovery of
analytical geometry, and then with the invention of the infinitesimal
calculus by Newton and Leibniz. Truly, Pythagoras, if he could have
foreseen the issue of the train of thought which he had set going would
have felt himself fully justified in his brotherhood with its excitement
of mysterious rites.

The point which I now want to make is that this dominance of the idea of
functionality in the abstract sphere of mathematics found itself
reflected in the order of nature under the guise of mathematically
expressed laws of nature. Apart from this progress of mathematics, the
seventeenth century developments of science would have been impossible.
Mathematics supplied the background of imaginative thought with which
the men of science approached the observation of nature. Galileo
produced formulae, Descartes produced formulae, Huyghens produced
formulae, Newton produced formulae.

As a particular example of the effect of the abstract development of
mathematics upon the science of those times, consider the notion of
periodicity. The general recurrences of things are very obvious in our
ordinary experience. Days recur, lunar phases recur, the seasons of the
year recur, rotating bodies recur to their old positions, beats of the
heart recur, breathing recurs. On every side, we are met by recurrence.
Apart from recurrence, knowledge would be impossible; for nothing could
be referred to our past experience. Also, apart from some regularity of
recurrence, measurement would be impossible. In our experience, as we
gain the idea of exactness, recurrence is fundamental.

In the sixteenth and seventeenth centuries, the theory of periodicity
took a fundamental place in science. Kepler divined a law connecting the
major axes of the planetary orbits with the periods in which the planets
respectively described their orbits: Galileo observed the periodic
vibrations of pendulums: Newton explained sound as being due to the
disturbance of air by the passage through it of periodic waves of
condensation and rarefaction: Huyghens explained light as being due to
the transverse waves of vibration of a subtle ether: Mersenne connected
the period of the vibration of a violin string with its density,
tension, and length. The birth of modern physics depended upon the
application of the abstract idea of periodicity to a variety of concrete
instances. But this would have been impossible, unless mathematicians
had already worked out in the abstract the various abstract ideas which
cluster round the notions of periodicity. The science of trigonometry
arose from that of the relations of the angles of a right-angled
triangle, to the ratios between the sides and hypotenuse of the
triangle. Then, under the influence of the newly discovered mathematical
science of the analysis of functions, it broadened out into the study of
the simple abstract periodic functions which these ratios exemplify.
Thus trigonometry became completely abstract; and in thus becoming
abstract, it became useful. It illuminated the underlying analogy
between sets of utterly diverse physical phenomena; and at the same time
it supplied the weapons by which any one such set could have its various
features analysed and related to each other.[2]

Nothing is more impressive than the fact that, as mathematics withdrew
increasingly into the upper regions of ever greater extremes of abstract
thought, it returned back to earth with a corresponding growth of
importance for the analysis of concrete fact. The history of the
seventeenth century science reads as though it were some vivid dream of
Plato or Pythagoras. In this characteristic the seventeenth century was
only the forerunner of its successors.

Footnote 2:

  For a more detailed consideration of the nature and function of pure
  mathematics _cf._ my _Introduction to Mathematics_, Home University
  Library, Williams and Norgate, London.

The paradox is now fully established that the utmost abstractions are
the true weapons with which to control our thought of concrete fact. As
the result of the prominence of mathematicians in the seventeenth
century, the eighteenth century was mathematically minded, more
especially where French influence predominated. An exception must be
made of the English empiricism derived from Locke. Outside France,
Newton’s direct influence on philosophy is best seen in Kant, and not in
Hume.

In the nineteenth century, the general influence of mathematics waned.
The romantic movement in literature, and the idealistic movement in
philosophy were not the products of mathematical minds. Also, even in
science, the growth of geology, of zoology, and of the biological
sciences generally, was in each case entirely disconnected from any
reference to mathematics. The chief scientific excitement of the century
was the Darwinian theory of evolution. Accordingly, mathematicians were
in the background, so far as the general thought of that age was
concerned. But this does not mean that mathematics was being neglected,
or even that it was uninfluential. During the nineteenth century pure
mathematics made almost as much progress as during all the preceding
centuries from Pythagoras onwards. Of course progress was easier,
because the technique had been perfected. But allowing for that, the
change in mathematics between the years 1800 and 1900 is very
remarkable. If we add in the previous hundred years, and take the two
centuries preceding the present time, one is almost tempted to date the
foundation of mathematics somewhere in the last quarter of the
seventeenth century. The period of the discovery of the elements
stretches from Pythagoras to Descartes, Newton, and Leibniz, and the
developed science has been created during the last two hundred and fifty
years. This is not a boast as to the superior genius of the modern
world; for it is harder to discover the elements than to develop the
science.

Throughout the nineteenth century, the influence of the science was its
influence on dynamics and physics, and thence derivatively on
engineering and chemistry. It is difficult to overrate its indirect
influence on human life through the medium of these sciences. But there
was no direct influence of mathematics upon the general thought of the
age.

In reviewing this rapid sketch of the influence of mathematics
throughout European history, we see that it had two great periods of
direct influence upon general thought, both periods lasting for about
two hundred years. The first period was that stretching from Pythagoras
to Plato, when the possibility of the science, and its general
character, first dawned upon the Grecian thinkers. The second period
comprised the seventeenth and eighteenth centuries of our modern epoch.
Both periods had certain common characteristics. In the earlier, as in
the later period, the general categories of thought in many spheres of
human interest, were in a state of disintegration. In the age of
Pythagoras, the unconscious Paganism, with its traditional clothing of
beautiful ritual and of magical rites, was passing into a new phase
under two influences. There were waves of religious enthusiasm, seeking
direct enlightenment into the secret depths of being; and at the
opposite pole, there was the awakening of critical analytical thought,
probing with cool dispassionateness into ultimate meanings. In both
influences, so diverse in their outcome, there was one common element—an
awakened curiosity, and a movement towards the reconstruction of
traditional ways. The pagan mysteries may be compared to the Puritan
reaction and to the Catholic reaction; critical scientific interest was
alike in both epochs, though with minor differences of substantial
importance.

In each age, the earlier stages were placed in periods of rising
prosperity, and of new opportunities. In this respect, they differed
from the period of gradual declension in the second and third centuries
when Christianity was advancing to the conquest of the Roman world. It
is only in a period, fortunate both in its opportunities for
disengagement from the immediate pressure of circumstances, and in its
eager curiosity, that the Age-Spirit can undertake any direct revision
of those final abstractions which lie hidden in the more concrete
concepts from which the serious thought of an age takes its start. In
the rare periods when this task can be undertaken, mathematics becomes
relevant to philosophy. For mathematics is the science of the most
complete abstractions to which the human mind can attain.

The parallel between the two epochs must not be pressed too far. The
modern world is larger and more complex than the ancient civilization
round the shores of the Mediterranean, or even than that of the Europe
which sent Columbus and the Pilgrim Fathers across the ocean. We cannot
now explain our age by some simple formula which becomes dominant and
will then be laid to rest for a thousand years. Thus the temporary
submergence of the mathematical mentality from the time of Rousseau
onwards appears already to be at an end. We are entering upon an age of
reconstruction, in religion, in science, and in political thought. Such
ages, if they are to avoid mere ignorant oscillation between extremes,
must seek truth in its ultimate depths. There can be no vision of this
depth of truth apart from a philosophy which takes full account of those
ultimate abstractions, whose interconnections it is the business of
mathematics to explore.

In order to explain exactly how mathematics is gaining in general
importance at the present time, let us start from a particular
scientific perplexity and consider the notions to which we are naturally
led by some attempt to unravel its difficulties. At present physics is
troubled by the quantum theory. I need not now explain[3] what this
theory is, to those who are not already familiar with it. But the point
is that one of the most hopeful lines of explanation is to assume that
an electron does not continuously traverse its path in space. The
alternative notion as to its mode of existence is that it appears at a
series of discrete positions in space which it occupies for successive
durations of time. It is as though an automobile moving at the average
rate of thirty miles an hour along a road, did not traverse the road
continuously; but appeared successively at the successive milestones,
remaining for two minutes at each milestone.

Footnote 3:

  _Cf._ Chapter VIII.

In the first place there is required the purely technical use of
mathematics to determine whether this conception does in fact explain
the many perplexing characteristics of the quantum theory. If the notion
survives this test, undoubtedly physics will adopt it. So far the
question is purely one for mathematics and physical science to settle
between them, on the basis of mathematical calculations and physical
observations.

But now a problem is handed over to the philosophers. This discontinuous
existence in space, thus assigned to electrons, is very unlike the
continuous existence of material entities which we habitually assume as
obvious. The electron seems to be borrowing the character which some
people have assigned to the Mahatmas of Tibet. These electrons, with the
correlative protons, are now conceived as being the fundamental entities
out of which the material bodies of ordinary experience are composed.
Accordingly, if this explanation is allowed, we have to revise all our
notions of the ultimate character of material existence. For when we
penetrate to these final entities, this startling discontinuity of
spatial existence discloses itself.

There is no difficulty in explaining the paradox, if we consent to apply
to the apparently steady undifferentiated endurance of matter the same
principles as those now accepted for sound and light. A steadily
sounding note is explained as the outcome of vibrations in the air: a
steady colour is explained as the outcome of vibrations in ether. If we
explain the steady endurance of matter on the same principle, we shall
conceive each primordial element as a vibratory ebb and flow of an
underlying energy, or activity. Suppose we keep to the physical idea of
energy: then each primordial element will be an organized system of
vibratory streaming of energy. Accordingly there will be a definite
period associated with each element; and within that period the
stream-system will sway from one stationary maximum to another
stationary maximum,—or, taking a metaphor from the ocean tides, the
system will sway from one high tide to another high tide. This system,
forming the primordial element, is nothing at any instant. It requires
its whole period in which to manifest itself. In an analogous way, a
note of music is nothing at an instant, but it also requires its whole
period in which to manifest itself.

Accordingly, in asking where the primordial element is, we must settle
on its average position at the centre of each period. If we divide time
into smaller elements, the vibratory system as one electronic entity has
no existence. The path in space of such a vibratory entity—where the
entity is _constituted by_ the vibrations—must be represented by a
series of detached positions in space, analogously to the automobile
which is found at successive milestones and at nowhere between.

We first must ask whether there is any evidence to associate the quantum
theory with vibration. This question is immediately answered in the
affirmative. The whole theory centres round the radiant energy from an
atom, and is intimately associated with the periods of the radiant
wave-systems. It seems, therefore, that the hypothesis of essentially
vibratory existence is the most hopeful way of explaining the paradox of
the discontinuous orbit.

In the second place, a new problem is now placed before philosophers and
physicists, if we entertain the hypothesis that the ultimate elements of
matter are in their essence vibratory. By this I mean that apart from
being a periodic system, such an element would have no existence. With
this hypothesis we have to ask, what are the ingredients which form the
vibratory organism. We have already got rid of the matter with its
appearance of undifferentiated endurance. Apart from some metaphysical
compulsion, there is no reason to provide another more subtle stuff to
take the place of the matter which has just been explained away. The
field is now open for the introduction of some new doctrine of organism
which may take the place of the materialism with which, since the
seventeenth century, science has saddled philosophy. It must be
remembered that the physicists’ energy is obviously an abstraction. The
concrete fact, which is the organism, must be a complete expression of
the character of a real occurrence. Such a displacement of scientific
materialism, if it ever takes place, cannot fail to have important
consequences in every field of thought.

Finally, our last reflection must be, that we have in the end come back
to a version of the doctrine of old Pythagoras, from whom mathematics,
and mathematical physics, took their rise. He discovered the importance
of dealing with abstractions; and in particular directed attention to
number as characterizing the periodicities of notes of music. The
importance of the abstract idea of periodicity was thus present at the
very beginning both of mathematics and of European philosophy.

In the seventeenth century, the birth of modern science required a new
mathematics, more fully equipped for the purpose of analysing the
characteristics of vibratory existence. And now in the twentieth century
we find physicists largely engaged in analysing the periodicities of
atoms. Truly, Pythagoras in founding European philosophy and European
mathematics, endowed them with the luckiest of lucky guesses—or, was it
a flash of divine genius, penetrating to the inmost nature of things?




                              CHAPTER III

                         THE CENTURY OF GENIUS


The previous chapters were devoted to the antecedent conditions which
prepared the soil for the scientific outburst of the seventeenth
century. They traced the various elements of thought and instinctive
belief, from their first efflorescence in the classical civilisation of
the ancient world, through the transformations which they underwent in
the Middle Ages, up to the historical revolt of the sixteenth century.
Three main factors arrested attention,—the rise of mathematics, the
instinctive belief in a detailed order of nature, and the unbridled
rationalism of the thought of the later Middle Ages. By this rationalism
I mean the belief that the avenue to truth was predominantly through a
metaphysical analysis of the nature of things, which would thereby
determine how things acted and functioned. The historical revolt was the
definite abandonment of this method in favour of the study of the
empirical facts of antecedents and consequences. In religion, it meant
the appeal to the origins of Christianity; and in science it meant the
appeal to experiment and the inductive method of reasoning.

A brief, and sufficiently accurate, description of the intellectual life
of the European races during the succeeding two centuries and a quarter
up to our own times is that they have been living upon the accumulated
capital of ideas provided for them by the genius of the seventeenth
century. The men of this epoch inherited a ferment of ideas attendant
upon the historical revolt of the sixteenth century, and they bequeathed
formed systems of thought touching every aspect of human life. It is the
one century which consistently, and throughout the whole range of human
activities, provided intellectual genius adequate for the greatness of
its occasions. The crowded stage of this hundred years is indicated by
the coincidences which mark its literary annals. At its dawn Bacon’s
_Advancement of Learning_ and Cervantes’ _Don Quixote_ were published in
the same year (1605), as though the epoch would introduce itself with a
forward and a backward glance. The first quarto edition of _Hamlet_
appeared in the preceding year, and a slightly variant edition in the
same year. Finally Shakespeare and Cervantes died on the same day, April
23, 1616. In the spring of this same year Harvey is believed to have
first expounded his theory of the circulation of the blood in a course
of lectures before the College of Physicians in London. Newton was born
in the year that Galileo died (1642), exactly one hundred years after
the publication of Copernicus’ _De Revolutionibus_. One year earlier
Descartes published his _Meditationes_ and two years later his
_Principia Philosophiae_. There simply was not time for the century to
space out nicely its notable events concerning men of genius.

I cannot now enter upon a chronicle of the various stages of
intellectual advance included within this epoch. It is too large a topic
for one lecture, and would obscure the ideas which it is my purpose to
develop. A mere rough catalogue of some names will be sufficient, names
of men who published to the world important work within these limits of
time: Francis Bacon, Harvey, Kepler, Galileo, Descartes, Pascal,
Huyghens, Boyle, Newton, Locke, Spinoza, Leibniz. I have limited the
list to the sacred number of twelve, a number much too small to be
properly representative. For example, there is only one Italian there,
whereas Italy could have filled the list from its own ranks. Again
Harvey is the only biologist, and also there are too many Englishmen.
This latter defect is partly due to the fact that the lecturer is
English, and that he is lecturing to an audience which, equally with
him, owns this English century. If he had been Dutch, there would have
been too many Dutchmen; if Italian, too many Italians; and if French,
too many Frenchmen. The unhappy Thirty Years’ War was devastating
Germany; but every other country looks back to this century as an epoch
which witnessed some culmination of its genius. Certainly this was a
great period of English thought; as at a later time Voltaire impressed
upon France.

The omission of physiologists, other than Harvey, also requires
explanation. There were, of course, great advances in biology within the
century, chiefly associated with Italy and the University of Padua. But
my purpose is to trace the philosophic outlook, derived from science and
presupposed by science, and to estimate some of its effects on the
general climate of each age. Now the scientific philosophy of this age
was dominated by physics; so as to be the most obvious rendering, in
terms of general ideas, of the state of physical knowledge of that age
and of the two succeeding centuries. As a matter of fact, these concepts
are very unsuited to biology; and set for it an insoluble problem of
matter and life and organism, with which biologists are now wrestling.
But the science of living organisms is only now coming to a growth
adequate to impress its conceptions upon philosophy. The last half
century before the present time has witnessed unsuccessful attempts to
impress biological notions upon the materialism of the seventeenth
century. However this success be estimated, it is certain that the root
ideas of the seventeenth century were derived from the school of thought
which produced Galileo, Huyghens and Newton, and not from the
physiologists of Padua. One unsolved problem of thought, so far as it
derives from this period, is to be formulated thus: Given configurations
of matter with locomotion in space as assigned by physical laws, to
account for living organisms.

My discussion of the epoch will be best introduced by a quotation from
Francis Bacon, which forms the opening of Section (or ‘Century’) IX of
his _Natural History_, I mean his _Silva Silvarum_. We are told in the
contemporary memoir by his chaplain, Dr. Rawley, that this work was
composed in the last five years of his life, so it must be dated between
1620 and 1626. The quotation runs thus:

“It is certain that all bodies whatsoever, though they have no sense,
yet they have perception; for when one body is applied to another, there
is a kind of election to embrace that which is agreeable, and to exclude
or expel that which is ingrate; and whether the body be alterant or
altered, evermore a perception precedeth operation; for else all bodies
would be like one to another. And sometimes this perception, in some
kind of bodies, is far more subtile than sense; so that sense is but a
dull thing in comparison of it: we see a weatherglass will find the
least difference of the weather in heat or cold, when we find it not.
And this perception is sometimes at a distance, as well as upon the
touch; as when the loadstone draweth iron; or flame naphtha of Babylon,
a great distance off. It is therefore a subject of a very noble enquiry,
to enquire of the more subtile perceptions; for it is another key to
open nature, as well as the sense; and sometimes better. And besides, it
is a principal means of natural divination; for that which in these
perceptions appeareth early, in the great effects cometh long after.”

There are a great many points of interest about this quotation, some of
which will emerge into importance in succeeding lectures. In the first
place, note the careful way in which Bacon discriminates between
_perception_, or _taking account of_, on the one hand, and _sense_, or
_cognitive experience_, on the other hand. In this respect Bacon is
outside the physical line of thought which finally dominated the
century. Later on, people thought of passive matter which was operated
on externally by forces. I believe Bacon’s line of thought to have
expressed a more fundamental truth than do the materialistic concepts
which were then being shaped as adequate for physics. We are now so used
to the materialistic way of looking at things, which has been rooted in
our literature by the genius of the seventeenth century, that it is with
some difficulty that we understand the possibility of another mode of
approach to the problems of nature.

In the particular instance of the quotation which I have just made, the
whole passage and the context in which it is embedded, are permeated
through and through by the experimental method, that is to say, by
attention to ‘irreducible and stubborn facts’, and by the inductive
method of eliciting general laws. Another unsolved problem which has
been bequeathed to us by the seventeenth century is the rational
justification of this method of Induction. The explicit realisation of
the antithesis between the deductive rationalism of the scholastics and
the inductive observational methods of the moderns must chiefly be
ascribed to Bacon; though, of course, it was implicit in the mind of
Galileo and of all the men of science of those times. But Bacon was one
of the earliest of the whole group, and also had the most direct
apprehension of the full extent of the intellectual revolution which was
in progress. Perhaps the man who most completely anticipated both Bacon
and the whole modern point of view was the artist Leonardo Da Vinci, who
lived almost exactly a century before Bacon. Leonardo also illustrates
the theory which I was advancing in my last lecture, that the rise of
naturalistic art was an important ingredient in the formation of our
scientific mentality. Indeed, Leonardo was more completely a man of
science than was Bacon. The practice of naturalistic art is more akin to
the practice of physics, chemistry and biology than is the practice of
law. We all remember the saying of Bacon’s contemporary, Harvey, the
discoverer of the circulation of the blood, that Bacon ‘wrote of science
like a Lord Chancellor.’ But at the beginning of the modern period Da
Vinci and Bacon stand together as illustrating the various strains which
have combined to form the modern world, namely, legal mentality and the
patient observational habits of the naturalistic artists.

In the passage which I have quoted from Bacon’s writings there is no
explicit mention of the method of inductive reasoning. It is unnecessary
for me to prove to you by any quotations that the enforcement of the
importance of this method, and of the importance, to the welfare of
mankind, of the secrets of nature to be thus discovered, was one of the
main themes to which Bacon devoted himself in his writings. Induction
has proved to be a somewhat more complex process than Bacon anticipated.
He had in his mind the belief that with a sufficient care in the
collection of instances the general law would stand out of itself. We
know now, and probably Harvey knew then, that this is a very inadequate
account of the processes which issue in scientific generalisations. But
when you have made all the requisite deductions, Bacon remains as one of
the great builders who constructed the mind of the modern world.

The special difficulties raised by induction emerged in the eighteenth
century, as the result of Hume’s criticism. But Bacon was one of the
prophets of the historical revolt, which deserted the method of
unrelieved rationalism, and rushed into the other extreme of basing all
fruitful knowledge upon inference from particular occasions in the past
to particular occasions in the future. I do not wish to throw any doubt
upon the validity of induction, when it has been properly guarded. My
point is, that the very baffling task of applying reason to elicit the
general characteristics of the immediate occasion, as set before us in
direct cognition, is a necessary preliminary, if we are to justify
induction; unless indeed we are content to base it upon our vague
instinct that of course it is all right. Either there is something about
the immediate occasion which affords knowledge of the past and the
future, or we are reduced to utter scepticism as to memory and
induction. It is impossible to over-emphasise the point that the key to
the process of induction, as used either in science or in our ordinary
life, is to be found in the right understanding of the immediate
occasion of knowledge in its full concreteness. It is in respect to our
grasp of the character of these occasions in their concreteness that the
modern developments of physiology and of psychology are of critical
importance. I shall illustrate this point in my subsequent lectures. We
find ourselves amid insoluble difficulties when we substitute for this
concrete occasion a mere abstract in which we only consider material
objects in a flux of configurations in time and space. It is quite
obvious that such objects can tell us only that they are where they are.

Accordingly, we must recur to the method of the school-divinity as
explained by the Italian medievalists whom I quoted in the first
lecture. We must observe the immediate occasion, and _use reason_ to
elicit a general description of its nature. Induction presupposes
metaphysics. In other words, it rests upon an antecedent rationalism.
You cannot have a rational justification for your appeal to history till
your metaphysics has assured you that there _is_ a history to appeal to;
and likewise your conjectures as to the future presuppose some basis of
knowledge that there _is_ a future already subjected to some
determinations. The difficulty is to make sense of either of these
ideas. But unless you have done so, you have made nonsense of induction.

You will observe that I do not hold Induction to be in its essence the
derivation of general laws. It is the divination of some characteristics
of a particular future from the known characteristics of a particular
past. The wider assumption of general laws holding for all cognisable
occasions appears a very unsafe addendum to attach to this limited
knowledge. All we can ask of the present occasion is that it shall
determine a particular community of occasions, which are in some
respects mutually qualified by reason of their inclusion within that
same community. That community of occasions considered in physical
science is the set of happenings which fit on to each other—as we say—in
a common space-time, so that we can trace the transitions from one to
the other. Accordingly, we refer to _the_ common space-time indicated in
our immediate occasion of knowledge. Inductive reasoning proceeds from
the particular occasion to the particular community of occasions, and
from the particular community to relations between particular occasions
within that community. Until we have taken into account other scientific
concepts, it is impossible to carry the discussion of induction further
than this preliminary conclusion.

The third point to notice about this quotation from Bacon is the purely
qualitative character of the statements made in it. In this respect
Bacon completely missed the tonality which lay behind the success of
seventeenth century science. Science was becoming, and has remained,
primarily quantitative. Search for measurable elements among your
phenomena, and then search for relations between these measures of
physical quantities. Bacon ignores this rule of science. For example, in
the quotation given he speaks of action at a distance; but he is
thinking qualitatively and not quantitatively. We cannot ask that he
should anticipate his younger contemporary Galileo, or his distant
successor Newton. But he gives no hint that there should be a search for
quantities. Perhaps he was misled by the current logical doctrines which
had come down from Aristotle. For, in effect, these doctrines said to
the physicist ‘_classify_’ when they should have said ‘_measure_.’

By the end of the century physics had been founded on a satisfactory
basis of measurement. The final and adequate exposition was given by
Newton. The common measurable element of _mass_ was discerned as
characterising all bodies in different amounts. Bodies which are
apparently identical in substance, shape, and size have very
approximately the same mass: the closer the identity, the nearer the
equality. The force acting on a body, whether by touch or by action at a
distance, was [in effect] defined as being equal to the mass of the body
multiplied by the rate of change of the body’s velocity, so far as this
rate of change is produced by that force. In this way the force is
discerned by its effect on the motion of the body. The question now
arises whether this conception of the magnitude of a force leads to the
discovery of simple quantitative laws involving the alternative
determination of forces by circumstances of the configuration of
substances and of their physical characters. The Newtonian conception
has been brilliantly successful in surviving this test throughout the
whole modern period. Its first triumph was the law of gravitation. Its
cumulative triumph has been the whole development of dynamical
astronomy, of engineering, and of physics.

This subject of the formation of the three laws of motion and of the law
of gravitation deserves critical attention. The whole development of
thought occupied exactly two generations. It commenced with Galileo and
ended with Newton’s _Principia_; and Newton was born in the year that
Galileo died. Also the lives of Descartes and Huyghens fall within the
period occupied by these great terminal figures. The issue of the
combined labours of these four men has some right to be considered as
the greatest single intellectual success which mankind has achieved. In
estimating its size, we must consider the completeness of its range. It
constructs for us a vision of the material universe, and it enables us
to calculate the minutest detail of a particular occurrence. Galileo
took the first step in hitting on the right line of thought. He noted
that the critical point to attend to was not the motion of bodies but
the changes of their motions. Galileo’s discovery is formularised by
Newton in his first law of motion:—“Every body continues in its state of
rest, or of uniform motion in a straight line, except so far as it may
be compelled by force to change that state.”

This formula contains the repudiation of a belief which had blocked the
progress of physics for two thousand years. It also deals with a
fundamental concept which is essential to scientific theory; I mean, the
concept of an ideally isolated system. This conception embodies a
fundamental character of things, without which science, or indeed any
knowledge on the part of finite intellects, would be impossible. The
‘isolated’ system is not a solipsist system, apart from which there
would be nonentity. It is isolated as within the universe. This means
that there are truths respecting this system which require reference
only to the remainder of things by way of a uniform systematic scheme of
relationships. Thus the conception of an isolated system is not the
conception of substantial independence from the remainder of things, but
of freedom from casual contingent dependence upon detailed items within
the rest of the universe. Further, this freedom from casual dependence
is required only in respect to certain abstract characteristics which
attach to the isolated system, and not in respect to the system in its
full concreteness.

The first law of motion asks what is to be said of a dynamically
isolated system so far as concerns its motion as a whole, abstracting
from its orientation and its internal arrangement of parts. Aristotle
said that you must conceive such a system to be at rest. Galileo added
that the state of rest is only a particular case, and that the general
statement is ‘either in a state of rest, or of uniform motion in a
straight line.’ Accordingly, an Aristotelean would conceive the forces
arising from the reaction of alien bodies as being quantitatively
measurable in terms of the velocity they sustain, and as directively
determined by the direction of that velocity; while the Galilean would
direct attention to the magnitude of the acceleration and to its
direction. This difference is illustrated by contrasting Kepler and
Newton. They both speculated as to the forces sustaining the planets in
their orbits. Kepler looked for tangential forces pushing the planets
along, whereas Newton looked for radial forces diverting the directions
of the planets’ motions.

Instead of dwelling upon the mistake which Aristotle made, it is more
profitable to emphasise the justification which he had for it, if we
consider the obvious facts of our experience. All the motions which
enter into our normal everyday experience cease unless they are
evidently sustained from the outside. Apparently, therefore, the sound
empiricist must devote his attention to this question of the sustenance
of motion. We here hit upon one of the dangers of unimaginative
empiricism. The seventeenth century exhibits another example of this
same danger; and, of all people in the world, Newton fell into it.
Huyghens had produced the wave theory of light. But this theory failed
to account for the most obvious facts about light as in our ordinary
experience, namely, that shadows cast by obstructing objects are defined
by rectilinear rays. Accordingly, Newton rejected this theory and
adopted the corpuscular theory which completely explained shadows. Since
then both theories have had their periods of triumph. At the present
moment the scientific world is seeking for a combination of the two.
These examples illustrate the danger of refusing to entertain an idea
because of its failure to explain one of the most obvious facts in the
subject matter in question. If you have had your attention directed to
the novelties in thought in your own lifetime, you will have observed
that almost all really new ideas have a certain aspect of foolishness
when they are first produced.

Returning to the laws of motion, it is noticeable that no reason was
produced in the seventeenth century for the Galilean as distinct from
the Aristotelian position. It was an ultimate fact. When in the course
of these lectures we come to the modern period, we shall see that the
theory of relativity throws complete light on this question; but only by
rearranging our whole ideas as to space and time.

It remained for Newton to direct attention to _mass_ as a physical
quantity inherent in the nature of a material body. Mass remained
permanent during all changes of motion. But the proof of the permanence
of mass amid chemical transformations had to wait for Lavoisier, a
century later. Newton’s next task was to find some estimate of the
magnitude of the alien force in terms of the mass of the body and of its
acceleration. He here had a stroke of luck. For, from the point of view
of a mathematician, the simplest possible law, namely the product of the
two, proved to be the successful one. Again the modern relativity theory
modifies this extreme simplicity. But luckily for science the delicate
experiments of the physicists of to-day were not then known, or even
possible. Accordingly, the world was given the two centuries which it
required in order to digest Newton’s laws of motion.

Having regard to this triumph, can we wonder that scientists placed
their ultimate principles upon a materialistic basis, and thereafter
ceased to worry about philosophy? We shall grasp the course of thought,
if we understand exactly what this basis is, and what difficulties it
finally involves. When you are criticising the philosophy of an epoch,
do not chiefly direct your attention to those intellectual positions
which its exponents feel it necessary explicitly to defend. There will
be some fundamental assumptions which adherents of all the variant
systems within the epoch unconsciously presuppose. Such assumptions
appear so obvious that people do not know what they are assuming because
no other way of putting things has ever occurred to them. With these
assumptions a certain limited number of types of philosophic systems are
possible, and this group of systems constitutes the philosophy of the
epoch.

One such assumption underlies the whole philosophy of nature during the
modern period. It is embodied in the conception which is supposed to
express the most concrete aspect of nature. The Ionian philosophers
asked, What is nature made of? The answer is couched in terms of stuff,
or matter, or material,—the particular name chosen is indifferent—which
has the property of simple location in space and time, or, if you adopt
the more modern ideas, in space-time. What I mean by matter, or
material, is anything which has this property of _simple location_. By
simple location I mean one major characteristic which refers equally
both to space and to time, and other minor characteristics which are
diverse as between space and time.

The characteristic common both to space and time is that material can be
said to be _here_ in space and _here_ in time, or _here_ in space-time,
in a perfectly definite sense which does not require for its explanation
any reference to other regions of space-time. Curiously enough this
character of simple location holds whether we look on a region of
space-time as determined absolutely or relatively. For if a region is
merely a way of indicating a certain set of relations to other entities,
then this characteristic, which I call simple location, is that material
can be said to have just these relations of position to the other
entities without requiring for its explanation any reference to other
regions constituted by analogous relations of position to the same
entities. In fact, as soon as you have settled, however you do settle,
what you mean by a definite place in space-time, you can adequately
state the relation of a particular material body to space-time by saying
that it is just there, in that place; and, so far as simple location is
concerned, there is nothing more to be said on the subject.

There are, however, some subordinate explanations to be made which bring
in the minor characteristics which I have already mentioned. First, as
regards time, if material has existed during any period, it has equally
been in existence during any portion of that period. In other words,
dividing the time does not divide the material. Secondly, in respect to
space, dividing the volume does divide the material. Accordingly, if
material exists throughout a volume, there will be less of that material
distributed through any definite half of that volume. It is from this
property that there arises our notion of density at a point of space.
Anyone who talks about density is not assimilating time and space to the
extent that some extremists of the modern school of relativists very
rashly desire. For the division of time functions, in respect to
material, quite differently from the division of space.

Furthermore, this fact that the material is indifferent to the division
of time leads to the conclusion that the lapse of time is an accident,
rather than of the essence, of the material. The material is fully
itself in any sub-period however short. Thus the transition of time has
nothing to do with the character of the material. The material is
equally itself at an instant of time. Here an instant of time is
conceived as in itself without transition, since the temporal transition
is the succession of instants.

The answer, therefore, which the seventeenth century gave to the ancient
question of the Ionian thinkers, ‘What is the world made of?’ was that
the world is a succession of instantaneous configurations of matter,—or
of material, if you wish to include stuff more subtle than ordinary
matter, the ether for example.

We cannot wonder that science rested content with this assumption as to
the fundamental elements of nature. The great forces of nature, such as
gravitation, were entirely determined by the configurations of masses.
Thus the configurations determined their own changes, so that the circle
of scientific thought was completely closed. This is the famous
mechanistic theory of nature, which has reigned supreme ever since the
seventeenth century. It is the orthodox creed of physical science.
Furthermore, the creed justified itself by the pragmatic test. It
worked. Physicists took no more interest in philosophy. They emphasized
the anti-rationalism of the Historical Revolt. But the difficulties of
this theory of materialistic mechanism very soon became apparent. The
history of thought in the eighteenth and nineteenth centuries is
governed by the fact that the world had got hold of a general idea which
it could neither live with nor live without.

This simple location of instantaneous material configurations is what
Bergson has protested against, so far as it concerns time and so far as
it is taken to be the fundamental fact of concrete nature. He calls it a
distortion of nature due to the intellectual ‘spatialisation’ of things.
I agree with Bergson in his protest: but I do not agree that such
distortion is a vice necessary to the intellectual apprehension of
nature. I shall in subsequent lectures endeavour to show that this
spatialisation is the expression of more concrete facts under the guise
of very abstract logical constructions. There is an error; but it is
merely the accidental error of mistaking the abstract for the concrete.
It is an example of what I will call the ‘Fallacy of Misplaced
Concreteness.’ This fallacy is the occasion of great confusion in
philosophy. It is not necessary for the intellect to fall into the trap,
though in this example there has been a very general tendency to do so.

It is at once evident that the concept of simple location is going to
make great difficulties for induction. For, if in the location of
configurations of matter throughout a stretch of time there is no
inherent reference to any other times, past or future, it immediately
follows that nature within any period does not refer to nature at any
other period. Accordingly, induction is not based on anything which can
be observed as inherent in nature. Thus we cannot look to nature for the
justification of our belief in any law such as the law of gravitation.
In other words, the order of nature cannot be justified by the mere
observation of nature. For there is nothing in the present fact which
inherently refers either to the past or to the future. It looks,
therefore, as though memory, as well as induction, would fail to find
any justification within nature itself.

I have been anticipating the course of future thought, and have been
repeating Hume’s argument. This train of thought follows so immediately
from the consideration of simple location, that we cannot wait for the
eighteenth century before considering it. The only wonder is that the
world did in fact wait for Hume before noting the difficulty. Also it
illustrates the anti-rationalism of the scientific public that, when
Hume did appear, it was only the religious implications of his
philosophy which attracted attention. This was because the clergy were
in principle rationalists, whereas the men of science were content with
a simple faith in the order of nature. Hume himself remarks, no doubt
scoffingly, ‘Our holy religion is founded on faith.’ This attitude
satisfied the Royal Society but not the Church. It also satisfied Hume
and has satisfied subsequent empiricists.

There is another presupposition of thought which must be put beside the
theory of simple location. I mean the two correlative categories of
Substance and quality. There is, however this difference. There were
different theories as to the adequate description of the status of
space. But whatever its status, no one had any doubt but that the
connection with space enjoyed by entities, which are said to be in
space, is that of simple location. We may put this shortly by saying
that it was tacitly assumed that space is the locus of simple locations.
Whatever is in space is _simpliciter_ in some definite portion of space.
But in respect to substance and quality the leading minds of the
seventeenth century were definitely perplexed; though, with their usual
genius, they at once constructed a theory which was adequate for their
immediate purposes.

Of course, substance and quality, as well as simple location, are the
most natural ideas for the human mind. It is the way in which we think
of things, and without these ways of thinking we could not get our ideas
straight for daily use. There is no doubt about this. The only question
is, How concretely are we thinking when we consider nature under these
conceptions? My point will be, that we are presenting ourselves with
simplified editions of immediate matters of fact. When we examine the
primary elements of these simplified editions, we shall find that they
are in truth only to be justified as being elaborate logical
constructions of a high degree of abstraction. Of course, as a point of
individual psychology, we get at the ideas by the rough and ready method
of suppressing what appear to be irrelevant details. But when we attempt
to justify this suppression of irrelevance, we find that, though there
are entities left corresponding to the entities we talk about, yet these
entities are of a high degree of abstraction.

Thus I hold that substance and quality afford another instance of the
fallacy of misplaced concreteness. Let us consider how the notions of
substance and quality arise. We observe an object as an entity with
certain characteristics. Furthermore, each individual entity is
apprehended through its characteristics. For example, we observe a body;
there is something about it which we note. Perhaps, it is hard, and
blue, and round, and noisy. We observe something which possesses these
qualities: apart from these qualities we do not observe anything at all.
Accordingly, the entity is the substratum, or substance, of which we
predicate qualities. Some of the qualities are essential, so that apart
from them the entity would not be itself; while other qualities are
accidental and changeable. In respect to material bodies, the qualities
of having a quantitative mass, and of simple location somewhere, were
held by John Locke at the close of the seventeenth century to be
essential qualities. Of course, the location was changeable, and the
unchangeability of mass was merely an experimental fact except for some
extremists.

So far, so good. But when we pass to blueness and noisiness a new
situation has to be faced. In the first place, the body may not be
always blue, or noisy. We have already allowed for this by our theory of
accidental qualities, which for the moment we may accept as adequate.
But in the second place, the seventeenth century exposed a real
difficulty. The great physicists elaborated transmission theories of
light and sound, based upon their materialistic views of nature. There
were two hypotheses as to light: either it was transmitted by the
vibratory waves of a materialistic ether, or—according to Newton—it was
transmitted by the motion of incredibly small corpuscles of some subtle
matter. We all know that the wave theory of Huyghens held the field
during the nineteenth century, and that at present physicists are
endeavouring to explain some obscure circumstances attending radiation
by a combination of both theories. But whatever theory you choose, there
is no light or colour as a fact in external nature. There is merely
motion of material. Again, when the light enters your eyes and falls on
the retina, there is merely motion of material. Then your nerves are
affected and your brain is affected, and again this is merely motion of
material. The same line of argument holds for sound, substituting waves
in the air for waves in the ether, and ears for eyes.

We then ask in what sense are blueness and noisiness qualities of the
body. By analogous reasoning, we also ask in what sense is its scent a
quality of the rose.

Galileo considered this question, and at once pointed out that, apart
from eyes, ears, or noses, there would be no colours, sounds, or smells.
Descartes and Locke elaborated a theory of primary and secondary
qualities. For example, Descartes in his ‘Sixth Meditation’ says:[4]
“And indeed, as I perceive different sorts of colours, sounds, odours,
tastes, heat, hardness, etc., I safely conclude that there are in the
bodies from which the diverse perceptions of the senses proceed, certain
varieties corresponding to them, although, perhaps, not in reality like
them;....”

Footnote 4:

  Translation by Professor John Veitch.

Also in his _Principles of Philosophy_, he says: “That by our senses we
know nothing of external objects beyond their figure [or situation],
magnitude, and motion.”

Locke, writing with a knowledge of Newtonian dynamics, places mass among
the primary qualities of bodies. In short, he elaborates a theory of
primary and secondary qualities in accordance with the state of physical
science at the close of the seventeenth century. The primary qualities
are the essential qualities of substances whose spatio-temporal
relationships constitute nature. The orderliness of these relationships
constitutes nature. The orderliness of these relationships constitutes
the order of nature. The occurrences of nature are in some way
apprehended by minds, which are associated with living bodies.
Primarily, the mental apprehension is aroused by the occurrences in
certain parts of the correlated body, the occurrences in the brain, for
instance. But the mind in apprehending also experiences sensations
which, properly speaking, are qualities of the mind alone. These
sensations are projected by the mind so as to clothe appropriate bodies
in external nature. Thus the bodies are perceived as with qualities
which in reality do not belong to them, qualities which in fact are
purely the offspring of the mind. Thus nature gets credit which should
in truth be reserved for ourselves: the rose for its scent: the
nightingale for his song: and the sun for his radiance. The poets are
entirely mistaken. They should address their lyrics to themselves, and
should turn them into odes of self-congratulation on the excellency of
the human mind. Nature is a dull affair, soundless, scentless,
colourless; merely the hurrying of material, endlessly, meaninglessly.

However you disguise it, this is the practical outcome of the
characteristic scientific philosophy which closed the seventeenth
century.

In the first place, we must note its astounding efficiency as a system
of concepts for the organisation of scientific research. In this
respect, it is fully worthy of the genius of the century which produced
it. It has held its own as the guiding principle of scientific studies
ever since. It is still reigning. Every university in the world
organises itself in accordance with it. No alternative system of
organising the pursuit of scientific truth has been suggested. It is not
only reigning, but it is without a rival.

And yet—it is quite unbelievable. This conception of the universe is
surely framed in terms of high abstractions, and the paradox only arises
because we have mistaken our abstractions for concrete realities.

No picture, however generalised, of the achievements of scientific
thought in this century can omit the advance in mathematics. Here as
elsewhere the genius of the epoch made itself evident. Three great
Frenchmen, Descartes, Desargues, Pascal, initiated the modern period in
geometry. Another Frenchman, Fermat, laid the foundations of modern
analysis, and all but perfected the methods of the differential
calculus. Newton and Leibniz, between them, actually did create the
differential calculus as a practical method of mathematical reasoning.
When the century ended, mathematics as an instrument for application to
physical problems was well established in something of its modern
proficiency. Modern pure mathematics, if we except geometry, was in its
infancy, and had given no signs of the astonishing growth it was to make
in the nineteenth century. But the mathematical physicist had appeared,
bringing with him the type of mind which was to rule the scientific
world in the next century. It was to be the age of ‘Victorious
Analysis.’

The seventeenth century had finally produced a scheme of scientific
thought framed by mathematicians, for the use of mathematicians. The
great characteristic of the mathematical mind is its capacity for
dealing with abstractions; and for eliciting from them clear-cut
demonstrative trains of reasoning, entirely satisfactory so long as it
is those abstractions which you want to think about. The enormous
success of the scientific abstractions, yielding on the one hand
_matter_ with its _simple location_ in space and time, and on the other
hand _mind_, perceiving, suffering, reasoning, but not interfering, has
foisted onto philosophy the task of accepting them as the most concrete
rendering of fact.

Thereby, modern philosophy has been ruined. It has oscillated in a
complex manner between three extremes. There are the dualists, who
accept matter and mind as on equal basis, and the two varieties of
monists, those who put mind inside matter, and those who put matter
inside mind. But this juggling with abstractions can never overcome the
inherent confusion introduced by the ascription of _misplaced
concreteness_ to the scientific scheme of the seventeenth century.




                               CHAPTER IV

                         THE EIGHTEENTH CENTURY


In so far as the intellectual climates of different epochs can be
contrasted, the eighteenth century in Europe was the complete antithesis
to the Middle Ages. The contrast is symbolised by the difference between
the cathedral of Chartres and the Parisian salons, where D’Alembert
conversed with Voltaire. The Middle Ages were haunted with the desire to
rationalise the infinite: the men of the eighteenth century rationalised
the social life of modern communities, and based their sociological
theories on an appeal to the facts of nature. The earlier period was the
age of faith, based upon reason. In the later period, they let sleeping
dogs lie: it was the age of reason, based upon faith. To illustrate my
meaning:—St. Anselm would have been distressed if he had failed to find
a convincing argument for the existence of God, and on this argument he
based his edifice of faith, whereas Hume based his _Dissertation on the
Natural History of Religion_ upon his faith in the order of nature. In
comparing these epochs it is well to remember that reason can err, and
that faith may be misplaced.

In my previous lecture I traced the evolution, during the seventeenth
century, of the scheme of scientific ideas which has dominated thought
ever since. It involves a fundamental duality, with _material_ on the
one hand, and on the other hand _mind_. In between there lie the
concepts of life, organism, function, instantaneous reality,
interaction, order of nature, which collectively form the Achilles heel
of the whole system.

I also expressed my conviction that if we desired to obtain a more
fundamental expression of the concrete character of natural fact, the
element in this scheme which we should first criticise is the concept of
_simple location_. In view therefore of the importance which this idea
will assume in these lectures, I will repeat the meaning which I have
attached to this phrase. To say that a bit of matter has _simple
location_ means that, in expressing its spatio-temporal relations, it is
adequate to state that it is where it is, in a definite finite region of
space, and throughout a definite finite duration of time, apart from any
essential reference of the relations of that bit of matter to other
regions of space and to other durations of time. Again, this concept of
simple location is independent of the controversy between the absolutist
and the relativist views of space or of time. So long as any theory of
space, or of time, can give a meaning, either absolute or relative, to
the idea of a definite region of space, and of a definite duration of
time, the idea of simple location has a perfectly definite meaning. This
idea is the very foundation of the seventeenth century scheme of nature.
Apart from it, the scheme is incapable of expression. I shall argue that
among the primary elements of nature as apprehended in our immediate
experience, there is no element whatever which possesses this character
of simple location. It does not follow, however, that the science of the
seventeenth century was simply wrong. I hold that by a process of
constructive abstraction we can arrive at abstractions which are the
simply-located bits of material, and at other abstractions which are the
minds included in the scientific scheme. Accordingly, the real error is
an example of what I have termed: The Fallacy of Misplaced Concreteness.

The advantage of confining attention to a definite group of
abstractions, is that you confine your thoughts to clear-cut definite
things, with clear-cut definite relations. Accordingly, if you have a
logical head, you can deduce a variety of conclusions respecting the
relationships between these abstract entities. Furthermore, if the
abstractions are well-founded, that is to say, if they do not abstract
from everything that is important in experience, the scientific thought
which confines itself to these abstractions will arrive at a variety of
important truths relating to our experience of nature. We all know those
clear-cut trenchant intellects, immovably encased in a hard shell of
abstractions. They hold you to their abstractions by the sheer grip of
personality.

The disadvantage of exclusive attention to a group of abstractions,
however well-founded, is that, by the nature of the case, you have
abstracted from the remainder of things. In so far as the excluded
things are important in your experience, your modes of thought are not
fitted to deal with them. You cannot think without abstractions;
accordingly, it is of the utmost importance to be vigilant in critically
revising your _modes_ of abstraction. It is here that philosophy finds
its niche as essential to the healthy progress of society. It is the
critic of abstractions. A civilisation which cannot burst through its
current abstractions is doomed to sterility after a very limited period
of progress. An active school of philosophy is quite as important for
the locomotion of ideas, as is an active school of railway engineers for
the locomotion of fuel.

Sometimes it happens that the service rendered by philosophy is entirely
obscured by the astonishing success of a scheme of abstractions in
expressing the dominant interests of an epoch. This is exactly what
happened during the eighteenth century. _Les philosophes_ were not
philosophers. They were men of genius, clear-headed and acute, who
applied the seventeenth century group of scientific abstractions to the
analysis of the unbounded universe. Their triumph, in respect to the
circle of ideas mainly interesting to their contemporaries, was
overwhelming. Whatever did not fit into their scheme was ignored,
derided, disbelieved. Their hatred of Gothic architecture symbolises
their lack of sympathy with dim perspectives. It was the age of reason,
healthy, manly, upstanding reason; but, of one-eyed reason, deficient in
its vision of depth. We cannot overrate the debt of gratitude which we
owe to these men. For a thousand years Europe had been a prey to
intolerant, intolerable visionaries. The common sense of the eighteenth
century, its grasp of the obvious facts of human suffering, and of the
obvious demands of human nature, acted on the world like a bath of moral
cleansing. Voltaire must have the credit, that he hated injustice, he
hated cruelty, he hated senseless repression, and he hated hocus-pocus.
Furthermore, when he saw them, he knew them. In these supreme virtues,
he was typical of his century, on its better side. But if men cannot
live on bread alone, still less can they do so on disinfectants. The age
had its limitations; yet we cannot understand the passion with which
some of its main positions are still defended, especially in the schools
of science, unless we do full justice to its positive achievements. The
seventeenth century scheme of concepts was proving a perfect instrument
for research.

This triumph of materialism was chiefly in the sciences of rational
dynamics, physics, and chemistry. So far as dynamics and physics were
concerned, progress was in the form of direct developments of the main
ideas of the previous epoch. Nothing fundamentally new was introduced,
but there was an immense detailed development. Special case after
special case was unravelled. It was as though the very Heavens were
being opened, on a set plan. In the second half of the century,
Lavoisier practically founded chemistry on its present basis. He
introduced into it the principle that no material is lost or gained in
any chemical transformations. This was the last success of materialistic
thought, which has not ultimately proved to be double-edged. Chemical
science now only waited for the atomic theory, in the next century.

In this century the notion of the mechanical explanation of all the
processes of nature finally hardened into a dogma of science. The notion
won through on its merits by reason of an almost miraculous series of
triumphs achieved by the mathematical physicists, culminating in the
_Méchanique Analytique_ of Lagrange, which was published in 1787.
Newton’s _Principia_ was published in 1687, so that exactly one hundred
years separates the two great books. This century contains the first
period of mathematical physics of the modern type. The publication of
Clerk Maxwell’s _Electricity and Magnetism_ in 1873 marks the close of
the second period. Each of these three books introduces new horizons of
thought affecting everything which comes after them.

In considering the various topics to which mankind has bent its
systematic thought, it is impossible not to be struck with the unequal
distribution of ability among the different fields. In almost all
subjects there are a few outstanding names. For it requires genius to
create a subject as a distinct topic for thought. But in the case of
many topics, after a good beginning very relevant to its immediate
occasion, the subsequent development appears as a weak series of
flounderings, so that the whole subject gradually loses its grip on the
evolution of thought. It was far otherwise with mathematical physics.
The more you study this subject, the more you will find yourself
astonished by the almost incredible triumphs of intellect which it
exhibits. The great mathematical physicists of the eighteenth and first
few years of the nineteenth century, most of them French, are a case in
point: Maupertuis, Clairaut, D’Alembert, Lagrange, Laplace, Fourier,
form a series of names, such that each recalls to mind some achievement
of the first rank. When Carlyle, as the mouthpiece of the subsequent
Romantic Age, scoffingly terms the period the Age of Victorious
Analysis, and mocks at Maupertuis as a ‘sublimish gentleman in a white
periwig,’ he only exhibits the narrow side of the Romanticists whom he
is then voicing.

It is impossible to explain intelligently, in a short time and without
technicalities, the details of the progress made by this school. I will,
however, endeavour to explain the main point of a joint achievement of
Maupertuis and Lagrange. Their results, in conjunction with some
subsequent mathematical methods due to two great German mathematicians
of the first half of the nineteenth century, Gauss and Riemann, have
recently proved themselves to be the preparatory work necessary for the
new ideas which Herz and Einstein have introduced into mathematical
physics. Also they inspired some of the best ideas in Clerk Maxwell’s
treatise, already mentioned in this lecture.

They aimed at discovering something more fundamental and more general
than Newton’s laws of motion which were discussed in the previous
lecture. They wanted to find some wider ideas, and in the case of
Lagrange some more general means of mathematical exposition. It was an
ambitious enterprise, and they were completely successful. Maupertuis
lived in the first half of the eighteenth century, and Lagrange’s active
life lay in its second half. We find in Maupertuis a tinge of the
theologic age which preceded his birth. He started with the idea that
the whole path of a material particle between any limits of time must
achieve some perfection worthy of the providence of God. There are two
points of interest in this motive principle. In the first place, it
illustrates the thesis which I was urging in my first lecture that the
way in which the medieval church had impressed on Europe the notion of
the detailed providence of a rational personal God was one of the
factors by which the trust in the order of nature had been generated. In
the second place, though we are now all convinced that such modes of
thought are of no direct use in detailed scientific enquiry, Maupertuis’
success in this particular case shows that almost any idea which jogs
you out of your current abstractions may be better than nothing. In the
present case what the idea in question did for Maupertuis was to lead
him to enquire what general property of the path as a whole could be
deduced from Newton’s laws of motion. Undoubtedly this was a very
sensible procedure whatever one’s theological notions. Also his general
idea led him to conceive that the property found would be a quantitative
sum, such that any slight deviation from the path would increase it. In
this supposition he was generalising Newton’s first law of motion. For
an isolated particle takes the shortest route with uniform velocity. So
Maupertuis conjectured that a particle travelling through a field of
force would realise the least possible amount of some quantity. He
discovered such a quantity and called it the integral action between the
time limits considered. In modern phraseology it is the sum through
successive small lapses of time of the difference between the kinetic
and potential energies of the particle at each successive instant. This
action, therefore, has to do with the interchange between the energy
arising from motion and the energy arising from position. Maupertuis had
discovered the famous theorem of least action. Maupertuis was not quite
of the first rank in comparison with such a man as Lagrange. In his
hands and in those of his immediate successors, his principle did not
assume any dominating importance. Lagrange put the same question on a
wider basis so as to make its answer relevant to actual procedure in the
development of dynamics. His Principle of Virtual Work as applied to
systems in motion is in effect Maupertuis’ principle conceived as
applying at each instant of the path of the system. But Lagrange saw
further than Maupertuis. He grasped that he had gained a method of
stating dynamical truths in a way which is perfectly indifferent to the
particular methods of measurement employed in fixing the positions of
the various parts of the system. Accordingly, he went on to deduce
equations of motion which are equally applicable whatever quantitative
measurements have been made, provided that they are adequate to fix
positions. The beauty and almost divine simplicity of these equations is
such that these formulae are worthy to rank with those mysterious
symbols which in ancient times were held directly to indicate the
Supreme Reason at the base of all things. Later Herz—inventor of
electromagnetic waves—based mechanics on the idea of every particle
traversing the shortest path open to it under the circumstances
constraining its motion; and finally Einstein, by the use of the
geometrical theories of Gauss and Riemann, showed that these
circumstances could be construed as being inherent in the character of
space-time itself. Such, in barest outline, is the story of dynamics
from Galileo to Einstein.

Meanwhile Galvani and Volta lived and made their electric discoveries;
and the biological sciences slowly gathered their material, but still
waited for dominating ideas. Psychology, also, was beginning to
disengage itself from its dependence on general philosophy. This
independent growth of psychology was the ultimate result of its
invocation by John Locke as a critic of metaphysical licence. All the
sciences dealing with life were still in an elementary observational
stage, in which classification and direct description were dominant. So
far the scheme of abstractions was adequate to the occasion.

In the realm of practice, the age which produced enlightened rulers,
such as the Emperor Joseph of the House of Hapsburg, Frederick the
Great, Walpole, the great Lord Chatham, George Washington, cannot be
said to have failed. Especially when to these rulers, it adds the
invention of parliamentary cabinet government in England, of federal
presidential government in the United States, and of the humanitarian
principles of the French Revolution. Also in technology it produced the
steam-engine, and thereby ushered in a new era of civilisation.
Undoubtedly, as a practical age the eighteenth century was a success. If
you had asked one of the wisest and most typical of its ancestors, who
just saw its commencement, I mean John Locke, what he expected from it,
he would hardly have pitched his hopes higher than its actual
achievements.

In developing a criticism of the scientific scheme of the eighteenth
century, I must first give my main reason for ignoring nineteenth
century idealism—I am speaking of the philosophic idealism which finds
the ultimate meaning of reality in mentality that is fully cognitive.
This idealistic school, as hitherto developed, has been too much
divorced from the scientific outlook. It has swallowed the scientific
scheme in its entirety as being the only rendering of the facts of
nature, and has then explained it as being an idea in the ultimate
mentality. In the case of absolute idealism, the world of nature is just
one of the ideas, somehow differentiating the unity of the Absolute: in
the case of pluralistic idealism involving monadic mentalities, this
world is the greatest common measure of the various ideas which
differentiate the various mental unities of the various monads. But,
however you take it, these idealistic schools have conspicuously failed
to connect, in any organic fashion, the fact of nature with their
idealistic philosophies. So far as concerns what will be said in these
lectures, your ultimate outlook may be realistic or idealistic. My point
is that a further stage of provisional realism is required in which the
scientific scheme is recast, and founded upon the ultimate concept of
_organism_.

In outline, my procedure is to start from the analysis of the status of
space and of time, or in modern phraseology, the status of space-time.
There are two characters of either. Things are separated by space, and
are separated by time: but they are also together in space, and together
in time, even if they be not contemporaneous. I will call these
characters the ‘_separative_’ and the ‘_prehensive_’ characters of
space-time. There is yet a third character of space-time. Everything
which is in space receives a definite limitation of some sort, so that
in a sense it has just that shape which it does have and no other, also
in some sense it is just in this place and in no other. Analogously for
time, a thing endures during a certain period, and through no other
period. I will call this the ‘_modal_’ character of space-time. It is
evident that the modal character taken by itself gives rise to the idea
of simple location. But it must be conjoined with the separative and
prehensive characters.

For simplicity of thought, I will first speak of space only, and will
afterwards extend the same treatment to time.

The volume is the most concrete element of space. But the separative
character of space, analyses a volume into sub-volumes, and so on
indefinitely. Accordingly, taking the separative character in isolation,
we should infer that a volume is a mere multiplicity of non-voluminous
elements, of points in fact. But it is the unity of volume which is the
ultimate fact of experience, for example, the voluminous space of this
hall. This hall as a mere multiplicity of points is a construction of
the logical imagination.

Accordingly, the prime fact is the prehensive unity of volume, and this
unity is mitigated or limited by the separated unities of the
innumerable contained parts. We have a prehensive unity, which is yet
held apart as an aggregate of contained parts. But the prehensive unity
of the volume is not the unity of a mere logical aggregate of parts. The
parts form an ordered aggregate, in the sense that each part is
something from the standpoint of every other part, and also from the
same standpoint every other part is something in relation to it. Thus if
A and B and C are volumes of space, B has an aspect from the standpoint
of A, and so has C, and so has the relationship of B and C. This aspect
of B from A is of the essence of A. The volumes of space have no
independent existence. They are only entities as within the totality;
you cannot extract them from their environment without destruction of
their very essence. Accordingly, I will say that the aspect of B from A
is the _mode_ in which B enters into the composition of A. This is the
modal character of space, that the prehensive unity of A is the
prehension into unity of the aspects of all other volumes from the
standpoint of A. The shape of a volume is the formula from which the
totality of its aspects can be derived. Thus the shape of a volume is
more abstract than its aspects. It is evident that I can use Leibniz’s
language, and say that every volume mirrors in itself every other volume
in space.

Exactly analogous considerations hold with respect to durations in time.
An instant of time, without duration, is an imaginative logical
construction. Also each duration of time mirrors in itself all temporal
durations.

But in two ways I have introduced a false simplicity. In the first
place, I should have conjoined space and time, and conducted my
explanation in respect to four-dimensional regions of space-time. I have
nothing to add in the way of explanation. In your minds, substitute such
four-dimensional regions for the spatial volumes of the previous
explanations.

Secondly, my explanation has involved itself in a vicious circle. For I
have made the prehensive unity of the region A to consist of the
prehensive unification of the modal presences in A of other regions.
This difficulty arises because space-time cannot in reality be
considered as a self-subsistent entity. It is an abstraction, and its
explanation requires reference to that from which it has been extracted.
Space-time is the specification of certain general characters of events
and of their mutual ordering. This recurrence to concrete fact brings me
back to the eighteenth century, and indeed to Francis Bacon in the
seventeenth century. We have to consider the development in those
epochs, of the criticism of the reigning scientific scheme.

No epoch is homogeneous; whatever you may have assigned as the dominant
note of a considerable period, it will always be possible to produce
men, and great men, belonging to the same time, who exhibit themselves
as antagonistic to the tone of their age. This is certainly the case
with the eighteenth century. For example, the names of John Wesley and
of Rousseau must have occurred to you while I was drawing the character
of that time. But I do not want to speak of them, or of others. The man,
whose ideas I must consider at some length, is Bishop Berkeley. Quite at
the commencement of the epoch, he made all the right criticisms, at
least in principle. It would be untrue to say that he produced no
effect. He was a famous man. The wife of George II was one of the few
queens who, in any country, have been clever enough, and wise enough, to
patronise learning judiciously; accordingly, Berkeley was made a bishop,
in days when bishops in Great Britain were relatively far greater men
than they are now. Also, what was more important than his bishopric,
Hume studied him, and developed one side of his philosophy in a way
which might have disturbed the ghost of the great ecclesiastic. Then
Kant studied Hume. So, to say that Berkeley was uninfluential during the
century, would certainly be absurd. But all the same, he failed to
affect the main stream of scientific thought. It flowed on as if he had
never written. Its general success made it impervious to criticism, then
and since. The world of science has always remained perfectly satisfied
with its peculiar abstractions. They work, and that is sufficient for
it.

The point before us is that this scientific field of thought is now, in
the twentieth century, too narrow for the concrete facts which are
before it for analysis. This is true even in physics, and is more
especially urgent in the biological sciences. Thus, in order to
understand the difficulties of modern scientific thought and also its
reactions on the modern world, we should have in our minds some
conception of a wider field of abstraction, a more concrete analysis,
which shall stand nearer to the complete concreteness of our intuitive
experience. Such an analysis should find in itself a niche for the
concepts of matter and spirit, as abstractions in terms of which much of
our physical experience can be interpreted. It is in the search for this
wider basis for scientific thought that Berkeley is so important. He
launched his criticism shortly after the schools of Newton and Locke had
completed their work, and laid his finger exactly on the weak spots
which they had left. I do not propose to consider either the subjective
idealism which has been derived from him, or the schools of development
which trace their descent from Hume and Kant respectively. My point will
be that—whatever the final metaphysics you may adopt—there is another
line of development embedded in Berkeley, pointing to the analysis which
we are in search of. Berkeley overlooked it, partly by reason of the
over-intellectualism of philosophers, and partly by his haste to have
recourse to an idealism with its objectivity grounded in the mind of
God. You will remember that I have already stated that the key of the
problem lies in the notion of simple location. Berkeley, in effect,
criticises this notion. He also raises the question, What do we mean by
things being realised in the world of nature?

In Sections 23 and 24 of his _Principles of Human Knowledge_, Berkeley
gives his answer to this latter question. I will quote some detached
sentences from those Sections:

“23. But, say you, surely there is nothing easier than for me to imagine
trees, for instance, in a park, or books existing in a closet, and
nobody by to perceive them. I answer, you may so, there is no difficulty
in it; but what is all this, I beseech you, more than framing in your
mind certain ideas which you call books and trees, and at the same time
omitting to frame the idea of any one that may perceive them?...”

“When we do our utmost to conceive the existence of external bodies, we
are all the while only contemplating our own ideas. But the mind _taking
no notice of itself_, is deluded to think it can and does conceive
bodies existing unthought of or without the mind, though at the same
time they are apprehended by or exist in itself....”

“24. It is very obvious, upon the least inquiry into our thoughts, to
know whether it be possible for us to understand what is meant by the
_absolute existence of sensible objects in themselves, or without the
mind_. To me it is evident those words mark out either a direct
contradiction, or else nothing at all....”

Again there is a very remarkable passage in Section 10, of the fourth
Dialogue of Berkeley’s _Alciphron_. I have already quoted it, at greater
length, in my _Principles of Natural Knowledge_:

“_Euphranor._ Tell me, Alciphron, can you discern the doors, window and
battlements of that same castle?

_Alciphron._ I cannot. At this distance it seems only a small round
tower.

_Euph._ But I, who have been at it, know that it is no small round
tower, but a large square building with battlements and turrets, which
it seems you do not see.

_Alc_. What will you infer from thence?

_Euph._ I would infer that the very object which you strictly and
properly perceive by sight is not that thing which is several miles
distant.

_Alc._ Why so?

_Euph._ Because a little round object is one thing, and a great square
object is another. Is it not so?...”

Some analogous examples concerning a planet and a cloud are then cited
in the dialogue, and this passage finally concludes with:

“_Euphranor._ Is it not plain, therefore, that neither the castle, the
planet, nor the cloud, _which you see here_, are those real ones which
you suppose exist at a distance?”

It is made explicit in the first passage, already quoted, that Berkeley
himself adopts an extreme idealistic interpretation. For him mind is the
only absolute reality, and the unity of nature is the unity of ideas in
the mind of God. Personally, I think that Berkeley’s solution of the
metaphysical problem raises difficulties not less than those which he
points out as arising from a realistic interpretation of the scientific
scheme. There is, however, another possible line of thought, which
enables us to adopt anyhow an attitude of provisional realism, and to
widen the scientific scheme in a way which is useful for science itself.

I recur to the passage from Francis Bacon’s _Natural History_, already
quoted in the previous lecture:

“It is certain that all bodies whatsoever, though they have no sense,
yet they have perception: ... and whether the body be alterant or
altered, evermore a perception precedeth operation; for else all bodies
would be alike one to another....”

Also in the previous lecture I construed _perception_ (as used by Bacon)
as meaning _taking account_ of the essential character of the thing
perceived, and I construed _sense_ as meaning _cognition_. We certainly
do take account of things of which at the time we have no explicit
cognition. We can even have a cognitive memory of the taking account,
without having had a contemporaneous cognition. Also, as Bacon points
out by his statement, “... for else all bodies would be alike one to
another,” it is evidently some element of the essential character which
we take account of, namely something on which diversity is founded and
not mere bare logical diversity.

The word ‘_perceive_’ is, in our common usage, shot through and through
with the notion of cognitive apprehension. So is the word
‘_apprehension_’, even with the adjective _cognitive_ omitted. I will
use the word ‘_prehension_’ for _uncognitive apprehension_: by this I
mean _apprehension_ which may or or may not be cognitive. Now take
Euphranor’s last remark:

“Is it not plain, therefore, that neither the castle, the planet, nor
the cloud, _which you see here_, are those real ones which you suppose
exist at distance?” Accordingly, there is a prehension, _here_ in this
place, of things which have a reference to _other_ places.

Now go back to Berkeley’s sentences, quoted from his _Principles of
Human Knowledge_. He contends that what constitutes the realisation of
natural entities is the being perceived within the unity of mind.

We can substitute the concept, that the realisation is a gathering of
things into the unity of a prehension; and that what is thereby realised
is the prehension, and not the things. This unity of a prehension
defines itself as a _here_ and a _now_, and the things so gathered into
the grasped unity have essential reference to other places and other
times. For Berkeley’s _mind_, I substitute a process of prehensive
unification. In order to make intelligible this concept of the
progressive realisation of natural occurrences, considerable expansion
is required, and confrontation with its actual implications in terms of
concrete experience. This will be the task of the subsequent lectures.
In the first place, note that the idea of simple location has gone. The
things which are grasped into a realised unity, here and now, are not
the castle, the cloud, and the planet simply in themselves; but they are
the castle, the cloud, and the planet from the standpoint, in space and
time, of the prehensive unification. In other words, it is the
perspective of the castle over there from the standpoint of the
unification here. It is, therefore, aspects of the castle, the cloud,
and the planet which are grasped into unity here. You will remember that
the idea of perspectives is quite familiar in philosophy. It was
introduced by Leibniz, in the notion of his monads mirroring
perspectives of the universe. I am using the same notion, only I am
toning down his monads into the unified events in space and time. In
some ways, there is a greater analogy with Spinoza’s modes; that is why
I use the terms ‘_mode_’ and ‘_modal_.’ In the analogy with Spinoza, his
one substance is for me the one underlying activity of realisation
individualising itself in an interlocked plurality of modes. Thus,
concrete fact is process. Its primary analysis is into underlying
activity of prehension, and into realised prehensive events. Each event
is an individual matter of fact issuing from an individualisation of the
substrate activity. But individualisation does not mean substantial
independence.

An entity of which we become aware in sense perception is the terminus
of our act of perception. I will call such an entity, a
‘_sense-object_’. For example, green of a definite shade is a
sense-object; so is a sound of definite quality and pitch; and so is a
definite scent; and a definite quality of touch. The way in which such
an entity is related to space during a definite lapse of time is
complex. I will say that a sense-object has ‘_ingression_’ into
space-time. The cognitive perception of a sense-object is the awareness
of the prehensive unification (into a standpoint A) of various modes of
various sense-objects, including the sense-object in question. The
standpoint A is, of course, a region of space-time; that is to say, it
is a volume of space through a duration of time. But as one entity, this
standpoint is a unit of realised experience. A mode of a sense-object at
A (as abstracted from the sense-object whose relationship to A the mode
is conditioning) is the aspect from A of some other region B. Thus the
sense-object is present in A with the mode of location in B. Thus if
green be the sense-object in question, green is not simply at A where it
is being perceived, nor is it simply at B where it is perceived as
located; but it is present at A with the mode of location in B. There is
no particular mystery about this. You have only got to look into a
mirror and to see the image in it of some green leaves behind your back.
For you at A there will be green; but not green simply at A where you
are. The green at A will be green with the mode of having location at
the image of the leaf behind the mirror. Then turn round and look at the
leaf. You are now perceiving the green in the same way as you did
before, except that now the green has the mode of being located in the
actual leaf. I am merely describing what we do perceive: we are aware of
green as being one element in a prehensive unification of sense-objects;
each sense-object, and among them green, having its particular mode,
which is expressible as location elsewhere. There are various types of
modal location. For example, sound is voluminous: it fills a hall, and
so sometimes does diffused colour. But the modal location of a colour
may be that of being the remote boundary of a volume, as for example the
colours on the walls of a room. Thus primarily space-time is the locus
of the modal ingression of sense-objects. This is the reason why space
and time (if for simplicity we disjoin them) are given in their
entireties. For each volume of space, or each lapse of time, includes in
its essence aspects of all volumes of space, or of all lapses of time.
The difficulties of philosophy in respect to space and time are founded
on the error of considering them as primarily the loci of simple
locations. Perception is simply the cognition of prehensive unification;
or more shortly, perception is cognition of prehension. The actual world
is a manifold of prehensions; and a ‘prehension’ is a ‘prehensive
occasion’; and a prehensive occasion is the most concrete finite entity,
conceived as what it is in itself and for itself, and not as from its
aspect in the essence of another such occasion. Prehensive unification
might be said to have simple location in its volume A. But this would be
a mere tautology. For space and time are simply abstractions from the
totality of prehensive unifications as mutually patterned in each other.
Thus a prehension has simple location at the volume A in the same way as
that in which a man’s face fits on to the smile which spreads over it.
There is, so far as we have gone, more sense in saying that an act of
perception has simple location; for it may be conceived as being simply
at the cognised prehension.

There are more entities involved in nature than the mere sense-objects,
so far considered. But, allowing for the necessity of revision
consequent on a more complete point of view, we can frame our answer to
Berkeley’s question as to the character of the reality to be assigned to
nature. He states it to be the reality of ideas in mind. A complete
metaphysic which has attained to some notion of mind, and to some notion
of ideas, may perhaps ultimately adopt that view. It is unnecessary for
the purpose of these lectures to ask such a fundamental question. We can
be content with a provisional realism in which nature is conceived as a
complex of prehensive unifications. Space and time exhibit the general
scheme of interlocked relations of these prehensions. You cannot tear
any one of them out of its context. Yet each one of them within its
context has all the reality that attaches to the whole complex.
Conversely, the totality has the same reality as each prehension; for
each prehension unifies the modalities to be ascribed, from its
standpoint, to every part of the whole. A prehension is a process of
unifying. Accordingly, nature is a process of expansive development,
necessarily transitional from prehension to prehension. What is achieved
is thereby passed beyond, but it is also retained as having aspects of
itself present to prehensions which lie beyond it.

Thus nature is a structure of evolving processes. The reality is the
process. It is nonsense to ask if the colour red is real. The colour red
is ingredient in the process of realisation. The realities of nature are
the prehensions in nature, that is to say, the events in nature.

Now that we have cleared space and time from the taint of simple
location, we may partially abandon the awkward term prehension. This
term was introduced to signify the essential unity of an event, namely,
the event as one entity, and not as a mere assemblage of parts or of
ingredients. It is necessary to understand that space-time is nothing
else than a system of pulling together of assemblages into unities. But
the word _event_ just means one of these spatio-temporal unities.
Accordingly, it may be used instead of the term ‘prehension’ as meaning
the thing prehended.

An event has contemporaries. This means that an event mirrors within
itself the modes of its contemporaries as a display of immediate
achievement. An event has a past. This means that an event mirrors
within itself the modes of its predecessors, as memories which are fused
into its own content. An event has a future. This means that an event
mirrors within itself such aspects as the future throws back onto the
present, or, in other words, as the present has determined concerning
the future. Thus an event has anticipation:

         “The prophetic soul
         Of the wide world dreaming on things to come.” [cvii]

These conclusions are essential for any form of realism. For there is in
the world for our cognisance, memory of the past, immediacy of
realisation, and indication of things to come.

In this sketch of an analysis more concrete than that of the scientific
scheme of thought, I have started from our own psychological field, as
it stands for our cognition. I take it for what it claims to be: the
self-knowledge of our bodily event. I mean the total event, and not the
inspection of the details of the body. This self-knowledge discloses a
prehensive unification of modal presences of entities beyond itself. I
generalise by the use of the principle that this total bodily event is
on the same level as all other events, except for an unusual complexity
and stability of inherent pattern. The strength of the theory of
materialistic mechanism has been the demand, that no arbitrary breaks be
introduced into nature, to eke out the collapse of an explanation. I
accept this principle. But if you start from the immediate facts of our
psychological experience, as surely an empiricist should begin, you are
at once led to the organic conception of nature of which the description
has been commenced in this lecture.

It is the defect of the eighteenth century scientific scheme that it
provides none of the elements which compose the immediate psychological
experiences of mankind. Nor does it provide any elementary trace of the
organic unity of a whole, from which the organic unities of electrons,
protons, molecules, and living bodies can emerge. According to that
scheme, there is no reason in the nature of things why portions of
material should have any physical relations to each other. Let us grant
that we cannot hope to be able to discern the laws of nature to be
necessary. But we can hope to see that it is necessary that there should
be an order of nature. The concept of the order of nature is bound up
with the concept of nature as the locus of organisms in process of
development.

  NOTE. In connection with the latter portion of this chapter a sentence
  from Descartes’ ‘Reply to Objections ... against the Meditations’ is
  interesting:—“Hence the idea of the sun will be the sun itself
  existing in the mind, not indeed formally, as it exists in the sky,
  but objectively, _i.e._, in the way in which objects are wont to exist
  in the mind; and this mode of being is truly much less perfect than
  that in which things exist outside the mind, but it is not on that
  account mere nothing, as I have already said.” [Reply to Objections I,
  Translation by Haldane and Ross, vol. ii, p. 10.] I find difficulty in
  reconciling this theory of ideas (with which I agree) with other parts
  of the Cartesian philosophy.




                               CHAPTER V

                         THE ROMANTIC REACTION


My last lecture described the influence upon the eighteenth century of
the narrow and efficient scheme of scientific concepts which it had
inherited from its predecessor. That scheme was the product of a
mentality which found the Augustinian theology extremely congenial. The
Protestant Calvinism and the Catholic Jansenism exhibited man as
helpless to co-operate with Irresistible Grace: the contemporary scheme
of science exhibited man as helpless to co-operate with the irresistable
mechanism of nature. The mechanism of God and the mechanism of matter
were the monstrous issues of limited metaphysics and clear logical
intellect. Also the seventeenth century had genius, and cleared the
world of muddled thought. The eighteenth century continued the work of
clearance, with ruthless efficiency. The scientific scheme has lasted
longer than the theological scheme. Mankind soon lost interest in
Irresistible Grace; but it quickly appreciated the competent engineering
which was due to science. Also in the first quarter of the eighteenth
century, George Berkeley launched his philosophical criticism against
the whole basis of the system. He failed to disturb the dominant current
of thought. In my last lecture I developed a parallel line of argument,
which would lead to a system of thought basing nature upon the concept
of organism, and not upon the concept of matter. In the present lecture,
I propose in the first place to consider how the concrete educated
thought of men has viewed this opposition of mechanism and organism. It
is in literature that the concrete outlook of humanity receives its
expression. Accordingly it is to literature that we must look,
particularly in its more concrete forms, namely in poetry and in drama,
if we hope to discover the inward thoughts of a generation.

We quickly find that the Western peoples exhibit on a colossal scale a
peculiarity which is popularly supposed to be more especially
characteristic of the Chinese. Surprise is often expressed that a
Chinaman can be of two religions, a Confucian for some occasions and a
Buddhist for other occasions. Whether this is true of China I do not
know; nor do I know whether, if true, these two attitudes are really
inconsistent. But there can be no doubt that an analogous fact is true
of the West, and that the two attitudes involved are inconsistent. A
scientific realism, based on mechanism, is conjoined with an unwavering
belief in the world of men and of the higher animals as being composed
of self-determining organisms. This radical inconsistency at the basis
of modern thought accounts for much that is half-hearted and wavering in
our civilisation. It would be going too far to say that it distracts
thought. It enfeebles it, by reason of the inconsistency lurking in the
background. After all, the men of the Middle Ages were in pursuit of an
excellency of which we have nearly forgotten the existence. They set
before themselves the ideal of the attainment of a harmony of the
understanding. We are content with superficial orderings from diverse
arbitrary starting points. For instance, the enterprises produced by the
individualistic energy of the European peoples presupposes physical
actions directed to final causes. But the science which is employed in
their development is based on a philosophy which asserts that physical
causation is supreme, and which disjoins the physical cause from the
final end. It is not popular to dwell on the absolute contradiction here
involved. It is the fact, however you gloze it over with phrases. Of
course, we find in the eighteenth century Paley’s famous argument, that
mechanism presupposes a God who is the author of nature. But even before
Paley put the argument into its final form, Hume had written the retort,
that the God whom you will find will be the sort of God who makes that
mechanism. In other words, that mechanism can, at most, presuppose a
mechanic, and not merely _a_ mechanic but _its_ mechanic. The only way
of mitigating mechanism is by the discovery that it is not mechanism.

When we leave apologetic theology, and come to ordinary literature, we
find, as we might expect, that the scientific outlook is in general
simply ignored. So far as the mass of literature is concerned, science
might never have been heard of. Until recently nearly all writers have
been soaked in classical and renaissance literature. For the most part,
neither philosophy nor science interested them, and their minds were
trained to ignore it.

There are exceptions to this sweeping statement; and, even if we confine
ourselves to English literature, they concern some of the greatest
names; also the indirect influence of science has been considerable.

A side light on this distracting inconsistency in modern thought is
obtained by examining some of those great serious poems in English
literature, whose general scale gives them a didactic character. The
relevant poems are Milton’s _Paradise Lost_, Pope’s _Essay on Man_,
Wordsworth’s _Excursion_, Tennyson’s _In Memoriam_. Milton, though he is
writing after the Restoration, voices the theological aspect of the
earlier portion of his century, untouched by the influence of the
scientific materialism. Pope’s poem represents the effect on popular
thought of the intervening sixty years which includes the first period
of assured triumph for the scientific movement. Wordsworth in his whole
being expresses a conscious reaction against the mentality of the
eighteenth century. This mentality means nothing else than the
acceptance of the scientific ideas at their full face value. Wordsworth
was not bothered by any intellectual antagonism. What moved him was a
moral repulsion. He felt that something had been left out, and that what
had been left out comprised everything that was most important. Tennyson
is the mouthpiece of the attempts of the waning romantic movement in the
second quarter of the nineteenth century to come to terms with science.
By this time the two elements in modern thought had disclosed their
fundamental divergence by their jarring interpretations of the course of
nature and the life of man. Tennyson stands in this poem as the perfect
example of the distraction which I have already mentioned. There are
opposing visions of the world, and both of them command his assent by
appeals to ultimate intuitions from which there seems no escape.
Tennyson goes to the heart of the difficulty. It is the problem of
mechanism which appalls him,

              “‘The stars,’ she whispers, ‘blindly run.’”

This line states starkly the whole philosophic problem implicit in the
poem. Each molecule blindly runs. The human body is a collection of
molecules. Therefore, the human body blindly runs, and therefore there
can be no individual responsibility for the actions of the body. If you
once accept that the molecule is definitely determined to be what it is,
independently of any determination by reason of the total organism of
the body, and if you further admit that the blind run is settled by the
general mechanical laws, there can be no escape from this conclusion.
But mental experiences are derivative from the actions of the body,
including of course its internal behaviour. Accordingly, the sole
function of the mind is to have at least some of its experiences settled
for it, and to add such others as may be open to it independently of the
body’s motions, internal and external.

There are then two possible theories as to the mind. You can either deny
that it can supply for itself any experiences other than those provided
for it by the body, or you can admit them.

If you refuse to admit the additional experiences, then all individual
moral responsibility is swept away. If you do admit them, then a human
being may be responsible for the state of his mind though he has no
responsibility for the actions of his body. The enfeeblement of thought
in the modern world is illustrated by the way in which this plain issue
is avoided in Tennyson’s poem. There is something kept in the
background, a skeleton in the cupboard. He touches on almost every
religious and scientific problem, but carefully avoids more than a
passing allusion to this one.

This very problem was in full debate at the date of the poem. John
Stuart Mill was maintaining his doctrine of determinism. In this
doctrine volitions are determined by motives, and motives are
expressible in terms of antecedent conditions including states of mind
as well as states of the body.

It is obvious that this doctrine affords no escape from the dilemma
presented by a thoroughgoing mechanism. For if the volition affects the
state of the body, then the molecules in the body do not blindly run. If
the volition does not affect the state of the body, the mind is still
left in its uncomfortable position.

Mill’s doctrine is generally accepted, especially among scientists, as
though in some way it allowed you to accept the extreme doctrine of
materialistic mechanism, and yet mitigated its unbelievable
consequences. It does nothing of the sort. Either the bodily molecules
blindly run, or they do not. If they do blindly run, the mental states
are irrelevant in discussing the bodily actions.

I have stated the arguments concisely, because in truth the issue is a
very simple one. Prolonged discussion is merely a source of confusion.
The question as to the metaphysical status of molecules does not come
in. The statement that they are mere formulae has no bearing on the
argument. For presumably the formulae mean something. If they mean
nothing, the whole mechanical doctrine is likewise without meaning, and
the question drops. But if the formulae mean anything, the argument
applies to exactly what they do mean. The traditional way of evading the
difficulty—other than the simple way of ignoring it—is to have recourse
to some form of what is now termed ‘vitalism.’ This doctrine is really a
compromise. It allows a free run to mechanism throughout the whole of
inanimate nature, and holds that the mechanism is partially mitigated
within living bodies. I feel that this theory is an unsatisfactory
compromise. The gap between living and dead matter is too vague and
problematical to bear the weight of such an arbitrary assumption, which
involves an essential dualism somewhere.

The doctrine which I am maintaining is that the whole concept of
materialism only applies to very abstract entities, the products of
logical discernment. The concrete enduring entities are organisms, so
that the plan of the _whole_ influences the very characters of the
various subordinate organisms which enter into it. In the case of an
animal, the mental states enter into the plan of the total organism and
thus modify the plans of the successive subordinate organisms until the
ultimate smallest organisms, such as electrons, are reached. Thus an
electron within a living body is different from an electron outside it,
by reason of the plan of the body. The electron blindly runs either
within or without the body; but it runs within the body in accordance
with its character within the body; that is to say, in accordance with
the general plan of the body, and this plan includes the mental state.
But this principle of modification is perfectly general throughout
nature, and represents no property peculiar to living bodies. In
subsequent lectures it will be explained that this doctrine involves the
abandonment of the traditional scientific materialism, and the
substitution of an alternative doctrine of organism.

I shall not discuss Mill’s determinism, as it lies outside the scheme of
these lectures. The foregoing discussion has been directed to secure
that either determinism or free will shall have some relevance,
unhampered by the difficulties introduced by materialistic mechanism, or
by the compromise of vitalism. I would term the doctrine of these
lectures, the theory of _organic mechanism_. In this theory, the
molecules may blindly run in accordance with the general laws, but the
molecules differ in their intrinsic characters according to the general
organic plans of the situations in which they find themselves.

The discrepancy between the materialistic mechanism of science and the
moral intuitions, which are presupposed in the concrete affairs of life,
only gradually assumed its true importance as the centuries advanced.
The different tones of the successive epochs to which the poems, already
mentioned, belong are curiously reflected in their opening passages.
Milton ends his introduction with the prayer,

               “That to the height of this great argument
               I may assert eternal Providence,
               And justify the ways of God to men.”

To judge from many modern writers on Milton, we might imagine that the
_Paradise Lost_ and the _Paradise Regained_ were written as a series of
experiments in blank verse. This was certainly not Milton’s view of his
work. To ‘justify the ways of God to men’ was very much his main object.
He recurs to the same idea in the _Samson Agonistes_,

                       “Just are the ways of God
                       And justifiable to men;”

We note the assured volume of confidence, untroubled by the coming
scientific avalanche. The actual date of the publication of the
_Paradise Lost_ lies just beyond the epoch to which it belongs. It is
the swansong of a passing world of untroubled certitude.

A comparison between Pope’s _Essay on Man_ and the _Paradise Lost_
exhibits the change of tone in English thought in the fifty or sixty
years which separate the age of Milton from the age of Pope. Milton
addresses his poem to God, Pope’s poem is addressed to Lord Bolingbroke,

              “Awake, my St. John! leave all meaner things
              To low ambition and the pride of kings.
              Let us (since life can little more supply
              Than just to look about us and to die)
              Expatiate free o’er all this scene of man;
              A mighty maze! but not without a plan;”

Compare the jaunty assurance of Pope,

                “A mighty maze! but not without a plan.”

with Milton’s

                       “Just are the ways of God
                       And justifiable to men;”

But the real point to notice is that Pope as well as Milton was
untroubled by the great perplexity which haunts the modern world. The
clue which Milton followed was to dwell on the ways of God in dealings
with man. Two generations later we find Pope equally confident that the
enlightened methods of modern science provided a plan adequate as a map
of the ‘mighty maze.’

Wordsworth’s _Excursion_ is the next English poem on the same subject. A
prose preface tells us that it is a fragment of a larger projected work,
described as ‘A philosophical poem containing views of Man, Nature, and
Society.’

Very characteristically the poem begins with the line,

             “’Twas summer, and the sun had mounted high:”

Thus the romantic reaction started neither with God nor with Lord
Bolingbroke, but with nature. We are here witnessing a conscious
reaction against the whole tone of the eighteenth century. That century
approached nature with the abstract analysis of science, whereas
Wordsworth opposes to the scientific abstractions his full concrete
experience.

A generation of religious revival and of scientific advance lies between
the _Excursion_ and Tennyson’s _In Memoriam_. The earlier poets had
solved the perplexity by ignoring it. That course was not open to
Tennyson. Accordingly his poem begins thus:

                 “Strong Son of God, immortal Love,
                 Whom we, that have not seen Thy face,
                 By faith, and faith alone, embrace,
                 Believing where we cannot prove;”

The note of perplexity is struck at once. The nineteenth century has
been a perplexed century, in a sense which is not true of any of its
predecessors of the modern period. In the earlier times there were
opposing camps, bitterly at variance on questions which they deemed
fundamental. But, except for a few stragglers, either camp was
whole-hearted. The importance of Tennyson’s poem lies in the fact that
it exactly expressed the character of its period. Each individual was
divided against himself. In the earlier times, the deep thinkers were
the clear thinkers,—Descartes, Spinoza, Locke, Leibniz. They knew
exactly what they meant and said it. In the nineteenth century, some of
the deeper thinkers among theologians and philosophers were muddled
thinkers. Their assent was claimed by incompatible doctrines; and their
efforts at reconciliation produced inevitable confusion.

Matthew Arnold, even more than Tennyson, was the poet who expressed this
mood of individual distraction which was so characteristic of this
century. Compare with _In Memoriam_ the closing lines of Arnold’s _Dover
Beach_:

           “And we are here as on a darkling plain
           Swept with confused alarms of struggle and flight,
           Where ignorant armies clash by night.”

Cardinal Newman in his _Apologia pro Vitâ Suâ_ mentions it as a
peculiarity of Pusey, the great Anglican ecclesiastic, “He was haunted
by no intellectual perplexities.” In this respect Pusey recalls Milton,
Pope, Wordsworth, as in contrast with Tennyson, Clough, Matthew Arnold,
and Newman himself.

So far as concerns English literature we find, as might be anticipated,
the most interesting criticism of the thoughts of science among the
leaders of the romantic reaction which accompanied and succeeded the
epoch of the French Revolution. In English literature, the deepest
thinkers of this school were Coleridge, Wordsworth, and Shelley. Keats
is an example of literature untouched by science. We may neglect
Coleridge’s attempt at an explicit philosophical formulation. It was
influential in his own generation; but in these lectures it is my object
only to mention those elements of the thought of the past which stand
for all time. Even with this limitation, only a selection is possible.
For our purposes Coleridge is only important by his influence on
Wordsworth. Thus Wordsworth and Shelley remain.

Wordsworth was passionately absorbed in nature. It has been said of
Spinoza, that he was drunk with God. It is equally true that Wordsworth
was drunk with nature. But he was a thoughtful, well-read man, with
philosophical interests, and sane even to the point of prosiness. In
addition, he was a genius. He weakens his evidence by his dislike of
science. We all remember his scorn of the poor man whom he somewhat
hastily accuses of peeping and botanising on his mother’s grave. Passage
after passage could be quoted from him, expressing this repulsion. In
this respect, his characteristic thought can be summed up in his phrase,
‘We murder to dissect.’

In this latter passage, he discloses the intellectual basis of his
criticism of science. He alleges against science its absorption in
abstractions. His consistent theme is that the important facts of nature
elude the scientific method. It is important therefore to ask, what
Wordsworth found in nature that failed to receive expression in science.
I ask this question in the interest of science itself; for one main
position in these lectures is a protest against the idea that the
abstractions of science are irreformable and unalterable. Now it is
emphatically not the case that Wordsworth hands over inorganic matter to
the mercy of science, and concentrates on the faith that in the living
organism there is some element that science cannot analyse. Of course he
recognises, what no one doubts, that in some sense living things are
different from lifeless things. But that is not his main point. It is
the brooding presence of the hills which haunts him. His theme is nature
_in solido_, that is to say, he dwells on that mysterious presence of
surrounding things, which imposes itself on any separate element that we
set up as an individual for its own sake. He always grasps the whole of
nature as involved in the tonality of the particular instance. That is
why he laughs with the daffodils, and finds in the primrose “thoughts
too deep for terms.”

Wordsworth’s greatest poem is, by far, the first book of _The Prelude_.
It is pervaded by this sense of the haunting presences of nature. A
series of magnificent passages, too long for quotation, express this
idea. Of course, Wordsworth is a poet writing a poem, and is not
concerned with dry philosophical statements. But it would hardly be
possible to express more clearly a feeling for nature, as exhibiting
entwined prehensive unities, each suffused with modal presences of
others:

             “Ye Presences of Nature in the sky
             And on the earth! Ye Visions of the hills!
             And Souls of lonely places! can I think
             A vulgar hope was yours when ye employed
             Such ministry, when ye through many a year
             Haunting me thus among my boyish sports,
             On caves and trees, upon the woods and hills,
             Impressed upon all forms the characters
             Of danger or desire; and thus did make
             The surface of the universal earth
             With triumph and delight, with hope and fear,
             Work like a sea?...”

In thus citing Wordsworth, the point which I wish to make is that we
forget how strained and paradoxical is the view of nature which modern
science imposes on our thoughts. Wordsworth, to the height of genius,
expresses the concrete facts of our apprehension, facts which are
distorted in the scientific analysis. Is it not possible that the
standardised concepts of science are only valid within narrow
limitations, perhaps too narrow for science itself?

Shelley’s attitude to science was at the opposite pole to that of
Wordsworth. He loved it, and is never tired of expressing in poetry the
thoughts which it suggests. It symbolises to him joy, and peace, and
illumination. What the hills were to the youth of Wordsworth, a chemical
laboratory was to Shelley. It is unfortunate that Shelley’s literary
critics have, in this respect, so little of Shelley in their own
mentality. They tend to treat as a casual oddity of Shelley’s nature
what was, in fact, part of the main structure of his mind, permeating
his poetry through and through. If Shelley had been born a hundred years
later, the twentieth century would have seen a Newton among chemists.

For the sake of estimating the value of Shelley’s evidence it is
important to realise this absorption of his mind in scientific ideas. It
can be illustrated by lyric after lyric. I will choose one poem only,
the fourth act of his _Prometheus Unbound_. The Earth and the Moon
converse together in the language of accurate science. Physical
experiments guide his imagery. For example, the Earth’s exclamation,

             “The vaporous exultation not to be confined!”

is the poetic transcript of ‘the expansive force of gases,’ as it is
termed in books on science. Again, take the Earth’s stanza,

      “I spin beneath my pyramid of night,
      Which points into the heavens,—dreaming delight,
      Murmuring victorious joy in my enchanted sleep;
      As a youth lulled in love-dreams faintly sighing,
      Under the shadow of his beauty lying,
      Which round his rest a watch of light and warmth doth keep.”

This stanza could only have been written by someone with a definite
geometrical diagram before his inward eye—a diagram which it has often
been my business to demonstrate to mathematical classes. As evidence,
note especially the last line which gives poetical imagery to the light
surrounding night’s pyramid. This idea could not occur to anyone without
the diagram. But the whole poem and other poems are permeated with
touches of this kind.

Now the poet, so sympathetic with science, so absorbed in its ideas, can
simply make nothing of the doctrine of secondary qualities which is
fundamental to its concepts. For Shelley nature retains its beauty and
its colour. Shelley’s nature is in its essence a nature of organisms,
functioning with the full content of our perceptual experience. We are
so used to ignoring the implications of orthodox scientific doctrine,
that it is difficult to make evident the criticism upon it which is
thereby implied. If anybody could have treated it seriously, Shelley
would have done so.

Furthermore Shelley is entirely at one with Wordsworth as to the
interfusing of the Presence in nature. Here is the opening stanza of his
poem entitled _Mont Blanc_:

           “The everlasting universe of Things
           Flows through the Mind, and rolls its rapid waves,
           Now dark—now glittering—now reflecting gloom—
           Now lending splendour, where from secret springs
           The source of human thought its tribute brings
           Of waters,—with a sound but half its own,
           Such as a feeble brook will oft assume
           In the wild woods, among the Mountains lone,
           Where waterfalls around it leap for ever,
           Where woods and winds contend, and a vast river
           Over its rocks ceaselessly bursts and raves.”

Shelley has written these lines with explicit reference to some form of
idealism, Kantian or Berkeleyan or Platonic. But however you construe
him, he is here an emphatic witness to a prehensive unification as
constituting the very being of nature.

Berkeley, Wordsworth, Shelley are representative of the intuitive
refusal seriously to accept the abstract materialism of science.

There is an interesting difference in the treatment of nature by
Wordsworth and by Shelley, which brings forward the exact questions we
have got to think about. Shelley thinks of nature as changing,
dissolving, transforming as it were at a fairy’s touch. The leaves fly
before the West Wind

                “Like ghosts from an enchanter fleeing.”

In his poem _The Cloud_ it is the transformations of water which excite
his imagination. The subject of the poem is the endless, eternal,
elusive change of things:

                      “I change but I cannot die.”

This is one aspect of nature, its elusive change: a change not merely to
be expressed by locomotion, but a change of inward character. This is
where Shelley places his emphasis, on the change of what cannot die.

Wordsworth was born among hills; hills mostly barren of trees, and thus
showing the minimum of change with the seasons. He was haunted by the
enormous permanences of nature. For him change is an incident which
shoots across a background of endurance,

                   “Breaking the silence of the seas
                   Among the farthest Hebrides.”

Every scheme for the analysis of nature has to face these two facts,
_change_ and _endurance_. There is yet a third fact to be placed by it,
_eternality_, I will call it. The mountain endures. But when after ages
it has been worn away, it has gone. If a replica arises, it is yet a new
mountain. A colour is eternal. It haunts time like a spirit. It comes
and it goes. But where it comes, it is the same colour. It neither
survives nor does it live. It appears when it is wanted. The mountain
has to time and space a different relation from that which colour has.
In the previous lecture, I was chiefly considering the relation to
space-time of things which, in my sense of the term, are eternal. It was
necessary to do so before we can pass to the consideration of the things
which endure.

Also we must recollect the basis of our procedure. I hold that
philosophy is the critic of abstractions. Its function is the double
one, first of harmonising them by assigning to them their right relative
status as abstractions, and secondly of completing them by direct
comparison with more concrete intuitions of the universe, and thereby
promoting the formation of more complete schemes of thought. It is in
respect to this comparison that the testimony of great poets is of such
importance. Their survival is evidence that they express deep intuitions
of mankind penetrating into what is universal in concrete fact.
Philosophy is not one among the sciences with its own little scheme of
abstractions which it works away at perfecting and improving. It is the
survey of sciences, with the special objects of their harmony, and of
their completion. It brings to this task, not only the evidence of the
separate sciences, but also its own appeal to concrete experience. It
confronts the sciences with concrete fact.

The literature of the nineteenth century, especially its English poetic
literature, is a witness to the discord between the aesthetic intuitions
of mankind and the mechanism of science. Shelley brings vividly before
us the elusiveness of the eternal objects of sense as they haunt the
change which infects underlying organisms. Wordsworth is the poet of
nature as being the field of enduring permanences carrying within
themselves a message of tremendous significance. The eternal objects are
also there for him,

              “The light that never was, on sea or land.”

Both Shelley and Wordsworth emphatically bear witness that nature cannot
be divorced from its aesthetic values; and that these values arise from
the cumulation, in some sense, of the brooding presence of the whole
onto its various parts. Thus we gain from the poets the doctrine that a
philosophy of nature must concern itself at least with these five
notions: change, value, eternal objects, endurance, organism,
interfusion.

We see that the literary romantic movement at the beginning of the
nineteenth century, just as much as Berkeley’s philosophical idealistic
movement a hundred years earlier, refused to be confined within the
materialistic concepts of the orthodox scientific theory. We know also
that when in these lectures we come to the twentieth century, we shall
find a movement in science itself to reorganise its concepts, driven
thereto by its own intrinsic development.

It is, however, impossible to proceed until we have settled whether
this refashioning of ideas is to be carried out on an objectivist
basis or on a subjectivist basis. By a subjectivist basis I mean the
belief that the nature of our immediate experience is the outcome of
the perceptive peculiarities of the subject enjoying the experience.
In other words, I mean that for this theory what is perceived is not a
partial vision of a complex of things generally independent of that
act of cognition; but that it merely is the expression of the
individual peculiarities of the cognitive act. Accordingly what is
common to the multiplicity of cognitive acts is the ratiocination
connected with them. Thus, though there is a common world of thought
associated with our sense-perceptions, there is no common world to
think about. What we do think about is a common conceptual world
applying indifferently to our individual experiences which are
strictly personal to ourselves. Such a conceptual world will
ultimately find its complete expression in the equations of applied
mathematics. This is the extreme subjectivist position. There is of
course the half-way house of those who believe that our perceptual
experience does tell us of a common objective world; but that the
things perceived are merely the outcome for us of this world, and are
not _in themselves_ elements in the common world itself.

Also there is the objectivist position. This creed is that the actual
elements perceived by our senses are _in themselves_ the elements of a
common world; and that this world is a complex of things, including
indeed our acts of cognition, but transcending them. According to this
point of view the things experienced are to be distinguished from our
knowledge of them. So far as there is dependence, the _things_ pave the
way for the _cognition_, rather than _vice versa_. But the point is that
the actual things experienced enter into a common world which transcends
knowledge, though it includes knowledge. The intermediate subjectivists
would hold that the things experienced only indirectly enter into the
common world by reason of their dependence on the subject who is
cognising. The objectivist holds that the things experienced and the
cognisant subject enter into the common world on equal terms. In these
lectures I am giving the outline of what I consider to be the essentials
of an objectivist philosophy adapted to the requirement of science and
to the concrete experience of mankind. Apart from the detailed criticism
of the difficulties raised by subjectivism in any form, my broad reasons
for distrusting it are three in number. One reason arises from the
direct interrogation of our perceptive experience. It appears from this
interrogation that we are _within_ a world of colours, sounds, and other
sense-objects, related in space and time to enduring objects such as
stones, trees, and human bodies. We seem to be ourselves elements of
this world in the same sense as are the other things which we perceive.
But the subjectivist, even the moderate intermediate subjectivist, makes
this world, as thus described, depend on us, in a way which directly
traverses our naïve experience. I hold that the ultimate appeal is to
naïve experience and that is why I lay such stress on the evidence of
poetry. My point is, that in our sense-experience we know away from and
beyond our own personality; whereas the subjectivist holds that in such
experience we merely know about our own personality. Even the
intermediate subjectivist places our personality between the world we
know of and the common world which he admits. The world we know of is
for him the internal strain of our personality under the stress of the
common world which lies behind.

My second reason for distrusting subjectivism is based on the particular
content of experience. Our historical knowledge tells us of ages in the
past when, so far as we can see, no living being existed on earth. Again
it also tells us of countless star-systems, whose detailed history
remains beyond our ken. Consider even the moon and the earth. What is
going on within the interior of the earth, and on the far side of the
moon! Our perceptions lead us to infer that there is something happening
in the stars, something happening within the earth, and something
happening on the far side of the moon. Also they tell us that in remote
ages there were things happening. But all these things which it appears
certainly happened, are either unknown in detail, or else are
reconstructed by inferential evidence. In the face of this content of
our personal experience, it is difficult to believe that the experienced
world is an attribute of our own personality. My third reason is based
upon the instinct for action. Just as sense-perception seems to give
knowledge of what lies beyond individuality, so action seems to issue in
an instinct for self-transcendence. The activity passes beyond self into
the known transcendent world. It is here that final ends are of
importance. For it is not activity urged from behind, which passes out
into the veiled world of the intermediate subjectivist. It is activity
directed to determinate ends in the known world; and yet it is activity
transcending self and it is activity within the known world. It follows
therefore that the world, as known, transcends the subject which is
cognisant of it.

The subjectivist position has been popular among those who have been
engaged in giving a philosophical interpretation to the recent theories
of relativity in physical science. The dependence of the world of sense
on the individual percipient seems an easy mode of expressing the
meanings involved. Of course, with the exception of those who are
content with themselves as forming the entire universe, solitary amid
nothing, everyone wants to struggle back to some sort of objectivist
position. I do not understand how a common world of thought can be
established in the absence of a common world of sense. I will not argue
this point in detail; but in the absence of a transcendence of thought,
or a transcendence of the world of sense, it is difficult to see how the
subjectivist is to divest himself of his solitariness. Nor does the
intermediate subjectivist appear to get any help from his unknown world
in the background.

The distinction between realism and idealism does not coincide with that
between objectivism and subjectivism. Both realists and idealists can
start from an objective standpoint. They may both agree that the world
disclosed in sense-perception is a common world, transcending the
individual percipient. But the objective idealist, when he comes to
analyse what the reality of this world involves, finds that cognitive
mentality is in some way inextricably concerned in every detail. This
position the realist denies. Accordingly these two classes of
objectivists do not part company till they have arrived at the ultimate
problem of metaphysics. There is a great deal which they share in
common. This is why, in my last lecture, I said that I adopted a
position of provisional realism.

In the past, the objectivist position has been distorted by the supposed
necessity of accepting the classical scientific materialism, with its
doctrine of simple location. This has necessitated the doctrine of
secondary and primary qualities. Thus the secondary qualities, such as
the sense-objects, are dealt with on subjectivist principles. This is a
half-hearted position which falls an easy prey to subjectivist
criticism.

If we are to include the secondary qualities in the common world, a very
drastic reorganisation of our fundamental concepts is necessary. It is
an evident fact of experience that our apprehensions of the external
world depend absolutely on the occurrences within the human body. By
playing appropriate tricks on the body a man can be got to perceive, or
not to perceive, almost anything. Some people express themselves as
though bodies, brains, and nerves were the only real things in an
entirely imaginary world. In other words, they treat bodies on
objectivist principles, and the rest of the world on subjectivist
principles. This will not do; especially, when we remember that it is
the experimenter’s perception of another person’s body which is in
question as evidence.

But we have to admit that the body is the organism whose states regulate
our cognisance of the world. The unity of the perceptual field therefore
must be a unity of bodily experience. In being aware of the bodily
experience, we must thereby be aware of aspects of the whole
spatio-temporal world as mirrored within the bodily life. This is the
solution of the problem which I gave in my last lecture. I will not
repeat myself now, except to remind you that my theory involves the
entire abandonment of the notion that simple location is the primary way
in which things are involved in space-time. In a certain sense,
everything is everywhere at all times. For every location involves an
aspect of itself in every other location. Thus every spatio-temporal
standpoint mirrors the world.

If you try to imagine this doctrine in terms of our conventional views
of space and time, which presuppose simple location, it is a great
paradox. But if you think of it in terms of our naïve experience, it is
a mere transcript of the obvious facts. You are in a certain place
perceiving things. Your perception takes place where you are, and is
entirely dependent on how your body is functioning. But this functioning
of the body in one place, exhibits for your cognisance an aspect of the
distant environment, fading away into the general knowledge that there
are things beyond. If this cognisance conveys knowledge of a
transcendent world, it must be because the event which is the bodily
life unifies in itself aspects of the universe.

This is a doctrine extremely consonant with the vivid expression of
personal experience which we find in the nature-poetry of imaginative
writers such as Wordsworth or Shelley. The brooding, immediate presences
of things are an obsession to Wordsworth. What the theory does do is to
edge cognitive mentality away from being the necessary substratum of the
unity of experience. That unity is now placed in the unity of an event.
Accompanying this unity, there may or there may not be cognition.

At this point we come back to the great question which was posed before
us by our examination of the evidence afforded by the poetic insight of
Wordsworth and Shelley. This single question has expanded into a group
of questions. What are enduring things, as distinguished from the
eternal objects, such as colour and shape? How are they possible? What
is their status and meaning in the universe? It comes to this: What is
the status of the enduring stability of the order of nature? There is
the summary answer, which refers nature to some greater reality standing
behind it. This reality occurs in the history of thought under many
names, The Absolute, Brahma, The Order of Heaven, God. The delineation
of final metaphysical truth is no part of this lecture. My point is that
any summary conclusion jumping from our conviction of the existence of
such an order of nature to the easy assumption that there is an ultimate
reality which, in some unexplained way, is to be appealed to for the
removal of perplexity, constitutes the great refusal of rationality to
assert its rights. We have to search whether nature does not in its very
being show itself as self-explanatory. By this I mean, that the sheer
statement, of what things are, may contain elements explanatory of why
things are. Such elements may be expected to refer to depths beyond
anything which we can grasp with a clear apprehension. In a sense, all
explanation must end in an ultimate arbitrariness. My demand is, that
the ultimate arbitrariness of matter of fact from which our formulation
starts should disclose the same general principles of reality, which we
dimly discern as stretching away into regions beyond our explicit powers
of discernment. Nature exhibits itself as exemplifying a philosophy of
the evolution of organisms subject to determinate conditions. Examples
of such conditions are the dimensions of space, the laws of nature, the
determinate enduring entities, such as atoms and electrons, which
exemplify these laws. But the very nature of these entities, the very
nature of their spatiality and temporality, should exhibit the
arbitrariness of these conditions as the outcome of a wider evolution
beyond nature itself, and within which nature is but a limited mode.

One all-pervasive fact, inherent in the very character of what is real
is the transition of things, the passage one to another. This passage is
not a mere linear procession of discrete entities. However we fix a
determinate entity, there is always a narrower determination of
something which is presupposed in our first choice. Also there is always
a wider determination into which our first choice fades by transition
beyond itself. The general aspect of nature is that of evolutionary
expansiveness. These unities, which I call events, are the emergence
into actuality of something. How are we to characterise the something
which thus emerges? The name ‘_event_’ given to such a unity, draws
attention to the inherent transitoriness, combined with the actual
unity. But this abstract word cannot be sufficient to characterise what
the fact of the reality of an event is in itself. A moment’s thought
shows us that no one idea can in itself be sufficient. For every idea
which finds its significance in each event must represent something
which contributes to what realisation is in itself. Thus no one word can
be adequate. But conversely, nothing must be left out. Remembering the
poetic rendering of our concrete experience, we see at once that the
element of value, of being valuable, of having value, of being an end in
itself, of being something which is for its own sake, must not be
omitted in any account of an event as the most concrete actual
something. ‘Value’ is the word I use for the intrinsic reality of an
event. Value is an element which permeates through and through the
poetic view of nature. We have only to transfer to the very texture of
realisation in itself that value which we recognise so readily in terms
of human life. This is the secret of Wordsworth’s worship of nature.
Realization therefore is in itself the attainment of value. But there is
no such thing as mere value. Value is the outcome of limitation. The
definite finite entity is the selected mode which is the shaping of
attainment; apart from such shaping into individual matter of fact there
is no attainment. The mere fusion of all that there is would be the
nonentity of indefiniteness. The salvation of reality is its obstinate,
irreducible, matter-of-fact entities, which are limited to be no other
than themselves. Neither science, nor art, nor creative action can tear
itself away from obstinate, irreducible, limited facts. The endurance of
things has its significance in the self-retention of that which imposes
itself as a definite attainment for its own sake. That which endures is
limited, obstructive, intolerant, infecting its environment with its own
aspects. But it is not self-sufficient. The aspects of all things enter
into its very nature. It is only itself as drawing together into its own
limitation the larger whole in which it finds itself. Conversely it is
only itself by lending its aspects to this same environment in which it
finds itself. The problem of evolution is the development of enduring
harmonies of enduring shapes of value, which merge into higher
attainments of things beyond themselves. Aesthetic attainment is
interwoven in the texture of realisation. The endurance of an entity
represents the attainment of a limited aesthetic success, though if we
look beyond it to its external effects, it may represent an aesthetic
failure. Even within itself, it may represent the conflict between a
lower success and a higher failure. The conflict is the presage of
disruption.

The further discussion of the nature of enduring objects and of the
conditions they require will be relevant to the consideration of the
doctrine of evolution which dominated the latter half of the nineteenth
century. The point which in this lecture I have endeavoured to make
clear is that the nature-poetry of the romantic revival was a protest on
behalf of the organic view of nature, and also a protest against the
exclusion of value from the essence of matter of fact. In this aspect of
it, the romantic movement may be conceived as a revival of Berkeley’s
protest which had been launched a hundred years earlier. The romantic
reaction was a protest on behalf of value.




                               CHAPTER VI

                         THE NINETEENTH CENTURY


My previous lecture was occupied with the comparison of the
nature-poetry of the romantic movement in England with the materialistic
scientific philosophy inherited from the eighteenth century. It noted
the entire disagreement of the two movements of thought. The lecture
also continued the endeavour to outline an objectivist philosophy,
capable of bridging the gap between science and that fundamental
intuition of mankind which finds its expression in poetry and its
practical exemplification in the presuppositions of daily life. As the
nineteenth century passed on, the romantic movement died down. It did
not die away, but it lost its clear unity of tidal stream, and dispersed
itself into many estuaries as it coalesced with other human interests.
The faith of the century was derived from three sources: one source was
the romantic movement, showing itself in religious revival, in art, and
in political aspiration: another source was the gathering advance of
science which opened avenues of thought: the third source was the
advance in technology which completely changed the conditions of human
life.

Each of these springs of faith had its origin in the previous period.
The French Revolution itself was the first child of romanticism in the
form in which it tinged Rousseau. James Watt obtained his patent for his
steam-engine in 1769. The scientific advance was the glory of France and
of French influence, throughout the same century.

Also even during this earlier period, the streams interacted, coalesced,
and antagonised each other. But it was not until the nineteenth century
that the threefold movement came to that full development and peculiar
balance characteristic of the sixty years following the battle of
Waterloo.

What is peculiar and new to the century, differentiating it from all its
predecessors, is its technology. It was not merely the introduction of
some great isolated inventions. It is impossible not to feel that
something more than that was involved. For example, writing was a
greater invention than the steam-engine. But in tracing the continuous
history of the growth of writing we find an immense difference from that
of the steam-engine. We must, of course, put aside minor and sporadic
anticipations of both; and confine attention to the periods of their
effective elaboration. The scale of time is so absolutely disparate. For
the steam-engine, we may give about a hundred years; for writing, the
time period is of the order of a thousand years. Further, when writing
was finally popularised, the world was not then expecting the next step
in technology. The process of change was slow, unconscious, and
unexpected.

In the nineteenth century, the process became quick, conscious, and
expected. The earlier half of the century was the period in which this
new attitude to change was first established and enjoyed. It was a
peculiar period of hope, in the sense in which, sixty or seventy years
later, we can now detect a note of disillusionment, or at least of
anxiety.

The greatest invention of the nineteenth century was the invention of
the method of invention. A new method entered into life. In order to
understand our epoch, we can neglect all the details of change, such as
railways, telegraphs, radios, spinning machines, synthetic dyes. We must
concentrate on the method in itself; that is the real novelty, which has
broken up the foundations of the old civilisation. The prophecy of
Francis Bacon has now been fulfilled; and man, who at times dreamt of
himself as a little lower than the angels, has submitted to become the
servant and the minister of nature. It still remains to be seen whether
the same actor can play both parts.

The whole change has arisen from the new scientific information.
Science, conceived not so much in its principles as in its results, is
an obvious storehouse of ideas for utilisation. But, if we are to
understand what happened during the century, the analogy of a mine is
better than that of a storehouse. Also, it is a great mistake to think
that the bare scientific idea is the required invention, so that it has
only to be picked up and used. An intense period of imaginative design
lies between. One element in the new method is just the discovery of how
to set about bridging the gap between the scientific ideas, and the
ultimate product. It is a process of disciplined attack upon one
difficulty after another.

The possibilities of modern technology were first in practice realised
in England, by the energy of a prosperous middle class. Accordingly, the
industrial revolution started there. But the Germans explicitly realised
the methods by which the deeper veins in the mine of science could be
reached. They abolished haphazard methods of scholarship. In their
technological schools and universities progress did not have to wait for
the occasional genius, or the occasional lucky thought. Their feats of
scholarship during the nineteenth century were the admiration of the
world. This discipline of knowledge applies beyond technology to pure
science, and beyond science to general scholarship. It represents the
change from amateurs to professionals.

There have always been people who devoted their lives to definite
regions of thought. In particular, lawyers and the clergy of the
Christian churches form obvious examples of such specialism. But the
full self-conscious realisation of the power of professionalism in
knowledge in all its departments, and of the way to produce the
professionals, and of the importance of knowledge to the advance of
technology, and of the methods by which abstract knowledge can be
connected with technology, and of the boundless possibilities of
technological advance,—the realisation of all these things was first
completely attained in the nineteenth century; and among the various
countries, chiefly in Germany.

In the past human life was lived in a bullock cart; in the future it
will be lived in an aeroplane; and the change of speed amounts to a
difference in quality.

The transformation of the field of knowledge, which has been thus
effected, has not been wholly a gain. At least, there are dangers
implicit in it, although the increase of efficiency is undeniable. The
discussion of various effects on social life arising from the new
situation is reserved for my last lecture. For the present it is
sufficient to note that this novel situation of disciplined progress is
the setting within which the thought of the century developed.

In the period considered four great novel ideas were introduced into
theoretical science. Of course, it is possible to show good cause for
increasing my list far beyond the number _four_. But I am keeping to
ideas which, if taken in their broadest signification, are vital to
modern attempts at reconstructing the foundations of physical science.

Two of these ideas are antithetical, and I will consider them together.
We are not concerned with details, but with ultimate influences on
thought. One of the ideas is that of a field of physical activity
pervading all space, even where there is an apparent vacuum. This notion
had occurred to many people, under many forms. We remember the medieval
axiom, nature abhors a vacuum. Also, Descartes’ vortices at one time, in
the seventeenth century, seemed as if established among scientific
assumptions. Newton believed that gravitation was caused by something
happening in a medium. But, on the whole, in the eighteenth century
nothing was made of any of these ideas. The passage of light was
explained in Newton’s fashion by the flight of minute corpuscles, which
of course left room for a vacuum. Mathematical physicists were far too
busy deducing the consequences of the theory of gravitation to bother
much about the causes; nor did they know where to look, if they had
troubled themselves over the question. There were speculations, but
their importance was not great. Accordingly, when the nineteenth century
opened, the notion of physical occurrences pervading all space held no
effective place in science. It was revived from two sources. The
undulatory theory of light triumphed, thanks to Thomas Young and
Fresnel. This demands that there shall be something throughout space
which can undulate. Accordingly, the ether was produced, as a sort of
all pervading subtle material. Again the theory of electromagnetism
finally, in Clerk Maxwell’s hands, assumed a shape in which it demanded
that there should be electromagnetic occurrences throughout all space.
Maxwell’s complete theory was not shaped until the eighteen-seventies.
But it had been prepared for by many great men, Ampère, Oersted,
Faraday. In accordance with the current materialistic outlook, these
electromagnetic occurrences also required a material in which to happen.
So again the ether was requisitioned. Then Maxwell, as the immediate
first-fruits of his theory, demonstrated that the waves of light were
merely waves of his electromagnetic occurrences. Accordingly, the theory
of electromagnetism swallowed up the theory of light. It was a great
simplification, and no one doubts its truth. But it had one unfortunate
effect so far as materialism was concerned. For, whereas quite a simple
sort of elastic ether sufficed for light when taken by itself, the
electromagnetic ether has to be endowed with just those properties
necessary for the production of the electromagnetic occurrences. In
fact, it becomes a mere name for the material which is postulated to
underlie these occurrences. If you do not happen to hold the
metaphysical theory which makes you postulate such an ether, you can
discard it. For it has no independent vitality.

Thus in the seventies of the last century, some main physical sciences
were established on a basis which presupposed the idea of _continuity_.
On the other hand, the idea of _atomicity_ had been introduced by John
Dalton, to complete Lavoisier’s work on the foundation of chemistry.
This is the second great notion. Ordinary matter was conceived as
atomic: electromagnetic effects were conceived as arising from a
continuous field.

There was no contradiction. In the first place, the notions are
antithetical; but, apart from special embodiments, are not logically
contradictory. Secondly, they were applied to different regions of
science, one to chemistry, and the other to electromagnetism. And, as
yet, there were but faint signs of coalescence between the two.

The notion of matter as atomic has a long history. Democritus and
Lucretius will at once occur to your minds. In speaking of these ideas
as novel, I merely mean _relatively novel_, having regard to the
settlement of ideas which formed the efficient basis of science
throughout the eighteenth century. In considering the history of
thought, it is necessary to distinguish the real stream, determining a
period, from ineffectual thoughts casually entertained. In the
eighteenth century every well-educated man read Lucretius, and
entertained ideas about atoms. But John Dalton made them efficient in
the stream of science; and in this function of efficiency atomicity was
a new idea.

The influence of atomicity was not limited to chemistry. The living cell
is to biology what the electron and the proton are to physics. Apart
from cells and from aggregates of cells there are no biological
phenomena. The cell theory was introduced into biology contemporaneously
with, and independently of, Dalton’s atomic theory. The two theories are
independent exemplifications of the same idea of ‘atomism.’ The
biological cell theory was a gradual growth, and a mere list of dates
and names illustrates the fact that the biological sciences, as
effective schemes of thought, are barely one hundred years old. Bichât
in 1801 elaborated a tissue theory: Johannes Müller in 1835 described
‘cells’ and demonstrated facts concerning their nature and relations:
Schleiden in 1838 and Schwann in 1839 finally established their
fundamental character. Thus by 1840 both biology and chemistry were
established on an atomic basis. The final triumph of atomism had to wait
for the arrival of electrons at the end of the century. The importance
of the imaginative background is illustrated by the fact that nearly
half a century after Dalton had done his work, another chemist, Louis
Pasteur, carried over these same ideas of atomicity still further into
the region of biology. The cell theory and Pasteur’s work were in some
respects more revolutionary than that of Dalton. For they introduced the
notion of _organism_ into the world of minute beings. There had been a
tendency to treat the atom as an ultimate entity, capable only of
external relations. This attitude of mind was breaking down under the
influence of Mendeleef’s periodic law. But Pasteur showed the decisive
importance of the idea of organism at the stage of infinitesimal
magnitude. The astronomers had shown us how big is the universe. The
chemists and biologists teach us how small it is. There is in modern
scientific practice a famous standard of length. It is rather small: to
obtain it, you must divide a centimetre into one hundred million parts,
and take one of them. Pasteur’s organisms are a good deal bigger than
this length. In connection with atoms, we now know that there are
organisms for which such distances are uncomfortably great.

The remaining pair of new ideas to be ascribed to this epoch are both of
them connected with the notion of transition or change. They are the
doctrine of the conservation of energy, and the doctrine of evolution.

The doctrine of energy has to do with the notion of quantitative
permanence underlying change. The doctrine of evolution has to do with
the emergence of novel organisms as the outcome of change. The theory of
energy lies in the province of physics. The theory of evolution lies
mainly in the province of biology, although it had previously been
touched upon by Kant and Laplace in connection with the formation of
suns and planets.

The convergent effect of the new power for scientific advance, which
resulted from these four ideas, transformed the middle period of the
century into an orgy of scientific triumph. Clear-sighted men, of the
sort who are so clearly wrong, now proclaimed that the secrets of the
physical universe were finally disclosed. If only you ignored everything
which refused to come into line, your powers of explanation were
unlimited. On the other side, muddle-headed men muddled themselves into
the most indefensible positions. Learned dogmatism, conjoined with
ignorance of the crucial facts, suffered a heavy defeat from the
scientific advocates of new ways. Thus to the excitement derived from
technological revolution, there was now added the excitement arising
from the vistas disclosed by scientific theory. Both the material and
the spiritual bases of social life were in process of transformation.
When the century entered upon its last quarter, its three sources of
inspiration, the romantic, the technological, and the scientific had
done their work.

Then, almost suddenly, a pause occurred; and in its last twenty years
the century closed with one of the dullest stages of thought since the
time of the First Crusade. It was an echo of the eighteenth century,
lacking Voltaire and the reckless grace of the French aristocrats. The
period was efficient, dull, and half-hearted. It celebrated the triumph
of the professional man.

But looking backwards upon this time of pause, we can now discern signs
of change. In the first place, the modern conditions of systematic
research prevent absolute stagnation. In every branch of science, there
was effective progress, indeed rapid progress, although it was confined
somewhat strictly within the accepted ideas of each branch. It was an
age of successful scientific orthodoxy, undisturbed by much thought
beyond the conventions.

In the second place, we can now see that the adequacy of scientific
materialism as a scheme of thought for the use of science was
endangered. The conservation of energy provided a new type of
quantitative permanence. It is true that energy could be construed as
something subsidiary to matter. But, anyhow, the notion of _mass_ was
losing its unique preeminence as being the one final permanent quantity.
Later on, we find the relations of mass and energy inverted; so that
mass now becomes the name for a quantity of energy considered in
relation to some of its dynamical effects. This train of thought leads
to the notion of energy being fundamental, thus displacing matter from
that position. But energy is merely the name for the quantitative aspect
of a structure of happenings; in short, it depends on the notion of the
functioning of an organism. The question is, can we define an organism
without recurrence to the concept of matter in simple location? We must,
later on, consider this point in more detail.

The same relegation of matter to the background occurs in connection
with the electromagnetic fields. The modern theory presupposes
happenings in that field which are divorced from immediate dependence
upon matter. It is usual to provide an ether as a substratum. But the
ether does not really enter into the theory. Thus again the notion of
material loses its fundamental position. Also, the atom is transforming
itself into an organism; and finally the evolution theory is nothing
else than the analysis of the conditions for the formation and survival
of various types of organisms. In truth, one most significant fact of
this later period is the advance in biological sciences. These sciences
are essentially sciences concerning organisms. During the epoch in
question, and indeed also at the present moment, the prestige of the
more perfect scientific form belongs to the physical sciences.
Accordingly, biology apes the manners of physics. It is orthodox to
hold, that there is nothing in biology but what is physical mechanism
under somewhat complex circumstances.

One difficulty in this position is the present confusion as to the
foundational concepts of physical science. This same difficulty also
attaches to the opposed doctrine of vitalism. For, in this later theory,
the fact of mechanism is accepted—I mean, mechanism based upon
materialism—and an additional vital control is introduced to explain the
actions of living bodies. It cannot be too clearly understood that the
various physical laws which appear to apply to the behaviour of atoms
are not mutually consistent as at present formulated. The appeal to
mechanism on behalf of biology was in its origin an appeal to the
well-attested self-consistent physical concepts as expressing the basis
of all natural phenomena. But at present there is no such system of
concepts.

Science is taking on a new aspect which is neither purely physical, nor
purely biological. It is becoming the study of organisms. Biology is the
study of the larger organisms; whereas physics is the study of the
smaller organisms. There is another difference between the two divisions
of science. The organisms of biology include as ingredients the smaller
organisms of physics; but there is at present no evidence that the
smaller of the physical organisms can be analysed into component
organisms. It may be so. But anyhow we are faced with the question as to
whether there are not primary organisms which are incapable of further
analysis. It seems very unlikely that there should be any infinite
regress in nature. Accordingly, a theory of science which discards
materialism must answer the question as to the character of these
primary entities. There can be only one answer on this basis. We must
start with the event as the ultimate unit of natural occurrence. An
event has to do with all that there is, and in particular with all other
events. This interfusion of events is effected by the aspects of those
eternal objects, such as colours, sounds, scents, geometrical
characters, which are required for nature and are not emergent from it.
Such an eternal object will be an ingredient of one event under the
guise, or aspect, of qualifying another event. There is a reciprocity of
aspects, and there are patterns of aspects. Each event corresponds to
two such patterns; namely, the pattern of aspects of other events which
it grasps into its own unity, and the pattern of its aspects which other
events severally grasp into their unities. Accordingly, a
non-materialistic philosophy of nature will identify a primary organism
as being the emergence of some particular pattern as grasped in the
unity of a real event. Such a pattern will also include the aspects of
the event in question as grasped in other events, whereby those other
events receive a modification, or partial determination. There is thus
an intrinsic and an extrinsic reality of an event, namely, the event as
in its own prehension, and the event as in the prehension of other
events. The concept of an organism includes, therefore, the concept of
the interaction of organisms. The ordinary scientific ideas of
transmission and continuity are, relatively speaking, details concerning
the empirically observed characters of these patterns throughout space
and time. The position here maintained is that the relationships of an
event are internal, so far as concerns the event itself; that is to say,
that they are constitutive of what the event is in itself.

Also in the previous lecture, we arrived at the notion that an actual
event is an achievement for its own sake, a grasping of diverse
entities into a value by reason of their real togetherness in that
pattern, to the exclusion of other entities. It is not the mere
logical togetherness of merely diverse things. For in that case, to
modify Bacon’s words, “all eternal objects would be alike one to
another.” This reality means that each intrinsic essence, that is to
say, what each eternal object is in itself, becomes relevant to the
one limited value emergent in the guise of the event. But values
differ in importance. Thus though each event is necessary for the
community of events, the weight of its contribution is determined by
something intrinsic in itself. We have now to discuss what that
property is. Empirical observation shows that it is the property which
we may call indifferently _retention_, _endurance_ or _reiteration_.
This property amounts to the recovery, on behalf of value amid the
transitoriness of reality, of the self-identity which is also enjoyed
by the primary eternal objects. The reiteration of a particular shape
(or formation) of value within an event occurs when the event as a
whole repeats some shape which is also exhibited by each one of a
succession of its parts. Thus however you analyse the event according
to the flux of its parts through time, there is the same
thing-for-its-own-sake standing before you. Thus the event, in its own
intrinsic reality, mirrors in itself, as derived from its own parts,
aspects of the same patterned value as it realises in its complete
self. It thus realises itself under the guise of an enduring
individual entity, with a life history contained within itself.
Furthermore, the extrinsic reality of such an event, as mirrored in
other events, takes this same form of an enduring individuality; only
in this case, the individuality is implanted as a reiteration of
aspects of itself in the alien events composing the environment.

The total temporal duration of such an event bearing an enduring
pattern, constitutes its specious present. Within this specious present
the event realises itself as a totality, and also in so doing realises
itself as grouping together a number of aspects of its own temporal
parts. One and the same pattern is realised in the total event, and is
exhibited by each of these various parts through an aspect of each part
grasped into the togetherness of the total event. Also, the earlier
life-history of the same pattern is exhibited by its aspects in this
total event. There is, thus, in this event a memory of the antecedent
life-history of its own dominant pattern, as having formed an element of
value in its own antecedent environment. This concrete prehension, from
within, of the life-history of an enduring fact is analysable into two
abstractions, of which one is the enduring entity which has emerged as a
real matter of fact to be taken account of by other things, and the
other is the individualised embodiment of the underlying energy of
realisation.

The consideration of the general flux of events leads to this analysis
into an underlying eternal energy in whose nature there stands an
envisagement of the realm of all eternal objects. Such an envisagement
is the ground of the individualised thoughts which emerge as
thought-aspects grasped within the life-history of the subtler and more
complex enduring patterns. Also in the nature of the eternal activity
there must stand an envisagement of all values to be obtained by a real
togetherness of eternal objects, as envisaged in ideal situations. Such
ideal situations, apart from any reality, are devoid of intrinsic value,
but are valuable as elements in purpose. The individualised prehension
into individual events of aspects of these ideal situations takes the
form of individualised thoughts, and as such has intrinsic value. Thus
value arises because there is now a real togetherness of the ideal
aspects, as in thought, with the actual aspects, as in process of
occurrence. Accordingly no value is to be ascribed to the underlying
activity as divorced from the matter-of-fact events of the real world.

Finally, to sum up this train of thought, the underlying activity, as
conceived apart from the fact of realisation, has three types of
envisagement. These are: first, the envisagement of eternal objects;
secondly, the envisagement of possibilities of value in respect to the
synthesis of eternal objects; and lastly, the envisagement of the actual
matter of fact which must enter into the total situation which is
achievable by the addition of the future. But in abstraction from
actuality, the eternal activity is divorced from value. For the
actuality is the value. The individual perception arising from enduring
objects will vary in its individual depth and width according to the way
in which the pattern dominates its own route. It may represent the
faintest ripple differentiating the general substrate energy; or, in the
other extreme, it may rise to conscious thought, which includes poising
before self-conscious judgment the abstract possibilities of value
inherent in various situations of ideal togetherness. The intermediate
cases will group round the individual perception as envisaging (without
self-consciousness) that one immediate possibility of attainment which
represents the closest analogy to its own immediate past, having regard
to the actual aspects which are there for prehension. The laws of
physics represent the harmonised adjustment of development which results
from this unique principle of determination. Thus dynamics is dominated
by a principle of least action, whose detailed character has to be
learnt from observation.

The atomic material entities which are considered in physical science
are merely these individual enduring entities, conceived in abstraction
from everything except what concerns their mutual interplay in
determining each other’s historical routes of life-history. Such
entities are partially formed by the inheritance of aspects from their
own past. But they are also partially formed by the aspects of other
events forming their environments. The laws of physics are the laws
declaring how the entities mutually react among themselves. For physics
these laws are arbitrary, because that science has abstracted from what
the entities are in themselves. We have seen that this fact of what the
entities are in themselves is liable to modification by their
environments. Accordingly, the assumption that no modification of these
laws is to be looked for in environments, which have any striking
difference from the environments for which the laws have been observed
to hold, is very unsafe. The physical entities may be modified in very
essential ways, so far as these laws are concerned. It is even possible
that they may be developed into individualities of more fundamental
types, with wider embodiment of envisagement. Such envisagement might
reach to the attainment of the poising of alternative values with
exercise of choice lying outside the physical laws, and expressible only
in terms of purpose. Apart from such remote possibilities, it remains an
immediate deduction that an individual entity, whose own life-history is
a part within the life-history of some larger, deeper, more complete
pattern, is liable to have aspects of that larger pattern dominating its
own being, and to experience modifications of that larger pattern
reflected in itself as modifications of its own being. This is the
theory of organic mechanism.

According to this theory the evolution of laws of nature is concurrent
with the evolution of enduring pattern. For the general state of the
universe, as it now is, partly determines the very essences of the
entities whose modes of functioning these laws express. The general
principle is that in a new environment there is an evolution of the old
entities into new forms.

This rapid outline of a thoroughgoing organic theory of nature enables
us to understand the chief requisites of the doctrine of evolution. The
main work, proceeding during this pause at the end of the nineteenth
century, was the absorption of this doctrine as guiding the methodology
of all branches of science. By a blindness which is almost judicial as
being a penalty affixed to hasty, superficial thinking, many religious
thinkers opposed the new doctrine; although, in truth, a thoroughgoing
evolutionary philosophy is inconsistent with materialism. The aboriginal
stuff, or material, from which a materialistic philosophy starts is
incapable of evolution. This material is in itself the ultimate
substance. Evolution, on the materialistic theory, is reduced to the
rôle of being another word for the description of the changes of the
external relations between portions of matter. There is nothing to
evolve, because one set of external relations is as good as any other
set of external relations. There can merely be change, purposeless and
unprogressive. But the whole point of the modern doctrine is the
evolution of the complex organisms from antecedent states of less
complex organisms. The doctrine thus cries aloud for a conception of
organism as fundamental for nature. It also requires an underlying
activity—a substantial activity—expressing itself in individual
embodiments, and evolving in achievements of organism. The organism is a
unit of emergent value, a real fusion of the characters of eternal
objects, emerging for its own sake.

Thus in the process of analysing the character of nature in itself, we
find that the emergence of organisms depends on a selective activity
which is akin to purpose. The point is that the enduring organisms are
now the outcome of evolution; and that, beyond these organisms, there is
nothing else that endures. On the materialistic theory, there is
material—such as matter or electricity—which endures. On the organic
theory, the only endurances are structures of activity, and the
structures are evolved.

Enduring things are thus the outcome of a temporal process; whereas
eternal things are the elements required for the very being of the
process. We can give a precise definition of endurance in this way: Let
an event A be pervaded by an enduring structural pattern. Then A can be
exhaustively subdivided into a temporal succession of events. Let B be
any part of A, which is obtained by picking out any one of the events
belonging to a series which thus subdivides A. Then the enduring pattern
is a pattern of aspects within the complete pattern prehended into the
unity of A, and it is also a pattern within the complete pattern
prehended into the unity of any temporal slice of A, such as B. For
example, a molecule is a pattern exhibited in an event of one minute,
and of any second of that minute. It is obvious that such an enduring
pattern may be of more, or of less, importance. It may express some
slight fact connecting the underlying activities thus individualised; or
it may express some very close connection. If the pattern which endures
is merely derived from the direct aspects of the external environment,
mirrored in the standpoints of the various parts, then the endurance is
an extrinsic fact of slight importance. But if the enduring pattern is
wholly derived from the direct aspects of the various temporal sections
of the event in question, then the endurance is an important intrinsic
fact. It expresses a certain unity of character uniting the underlying
individualised activities. There is then an enduring object with a
certain unity for itself and for the rest of nature. Let us use the term
physical endurance to express endurance of this type. Then physical
endurance is the process of continuously inheriting a certain identity
of character transmitted throughout a historical route of events. This
character belongs to the whole route, and to every event of the route.
This is the exact property of material. If it has existed for ten
minutes, it has existed during every minute of the ten minutes, and
during every second of every minute. Only if you take _material_ to be
fundamental, this property of endurance is an arbitrary fact at the base
of the order of nature; but if you take _organism_ to be fundamental,
this property is the result of evolution.

It looks at first sight, as if a physical object, with its process of
inheritance from itself, were independent of the environment. But such a
conclusion is not justified. For let B and C be two successive slices in
the life of such an object, such that C succeeds B. Then the enduring
pattern in C is inherited from B, and from other analogous antecedent
parts of its life. It is transmitted through B to C. But what is
transmitted to C is the complete pattern of aspects derived from such
events as B. These complete patterns include the influence of the
environment on B, and on the other antecedent parts of the life of the
object. Thus the complete aspects of the antecedent life are inherited
as the partial pattern which endures throughout all the various periods
of the life. Thus a favourable environment is essential to the
maintenance of a physical object.

Nature, as we know it, comprises enormous permanences. There are the
permanences of ordinary matter. The molecules within the oldest rocks
known to geologists may have existed unchanged for over a thousand
million years, not only unchanged in themselves, but unchanged in their
relative dispositions to each other. In that length of time the number
of pulsations of a molecule vibrating with the frequency of yellow
sodium light would be about 16.3 × 10^{22} = 163,000 × (10^6)³. Until
recently, an atom was apparently indestructible. We know better now. But
the indestructible atom has been succeeded by the apparently
indestructible electron and the indestructible proton.

Another fact to be explained is the great similarity of these
practically indestructible objects. All electrons are very similar to
each other. We need not outrun the evidence, and say that they are
identical; but our powers of observation cannot detect any differences.
Analogously, all hydrogen nuclei are alike. Also we note the great
numbers of these analogous objects. There are throngs of them. It seems
as though a certain similarity were a favourable condition for
endurance. Common sense also suggests this conclusion. If organisms are
to survive, they must work together.

Accordingly, the key to the mechanism of evolution is the necessity for
the evolution of a favourable environment, conjointly with the evolution
of any specific type of enduring organisms of great permanence. Any
physical object which by its influence deteriorates its environment,
commits suicide.

One of the simplest ways of evolving a favourable environment
concurrently with the development of the individual organism, is that
the influence of each organism on the environment should be favourable
to the _endurance_ of other organisms of the same type. Further, if the
organism also favours the _development_ of other organisms of the same
type, you have then obtained a mechanism of evolution adapted to produce
the observed state of large multitudes of analogous entities, with high
powers of endurance. For the environment automatically develops with the
species, and the species with the environment.

The first question to ask is, whether there is any direct evidence for
such a mechanism for the evolution of enduring organisms. In surveying
nature, we must remember that there are not only basic organisms whose
ingredients are merely aspects of eternal objects. There are also
organisms of organisms. Suppose for the moment and for the sake of
simplicity, we assume, without any evidence, that electrons and hydrogen
nuclei are such basic organisms. Then the atoms, and the molecules, are
organisms of a higher type, which also represent a compact definite
organic unity. But when we come to the larger aggregations of matter,
the organic unity fades into the background. It appears to be but faint
and elementary. It is there; but the pattern is vague and indecisive. It
is a mere aggregation of effects. When we come to living beings, the
definiteness of pattern is recovered, and the organic character again
rises into prominence. Accordingly, the characteristic laws of inorganic
matter are mainly the statistical averages resulting from confused
aggregates. So far are they from throwing light on the ultimate nature
of things, that they blur and obliterate the individual characters of
the individual organisms. If we wish to throw light upon the facts
relating to organisms, we must study either the individual molecules and
electrons, or the individual living beings. In between we find
comparative confusion. Now the difficulty of studying the individual
molecule is that we know so little about its life history. We cannot
keep an individual under continuous observation. In general, we deal
with them in large aggregates. So far as individuals are concerned,
sometimes with difficulty a great experimenter throws, so to speak, a
flash light on one of them, and just observes one type of instantaneous
effect. Accordingly, the history of the functioning of individual
molecules, or electrons, is largely hidden from us.

But in the case of living beings, we can trace the history of
individuals. We now find exactly the mechanism which is here demanded.
In the first place, there is the propagation of the species from members
of the same species. There is also the careful provision of the
favourable environment for the endurance of the family, the race, or the
seed in the fruit.

It is evident, however, that I have explained the evolutionary mechanism
in terms which are far too simple. We find associated species of living
things, providing for each other a favourable environment. Thus just as
the members of the same species mutually favour each other, so do
members of associated species. We find the rudimentary fact of
association in the existence of the two species, electrons and hydrogen
nuclei. The simplicity of the dual association, and the apparent absence
of competition from other antagonistic species accounts for the massive
endurance which we find among them.

There are thus two sides to the machinery involved in the development of
nature. On one side, there is a given environment with organisms
adapting themselves to it. The scientific materialism of the epoch in
question emphasised this aspect. From this point of view, there is a
given amount of material, and only a limited number of organisms can
take advantage of it. The givenness of the environment dominates
everything. Accordingly, the last words of science appeared to be the
Struggle for Existence, and Natural Selection. Darwin’s own writings are
for all time a model of refusal to go beyond the direct evidence, and of
careful retention of every possible hypothesis. But those virtues were
not so conspicuous in his followers, and still less in his
camp-followers. The imagination of European sociologists and publicists
was stained by exclusive attention to this aspect of conflicting
interests. The idea prevailed that there was a peculiar strong-minded
realism in discarding ethical considerations in the determination of the
conduct of commercial and national interests.

The other side of the evolutionary machinery, the neglected side, is
expressed by the word _creativeness_. The organisms can create their own
environment. For this purpose, the single organism is almost helpless.
The adequate forces require societies of coöperating organisms. But with
such coöperation and in proportion to the effort put forward, the
environment has a plasticity which alters the whole ethical aspect of
evolution.

In the immediate past, and at present, a muddled state of mind is
prevalent. The increased plasticity of the environment for mankind,
resulting from the advances in scientific technology, is being construed
in terms of habits of thought which find their justification in the
theory of a fixed environment.

The riddle of the universe is not so simple. There is the aspect of
permanence in which a given type of attainment is endlessly repeated for
its own sake; and there is the aspect of transition to other things,—it
may be of higher worth, and it may be of lower worth. Also there are its
aspects of struggle and of friendly help. But romantic ruthlessness is
no nearer to real politics, than is romantic self-abnegation.




                              CHAPTER VII

                               RELATIVITY


In the previous lectures of this course we have considered the
antecedent conditions which led up to the scientific movement, and have
traced the progress of thought from the seventeenth to the nineteenth
century. In the nineteenth century this history falls into three parts,
so far as it is to be grouped around science. These divisions are, the
contact between the romantic movement and science, the development of
technology and physics in the earlier part of the century, and lastly
the theory of evolution combined with the general advance of the
biological sciences.

The dominating note of the whole period of three centuries is that the
doctrine of materialism afforded an adequate basis for the concepts of
science. It was practically unquestioned. When undulations were wanted,
an ether was supplied, in order to perform the duties of an undulatory
material. To show the full assumption thus involved, I have sketched in
outline an alternative doctrine of an organic theory of nature. In the
last lecture it was pointed out that the biological developments, the
doctrine of evolution, the doctrine of energy, and the molecular
theories were rapidly undermining the adequacy of the orthodox
materialism. But until the close of the century no one drew that
conclusion. Materialism reigned supreme.

The note of the present epoch is that so many complexities have
developed regarding material, space, time, and energy, that the simple
security of the old orthodox assumptions has vanished. It is obvious
that they will not do as Newton left them, or even as Clerk Maxwell left
them. There must be a reorganization. The new situation in the thought
of to-day arises from the fact that scientific theory is outrunning
common sense. The settlement as inherited by the eighteenth century was
a triumph of organised common sense. It had got rid of medieval
phantasies, and of Cartesian vortices. As a result it gave full reign to
its anti-rationalistic tendencies derived from the historical revolt of
the Reformation period. It grounded itself upon what every plain man
could see with his own eyes, or with a microscope of moderate power. It
measured the obvious things to be measured, and it generalised the
obvious things to be generalised. For example, it generalised the
ordinary notions of weight and massiveness. The eighteenth century
opened with the quiet confidence that at last nonsense had been got rid
of. To-day we are at the opposite pole of thought. Heaven knows what
seeming nonsense may not to-morrow be demonstrated truth. We have
recaptured some of the tone of the early nineteenth century, only on a
higher imaginative level.

The reason why we are on a higher imaginative level is not because we
have finer imagination, but because we have better instruments. In
science, the most important thing that has happened during the last
forty years is the advance in instrumental design. This advance is
partly due to a few men of genius such as Michelson and the German
opticians. It is also due to the progress of technological processes of
manufacture, particularly in the region of metallurgy. The designer has
now at his disposal a variety of material of differing physical
properties. He can thus depend upon obtaining the material he desires;
and it can be ground to the shapes he desires, within very narrow limits
of tolerance. These instruments have put thought onto a new level. A
fresh instrument serves the same purpose as foreign travel; it shows
things in unusual combinations. The gain is more than a mere addition;
it is a transformation. The advance in experimental ingenuity is,
perhaps, also due to the larger proportion of national ability which now
flows into scientific pursuits. Anyhow, whatever be the cause, subtle
and ingenious experiments have abounded within the last generation. The
result is, that a great deal of information has been accumulated in
regions of nature very far removed from the ordinary experience of
mankind.

Two famous experiments, one devised by Galileo at the outset of the
scientific movement, and the other by Michelson with the aid of his
famous interferometer, first carried out in 1881, and repeated in 1887
and 1905, illustrate the assertions I have made. Galileo dropped heavy
bodies from the top of the leaning tower of Pisa, and demonstrated that
bodies of different weights, if released simultaneously, would reach the
earth together. So far as experimental skill, and delicacy of apparatus
were concerned, this experiment could have been made at any time within
the preceding five thousand years. The ideas involved merely concerned
weight and speed of travel, ideas which are familiar in ordinary life.
The whole set of ideas might have been familiar to the family of King
Minos of Crete, as they dropped pebbles into the sea from high
battlements rising from the shore. We cannot too carefully realise that
science started with the organisation of ordinary experiences. It was in
this way that it coalesced so readily with the anti-rationalistic bias
of the historical revolt. It was not asking for ultimate meanings. It
confined itself to investigating the connections regulating the
succession of obvious occurrences.

Michelson’s experiment could not have been made earlier than it was. It
required the general advance in technology, and Michelson’s experimental
genius. It concerns the determination of the earth’s motion through the
ether, and it assumes that light consists of waves of vibration
advancing at a fixed rate through the ether in any direction. Also, of
course, the earth is moving through the ether, and Michelson’s apparatus
is moving with the earth. In the centre of the apparatus a ray of light
is divided so that one half-ray goes in one direction _along_ the
apparatus through a given distance, and is reflected back to the centre
by a mirror in the apparatus. The other half-ray goes the same distance
_across_ the apparatus in a direction at right angles to the former ray,
and it also is reflected back to the centre. These reunited rays are
then reflected onto a screen in the apparatus. If precautions are taken,
you will see interference bands; namely bands of blackness where the
crests of the waves of one ray have filled up the troughs of the other
rays, owing to a minute difference in the lengths of paths of the two
half-rays, up to certain parts of the screens. These differences in
length will be affected by the motion of the earth. For it is the
lengths of the paths in the ether which count. Thus, since the apparatus
is moving with the earth, the path of one half-ray will be disturbed by
the motion in a different manner from the path of the other half-ray.
Think of yourself as moving in a railway carriage, first along the train
and then across the train; and mark out your paths on the railway track
which in this analogy corresponds to the ether. Now the motion of the
earth is very slow compared to that of light. Thus in the analogy you
must think of the train almost at a standstill, and of yourself as
moving very quickly.

In the experiment this effect of the earth’s motion would affect the
positions on the screen of the interference bands. Also if you turn the
apparatus round, through a right-angle, the effect of the earth’s motion
on the two half-rays will be interchanged, and the positions of the
interference bands would be shifted. We can calculate the small shift
which should result owing to the earth’s motion round the sun. Also to
this effect, we have to add that due to the sun’s motion through the
ether. The delicacy of the instrument can be tested, and it can be
proved that these effects of shifting are large enough to be observed by
it. Now the point is, that nothing was observed. There was no shifting
as you turned the instrument round.

The conclusion is either that the earth is always stationary in the
ether, or that there is something wrong with the fundamental principles
on which the interpretation of the experiment relies. It is obvious
that, in this experiment, we are very far away from the thoughts and the
games of the children of King Minos. The ideas of an ether, of waves in
it, of interference, of the motion of the earth through the ether, and
of Michelson’s interferometer, are remote from ordinary experience. But
remote as they are, they are simple and obvious compared to the accepted
explanation of the nugatory result of the experiment.

The ground of the explanation is that the ideas of space and of time
employed in science are too simple-minded, and must be modified. This
conclusion is a direct challenge to common sense, because the earlier
science had only refined upon the ordinary notions of ordinary people.
Such a radical reorganization of ideas would not have been adopted,
unless it had also been supported by many other observations which we
need not enter upon. Some form of the relativity theory seems to be the
simplest way of explaining a large number of facts which otherwise would
each require some _ad hoc_ explanation. The theory, therefore, does not
merely depend upon the experiments which led to its origination.

The central point of the explanation is that every instrument, such as
Michelson’s apparatus as used in the experiment, necessarily records the
velocity of light as having one and the same definite speed relatively
to it. I mean that an interferometer in a comet and an interferometer on
the earth would necessarily bring out the velocity of light, relatively
to themselves, as at the same value. This is an obvious paradox, since
the light moves with a definite velocity through the ether. Accordingly
two bodies, the earth and the comet, moving with unequal velocities
through the ether, might be expected to have different velocities
relatively to rays of light. For example, consider two cars on a road,
moving at ten and twenty miles an hour respectively, and being passed by
another car at fifty miles an hour. The rapid car will pass one of the
two cars at the relative velocity of forty miles per hour, and the other
at the rate of thirty miles per hour. The allegation as to light is
that, if we substituted a ray of light for the rapid car, the velocity
of the light along the roadway would be exactly the same as its velocity
relatively to either of the two cars which it overtakes. The velocity of
light is immensely large, being about three hundred thousand kilometres
per second. We must have notions as to space and time such that just
this velocity has this peculiar character. It follows that all our
notions of relative velocity must be recast. But these notions are the
immediate outcome of our habitual notions as to space and time. So we
come back to the position, that there has been something overlooked in
the current expositions of what we mean by space and of what we mean by
time.

Now our habitual fundamental assumption is that there is a unique
meaning to be given to space and a unique meaning to be given to time,
so that whatever meaning is given to spatial relations in respect to the
instrument on the earth, the same meaning must be given to them in
respect to the instrument on the comet, and the same meaning for an
instrument at rest in the ether. In the theory of relativity, this is
denied. As far as concerns space, there is no difficulty in agreeing, if
you think of the obvious facts of relative motion. But even here the
change in meaning has to go further than would be sanctioned by common
sense. Also the same demand is made for time; so that the relative
dating of events and the lapses of time between them are to be reckoned
as different for the instrument on the earth, for the instrument in the
comet, and for the instrument at rest in the ether. This is a greater
strain on our credulity. We need not probe the question further than the
conclusion that for the earth and for the comet spatiality and
temporality are each to have different meanings amid different
conditions, such as those presented by the earth and the comet.
Accordingly velocity has different meanings for the two bodies. Thus the
modern scientific assumption is that if anything has the speed of light
by reference to any one meaning of space and time, then it has the same
speed according to any other meaning of space and time.

This is a heavy blow at the classical scientific materialism, which
presupposes a definite present instant at which all matter is
simultaneously real. In the modern theory there is no such unique
present instant. You can find a meaning for the notion of the
simultaneous instant throughout all nature, but it will be a different
meaning for different notions of temporality.

There has been a tendency to give an extreme subjectivist interpretation
to this new doctrine. I mean that the relativity of space and time has
been construed as though it were dependent on the choice of the
observer. It is perfectly legitimate to bring in the observer, if he
facilitates explanations. But it is the observer’s body that we want,
and not his mind. Even this body is only useful as an example of a very
familiar form of apparatus. On the whole, it is better to concentrate
attention on Michelson’s interferometer, and to leave Michelson’s body
and Michelson’s mind out of the picture. The question is, why did the
interferometer have black bands on its screen, and why did not these
bands slightly shift as the instrument turned. The new relativity
associates space and time with an intimacy not hitherto contemplated;
and presupposes that their separation in concrete fact can be achieved
by alternative modes of abstraction, yielding alternative meanings. But
each mode of abstraction is directing attention to something which is in
nature; and thereby is isolating it for the purpose of contemplation.
The fact relevant to experiment, is the relevance of the interferometer
to just one among the many alternative systems of these spatio-temporal
relations which hold between natural entities.

What we must now ask of philosophy is to give us an interpretation of
the status in nature of space and time, so that the possibility of
alternative meanings is preserved. These lectures are not suited for the
elaboration of details; but there is no difficulty in pointing out where
to look for the origin of the discrimination between space and time. I
am presupposing the organic theory of nature, which I have outlined as a
basis for a thoroughgoing objectivism.

An event is the grasping into unity of a pattern of aspects. The
effectiveness of an event beyond itself arises from the aspects of
itself which go to form the prehended unities of other events. Except
for the systematic aspects of geometrical shape, this effectiveness is
trivial, if the mirrored pattern attaches merely to the event as one
whole. If the pattern endures throughout the successive parts of the
event, and also exhibits itself in the whole, so that the event is the
life history of the pattern, then in virtue of that enduring pattern the
event gains in external effectiveness. For its own effectiveness is
reënforced by the analogous aspects of all its successive parts. The
event constitutes a patterned value with a permanence inherent
throughout its own parts; and by reason of this inherent endurance the
event is important for the modification of its environment.

It is in this endurance of pattern that time differentiates itself from
space. The pattern is spatially _now_; and this temporal determination
constitutes its relation to each partial event. For it is reproduced in
this temporal succession of these spatial parts of its own life. I mean
that this particular rule of temporal order allows the pattern to be
reproduced in each temporal slice of its history. So to speak, each
enduring object discovers in nature and requires from nature a principle
discriminating space from time. Apart from the fact of an enduring
pattern this principle might be there, but it would be latent and
trivial. Thus the importance of space as against time, and of time as
against space, has developed with the development of enduring organisms.
Enduring objects are significant of a differentiation of space from time
in respect to the patterns ingredient within events; and conversely the
differentiation of space from time in the patterns ingredient within
events expresses the patience of the community of events for enduring
objects. There might be the community without objects, but there could
not be the enduring objects without the community with its peculiar
patience for them.

It is very necessary that this point should not be misunderstood.
Endurance means that a pattern which is exhibited in the prehension of
one event is also exhibited in the prehension of those of its parts
which are discriminated by a certain rule. It is not true that any part
of the whole event will yield the same pattern as does the whole. For
example, consider the total bodily pattern exhibited in the life of a
human body during one minute. One of the thumbs during the same minute
is part of the whole bodily event. But the pattern of this part is the
pattern of the thumb, and is not the pattern of the whole body. Thus
endurance requires a definite rule for obtaining the parts. In the above
example, we know at once what the rule is: You must take the life of the
whole body during any portion of that same minute; for example, during a
second or a tenth of a second. In other words, the meaning of endurance
presupposes a meaning for the lapse of time within the spatio-temporal
continuum.

The question now arises whether all enduring objects discover the same
principle of differentiation of space from time; or even whether at
different stages of its own life-history one object may not vary in its
spatio-temporal discrimination. Up till a few years ago, everyone
unhesitatingly assumed that there was only one such principle to be
discovered. Accordingly, in dealing with one object, time would have
exactly the same meaning in reference to endurance as in dealing with
the endurance of another object. It would also follow then that spatial
relations would have one unique meaning. But now it seems that the
observed effectiveness of objects can only be explained by assuming that
objects in a state of motion relatively to each other are utilising, for
their endurance, meanings of space and of time which are not identical
from one object to another. Every enduring object is to be conceived as
at rest in its own proper space, and in motion throughout any space
defined in a way which is not that inherent in its peculiar endurance.
If two objects are mutually at rest, they are utilising the same
meanings of space and of time for the purposes of expressing their
endurance; if in relative motion, the spaces and times differ. It
follows that, if we can conceive a body at one stage of its life history
as in motion relatively to itself at another stage, then the body at
these two stages is utilising diverse meanings of space, and
correlatively diverse meanings of time.

In an organic philosophy of nature there is nothing to decide between
the old hypothesis of the uniqueness of the time discrimination and the
new hypothesis of its multiplicity. It is purely a matter for evidence
drawn from observations.[5]

Footnote 5:

  _Cf._ my _Principles of Natural Knowledge_, Sec. 52:3.

In an earlier lecture, I said that an event had contemporaries. It is an
interesting question whether, on the new hypothesis, such a statement
can be made without the qualification of a reference to a definite
space-time system. It is possible to do so, in the sense that in _some_
time-system or other the two events are simultaneous. In other
time-systems the two contemporary events will not be simultaneous,
though they may overlap. Analogously one event will precede another
without qualification, if in _every_ time-system this precedence occurs.
It is evident that if we start from a given event A, other events in
general are divided into two sets, namely, those which without
qualification are contemporaneous with A and those which either precede
or succeed A. But there will be a set left over, namely, those events
which bound the two sets. There we have a critical case. You will
remember that we have a critical velocity to account for, namely the
theoretical velocity of light _in vacuo_.[6] Also you will remember that
the utilisation of different spatio-temporal systems means the relative
motion of objects. When we analyse this critical relation of a special
set of events to any given event A, we find the explanation of the
critical velocity which we require. I am suppressing all details. It is
evident that exactness of statement must be introduced by the
introduction of points, and lines, and instants. Also that the origin of
geometry requires discussion; for example, the measurement of lengths,
the straightness of lines, and the flatness of planes, and
perpendicularity. I have endeavoured to carry out these investigations
in some earlier books, under the heading of the theory of extensive
abstraction; but they are too technical for the present occasion.

Footnote 6:

  This is not the velocity of light in a gravitational field or in a
  medium of molecules and electrons.

If there be no one definite meaning to the geometrical relations of
distance, it is evident that the law of gravitation needs restatement.
For the formula expressing that law is that two particles attract each
other in proportion to the product of their masses and the inverse
square of their distances. This enunciation tacitly assumes that there
is one definite meaning to be ascribed to the instant at which the
attraction is considered, and also one definite meaning to be ascribed
to _distance_. But distance is a purely spatial notion, so that in the
new doctrine, there are an indefinite number of such meanings according
to the space-time system which you adopt. If the two particles are
relatively at rest, then we might be content with the space-time systems
which they are both utilising. Unfortunately this suggestion gives no
hint as to procedure when they are not mutually at rest. It is,
therefore, necessary to reformulate the law in a way which does not
presuppose any particular space-time system. Einstein has done this.
Naturally the result is more complicated. He introduced into
mathematical physics certain methods of pure mathematics which render
the formulae independent of the particular systems of measurement
adopted. The new formula introduces various small effects which are
absent in Newton’s law. But for the major effects Newton’s law and
Einstein’s law agree. Now these extra effects of Einstein’s law serve to
explain irregularities of the planet Mercury’s orbit which by Newton’s
law were inexplicable. This is a strong confirmation of the new theory.
Curiously enough, there is more than one alternative formula, based on
the new theory of multiple space-time systems, having the property of
embodying Newton’s law and in addition of explaining the peculiarities
of Mercury’s motion. The only method of selection between them is to
wait for experimental evidence respecting those effects on which the
formulae differ. Nature is probably quite indifferent to the aesthetic
preferences of mathematicians.

It only remains to add that Einstein would probably reject the theory of
multiple space-time systems which I have been expounding to you. He
would interpret his formula in terms of contortions in space-time which
alter the invariance theory for measure properties, and of the proper
times of each historical route. His mode of statement has the greater
mathematical simplicity, and only allows of one law of gravitation,
excluding the alternatives. But, for myself, I cannot reconcile it with
the given facts of our experience as to simultaneity, and spatial
arrangement. There are also other difficulties of a more abstract
character.

The theory of the relationship between events at which we have now
arrived is based first upon the doctrine that the relatednesses of an
event are all internal relations, so far as concerns that event, though
not necessarily so far as concerns the other relata. For example, the
eternal objects, thus involved, are externally related to events. This
internal relatedness is the reason why an event can be found only just
where it is and how it is,—that is to say, in just one definite set of
relationships. For each relationship enters into the essence of the
event; so that, apart from that relationship, the event would not be
itself. This is what is meant by the very notion of internal relations.
It has been usual, indeed universal, to hold that spatio-temporal
relationships are external. This doctrine is what is here denied.

The conception of internal relatedness involves the analysis of the
event into two factors, one the underlying substantial activity of
individualisation, and the other the complex of aspects—that is to say,
the complex of relatednesses as entering into the essence of the given
event—which are unified by this individualised activity. In other words,
the concept of internal relations requires the concept of substance as
the activity synthesising the relationships into its emergent character.
The event is what it is, by reason of the unification in itself of a
multiplicity of relationships. The general scheme of these mutual
relationships is an abstraction which presupposes each event as an
independent entity, which it is not, and asks what remnant of these
formative relationships is then left in the guise of external
relationships. The scheme of relationships as thus impartially expressed
becomes the scheme of a complex of events variously related as wholes to
parts and as joint parts within some one whole. Even here, the internal
relationship forces itself on our attention; for the part evidently is
constitutive of the whole. Also an isolated event which has lost its
status in any complex of events is equally excluded by the very nature
of an event. So the whole is evidently constitutive of the part. Thus
the internal character of the relationship really shows through this
impartial scheme of abstract external relations.

But this exhibition of the actual universe as extensive and divisible
has left out the distinction between space and time. It has in fact left
out the process of realisation, which is the adjustment of the synthetic
activities by virtue of which the various events become their realised
selves. This adjustment is thus the adjustment of the underlying active
substances whereby these substances exhibit themselves as the
individualisations or modes of Spinoza’s one substance. This adjustment
is what introduces temporal process.

Thus, in some sense, time, in its character of the adjustment of the
process of synthetic realisation, extends beyond the spatio-temporal
continuum of nature.[7] There is no necessity that temporal process, in
this sense, should be constituted by one single series of linear
succession. Accordingly, in order to satisfy the present demands of
scientific hypothesis, we introduce the metaphysical hypothesis that
this is not the case. We do assume (basing ourselves upon direct
observation), however, that temporal process of realisation can be
analysed into a group of linear serial processes. Each of these linear
series is a space-time system. In support of this assumption of definite
serial processes, we appeal: (1) to the immediate presentation through
the senses of an extended universe beyond ourselves and _simultaneous_
with ourselves, (2) to the intellectual apprehension of a meaning to the
question which asks what is _now immediately happening_ in regions
beyond the cognisance of our senses, (3) to the analysis of what is
involved in the _endurance_ of emergent objects. This endurance of
objects involves the display of a pattern as now realised. This display
is the display of a pattern as inherent in an event, but also as
exhibiting a temporal slice of nature as lending aspects to eternal
objects (or, equally, of eternal objects as lending aspects to events).
The pattern is spatialised in a whole duration for the benefit of the
event into whose essence the pattern enters. The event is part of the
duration, _i.e._, is part of what is exhibited in the aspects inherent
in itself; and conversely the duration is the whole of nature
simultaneous with the event, in that sense of simultaneity. Thus an
event in realising itself displays a pattern, and this pattern requires
a definite duration determined by a definite meaning of simultaneity.
Each such meaning of simultaneity relates the pattern as thus displayed
to one definite space-time system. The actuality of the space-time
systems is constituted by the realisation of pattern; but it is inherent
in the general scheme of events as constituting its patience for the
temporal process of realisation.

Footnote 7:

  _Cf._ my _Concept of Nature_, Ch. III.

Notice that the pattern requires a duration involving a definite lapse
of time, and not merely an instantaneous moment. Such a moment is more
abstract, in that it merely denotes a certain relation of contiguity
between the concrete events. Thus a duration is spatialised; and by
‘spatialised’ is meant that the duration is the field for the realised
pattern constituting the character of the event. A duration, as the
field of the pattern realised in the actualisation of one of its
contained events, is an epoch, _i.e._, an arrest. Endurance is the
repetition of the pattern in successive events. Thus endurance requires
a succession of durations, each exhibiting the pattern. In this account
‘time’ has been separated from ‘extension’ and from the ‘divisibility’
which arises from the character of spatio-temporal extension’.
Accordingly we must not proceed to conceive time as another form of
extensiveness. Time is sheer succession of epochal durations. But the
entities which succeed each other in this account are durations. The
duration is that which is required for the realisation of a pattern in
the given event. Thus the divisibility and extensiveness is within the
given duration. The epochal duration is not realised _via_ its
_successive_ divisible parts, but is given _with_ its parts. In this
way, the objection which Zeno might make to the joint validity of two
passages from Kant’s _Critique of Pure Reason_ is met by abandoning the
earlier of the two passages. I refer to passages from the section ‘Of
the Axioms of Intuition’; the earlier from the subsection on _Extensive
Quantity_, and the latter from the subsection on _Intensive Quantity_
where considerations respecting quantity in general, extensive and
intensive, are summed up. The earlier passage runs thus:[8]

Footnote 8:

  Max Müller’s translation.

“I call an extensive quantity that in which the representation of the
whole is rendered possible by the representation of its parts, _and
therefore necessarily preceded by it_.[9] I cannot represent to myself
any line, however small it may be, without drawing it in thought, that
is, without producing all its parts one after the other, starting from a
given point, and thus, first of all, drawing its intuition. The same
applies to every, even the smallest portion of time. I can only think in
it the successive progress from one moment to another, thus producing in
the end, by all the portions of time, and their addition, a definite
quantity of time.”

Footnote 9:

  Italics mine, and also in the second passage.

The second passage runs thus:

“This peculiar property of quantities that no part of them is the
smallest possible part (no part indivisible) is called continuity. Time
and space are quanta continua, because there is no part of them that is
not enclosed between limits (points and moments), _no part that is not
itself again a space or a time. Space consists of spaces only, time of
times. Points and moments are only limits_, mere places of limitation,
and as places _presupposing always_ those intuitions which they are
meant to limit or to determine. Mere places or parts that might be given
before space or time, could never be compounded into space or time.”

I am in complete agreement with the second extract if ‘time and space’
is the extensive continuum; but it is inconsistent with its predecessor.
For Zeno would object that a vicious infinite regress is involved. Every
part of time involves some smaller part of itself, and so on. Also this
series regresses backwards ultimately to nothing; since the initial
moment is without duration and merely marks the relation of contiguity
to an earlier time. Thus time is impossible, if the two extracts are
both adhered to. I accept the later, and reject the earlier, passage.
Realisation is the becoming of time in the field of extension. Extension
is the complex of events, _quâ_ their potentialities. In realisation the
potentiality becomes actuality. But the potential pattern requires a
duration; and the duration must be exhibited as an epochal whole, by the
realisation of the pattern. Thus time is the succession of elements in
themselves divisible and contiguous. A duration, in becoming temporal,
thereby incurs realisation in respect to some enduring object.
Temporalisation is realisation. Temporalisation is not another
continuous process. It is an atomic succession. Thus time is atomic
(_i.e._, epochal), though what is temporalised is divisible. This
doctrine follows from the doctrine of events, and of the nature of
enduring objects. In the next chapter we must consider its relevance to
the quantum theory of recent science.

It is to be noted that this doctrine of the epochal character of time
does not depend on the modern doctrine of relativity, and holds
equally—and indeed, more simply—if this doctrine be abandoned. It does
depend on the analysis of the intrinsic character of an event,
considered as the most concrete finite entity.

In reviewing this argument, note first that the second quotation from
Kant, on which it is based, does not depend on any peculiar Kantian
doctrine. The latter of the two is in agreement with Plato as against
Aristotle.[10] In the second place, the argument assumes that Zeno
understated his argument. He should have urged it against the current
notion of time in itself, and not against motion, which involves
relations between time and space. For, what becomes has duration. But no
duration can become until a smaller duration (part of the former) has
antecedently come into being [Kant’s earlier statement]. The same
argument applies to this smaller duration, and so on. Also the infinite
regress of these durations converges to nothing—and even on the
Aristotelian view there is no first moment. Accordingly time would be an
irrational notion. Thirdly, in the epochal theory Zeno’s difficulty is
met by conceiving temporalisation as the realisation of a complete
organism. This organism is an event holding in its essence its
spatio-temporal relationships (both within itself, and beyond itself)
throughout the spatio-temporal continuum.

Footnote 10:

  _Cf._ ‘Euclid in Greek,’ by Sir T. L. Heath, Camb. Univ. Press, in a
  note on Points.




                              CHAPTER VIII

                           THE QUANTUM THEORY


The theory of relativity has justly excited a great amount of public
attention. But, for all its importance, it has not been the topic which
has chiefly absorbed the recent interest of physicists. Without question
that position is held by the quantum theory. The point of interest in
this theory is that, according to it, some effects which appear
essentially capable of gradual increase or gradual diminution are in
reality to be increased or decreased only by certain definite jumps. It
is as though you could walk at three miles per hour or at four miles per
hour, but not at three and a half miles per hour.

The effects in question are concerned with the radiation of light from a
molecule which has been excited by some collision. Light consists of
waves of vibration in the electromagnetic field. After a complete wave
has passed a given point everything at that point is restored to its
original state and is ready for the next wave which follows on. Picture
to yourselves the waves on the ocean, and reckon from crest to crest of
successive waves. The number of waves which pass a given point in one
second is called the frequency of that system of waves. A system of
light-waves of definite frequency corresponds to a definite colour in
the spectrum. Now a molecule, when excited, vibrates with a certain
number of definite frequencies. In other words, there are a definite set
of modes of vibration of the molecule, and each mode of vibration has
one definite frequency. Each mode of vibration can stir up in the
electromagnetic field waves of its own frequency. These waves carry away
the energy of the vibration; so that finally (when such waves are in
being) the molecule loses the energy of its excitement and the waves
cease. Thus a molecule can radiate light of certain definite colours,
that is to say, of certain definite frequencies.

You would think that each mode of vibration could be excited to any
intensity, so that the energy carried away by light of that frequency
could be of any amount. But this is not the case. There appear to be
certain minimum amounts of energy which cannot be subdivided. The case
is analogous to that of a citizen of the United States who, in paying
his debts in the currency of his country, cannot subdivide a cent so as
to correspond to some minute subdivision of the goods obtained. The cent
corresponds to the minimum quantity of the light energy, and the goods
obtained correspond to the energy of the exciting cause. This exciting
cause is either strong enough to procure the emission of one cent of
energy, or fails to procure the emission of any energy whatsoever. In
any case the molecule will only emit an integral number of cents of
energy. There is a further peculiarity which we can illustrate by
bringing an Englishman onto the scene. He pays his debts in English
currency, and his smallest unit is a farthing which differs in value
from the cent. The farthing is in fact about half a cent, to a very
rough approximation. In the molecule, different modes of vibration have
different frequencies. Compare each mode to a nation. One mode
corresponds to the United States, and another mode corresponds to
England. One mode can only radiate its energy in an integral number of
cents, so that a cent of energy is the least it can pay out; whereas the
other mode can only radiate its energy in an integral number of
farthings, so that a farthing of energy is the least that it can pay
out. Also a rule can be found to tell us the relative value of the cent
of energy of one mode to the farthing of energy of another mode. The
rule is childishly simple: Each smallest coin of energy has a value in
strict proportion to the frequency belonging to that mode. By this rule,
and comparing farthings with cents, the frequency of an American would
be about twice that of an Englishman. In other words, the American would
do about twice as many things in a second as an Englishman. I must leave
you to judge whether this corresponds to the reputed characters of the
two nations. Also I suggest that there are merits attaching to both ends
of the solar spectrum. Sometimes you want red light and sometimes violet
light.

There has been, I hope, no great difficulty in comprehending what the
quantum theory asserts about molecules. The perplexity arises from the
effort to fit the theory into the current scientific picture of what is
going on in the molecule or atom.

It has been the basis of the materialistic theory, that the happenings
of nature are to be explained in terms of the locomotion of material. In
accordance with this principle, the waves of light were explained in
terms of the locomotion of a material ether, and the internal happenings
of a molecule are now explained in terms of the locomotion of separate
material parts. In respect to waves of light, the material ether has
retreated to an indeterminate position in the background, and is rarely
talked about. But the principle is unquestioned as regards its
application to the atom. For example a neutral hydrogen atom is assumed
to consist of at least two lumps of material; one lump is the nucleus
consisting of a material called positive electricity, and the other is a
single electron which is negative electricity. The nucleus shows signs
of being complex, and of being subdivisible into smaller lumps, some of
positive electricity and others electronic. The assumption is, that
whatever vibration takes place in the atom is to be attributed to the
vibratory locomotion of some bit of material, detachable from the
remainder. The difficulty with the quantum theory is that, on this
hypothesis, we have to picture the atom as providing a limited number of
definite grooves, which are the sole tracks along which vibration can
take place, whereas the classical scientific picture provides none of
these grooves. The quantum theory wants trolley-cars with a limited
number of routes, and the scientific picture provides horses galloping
over prairies. The result is that the physical doctrine of the atom has
got into a state which is strongly suggestive of the epicycles of
astronomy before Copernicus.

On the organic theory of nature there are two sorts of vibrations which
radically differ from each other. There is vibratory locomotion, and
there is vibratory organic deformation; and the conditions for the two
types of change are of a different character. In other words, there is
vibratory locomotion of a given pattern as one whole, and there is
vibratory change of pattern.

A complete organism in the organic theory is what corresponds to a bit
of material on the materialistic theory. There will be a primary genus,
comprising a number of species of organisms, such that each primary
organism, belonging to a species of the primary genus, is not
decomposable into subordinate organisms. I will call any organism of the
primary genus a primate. There may be different species of primates.

It must be kept in mind that we are dealing with the abstractions of
physics. Accordingly, we are not thinking of what a primate is in
itself, as a pattern arising from the prehension of the concrete
aspects; nor are we thinking of what a primate is for its environment,
in respect to its concrete aspects prehended therein. We are thinking of
these various aspects merely in so far as their effects on patterns and
on locomotion are expressible in spatio-temporal terms. Accordingly, in
the language of physics, the aspects of a primate are merely its
contributions to the electromagnetic field. This is in fact exactly what
we know of electrons and protons. An electron for us is merely the
pattern of its aspects in its environment, so far as those aspects are
relevant to the electromagnetic field.

Now in discussing the theory of relativity, we saw that the relative
motion of two primates means simply that their organic patterns are
utilising diverse space-time systems. If two primates do not continue
either mutually at rest, or mutually in uniform relative motion, at
least one of them is changing its intrinsic space-time system. The laws
of motion express the conditions under which these changes of space-time
systems are effected. The conditions for vibratory _locomotion_ are
founded upon these general laws of motion.

But it is possible that certain species of primates are apt to go to
pieces under conditions which lead them to effect changes of space-time
systems. Such species would only experience a long range of endurance,
if they had succeeded in forming a favourable association among primates
of different species, such that in this association the tendency to
collapse is neutralised by the environment of the association. We can
imagine the atomic nucleus as composed of a large number of primates of
differing species, and perhaps with many primates of the same species,
the whole association being such as to favour stability. An example of
such an association is afforded by the association of a positive nucleus
with negative electrons to obtain a neutral atom. The neutral atom is
thereby shielded from any electric field which would otherwise produce
changes in the space-time system of the atom.

The requirements of physics now suggest an idea which is very consonant
with the organic philosophical theory. I put it in the form of a
question: Has our organic theory of endurance been tainted by the
materialistic theory in so far as it assumes without question that
endurance must mean undifferentiated sameness throughout the
life-history concerned? Perhaps you noticed that (in a previous chapter)
I used the word ‘reiteration’ as a synonym of ‘endurance.’ It obviously
is not quite synonymous in its meaning; and now I want to suggest that
_reiteration_ where it differs from _endurance_ is more nearly what the
organic theory requires. The difference is very analogous to that
between the Galileans and the Aristotelians: Aristotle said ‘rest’ where
Galileo added ‘or uniform motion in a straight line.’ Thus in the
organic theory, a pattern need not endure in undifferentiated sameness
through time. The pattern may be essentially one of aesthetic contrasts
requiring a lapse of time for its unfolding. A tune is an example of
such a pattern. Thus the endurance of the pattern now means the
reiteration of its succession of contrasts. This is obviously the most
general notion of endurance on the organic theory, and ‘reiteration’ is
perhaps the word which expresses it with most directness. But when we
translate this notion into the abstractions of physics, it at once
becomes the technical notion of ‘vibration.’ This vibration is not the
vibratory locomotion: it is the vibration of organic deformation. There
are certain indications in modern physics that for the rôle of
corpuscular organisms at the base of the physical field, we require
vibratory entities. Such corpuscles would be the corpuscles detected as
expelled from the nuclei of atoms, which then dissolve into waves of
light. We may conjecture that such a corpuscular body has no great
stability of endurance, when in isolation. Accordingly, an unfavourable
environment leading to rapid changes in its proper space-time system,
that is to say, an environment jolting it into violent accelerations,
causes the corpuscles to go to pieces and dissolve into light-waves of
the same period of vibration.

A proton, and perhaps an electron, would be an association of such
primates, superposed on each other, with their frequencies and spatial
dimensions so arranged as to promote the stability of the complex
organism, when jolted into accelerations of locomotion. The conditions
for stability would give the associations of periods possible for
protons. The expulsion of a primate would come from a jolt which leads
the proton either to settle down into an alternative association, or to
generate a new primate by the aid of the energy received.

A primate must be associated with a definite frequency of vibratory
organic deformation so that when it goes to pieces it dissolves into
light waves of the same frequency, which then carry off all its average
energy. It is quite easy (as a particular hypothesis) to imagine
stationary vibrations of the electromagnetic field of definite
frequency, and directed radially to and from a centre, which, in
accordance with the accepted electromagnetic laws, would consist of a
vibratory spherical nucleus satisfying one set of conditions and a
vibratory external field satisfying another set of conditions. This is
an example of vibratory organic deformation. Further [on this particular
hypothesis], there are two ways of determining the subsidiary conditions
so as to satisfy the ordinary requirements of mathematical physics. The
total energy, according to one of these ways, would satisfy the quantum
condition; so that it consists of an integral number of units or cents,
which are such that the cent of energy of any primate is proportional to
its frequency. I have not worked out the conditions for stability or for
a stable association. I have mentioned the particular hypothesis by way
of showing by example that the organic theory of nature affords
possibilities for the reconsideration of ultimate physical laws, which
are not open to the opposed materialistic theory.

In this particular hypothesis of vibratory primates, the Maxwellian
equations are supposed to hold throughout all space, including the
interior of a proton. They express the laws governing the vibratory
production and absorption of energy. The whole process for each primate
issues in a certain average energy characteristic of the primate, and
proportional to its mass. In fact the energy is the mass. There are
vibratory radial streams of energy, both without and within a primate.
Within the primate, there are vibratory distributions of electric
density. On the materialistic theory such density marks the presence of
material: on the organic theory of vibration, it marks the vibratory
production of energy. Such production is restricted to the interior of
the primate.

All science must start with some assumptions as to the ultimate analysis
of the facts with which it deals. These assumptions are justified partly
by their adherence to the types of occurrence of which we are directly
conscious, and partly by their success in representing the observed
facts with a certain generality, devoid of _ad hoc_ suppositions. The
general theory of the vibration of primates, which I have outlined, is
merely given as an example of the sort of possibilities which the
organic theory leaves open for physical science. The point is that it
adds the possibility of organic deformation to that of mere locomotion.
Light waves form one great example of organic deformation.

At any epoch the assumptions of a science are giving way, when they
exhibit symptoms of the epicyclic state from which astronomy was rescued
in the sixteenth century. Physical science is now exhibiting such
symptoms. In order to reconsider its foundations, it must recur to a
more concrete view of the character of real things, and must conceive
its fundamental notions as abstractions derived from this direct
intuition. It is in this way that it surveys the general possibilities
of revision which are open to it.

The discontinuities introduced by the quantum theory require revision of
physical concepts in order to meet them. In particular, it has been
pointed out that some theory of discontinuous existence is required.
What is asked from such a theory, is that an orbit of an electron can be
regarded as a series of detached positions, and not as a continuous
line.

The theory of a primate or a vibrating pattern, given above, together
with the distinction between temporality and extensiveness in the
previous chapter, yields exactly this result. It will be remembered that
the continuity of the complex of events arises from the relationships of
extensiveness; whereas the temporality arises from the realisation in a
subject-event of a pattern which requires for its display that the whole
of a duration be spatialised (_i.e._, arrested), as given by its aspects
in the event. Thus realization proceeds _viâ_ a succession of epochal
durations; and the continuous transition, _i.e._, the organic
deformation, is within the duration which is already given. The
vibratory organic deformation is in fact the reiteration of the pattern.
One complete period defines the duration required for the complete
pattern. Thus the primate is realised atomically in a succession of
durations, each duration to be measured from one maximum to another.
Accordingly, so far as the primate as one enduring whole entity is to be
taken account of, it is to be assigned to these durations successively.
If it is considered as one thing, its orbit is to be diagrammatically
exhibited by a series of detached dots. Thus the locomotion of the
primate is discontinuous in space and time. If we go below the quanta of
time which are the successive vibratory periods of the primate, we find
a succession of vibratory electromagnetic fields, each stationary in the
space-time of its own duration. Each of these fields exhibits a single
complete period of the electromagnetic vibration which constitutes the
primate. This vibration is not to be thought of as the becoming of
reality; it is what the primate is in one of its discontinuous
realisations. Also the successive durations in which the primate is
realised are contiguous; it follows that the life history of the primate
can be exhibited as being the continuous development of occurrences in
the electromagnetic field. But these occurrences enter into realisation
as whole atomic blocks, occupying definite periods of time.

There is no need to conceive that time is atomic in the sense that all
patterns must be realised in the same successive durations. In the first
place, even if the periods were the same in the case of two primates,
the durations of realisation may not be the same. In other words, the
two primates may be out of phase. Also if the periods are different, the
atomism of any one duration of one primate is necessarily subdivided by
the boundary moments of durations of the other primate.

The laws of the locomotion of primates express under what conditions any
primate will change its space-time system.

It is unnecessary to pursue this conception further. The justification
of the concept of vibratory existence must be purely experimental. The
point illustrated by this example is that the cosmological outlook,
which is here adopted, is perfectly consistent with the demands for
discontinuity which have been urged from the side of physics. Also if
this concept of temporalisation as a successive realisation of epochal
durations be adopted, the difficulty of Zeno is evaded. The particular
form, which has been given here to this concept, is purely for that
purpose of illustration and must necessarily require recasting before it
can be adapted to the results of experimental physics.




                               CHAPTER IX

                         SCIENCE AND PHILOSOPHY


In the present lecture, it is my object to consider some reactions of
science upon the stream of philosophic thought during the modern
centuries with which we are concerned. I shall make no attempt to
compress a history of modern philosophy within the limits of one
lecture. We shall merely consider some contacts between science and
philosophy, in so far as they lie within the scheme of thought which it
is the purpose of these lectures to develop. For this reason the whole
of the great German idealistic movement will be ignored, as being out of
effective touch with its contemporary science so far as reciprocal
modification of concepts is concerned. Kant, from whom this movement
took its rise, was saturated with Newtonian physics, and with the ideas
of the great French physicists—such as Clairaut,[11] for instance—who
developed the Newtonian ideas. But the philosophers who developed the
Kantian school of thought, or who transformed it into Hegelianism,
either lacked Kant’s background of scientific knowledge, or lacked his
potentiality of becoming a great physicist if philosophy had not
absorbed his main energies.

Footnote 11:

  _Cf._ the curious evidence of Kant’s scientific reading in the
  _Critique of Pure Reason, Transcendental Analytic, Second Analogy of
  Experience_, where he refers to the phenomenon of capillary action.
  This is an unnecessarily complex illustration; a book resting on a
  table would have equally well sufficed. But the subject had just been
  adequately treated for the first time by Clairaut in an appendix to
  his _Figure of the Earth_. Kant evidently had read this appendix, and
  his mind was full of it.

The origin of modern philosophy is analogous to that of science, and is
contemporaneous. The general trend of its development was settled in the
seventeenth century, partly at the hands of the same men who established
the scientific principles. This settlement of purpose followed upon a
transitional period dating from the fifteenth century. There was in fact
a general movement of European mentality, which carried along with its
stream, religion, science and philosophy. It may shortly be
characterised as being the direct recurrence to the original sources of
Greek inspiration on the part of men whose spiritual shape had been
derived from inheritance from the Middle Ages. There was therefore no
revival of Greek mentality. Epochs do not rise from the dead. The
principles of aesthetics and of reason, which animated the Greek
civilisation, were reclothed in a modern mentality. Between the two
there lay other religions, other systems of law, other anarchies, and
other racial inheritances, dividing the living from the dead.

Philosophy is peculiarly sensitive to such differences. For, whereas you
can make a replica of an ancient statue, there is no possible replica of
an ancient state of mind. There can be no nearer approximation than that
which a masquerade bears to real life. There may be understanding of the
past, but there is a difference between the modern and the ancient
reactions to the same stimuli.

In the particular case of philosophy, the distinction in tonality lies
on the surface. Modern philosophy is tinged with subjectivism, as
against the objective attitude of the ancients. The same change is to be
seen in religion. In the early history of the Christian Church, the
theological interest centred in discussions on the nature of God, the
meaning of the Incarnation, and apocalyptic forecasts of the ultimate
fate of the world. At the Reformation, the Church was torn asunder by
dissension as to the individual experiences of believers in respect to
justification. The individual subject of experience had been substituted
for the total drama of all reality. Luther asked, ‘How am I justified?’;
modern philosophers have asked, ‘How do I have knowledge?’ The emphasis
lies upon the subject of experience. This change of standpoint is the
work of Christianity in its pastoral aspect of shepherding the company
of believers. For century after century it insisted upon the infinite
worth of the individual human soul. Accordingly, to the instinctive
egotism of physical desires, it has superadded an instinctive feeling of
justification for an egotism of intellectual outlook. Every human being
is the natural guardian of his own importance. Without a doubt, this
modern direction of attention emphasises truths of the highest value.
For example, in the field of practical life, it has abolished slavery,
and has impressed upon the popular imagination the primary rights of
mankind.

Descartes, in his _Discourse on Method_, and in his _Meditations_,
discloses with great clearness the general conceptions which have since
influenced modern philosophy. There is a subject receiving experience:
in the _Discourse_ this subject is always mentioned in the first person,
that is to say, as being Descartes himself. Descartes starts with
himself as being a mentality, which in virtue of its consciousness of
its own inherent presentations of sense and of thought, is thereby
conscious of its own existence as a unit entity. The subsequent history
of philosophy revolves round the Cartesian formulation of the primary
datum. The ancient world takes its stand upon the drama of the Universe,
the modern world upon the inward drama of the Soul. Descartes, in his
_Meditations_, expressly grounds the existence of this inward drama upon
the possibility of error. There may be no correspondence with objective
fact, and thus there must be a soul with activities whose reality is
purely derivative from itself. For example, here is a quotation[12] from
_Meditation II_: “But it will be said that these presentations are
false, and that I am dreaming. Let it be so. At all events it is certain
that I seem to see light, hear a noise, and feel heat; this cannot be
false, and this is what in me is properly called perceiving (sentire),
which is nothing else than thinking. From this I begin to know what I am
with somewhat greater clearness and distinctness than heretofore.” Again
in _Meditation III_: “...; for, as I before remarked, although the
things which I perceive or imagine are perhaps nothing at all apart from
me, I am nevertheless assured that those modes of consciousness which I
call perceptions and imaginations, in as far only as they are modes of
consciousness, exist in me.”

Footnote 12:

  Quoted from Veitch’s translation.

The objectivism of the medieval and the ancient worlds passed over into
science. Nature is there conceived as for itself, with its own mutual
reactions. Under the recent influence of relativity, there has been a
tendency towards subjectivist formulations. But, apart from this recent
exception, nature, in scientific thought, has had its laws formulated
without any reference to dependence on individual observers. There is,
however, this difference between the older and the later attitudes
towards science. The anti-rationalism of the moderns has checked any
attempt to harmonise the ultimate concepts of science with ideas drawn
from a more concrete survey of the whole of reality. The material, the
space, the time, the various laws concerning the transition of material
configurations, are taken as ultimate stubborn facts, not to be tampered
with.

The effect of this antagonism to philosophy has been equally unfortunate
both for philosophy and for science. In this lecture we are concerned
with philosophy. Philosophers are rationalists. They are seeking to go
behind stubborn and irreducible facts: they wish to explain in the light
of universal principles the mutual reference between the various details
entering into the flux of things. Also, they seek such principles as
will eliminate mere arbitrariness; so that, whatever portion of fact is
assumed or given, the existence of the remainder of things shall satisfy
some demand of rationality. They demand meaning. In the words of Henry
Sidgwick[13]—“It is the primary aim of philosophy to unify completely,
bring into clear coherence, all departments of rational thought, and
this aim cannot be realised by any philosophy that leaves out of its
view the important body of judgments and reasonings which form the
subject matter of ethics.” Accordingly, the bias towards history on the
part of the physical and social sciences with their refusal to
rationalise below some ultimate mechanism, has pushed philosophy out of
the effective currents of modern life. It has lost its proper rôle as a
constant critic of partial formulations. It has retreated into the
subjectivist sphere of mind, by reason of its expulsion by science from
the objectivist sphere of matter. Thus the evolution of thought in the
seventeenth century coöperated with the enhanced sense of individual
personality derived from the Middle Ages. We see Descartes taking his
stand upon his own ultimate mind, which his philosophy assures him of;
and asking about its relations to the ultimate matter—exemplified, in
the second _Meditation_, by the human body and a lump of wax—which his
science assumes. There is Aaron’s rod, and the magicians’ serpents; and
the only question for philosophy is, which swallows which; or whether,
as Descartes thought, they all lived happily together. In this stream of
thought are to be found Locke, Berkeley, Hume, Kant. Two great names lie
outside this list, Spinoza and Leibniz. But there is a certain isolation
of both of them in respect to their philosophical influence so far as
science is concerned; as though they had strayed to extremes which lie
outside the boundaries of safe philosophy, Spinoza by retaining older
ways of thought, and Leibniz by the novelty of his monads.

Footnote 13:

  _Cf._ _Henry Sidgwick: A Memoir_, Appendix I.

The history of philosophy runs curiously parallel to that of science. In
the case of both, the seventeenth century set the stage for its two
successors. But with the twentieth century a new act commences. It is an
exaggeration to attribute a general change in a climate of thought to
any one piece of writing, or to any one author. No doubt Descartes only
expressed definitely and in decisive form what was already in the air of
his period. Analogously, in attributing to William James the
inauguration of a new stage in philosophy, we should be neglecting other
influences of his time. But, admitting this, there still remains a
certain fitness in contrasting his essay, _Does Consciousness Exist_,
published in 1904, with Descartes’ _Discourse on Method_, published in
1637. James clears the stage of the old paraphernalia; or rather he
entirely alters its lighting. Take for example these two sentences from
his essay: “To deny plumply that ‘consciousness’ exists seems so absurd
on the face of it—for undeniably ‘thoughts’ do exist—that I fear some
readers will follow me no farther. Let me then immediately explain that
I mean only to deny that the word stands for an entity, but to insist
most emphatically that it does stand for a function.”

The scientific materialism and the Cartesian Ego were both challenged at
the same moment, one by science and the other by philosophy, as
represented by William James with his psychological antecedents; and the
double challenge marks the end of a period which lasted for about two
hundred and fifty years. Of course, ‘matter’ and ‘consciousness’ both
express something so evident in ordinary experience that any philosophy
must provide some things which answer to their respective meanings. But
the point is that, in respect to both of them, the seventeenth century
settlement was infected with a presupposition which is now challenged.
James denies that consciousness is an entity, but admits that it is a
function. The discrimination between an entity and a function is
therefore vital to the understanding of the challenge which James is
advancing against the older modes of thought. In the essay in question,
the character which James assigns to consciousness is fully discussed.
But he does not unambiguously explain what he means by the notion of an
entity, which he refuses to apply to consciousness. In the sentence
which immediately follows the one which I have already quoted, he says:

“There is, I mean, no aboriginal stuff or quality of being, contrasted
with that of which material objects are made, out of which our thoughts
of them are made; but there is a function in experience which thoughts
perform, and for the performance of which this quality of being is
invoked. That function is _knowing_. ‘Consciousness’ is supposed
necessary to explain the fact that things not only are, but get
reported, are known.”

Thus James is denying that consciousness is a ‘stuff.’

The term ‘entity,’ or even that of ‘stuff,’ does not fully tell its own
tale. The notion of ‘entity’ is so general that it may be taken to mean
anything that can be thought about. You cannot think of mere nothing;
and the something which is an object of thought may be called an entity.
In this sense, a function is an entity. Obviously, this is not what
James had in his mind.

In agreement with the organic theory of nature which I have been
tentatively putting forward in these lectures, I shall for my own
purposes construe James as denying exactly what Descartes asserts in his
_Discourse_ and his _Meditations_. Descartes discriminates two species
of entities, _matter_ and _soul_. The essence of matter is spatial
extension; the essence of soul is its cogitation, in the full sense
which Descartes assigns to the word ‘_cogitare_.’ For example, in
Section Fifty-three of Part I of his _Principles of Philosophy_, he
enunciates: “That of every substance there is one principal attribute,
as thinking of the mind, extension of the body.” In the earlier,
Fifty-first Section, Descartes states: “By substance we can conceive
nothing else than a thing which exists in such a way as to stand in need
of nothing beyond itself in order to its existence.” Furthermore, later
on, Descartes says: “For example, because any substance which ceases to
endure ceases also to exist, duration is not distinct from substance
except in thought;....” Thus we conclude that, for Descartes, minds and
bodies exist in such a way as to stand in need of nothing beyond
themselves individually (God only excepted, as being the foundation of
all things); that both minds and bodies endure, because without
endurance they would cease to exist; that spatial extension is the
essential attribute of bodies; and that cogitation is the essential
attribute of minds.

It is difficult to praise too highly the genius exhibited by Descartes
in the complete sections of his _Principles_ which deal with these
questions. It is worthy of the century in which he writes, and of the
clearness of the French intellect. Descartes in his distinction between
time and duration, and in his way of grounding time upon motion, and in
his close relation between matter and extension, anticipates, as far as
it was possible at his epoch, modern notions suggested by the doctrine
of relativity, or by some aspects of Bergson’s doctrine of the
generation of things. But the fundamental principles are so set out as
to presuppose independently existing substances with simple location in
a community of temporal durations, and, in the case of bodies, with
simple location in the community of spatial extensions. Those principles
lead straight to the theory of a materialistic, mechanistic nature,
surveyed by cogitating minds. After the close of the seventeenth
century, science took charge of the materialistic nature, and philosophy
took charge of the cogitating minds. Some schools of philosophy admitted
an ultimate dualism; and the various idealistic schools claimed that
nature was merely the chief example of the cogitations of minds. But all
schools admitted the Cartesian analysis of the ultimate elements of
nature. I am excluding Spinoza and Leibniz from these statements as to
the main stream of modern philosophy, as derivative from Descartes;
though of course they were influenced by him, and in their turn
influenced philosophers. I am thinking mainly of the effective contacts
between science and philosophy.

This division of territory between science and philosophy was not a
simple business; and in fact it illustrated the weakness of the whole
cut-and-dried presupposition upon which it rested. We are aware of
nature as an interplay of bodies, colours, sounds, scents, tastes,
touches and other various bodily feelings, displayed as in space, in
patterns of mutual separation by intervening volumes, and of individual
shape. Also the whole is a flux, changing with the lapse of time. This
systematic totality is disclosed to us as one complex of things. But the
seventeenth century dualism cuts straight across it. The objective world
of science was confined to mere spatial material with simple location in
space and time, and subjected to definite rules as to its locomotion.
The subjective world of philosophy annexed the colours, sounds, scents,
tastes, touches, bodily feelings, as forming the subjective content of
the cogitations of the individual minds. Both worlds shared in the
general flux; but time, as measured, is assigned by Descartes to the
cogitations of the observer’s mind. There is obviously one fatal
weakness to this scheme. The cogitations of mind exhibit themselves as
holding up entities, such as colours for instance, before the mind as
the termini of contemplation. But in this theory these colours are,
after all, merely the furniture of the mind. Accordingly, the mind seems
to be confined to its own private world of cogitations. The
subject-object conformation of experience in its entirety lies within
the mind as one of its private passions. This conclusion from the
Cartesian data is the starting point from which Berkeley, Hume, and Kant
developed their respective systems. And, antecedently to them, it was
the point upon which Locke concentrated as being the vital question.
Thus the question as to how any knowledge is obtained of the truly
objective world of science becomes a problem of the first magnitude.
Descartes states that the objective body is perceived by the intellect.
He says (_Meditation II_): “I must, therefore, admit that I cannot even
comprehend by imagination what the piece of wax is, and that it is the
mind alone which perceives it. I speak of one piece in particular; for,
as to wax in general, this is still more evident. But what is the piece
of wax that can be perceived only by the mind?... The perception of it
is neither an act of sight, of touch, nor of imagination, and never was
either of these, though it might formerly seem so, but is simply an
_intuition_ (_inspectio_) of the mind,....” It must be noted that the
Latin word ‘inspectio’ is associated in its classical use with the
notion of theory as opposed to practice.

The two great preoccupations of modern philosophy now lie clearly before
us. The study of mind divides into psychology, or the study of mental
functionings as considered in themselves and in their mutual relations,
and into epistemology, or the theory of the knowledge of a common
objective world. In other words, there is the study of the cogitations,
_quâ_ passions of the mind, and their study _quâ_ leading to an
inspection (_intuition_) of an objective world. This is a very uneasy
division, giving rise to a host of perplexities whose consideration has
occupied the intervening centuries.

As long as men thought in terms of physical notions for the objective
world and of mentality for the subjective world, the setting out of the
problem, as achieved by Descartes, sufficed as a starting point. But the
balance has been upset by the rise of physiology. In the seventeenth
century men passed from the study of physics to the study of philosophy.
Towards the end of the nineteenth century, notably in Germany, men
passed from the study of physiology to the study of psychology. The
change in tone has been decisive. Of course, in the earlier period the
intervention of the human body was fully considered, for example, by
Descartes in Part V of the ‘_Discourse on Method_.’ But the
physiological instinct had not been developed. In considering the human
body, Descartes thought with the outfit of a physicist; whereas the
modern psychologists are clothed with the mentalities of medical
physiologists. The career of William James is an example of this change
in standpoint. He also possessed the clear, incisive genius which could
state in a flash the exact point at issue.

The reason why I have put Descartes and James in close juxtaposition is
now evident. Neither philosopher finished an epoch by a final solution
of a problem. Their great merit is of the opposite sort. They each of
them open an epoch by their clear formulation of terms in which thought
could profitably express itself at particular stages of knowledge, one
for the seventeenth century, the other for the twentieth century. In
this respect, they are both to be contrasted with St. Thomas Aquinas,
who expressed the culmination of Aristotelian scholasticism.

In many ways neither Descartes nor James were the most characteristic
philosophers of their respective epochs. I should be disposed to ascribe
these positions to Locke and to Bergson respectively, at least so far as
concerns their relations to the science of their times. Locke developed
the lines of thought which kept philosophy on the move; for example he
emphasized the appeal to psychology. He initiated the age of
epoch-making enquiries into urgent problems of limited scope.
Undoubtedly, in so doing, he infected philosophy with something of the
anti-rationalism of science. But the very groundwork of a fruitful
methodology is to start from those clear postulates which must be held
to be ultimate so far as concerns the occasion in question. The
criticism of such methodological postulates is thus reserved for another
opportunity. Locke discovered that the philosophical situation
bequeathed by Descartes involved the problems of epistemology and
psychology.

Bergson introduced into philosophy the organic conceptions of
physiological science. He has most completely moved away from the static
materialism of the seventeenth century. His protest against
spatialisation is a protest against taking the Newtonian conception of
nature as being anything except a high abstraction. His so-called
anti-intellectualism should be construed in this sense. In some respects
he recurs to Descartes; but the recurrence is accompanied with an
instinctive grasp of modern biology.

There is another reason for associating Locke and Bergson. The germ of
an organic theory of nature is to be found in Locke. His most recent
expositor, Professor Gibson,[14] states that Locke’s way of conceiving
the identity of self-consciousness ‘like that of a living organism,
involves a genuine transcending of the mechanical view of nature and of
mind, embodied in the composition theory.’ But it is to be noticed that
in the first place Locke wavers in his grasp of this position; and in
the second place, what is more important still, he only applies his idea
to self-consciousness. The physiological attitude has not yet
established itself. The effect of physiology was to put mind back into
nature. The neurologist traces first the effect of stimuli along the
bodily nerves, then integration at nerve centres, and finally the rise
of a projective reference beyond the body with a resulting motor
efficacy in renewed nervous excitement. In biochemistry, the delicate
adjustment of the chemical composition of the parts to the preservation
of the whole organism is detected. Thus the mental cognition is seen as
the reflective experience of a totality, reporting for itself what it is
in itself as one unit occurrence. This unit is the integration of the
sum of its partial happenings, but it is not their numerical aggregate.
It has its own unity as an event. This total unity, considered as an
entity for its own sake, is the prehension into unity of the patterned
aspects of the universe of events. Its knowledge of itself arises from
its own relevance to the things of which it prehends the aspects. It
knows the world as a system of mutual relevance, and thus sees itself as
mirrored in other things. These other things include more especially the
various parts of its own body.

Footnote 14:

  _Cf._ his book, _Locke’s Theory of Knowledge and its Historical
  Relations_, Camb. Univ. Press, 1917.

It is important to discriminate the bodily pattern, which endures, from
the bodily event, which is pervaded by the enduring pattern, and from
the parts of the bodily event. The parts of the bodily event are
themselves pervaded by their own enduring patterns, which form elements
in the bodily pattern. The parts of the body are really portions of the
environment of the total bodily event, but so related that their mutual
aspects, each in the other, are peculiarly effective in modifying the
pattern of either. This arises from the intimate character of the
relation of whole to part. Thus the body is a portion of the environment
for the part, and the part is a portion of the environment for the body;
only they are peculiarly sensitive, each to modifications of the other.
This sensitiveness is so arranged that the part adjusts itself to
preserve the stability of the pattern of the body. It is a particular
example of the favourable environment shielding the organism. The
relation of part to whole has the special reciprocity associated with
the notion of organism, in which the part is for the whole; but this
relation reigns throughout nature and does not start with the special
case of the higher organisms.

Further, viewing the question as a matter of chemistry, there is no need
to construe the actions of each molecule in a living body by its
exclusive particular reference to the pattern of the complete living
organism. It is true that each molecule is affected by the aspect of
this pattern as mirrored in it, so as to be otherwise than what it would
have been if placed elsewhere. In the same way, under some circumstances
an electron may be a sphere, and under other circumstances an egg-shaped
volume. The mode of approach to the problem, so far as science is
concerned, is merely to ask if molecules exhibit in living bodies
properties which are not to be observed amid inorganic surroundings. In
the same way, in a magnetic field soft iron exhibits magnetic properties
which are in abeyance elsewhere. The prompt self-preservative actions of
living bodies, and our experience of the physical actions of our bodies
following the determinations of will, suggest the modification of
molecules in the body as the result of the total pattern. It seems
possible that there may be physical laws expressing the modification of
the ultimate basic organisms when they form part of higher organisms
with adequate compactness of pattern. It would, however, be entirely in
consonance with the empirically observed action of environments, if the
direct effects of aspects as between the whole body and its parts were
negligible. We should expect transmission. In this way the modification
of total pattern would transmit itself by means of a series of
modifications of a descending series of parts, so that finally the
modification of the cell changes its aspect in the molecule, thus
effecting a corresponding alteration in the molecule,—or in some subtler
entity. Thus the question for physiology is the question of the physics
of molecules in cells of different characters.

We can now see the relation of psychology to physiology and to physics.
The private psychological field is merely the event considered from its
own standpoint. The unity of this field is the unity of the event. But
it is the event as one entity, and not the event as a sum of parts. The
relations of the parts, to each other and to the whole, are their
aspects, each in the other. A body for an external observer is the
aggregate of the aspects for him of the body as a whole, and also of the
body as a sum of parts. For the external observer the aspects of shape
and of sense-objects are dominant, at least for cognition. But we must
also allow for the possibility that we can detect in ourselves direct
aspects of the mentalities of higher organisms. The claim that the
cognition of alien mentalities must necessarily be by means of indirect
inferences from aspects of shape and of sense-objects is wholly
unwarranted by this philosophy of organism. The fundamental principle is
that whatever merges into actuality, implants its aspects in every
individual event.

Further, even for self-cognition, the aspects of the parts of our own
bodies partly take the form of aspects of shape, and of sense-objects.
But that part of the bodily event, in respect to which the cognitive
mentality is associated, is for itself the unit psychological field. Its
ingredients are not referent to the event itself; they are aspects of
what lies beyond that event. Thus the self-knowledge inherent in the
bodily event is the knowledge of itself as a complex unity, whose
ingredients involve all reality beyond itself, restricted under the
limitation of its pattern of aspects. Thus we know ourselves as a
function of unification of a plurality of things which are other than
ourselves. Cognition discloses an event as being an activity, organising
a real togetherness of alien things. But this psychological field does
not depend on its cognition; so that this field is still a unit event as
abstracted from its self-cognition.

Accordingly, consciousness will be the function of knowing. But what is
known is already a prehension of aspects of the one real universe. These
aspects are aspects of other events as mutually modifying, each the
others. In the pattern of aspects they stand in their pattern of mutual
relatedness.

The aboriginal data in terms of which the pattern weaves itself are the
aspects of shapes, of sense-objects, and of other eternal objects whose
self-identity is not dependent on the flux of things. Wherever such
objects have ingression into the general flux, they interpret events,
each to the other. They are here in the perceiver; but, as perceived by
him, they convey for him something of the total flux which is beyond
himself. The subject-object relation takes its origin in the double rôle
of these eternal objects. They are modifications of the subject, but
only in their character of conveying aspects of other subjects in the
community of the universe. Thus no individual subject can have
independent reality, since it is a prehension of limited aspects of
subjects other than itself.

The technical phrase ‘subject-object’ is a bad term for the fundamental
situation disclosed in experience. It is really reminiscent of the
Aristotelian ‘subject-predicate.’ It already presupposes the
metaphysical doctrine of diverse subjects qualified by their private
predicates. This is the doctrine of subjects with private worlds of
experience. If this be granted, there is no escape from solipsism. The
point is that the phrase ‘subject-object’ indicates a fundamental entity
underlying the objects. Thus the ‘objects,’ as thus conceived, are
merely the ghosts of Aristotelian predicates. The primary situation
disclosed in cognitive experience is ‘ego-object amid objects.’ By this
I mean that the primary fact is an impartial world transcending the
‘here-now’ which marks the ego-object, and transcending the ‘now’ which
is the spatial world of simultaneous realisation. It is a world also
including the actuality of the past, and the limited potentiality of the
future, together with the complete world of abstract potentiality, the
realm of eternal objects, which transcends, and finds exemplification in
and comparison with, the actual course of realisation. The ego-object,
as consciousness here-now, is conscious of its experient essence as
constituted by its internal relatedness to the world of realities, and
to the world of ideas. But the ego-object, in being thus constituted, is
within the world of realities, and exhibits itself as an organism
requiring the ingression of ideas for the purpose of this status among
realities. This question of consciousness must be reserved for treatment
on another occasion.

The point to be made for the purposes of the present discussion is that
a philosophy of nature as organic must start at the opposite end to that
requisite for a materialistic philosophy. The materialistic starting
point is from independently existing substances, matter and mind. The
matter suffers modifications of its external relations of locomotion,
and the mind suffers modifications of its contemplated objects. There
are, in this materialistic theory, two sorts of independent substances,
each qualified by their appropriate passions. The organic starting point
is from the analysis of process as the realisation of events disposed in
an interlocked community. The event is the unit of things real. The
emergent enduring pattern is the stabilisation of the emergent
achievement so as to become a fact which retains its identity throughout
the process. It will be noted that endurance is not primarily the
property of enduring beyond itself, but of enduring within itself. I
mean that endurance is the property of finding its pattern reproduced in
the temporal parts of the total event. It is in this sense that a total
event carries an enduring pattern. There is an intrinsic value identical
for the whole and for its succession of parts. Cognition is the
emergence, into some measure of individualised reality, of the general
substratum of activity, poising before itself possibility, actuality,
and purpose.

It is equally possible to arrive at this organic conception of the world
if we start from the fundamental notions of modern physics, instead of,
as above, from psychology and physiology. In fact by reason of my own
studies in mathematics and mathematical physics, I did in fact arrive at
my convictions in this way. Mathematical physics presumes in the first
place an electromagnetic field of activity pervading space and time. The
laws which condition this field are nothing else than the conditions
observed by the general activity of the flux of the world, as it
individualises itself in the events. In physics, there is an
abstraction. The science ignores what anything is in itself. Its
entities are merely considered in respect to their extrinsic reality,
that is to say, in respect to their aspects in other things. But the
abstraction reaches even further than that; for it is only the aspects
in other things, as modifying the spatio-temporal specifications of the
life histories of those other things, which count. The intrinsic reality
of the observer comes in: I mean what the observer is for himself is
appealed to. For example, the fact that he will see red or blue enters
into scientific statements. But the red which the observer sees does not
in truth enter into science. What is relevant is merely the bare
diversity of the observer’s red experiences from all of his other
experiences. Accordingly, the intrinsic character of the observer is
merely relevant in order to fix the self-identical individuality of the
physical entities. These entities are only considered as agencies in
fixing the routes in space and in time of the life histories of enduring
entities.

The phraseology of physics is derived from the materialistic ideas of
the seventeenth century. But we find that, even in its extreme
abstraction, what it is really presupposing is the organic theory of
aspects as explained above. First, consider any event in empty space
where the word ‘empty’ means devoid of electrons, or protons, or of any
other form of electric charge. Such an event has three rôles in physics.
In the first place, it is the actual scene of an adventure of energy,
either as its _habitat_ or as the locus of a particular stream of
energy: anyhow, in this rôle the energy is there, either as located in
space during the time considered, or as streaming through space.

In its second rôle, the event is a necessary link in the pattern of
transmission, by which the character of every event receives some
modification from the character of every other event.

In its third rôle, the event is the repository of a possibility, as to
what would happen to an electric charge, either by way of deformation or
of locomotion, if it should have happened to be there.

If we modify our assumption by considering an event which includes in
itself a portion of the life-history of an electric charge, then the
analysis of its three rôles still remains; except that the possibility
embodied in the third rôle is now transformed into an actuality. In this
replacement of possibility by actuality, we obtain the distinction
between empty and occupied events.

Recurring to the empty events, we note the deficiency in them of
individuality of intrinsic content. Considering the first rôle of an
empty event, as being a _habitat_ of energy, we note that there is no
individual discrimination of an individual bit of energy, either as
statically located, or as an element in the stream. There is simply a
quantitative determination of activity, without individualisation of the
activity in itself. This lack of individualisation is still more evident
in the second and third rôles. An empty event is something in itself,
but it fails to realise a stable individuality of content. So far as its
content is concerned, the empty event is one realised element in a
general scheme of organised activity.

Some qualification is required when the empty event is the scene of the
transmission of a definite train of recurrent wave-forms. There is now a
definite pattern which remains permanent in the event. We find here the
first faint trace of enduring individuality. But it is individuality
without the faintest capture of originality: for it is merely a
permanence arising solely from the implication of the event in a larger
scheme of patterning.

Turning now to the examination of an occupied event, the electron has a
determinate individuality. It can be traced throughout its life-history
through a variety of events. A collection of electrons, together with
the analogous atomic charges of positive electricity, forms a body such
as we ordinarily perceive. The simplest body of this kind is a molecule,
and a set of molecules forms a lump of ordinary matter, such as a chair,
or a stone. Thus a charge of electricity is the mark of individuality of
content, as additional to the individuality of an event in itself. This
individuality of content is the strong point of the materialistic
doctrine.

It can, however, be equally well explained on the theory of organism.
When we look into the function of the electric charge, we note that its
rôle is to mark the origination of a pattern which is transmitted
through space and time. It is the key of some particular pattern. For
example, the field of force in any event is to be constructed by
attention to the adventures of electrons and protons, and so also are
the streams and distributions of energy. Further, the electric waves
find their origin in the vibratory adventures of these charges. Thus the
transmitted pattern is to be conceived as the flux of aspects throughout
space and time derived from the life history of the atomic charge. The
individualisation of the charge arises by a conjunction of two
characters, in the first place by the continued identity of its mode of
functioning as a key for the determination of a diffusion of pattern;
and, in the second place, by the unity and continuity of its life
history.

We may conclude, therefore, that the organic theory represents directly
what physics actually does assume respecting its ultimate entities. We
also notice the complete futility of these entities, if they are
conceived as fully concrete individuals. So far as physics is concerned,
they are wholly occupied in moving each other about, and they have no
reality outside this function. In particular for physics, there is no
intrinsic reality.

It is obvious that the basing of philosophy upon the presupposition of
organism must be traced back to Leibniz.[15] His monads are for him the
ultimately real entities. But he retained the Cartesian substances with
their qualifying passions, as also equally expressing for him the final
characterisation of real things. Accordingly for him there was no
concrete reality of internal relations. He had therefore on his hands
two distinct points of view. One was that the final real entity is an
organising activity, fusing ingredients into a unity, so that this unity
is the reality. The other point of view is that the final real entities
are substances supporting qualities. The first point of view depends
upon the acceptance of internal relations binding together all reality.
The latter is inconsistent with the reality of such relations. To
combine these two points of view, his monads were therefore windowless;
and their passions merely mirrored the universe by the divine
arrangement of a preëstablished harmony. This system thus presupposed an
aggregate of independent entities. He did not discriminate the event, as
the unit of experience, from the enduring organism as its stabilisation
into importance, and from the cognitive organism as expressing an
increased completeness of individualisation. Nor did he admit the
many-termed relations, relating sense-data to various events in diverse
ways. These many-termed relations are in fact the perspectives which
Leibniz does admit, but only on the condition that they are purely
qualities of the organising monads. The difficulty really arises from
the unquestioned acceptance of the notion of simple location as
fundamental for space and time, and from the acceptance of the notion of
independent individual substance as fundamental for a real entity. The
only road open to Leibniz was thus the same as that later taken by
Berkeley [in a prevalent interpretation of his meaning], namely an
appeal to a _Deux ex machinâ_ who was capable of rising superior to the
difficulties of metaphysics.

Footnote 15:

  _Cf._ Bertrand Russell, _The Philosophy of Leibniz_, for the
  suggestion of this line of thought.

In the same way as Descartes introduced the tradition of thought which
kept subsequent philosophy in some measure of contact with the
scientific movement, so Leibniz introduced the alternative tradition
that the entities, which are the ultimate actual things, are in some
sense procedures of organisation. This tradition has been the foundation
of the great achievements of German philosophy. Kant reflected the two
traditions, one upon the other. Kant was a scientist, but the schools
derivative from Kant have had but slight effect on the mentality of the
scientific world. It should be the task of the philosophical schools of
this century to bring together the two streams into an expression of the
world-picture derived from science, and thereby end the divorce of
science from the affirmations of our aesthetic and ethical experiences.




                               CHAPTER X

                              ABSTRACTION


In the previous chapters I have been examining the reactions of the
scientific movement upon the deeper issues which have occupied modern
thinkers. No one man, no limited society of men, and no one epoch can
think of everything at once. Accordingly for the sake of eliciting the
various impacts of science upon thought, the topic has been treated
historically. In this retrospect I have kept in mind that the ultimate
issue of the whole story is the patent dissolution of the comfortable
scheme of scientific materialism which has dominated the three centuries
under review. Accordingly various schools of criticism of the dominant
opinions have been stressed; and I have endeavoured to outline an
alternative cosmological doctrine, which shall be wide enough to include
what is fundamental both for science and for its critics. In this
alternative scheme, the notion of material, as fundamental, has been
replaced by that of organic synthesis. But the approach has always been
from the consideration of the actual intricacies of scientific thought,
and of the peculiar perplexities which it suggests.

In the present chapter, and in the immediately succeeding chapter, we
will forget the peculiar problems of modern science, and will put
ourselves at the standpoint of a dispassionate consideration of the
nature of things, antecedently to any special investigation into their
details. Such a standpoint is termed ‘metaphysical.’ Accordingly those
readers who find metaphysics, even in two slight chapters, irksome, will
do well to proceed at once to the Chapter on ‘Religion and Science,’
which resumes the topic of the impact of science on modern thought.

These metaphysical chapters are purely descriptive. Their justification
is to be sought, (i) in our direct knowledge of the actual occasions
which compose our immediate experience, and (ii) in their success as
forming a basis for harmonising our systematised accounts of various
types of experience, and (iii) in their success as providing the
concepts in terms of which an epistemology can be framed. By (iii) I
mean that an account of the general character of what we know must
enable us to frame an account of how knowledge is possible as an adjunct
within things known.

In any occasion of cognition, that which is known is an actual occasion
of experience, as diversified[16] by reference to a realm of entities
which transcend that immediate occasion in that they have analogous or
different connections with other occasions of experience. For example a
definite shade of red may, in the immediate occasion, be implicated with
the shape of sphericity in some definite way. But that shade of red, and
that spherical shape, exhibit themselves as transcending that occasion,
in that either of them has other relationships to other occasions. Also,
apart from the actual occurrence of the same things in other occasions,
every actual occasion is set within a realm of alternative
interconnected entities. This realm is disclosed by all the untrue
propositions which can be predicated significantly of that occasion. It
is the realm of alternative suggestions, whose foothold in actuality
transcends each actual occasion. The real relevance of untrue
propositions for each actual occasion is disclosed by art, romance, and
by criticism in reference to ideals. It is the foundation of the
metaphysical position which I am maintaining that the understanding of
actuality requires a reference to ideality. The two realms are
intrinsically inherent in the total metaphysical situation. The truth
that some proposition respecting an actual occasion is untrue may
express the vital truth as to the aesthetic achievement. It expresses
the ‘great refusal’ which is its primary characteristic. An event is
decisive in proportion to the importance (for it) of its untrue
propositions: their relevance to the event cannot be dissociated from
what the event is in itself by way of achievement. These transcendent
entities have been termed ‘universals.’ I prefer to use the term
‘eternal objects,’ in order to disengage myself from presuppositions
which cling to the former term owing to its prolonged philosophical
history. Eternal objects are thus, in their nature, abstract. By
‘abstract’ I mean that what an eternal object is in itself—that is to
say, its essence—is comprehensible without reference to some one
particular occasion of experience. To be abstract is to transcend
particular concrete occasions of actual happening. But to transcend an
actual occasion does not mean being disconnected from it. On the
contrary, I hold that each eternal object has its own proper connection
with each such occasion, which I term its mode of ingression into that
occasion. Thus an eternal object is to be comprehended by acquaintance
with (i) its particular individuality, (ii) its general relationships to
other eternal objects as apt for realisation in actual occasions, and
(iii) the general principle which expresses its ingression in particular
actual occasions.

Footnote 16:

  _Cf._ my _Principles of Natural Knowledge_, Ch. V, Sec. 13.

These three headings express two principles. The first principle is that
each eternal object is an individual which, in its own peculiar fashion,
is what it is. This particular individuality is the individual essence
of the object, and cannot be described otherwise than as being itself.
Thus the individual essence is merely the essence considered in respect
to its uniqueness. Further, the essence of an eternal object is merely
the eternal object considered as adding its own unique contribution to
each actual occasion. This unique contribution is identical for all such
occasions in respect to the fact that the object in all modes of
ingression is just its identical self. But it varies from one occasion
to another in respect to the differences of its modes of ingression.
Thus the metaphysical status of an eternal object is that of a
possibility for an actuality. Every actual occasion is defined as to its
character by how these possibilities are actualised for that occasion.
Thus actualisation is a selection among possibilities. More accurately,
it is a selection issuing in a gradation of possibilities in respect to
their realisation in that occasion. This conclusion brings us to the
second metaphysical principle: An eternal object, considered as an
abstract entity, cannot be divorced from its reference to other eternal
objects, and from its reference to actuality generally; though it is
disconnected from its actual modes of ingression into definitive actual
occasions. This principle is expressed by the statement that each
eternal object has a ‘relational essence.’ This relational essence
determines how it is possible for the object to have ingression into
actual occasions.

In other words: If _A_ be an eternal object, then what _A_ is in itself
involves _A’s_ status in the universe, and _A_ cannot be divorced from
this status. In the essence of _A_ there stands a determinateness as to
the relationships of _A_ to other eternal objects, and an
indeterminateness as to the relationships of _A_ to actual occasions.
Since the relationships of _A_ to other eternal objects stand
determinately in the essence of _A_, it follows that they are internal
relations. I mean by this that these relationships are constitutive of
_A_; for an entity which stands in internal relations has no being as an
entity not in these relations. In other words, once with internal
relations, always with internal relations. The internal relationships of
_A_ conjointly form its significance.

Again an entity cannot stand in external relations unless in its essence
there stands an indeterminateness which is its patience for such
external relations. The meaning of the term ‘possibility’ as applied to
_A_ is simply that there stands in the essence of _A_ a patience for
relationships to actual occasions. The relationships of _A_ to an actual
occasion are simply how the eternal relationships of _A_ to other
eternal objects are graded as to their realisation in that occasion.

Thus the general principle which expresses _A’s_ ingression in the
particular actual occasion α is the indeterminateness which stands in
the essence of _A_ as to its ingression into α, and is the
determinateness which stands in the essence of α as to the ingression of
_Α_ into α. Thus the synthetic prehension, which is α, is the solution
of the indeterminateness of _Α_ into the determinateness of α.
Accordingly the relationship between _Α_ and α is external as regards
_Α_, and is internal as regards α. Every actual occasion α is the
solution of all modalities into actual categorical ingressions: truth
and falsehood take the place of possibility. The complete ingression of
_Α_ into α is expressed by all the true propositions which are about
both _Α_ and α, and also—it may be—about other things.

The determinate relatedness of the eternal object _Α_ to every other
eternal object is how _Α_ is systematically and by the necessity of its
nature related to every other eternal object. Such relatedness
represents a possibility for realisation. But a relationship is a fact
which concerns all the implicated relata, and cannot be isolated as if
involving only one of the relata. Accordingly there is a general fact of
systematic mutual relatedness which is inherent in the character of
possibility. The realm of eternal objects is properly described as a
‘realm,’ because each eternal object has its status in this general
systematic complex of mutual relatedness.

In respect to the ingression of _Α_ into an actual occasion α, the
mutual relationships of _Α_ to other eternal objects, as thus graded in
realisation, require for their expression a reference to the status of
_Α_ and of the other eternal objects in the spatio-temporal
relationship. Also this status is not expressible (for this purpose)
without a reference to the status of α and of other actual occasions in
the same spatio-temporal relationship. Accordingly the spatio-temporal
relationship, in terms of which the actual course of events is to be
expressed, is nothing else than a selective limitation within the
general systematic relationships among eternal objects. By ‘limitation,’
as applied to the spatio-temporal continuum, I mean those matter-of-fact
determinations—such as the three dimensions of space, and the four
dimensions of the spatio-temporal continuum—which are inherent in the
actual course of events, but which present themselves as arbitrary in
respect to a more abstract possibility. The consideration of these
general limitations at the base of actual things, as distinct from the
limitations peculiar to each actual occasion, will be more fully resumed
in the chapter on ‘God.’

Further, the status of all possibility in reference to actuality
requires a reference to this spatio-temporal continuum. In any
particular consideration of a possibility we may conceive this continuum
to be transcended. But in so far as there is any definite reference to
actuality, the definite _how_ of transcendence of that spatio-temporal
continuum is required. Thus primarily the spatio-temporal continuum is a
locus of relational possibility, selected from the more general realm of
systematic relationship. This limited locus of relational possibility
expresses one limitation of possibility inherent in the general system
of the process of realisation. Whatever possibility is generally
coherent with that system falls within this limitation. Also whatever is
abstractedly possible in relation to the general course of events—as
distinct from the particular limitations introduced by particular
occasions—pervades the spatio-temporal continuum in every alternative
spatial situation and at all alternative times.

Fundamentally, the spatio-temporal continuum is the general system of
relatedness of all possibilities, in so far as that system is limited by
its relevance to the general fact of actuality. Also it is inherent in
the nature of possibility that it should include this relevance to
actuality. For possibility is that in which there stands achievability,
abstracted from achievement.

It has already been emphasised that an actual occasion is to be
conceived as a limitation; and that this process of limitation can be
still further characterised as a gradation. This characteristic of an
actual occasion (α, say) requires further elucidation: An
indeterminateness stands in the essence of any eternal object (_Α_,
say). The actual occasion α synthesises in itself every eternal object;
and, in so doing, it includes the _complete_ determinate relatedness of
_Α_ to every other eternal object, or set of eternal objects. This
synthesis is a limitation of realisation but _not_ of content. Each
relationship preserves its inherent self-identity. But grades of entry
into this synthesis are inherent in each actual occasion, such as α.
These grades can be expressed only as relevance of value. This relevance
of value varies—as comparing different occasions—in grade from the
inclusion of the individual essence of _Α_ as an element in the
aesthetic synthesis (in some grade of inclusion) to the lowest grade
which is the exclusion of the individual essence of _Α_ as an element in
the aesthetic synthesis. In so far as it stands in this lowest grade,
every determinate relationship of _Α_ is merely ingredient in the
occasion in respect to the determinate _how_ this relationship is an
unfulfilled alternative, not contributing any aesthetic value, except as
forming an element in the systematic substratum of unfulfilled content.
In a higher grade, it may remain unfulfilled, but be aesthetically
relevant.

Thus _A_, conceived merely in respect to its relationships to other
eternal objects, is ‘_A_ conceived as _not-being_’; where ‘not-being’
means ‘abstracted from the determinate fact of inclusions in, and
exclusions from, actual events.’ Also ‘_A_ as _not-being_ in respect to
a definite occasion α’ means that _A_ in all its determinate
relationships is excluded from α. Again ‘_A_ as _being_ in respect to α’
means that _A_ in some of its determinate relationships is included in
α. But there can be no occasion which includes _A_ in all its
determinate relationships; for some of these relationships are
contraries. Thus, in regard to excluded relationships, _A_ will be
_not-being_ in α, even when in regard to other relationships _A_ will be
_being_ in α. In this sense, every occasion is a synthesis of _being_
and _not-being_. Furthermore, though some eternal objects are
synthesised in an occasion α merely _quâ not-being_, each eternal object
which is synthesised _quâ being_ is also synthesised _quâ not-being_.
‘_Being_’ here means ‘individually effective in the aesthetic
synthesis.’ Also the ‘aesthetic synthesis’ is the ‘experient synthesis’
viewed as self-creative, under the limitations laid upon it by its
internal relatedness to all other actual occasions. We thus
conclude—what has already been stated above—that the general fact of the
synthetic prehension of all eternal objects into every occasion wears
the double aspect of the indeterminate relatedness of each eternal
object to occasions generally, and of its determinate relatedness to
each particular occasion. This statement summarises the account of how
external relations are possible. But the account depends upon
disengaging the spatio-temporal continuum from its mere implication in
actual occasions—according to the usual explanation—and upon exhibiting
it in its origin from the general nature of abstract possibility, as
limited by the general character of the actual course of events.

The difficulty which arises in respect to internal relations is to
explain how any particular truth is possible. In so far as there are
internal relations, everything must depend upon everything else. But if
this be the case, we cannot know about anything till we equally know
everything else. Apparently, therefore, we are under the necessity of
saying everything at once. This supposed necessity is palpably untrue.
Accordingly it is incumbent on us to explain how there can be internal
relations, seeing that we admit finite truths.

Since actual occasions are selections from the realm of possibilities,
the ultimate explanation of how actual occasions have the general
character which they do have, must lie in an analysis of the general
character of the realm of possibility.

The _analytical character_ of the realm of eternal objects is the
primary metaphysical truth concerning it. By this character it is meant
that the status of any eternal object _A_ in this realm is capable of
analysis into an indefinite number of subordinate relationships of
limited scope. For example if _B_ and _C_ are two other eternal objects,
then there is some perfectly definite relationship _R(A, B, C)_ which
involves _A, B, C_ only, as to require the mention of no other definite
eternal objects in the capacity of relata. Of course, the relationship
_R(A, B, C)_ may involve subordinate relationships which are themselves
eternal objects, and _R(A, B, C)_ is also itself an eternal object. Also
there will be other relationships which in the same sense involve only
_A, B, C_. We have now to examine how, having regard to the internal
relatedness of eternal objects, this limited relationship _R(A, B, C)_
is possible.

The reason for the existence of finite relationships in the realm of
eternal objects is that relationships of these objects among themselves
are entirely unselective, and are systematically complete. We are
discussing possibility; so that every relationship which is possible is
thereby in the realm of possibility. Every such relationship of each
eternal object is founded upon the perfectly definite status of that
object as a relatum in the general scheme of relationships. This
definite status is what I have termed the ‘relational essence’ of the
object. This relational essence is determinable by reference to that
object alone, and does not require reference to any other objects,
except those which are specifically involved in its individual essence
when that essence is complex (as will be explained immediately). The
meaning of the words ‘any’ and ‘some’ springs from this principle—that
is to say, the meaning of the ‘variable’ in logic. The whole principle
is that a particular determination can be made of the _how_ of some
definite relationship of a definite eternal object _A_ to a definite
finite number _n_ of other eternal objects, _without_ any determination
of the other _n_ objects, X1, X2, ... Xn, except that they have, each of
them, the requisite status to play their respective parts in that
multiple relationship. This principle depends on the fact that the
relational essence of an eternal object is not unique to that object.
The mere relational essence of each eternal object determines the
complete uniform scheme of relational essences, since each object stands
internally in all its possible relationships. Thus the realm of
possibility provides a uniform scheme of relationships among finite sets
of eternal objects; and all eternal objects stand in all such
relationships, so far as the status of each permits.

Accordingly the relationships (as in possibility) do not involve the
individual essences of the eternal objects; they involve _any_ eternal
objects as relata, subject to the proviso that these relata have the
requisite relational essences. [It is this proviso which, automatically
and by the nature of the case, limits the ‘any’ of the phrase ‘any
eternal objects.’] This principle is the principle of the _Isolation of
Eternal Objects_ in the realm of possibility. The eternal objects are
isolated, because their relationships as possibilities are expressible
without reference to their respective individual essences. In contrast
to the realm of possibility, the inclusion of eternal objects within an
actual occasion means that in respect to some of their possible
relationships there is a togetherness of their individual essences. This
realised togetherness is the achievement of an emergent value
defined—or, shaped—by the definite eternal relatedness in respect to
which the real togetherness is achieved. Thus the eternal relatedness is
the form—the εἶδος—; the emergent actual occasion is the _superject_ of
informed value; value, as abstracted from any particular superject, is
the abstract matter—the ὕλη—which is common to all actual occasions; and
the synthetic activity which prehends valueless possibility into
superjicient informed value is the substantial activity. This
substantial activity is that which is omitted in any analysis of the
static factors in the metaphysical situation. The analysed elements of
the situation are the attributes of the substantial activity.

The difficulty inherent in the concept of finite internal relations
among eternal objects is thus evaded by two metaphysical principles, (i)
that the relationships of any eternal object _A_, considered as
constitutive of _A_, merely involve other eternal objects as bare relata
without reference to their individual essences, and (ii) that the
divisibility of the general relationship of _A_ into a multiplicity of
finite relationships of _A_ stands therefore in the essence of that
eternal object. The second principle obviously depends upon the first.
To understand _A_ is to understand the _how_ of a general scheme of
relationship. This scheme of relationship does not require the
individual uniqueness of the other relata for its comprehension. This
scheme also discloses itself as being analysable into a multiplicity of
limited relationships which have their own individuality and yet at the
same time presupposes the total relationship within possibility. In
respect to actuality there is first the general limitation of
relationships, which reduces this general unlimited scheme to the four
dimensional spatio-temporal scheme. This spatio-temporal scheme is, so
to speak, the greatest common measure of the schemes of relationship (as
limited by actuality) inherent in all the eternal objects. By this it is
meant that, _how_ select relationships of an eternal object (_A_) are
realised in any actual occasion, is always explicable by expressing the
status of _A_ in respect to this spatio-temporal scheme, and by
expressing in this scheme the relationship of the actual occasion to
other actual occasions. A definite finite relationship involving the
definite eternal objects of a limited set of such objects is itself an
eternal object: it is those eternal objects as in that relationship. I
will call such an eternal object ‘complex.’ The eternal objects which
are the relata in a complex eternal object will be called the
‘components’ of that eternal object. Also if any of these relata are
themselves complex, their components will be called ‘derivative
components’ of the original complex object. Also the components of
derivative components will also be called derivative components of the
original object. Thus the complexity of an eternal object means its
analysability into a relationship of component eternal objects. Also the
analysis of the general scheme of relatedness of eternal objects means
its exhibition as a multiplicity of complex eternal objects. An eternal
object, such as a definite shade of green, which cannot be analysed into
a relationship of components, will be called ‘simple.’

We can now explain how the analytical character of the realm of eternal
objects allows of an analysis of that realm into grades.

In the lowest grade of eternal objects are to be placed those objects
whose individual essences are simple. This is the grade of zero
complexity. Next consider any set of such objects, finite or infinite as
to the number of its members. For example, consider the set of three
eternal objects _A, B, C_, of which none is complex. Let us write _R(A,
B, C)_ for some definite possible relatedness of _A, B, C_. To take a
simple example, _A, B, C_ may be three definite colours with the
spatio-temporal relatedness to each other of three faces of a regular
tetrahedron, anywhere at any time. Then _R(A, B, C)_ is another eternal
object of the lowest complex grade. Analogously there are eternal
objects of successively higher grades. In respect to any complex eternal
object, _S(D1, D2, ... Dn)_, the eternal objects _D1, ... Dn_, whose
individual essences are constitutive of the individual essence of _S(D1,
... Dn)_, are called the components of _S(D1, ... Dn)_. It is obvious
that the grade of complexity to be ascribed to _S(D1, ... Dn)_ is to be
taken as one above the highest grade of complexity to be found among its
components.

There is thus an analysis of the realm of possibility into simple
eternal objects, and into various grades of complex eternal objects. A
complex eternal object is an abstract situation. There is a double sense
of ‘abstraction,’ in regard to the abstraction of _definite_ eternal
objects, _i.e._, non-mathematical abstraction. There is abstraction from
actuality, and abstraction from possibility. For example, _A_ and _R(A,
B, C)_ are both abstractions from the realm of possibility. Note that
_A_ must mean _A_ in all its possible relationships, and among them
_R(A, B, C)_. Also _R(A, B, C)_ means _R(A, B, C)_ in all its
relationships. But this meaning of _R(A, B, C)_ excludes other
relationships into which _A_ can enter. Hence _A_ as in _R(A, B, C)_ is
more abstract than _A simpliciter_. Thus as we pass from the grade of
simple eternal objects to higher and higher grades of complexity, we are
indulging in higher grades of abstraction from the realm of possibility.

We can now conceive the successive stages of a definite progress towards
some assigned mode of abstraction from the realm of possibility,
involving a progress (in thought) through successive grades of
increasing complexity. I will call any such route of progress ‘an
abstractive hierarchy.’ Any abstractive hierarchy, finite or infinite,
is based upon some definite group of simple eternal objects. This group
will be called the ‘base’ of the hierarchy. Thus the base of an
abstractive hierarchy is a set of objects of zero complexity. The formal
definition of an abstractive hierarchy is as follows:

An ‘abstractive hierarchy based upon _g_,’ where _g_ is a group of
simple eternal objects, is a set of eternal objects which satisfy the
following conditions,

(i) the members of _g_ belong to it, and are the only simple eternal
objects in the hierarchy,

(ii) the components of any complex eternal object in the hierarchy are
also members of the hierarchy, and

(iii) any set of eternal objects belonging to the hierarchy, whether all
of the same grade or whether differing among themselves as to grade, are
jointly among the components or derivative components of at least one
eternal object which also belongs to the hierarchy.

It is to be noticed that the components of an eternal object are
necessarily of a lower grade of complexity than itself. Accordingly any
member of such a hierarchy, which is of the first grade of complexity,
can have as components only members of the group _g_; and any member of
the second grade can have as components only members of the first grade,
and members of _g_; and so on for the higher grades.

The third condition to be satisfied by an abstractive hierarchy will be
called the condition of connexity. Thus an abstractive hierarchy springs
from its base; it includes every successive grade from its base either
indefinitely onwards, or to its maximum grade; and it is ‘connected’ by
the reappearance (in a higher grade) of any set of its members belonging
to lower grades, in the function of a set of components or derivative
components of at least one member of the hierarchy.

An abstractive hierarchy is called ‘finite’ if it stops at a finite
grade of complexity. It is called ‘infinite’ if it includes members
belonging respectively to all degrees of complexity.

It is to be noted that the base of an abstractive hierarchy may contain
any number of members, finite or infinite. Further, the infinity of the
number of the members of the base has nothing to do with the question as
to whether the hierarchy be finite or infinite.

A finite abstractive hierarchy will, by definition, possess a grade of
maximum complexity. It is characteristic of this grade that a member of
it is a component of no other eternal object belonging to any grade of
the hierarchy. Also it is evident that this grade of maximum complexity
must possess only one member; for otherwise the condition of connexity
would not be satisfied. Conversely any complex eternal object defines a
finite abstractive hierarchy to be discovered by a process of analysis.
This complex eternal object from which we start will be called the
‘vertex’ of the abstractive hierarchy: it is the sole member of the
grade of maximum complexity. In the first stage of the analysis we
obtain the components of the vertex. These components may be of varying
complexity; but there must be among them at least one member whose
complexity is of a grade one lower than that of the vertex. A grade
which is one lower than that of a given eternal object will be called
the ‘proximate grade’ for that object. We take then those components of
the vertex which belong to its proximate grade; and as the second stage
we analyse them into their components. Among these components there must
be some belonging to the proximate grade for the objects thus analysed.
Add to them the components of the vertex which also belong to this grade
of ‘second proximation’ from the vertex; and, at the third stage analyse
as before. We thus find objects belonging to the grade of third
proximation from the vertex; and we add to them the components belonging
to this grade, which have been left over from the preceding stages of
the analysis. We proceed in this way through successive stages, till we
reach the grade of simple objects. This grade forms the base of the
hierarchy.

It is to be noted that in dealing with hierarchies we are entirely
within the realm of possibility. Accordingly the eternal objects are
devoid of real togetherness: they remain within their ‘isolation.’

The logical instrument which Aristotle used for the analysis of actual
fact into more abstract elements was that of classification into species
and genera. This instrument has its overwhelmingly important application
for science in its preparatory stages. But its use in metaphysical
description distorts the true vision of the metaphysical situation. The
use of the term ‘universal’ is intimately connected with this
Aristotelian analysis: the term has been broadened of late; but still it
suggests that classificatory analysis. For this reason I have avoided
it.

In any actual occasion α, there will be a group _g_ of simple eternal
objects which are ingredient in that group in the most concrete mode.
This complete ingredience in an occasion, so as to yield the most
complete fusion of individual essence with other eternal objects in the
formation of the individual emergent occasion, is evidently of its own
kind and cannot be defined in terms of anything else. But it has a
peculiar characteristic which necessarily attaches to it. This
characteristic is that there is an _infinite_ abstractive hierarchy
based upon _g_ which is such that all its members are equally involved
in this complete inclusion in α.

The existence of such an infinite abstractive hierarchy is what is meant
by the statement that it is impossible to complete the description of an
actual occasion by means of concepts. I will call this infinite
abstractive hierarchy which is associated with α ‘the associated
hierarchy of α.’ It is also what is meant by the notion of the
connectedness of an actual occasion. This connectedness of an occasion
is necessary for its synthetic unity and for its intelligibility. There
is a connected hierarchy of concepts applicable to the occasion,
including concepts of all degrees of complexity. Also in the actual
occasion, the individual essences of the eternal objects involved in
these complex concepts achieve an aesthetic synthesis, productive of the
occasion as an experience for its own sake. This associated hierarchy is
the shape, or pattern, or form, of the occasion in so far as the
occasion is constituted of what enters into its full realisation.

Some confusion of thought has been caused by the fact that abstraction
from possibility runs in the opposite direction to an abstraction from
actuality, so far as degree of abstractness is concerned. For evidently
in describing an actual occasion α, we are nearer to the total concrete
fact when we describe α by predicating of it some member of its
associated hierarchy, which is of a high grade of complexity. We have
then said more about α. Thus, with a high grade of complexity we gain in
approach to the full concreteness of α, and with a low grade we lose in
this approach. Accordingly the simple eternal objects represent the
extreme of abstraction from an actual occasion; whereas simple eternal
objects represent the minimum of abstraction from the realm of
possibility. It will, I think, be found that, when a high degree of
abstraction is spoken of, abstraction from the realm of possibility is
what is usually meant—in other words, an elaborate logical construction.

So far I have merely been considering an actual occasion on the side of
its full concreteness. It is this side of the occasion in virtue of
which it is an event in nature. But a natural event, in this sense of
the term, is only an abstraction from a complete actual occasion. A
complete occasion includes that which in cognitive experience takes the
form of memory, anticipation, imagination, and thought. These elements
in an experient occasion are also modes of inclusion of complex eternal
objects in the synthetic prehension, as elements in the emergent value.
They differ from the concreteness of full inclusion. In a sense this
difference is inexplicable; for each mode of inclusion is of its own
kind, not to be explained in terms of anything else. But there is a
common difference which discriminates these modes of inclusion from the
full concrete ingression which has been discussed. This _differentia_ is
_abruptness_. By ‘abruptness’ I mean that what is remembered, or
anticipated, or imagined, or thought, is exhausted by a finite complex
concept. In each case there is one finite eternal object prehended
within the occasion as the vertex of a finite hierarchy. This breaking
off from an actual illimitability is what in any occasion marks off that
which is termed mental from that which belongs to the physical event to
which the mental functioning is referred.

In general there seems to be some loss of vividness in the apprehension
of the eternal objects concerned: for example, Hume speaks of ‘faint
copies.’ But this faintness seems to be a very unsafe ground for
differentiation. Often things realised in thought are more vivid than
the same things in inattentive physical experience. But the things
apprehended as mental are always subject to the condition that we come
to a stop when we attempt to explore ever higher grades of complexity in
their realised relationships. We always find that we have thought of
just this—whatever it may be—and of no more. There is a limitation which
breaks off the finite concept from the higher grades of illimitable
complexity.

Thus an actual occasion is a prehension of one infinite hierarchy (its
associated hierarchy) together with various finite hierarchies. The
synthesis into the occasion of the infinite hierarchy is according to
its specific mode of realisation, and that of the finite hierarchies is
according to various other specific modes of realisation. There is one
metaphysical principle which is essential for the rational coherence of
this account of the general character of an experient occasion. I call
this principle, ‘The Translucency of Realisation.’ By this I mean that
any eternal object is just itself in whatever mode of realisation it is
involved. There can be no distortion of the individual essence without
thereby producing a different eternal object. In the essence of each
eternal object there stands an indeterminateness which expresses its
indifferent patience for any mode of ingression into any actual
occasion. Thus in cognitive experience, there can be the cognition of
the same eternal object as in the same occasion having ingression with
implication in more than one grade of realisation. Thus the translucency
of realisation, and the possible multiplicity of modes of ingression
into the same occasion, together form the foundation for the
correspondence theory of truth.

In this account of an actual occasion in terms of its connection with
the realm of eternal objects, we have gone back to the train of thought
in our second chapter, where the nature of mathematics was discussed.
The idea, ascribed to Pythagoras, has been amplified, and put forward as
the first chapter in metaphysics. The next chapter is concerned with the
puzzling fact that there is an actual course of events which is in
itself a limited fact, in that metaphysically speaking it might have
been otherwise. But other metaphysical investigations are omitted; for
example, epistemology, and the classification of some elements in the
unfathomable wealth of the field of possibility. This last topic brings
metaphysics in sight of the special topics of the various sciences.




                               CHAPTER XI

                                  GOD


Aristotle found it necessary to complete his metaphysics by the
introduction of a Prime Mover—God. This, for two reasons, is an
important fact in the history of metaphysics. In the first place if we
are to accord to anyone the position of the greatest metaphysician,
having regard to genius of insight, to general equipment in knowledge,
and to the stimulus of his metaphysical ancestry, we must choose
Aristotle. Secondly, in his consideration of this metaphysical question
he was entirely dispassionate; and he is the last European metaphysician
of first rate importance for whom this claim can be made. After
Aristotle, ethical and religious interests began to influence
metaphysical conclusions. The Jews dispersed, first willingly and then
forcibly, and the Judaic-Alexandrian school arose. Then Christianity
closely followed by Mahometanism, intervened. The Greek gods who
surrounded Aristotle were subordinate metaphysical entities, well within
nature. Accordingly on the subject of his Prime Mover, he would have no
motive, except to follow his metaphysical train of thought whithersoever
it led him. It did not lead him very far towards the production of a God
available for religious purposes. It may be doubted whether any properly
general metaphysics can ever, without the illicit introduction of other
considerations, get much further than Aristotle. But his conclusion does
represent a first step without which no evidence on a narrower
experiential basis can be of much avail in shaping the conception. For
nothing, within any limited type of experience, can give intelligence to
shape our ideas of any entity at the base of all actual things, unless
the general character of things requires that there be such an entity.

The phrase, Prime Mover, warns us that Aristotle’s thought was enmeshed
in the details of an erroneous physics and an erroneous cosmology. In
Aristotle’s physics special causes were required to sustain the motions
of material things. These could easily be fitted into his system,
provided that the general cosmic motions could be sustained. For then in
relation to the general working system, each thing could be provided
with its true end. Hence the necessity for a Prime Mover who sustains
the motions of the spheres on which depend the adjustment of things.
To-day we repudiate the Aristotelian physics and the Aristotelian
cosmology, so that the exact form of the above argument manifestly
fails. But if our general metaphysics is in any way similar to that
outlined in the previous chapter, an analogous metaphysical problem
arises which can be solved only in an analogous fashion. In the place of
Aristotle’s God as Prime Mover, we require God as the Principle of
Concretion. This position can be substantiated only by the discussion of
the general implication of the course of actual occasions,—that is to
say, of the process of realisation.

We conceive actuality as in essential relation to an unfathomable
possibility. Eternal objects inform actual occasions with hierarchic
patterns, included and excluded in every variety of discrimination.
Another view of the same truth is that every actual occasion is a
limitation imposed on possibility, and that by virtue of this
limitation the particular value of that shaped togetherness of things
emerges. In this way we express how a single occasion is to be viewed
in terms of possibility, and how possibility is to be viewed in terms
of a single actual occasion. But there are no single occasions, in the
sense of isolated occasions. Actuality is through and through
togetherness—togetherness of otherwise isolated eternal objects, and
togetherness of all actual occasions. It is my task in this chapter to
describe the unity of actual occasions. The previous chapter centered
its interest in the abstract: the present chapter deals with the
concrete, _i.e._, that which has grown together.

Consider an occasion α:—we have to enumerate how other actual occasions
are in α, in the sense that their relationships with α are constitutive
of the essence of α. What α is in itself, is that it is a unit of
realised experience; accordingly we ask how other occasions are in the
experience which is α. Also for the present I am excluding cognitive
experience. The complete answer to this question is, that the
relationships among actual occasions are as unfathomable in their
variety of type as are those among eternal objects in the realm of
abstraction. But there are fundamental types of such relationships in
terms of which the whole complex variety can find its description.

A preliminary for the understanding of these types of entry (of one
occasion into the essence of another) is to note that they are involved
in the modes of realisation of abstractive hierarchies, discussed in the
previous chapter. The spatio-temporal relationships, involved in those
hierarchies as realised in α, have all a definition in terms of α and of
the occasions entrant in α. Thus the entrant occasions lend their
aspects to the hierarchies, and thereby convert spatio-temporal
modalities into categorical determinations; and the hierarchies lend
their forms to the occasions and thereby limit the entrant occasions to
being entrant only under those forms. Thus in the same way (as seen in
the previous chapter) that every occasion is a synthesis of all eternal
objects under the limitation of gradations of actuality, so every
occasion is a synthesis of all occasions under the limitation of
gradations of types of entry. Each occasion synthesises the totality of
content under its own limitations of mode.

In respect to these types of internal relationship between α and other
occasions, these other occasions (as constitutive of α) can be
classified in many alternative ways. These are all concerned with
different definitions of past, present, and future. It has been usual in
philosophy to assume that these various definitions must necessarily be
equivalent. The present state of opinion in physical science
conclusively shows that this assumption is without metaphysical
justification, even though any such discrimination may be found to be
unnecessary for physical science. This question has already been dealt
with in the chapter on Relativity. But the physical theory of relativity
touches only the fringe of the various theories which are metaphysically
tenable. It is important for my argument to insist upon the unbounded
freedom within which the actual is a unique categorical determination.

Every actual occasion exhibits itself as a process: it is a
becomingness. In so disclosing itself, it places itself as one among a
multiplicity of other occasions, without which it could not be itself.
It also defines itself as a particular individual achievement, focussing
in its limited way an unbounded realm of eternal objects.

Any one occasion α issues from other occasions which collectively form
its _past_. It displays for itself other occasions which collectively
form its _present_. It is in respect to its associated hierarchy, as
displayed in this immediate present, that an occasion finds its own
originality. It is that display which is its own contribution to the
output of actuality. It may be conditioned, and even completely
determined by the past from which it issues. But its display in the
present under those conditions is what directly emerges from its
prehensive activity. The occasion α also holds within itself an
indetermination in the form of a future, which has partial determination
by reason of its inclusion in α and also has determinate spatio-temporal
relatedness to α and to actual occasions of the past from α and of the
present for α.

This future is a synthesis in α of eternal objects as not-being and as
requiring the passage from α to other individualisations (with
determinate spatio-temporal relations to α) in which not-being becomes
being.

There is also in α what, in the previous chapter, I have termed the
‘abrupt’ realisation of finite eternal objects. This abrupt realisation
requires _either_ a reference of the basic objects of the finite
hierarchy to determinate occasions other than α (as their situations),
in past, present, future; _or_ requires a realisation of these eternal
objects in determinate relationships, but under the aspect of exemption
from inclusion in the spatio-temporal scheme of relatedness between
actual occasions. This abrupt synthesis of eternal objects in each
occasion is the inclusion in actuality of the analytical character of
the realm of eternality. This inclusion has those limited gradations of
actuality which characterise every occasion by reason of its essential
limitation. It is this realised extension of eternal relatedness beyond
the mutual relatedness of the actual occasions, which prehends into each
occasion the full sweep of eternal relatedness. I term this abrupt
realisation the ‘graded envisagement’ which each occasion prehends into
its synthesis. This graded envisagement is how the actual includes what
(in one sense) is not-being as a positive factor in its own achievement.
It is the source of error, of truth, of art, of ethics, and of religion.
By it, fact is confronted with alternatives.

This general concept, of an event as a process whose outcome is a unit
of experience, points to the analysis of an event into (i) substantial
activity, (ii) conditioned potentialities which are there for synthesis,
and (iii) the achieved outcome of the synthesis. The unity of all actual
occasions forbids the analysis of substantial activities into
independent entities. Each individual activity is nothing but the mode
in which the general activity is individualised by the imposed
conditions. The envisagement which enters into the synthesis is also a
character which conditions the synthesising activity. The general
activity is not an entity in the sense in which occasions or eternal
objects are entities. It is a general metaphysical character which
underlies all occasions, in a particular mode for each occasion. There
is nothing with which to compare it: it is Spinoza’s one infinite
substance. Its attributes are its character of individualisation into a
multiplicity of modes, and the realm of eternal objects which are
variously synthesised in these modes. Thus eternal possibility and modal
differentiation into individual multiplicity are the attributes of the
one substance. In fact each general element of the metaphysical
situation is an attribute of the substantial activity.

Yet another element in the metaphysical situation is disclosed by the
consideration that the general attribute of modality is limited. This
element must rank as an attribute of the substantial activity. In its
nature each mode is limited, so as not to be other modes. But, beyond
these limitations of particulars, the general modal individualisation is
limited in two ways: In the first place it is an actual course of
events, which might be otherwise so far as concerns eternal possibility,
but _is_ that course. This limitation takes three forms, (i) the special
logical relations which all events must conform to, (ii) the selection
of relationships to which the events do conform, and (iii) the
particularity which infects the course even within those general
relationships of logic and causation. Thus this first limitation is a
limitation of antecedent selection. So far as the general metaphysical
situation is concerned, there might have been an indiscriminate modal
pluralism apart from logical or other limitation. But there could not
then have been these modes, for each mode represents a synthesis of
actualities which are limited to conform to a standard. We here come to
the second way of limitation. Restriction is the price of value. There
cannot be value without antecedent standards of value, to discriminate
the acceptance or rejection of what is before the envisaging mode of
activity. Thus there is an antecedent limitation among values,
introducing contraries, grades, and oppositions.

According to this argument the fact that there is a process of actual
occasions, and the fact that the occasions are the emergence of values
which require such limitation, both require that the course of events
should have developed amid an antecedent limitation composed of
conditions, particularisation, and standards of value.

Thus as a further element in the metaphysical situation, there is
required a principle of limitation. Some particular _how_ is necessary,
and some particularisation in the _what_ of matter of fact is necessary.
The only alternative to this admission, is to deny the reality of actual
occasions. Their apparent irrational limitation must be taken as a proof
of illusion and we must look for reality behind the scene. If we reject
this alternative behind the scene, we must provide a ground for
limitation which stands among the attributes of the substantial
activity. This attribute provides the limitation for which no reason can
be given: for all reason flows from it. God is the ultimate limitation,
and His existence is the ultimate irrationality. For no reason can be
given for just that limitation which it stands in His nature to impose.
God is not concrete, but He is the ground for concrete actuality. No
reason can be given for the nature of God, because that nature is the
ground of rationality.

In this argument the point to notice is, that what is metaphysically
indeterminate has nevertheless to be categorically determinate. We have
come to the limit of rationality. For there is a categorical limitation
which does not spring from any metaphysical reason. There is a
metaphysical need for a principle of determination, but there can be no
metaphysical reason for what is determined. If there were such a reason,
there would be no need for any further principle: for metaphysics would
already have provided the determination. The general principle of
empiricism depends upon the doctrine that there is a principle of
concretion which is not discoverable by abstract reason. What further
can be known about God must be sought in the region of particular
experiences, and therefore rests on an empirical basis. In respect to
the interpretation of these experiences, mankind have differed
profoundly. He has been named respectively, Jehovah, Allah, Brahma,
Father in Heaven, Order of Heaven, First Cause, Supreme Being, Chance.
Each name corresponds to a system of thought derived from the
experiences of those who have used it.

Among medieval and modern philosophers, anxious to establish the
religious significance of God, an unfortunate habit has prevailed of
paying to Him metaphysical compliments. He has been conceived as the
foundation of the metaphysical situation with its ultimate activity. If
this conception be adhered to, there can be no alternative except to
discern in Him the origin of all evil as well as of all good. He is then
the supreme author of the play, and to Him must therefore be ascribed
its shortcomings as well as its success. If He be conceived as the
supreme ground for limitation, it stands in His very nature to divide
the Good from the Evil, and to establish Reason ‘within her dominions
supreme.’




                              CHAPTER XII

                          RELIGION AND SCIENCE


The difficulty in approaching the question of the relations between
Religion and Science is, that its elucidation requires that we have in
our minds some clear idea of what we mean by either of the terms,
‘religion’ and ‘science.’ Also I wish to speak in the most general way
possible, and to keep in the background any comparison of particular
creeds, scientific or religious. We have got to understand the type of
connection which exists between the two spheres, and then to draw some
definite conclusions respecting the existing situation which at present
confronts the world.

The _conflict_ between religion and science is what naturally occurs to
our minds when we think of this subject. It seems as though, during the
last half-century, the results of science and the beliefs of religion
had come into a position of frank disagreement, from which there can be
no escape, except by abandoning either the clear teaching of science, or
the clear teaching of religion. This conclusion has been urged by
controversialists on either side. Not by all controversialists, of
course, but by those trenchant intellects which every controversy calls
out into the open.

The distress of sensitive minds, and the zeal for truth, and the sense
of the importance of the issues, must command our sincerest sympathy.
When we consider what religion is for mankind, and what science is, it
is no exaggeration to say that the future course of history depends upon
the decision of this generation as to the relations between them. We
have here the two strongest general forces (apart from the mere impulse
of the various senses) which influence men, and they seem to be set one
against the other—the force of our religious intuitions, and the force
of our impulse to accurate observation and logical deduction.

A great English statesman once advised his countrymen to use large-scale
maps, as a preservative against alarms, panics, and general
misunderstanding of the true relations between nations. In the same way
in dealing with the clash between permanent elements of human nature, it
is well to map our history on a large scale, and to disengage ourselves
from our immediate absorption in the present conflicts. When we do this,
we immediately discover two great facts. In the first place, there has
always been a conflict between religion and science; and in the second
place, both religion and science have always been in a state of
continual development. In the early days of Christianity, there was a
general belief among Christians that the world was coming to an end in
the lifetime of people then living. We can make only indirect inferences
as to how far this belief was authoritatively proclaimed; but it is
certain that it was widely held, and that it formed an impressive part
of the popular religious doctrine. The belief proved itself to be
mistaken, and Christian doctrine adjusted itself to the change. Again in
the early Church individual theologians very confidently deduced from
the Bible opinions concerning the nature of the physical universe. In
the year A. D. 535, a monk named Cosmas[17] wrote a book which he
entitled, _Christian Topography_. He was a travelled man who had visited
India and Ethiopia; and finally he lived in a monastery at Alexandria,
which was then a great centre of culture. In this book, basing himself
upon the direct meaning of Biblical texts as construed by him in a
literal fashion, he denied the existence of the antipodes, and asserted
that the world is a flat parallelogram whose length is double its
breadth.

Footnote 17:

  _Cf._ Lecky’s _The Rise and Influence of Rationalism in Europe_, Ch.
  III.

In the seventeenth century the doctrine of the motion of the earth was
condemned by a Catholic tribunal. A hundred years ago the extension of
time demanded by geological science distressed religious people,
Protestant and Catholic. And to-day the doctrine of evolution is an
equal stumbling-block. These are only a few instances illustrating a
general fact.

But all our ideas will be in a wrong perspective if we think that this
recurring perplexity was confined to contradictions between religion and
science; and that in these controversies religion was always wrong, and
that science was always right. The true facts of the case are very much
more complex, and refuse to be summarised in these simple terms.

Theology itself exhibits exactly the same character of gradual
development, arising from an aspect of conflict between its own proper
ideas. This fact is a commonplace to theologians, but is often obscured
in the stress of controversy. I do not wish to overstate my case; so I
will confine myself to Roman Catholic writers. In the seventeenth
century a learned Jesuit, Father Petavius, showed that the theologians
of the first three centuries of Christianity made use of phrases and
statements which since the fifth century would be condemned as
heretical. Also Cardinal Newman devoted a treatise to the discussion of
the development of doctrine. He wrote it before he became a great Roman
Catholic ecclesiastic; but throughout his life, it was never retracted
and continually reissued.

Science is even more changeable than theology. No man of science could
subscribe without qualification to Galileo’s beliefs, or to Newton’s
beliefs, or to all his own scientific beliefs of ten years ago.

In both regions of thought, additions, distinctions, and modifications
have been introduced. So that now, even when the same assertion is made
to-day as was made a thousand, or fifteen hundred years ago, it is made
subject to limitations or expansions of meaning, which were not
contemplated at the earlier epoch. We are told by logicians that a
proposition must be either true or false, and that there is no middle
term. But in practice, we may know that a proposition expresses an
important truth, but that it is subject to limitations and
qualifications which at present remain undiscovered. It is a general
feature of our knowledge, that we are insistently aware of important
truths; and yet that the only formulations of these truths which we are
able to make presuppose a general standpoint of conceptions which may
have to be modified. I will give you two illustrations, both from
science: Galileo said that the earth moves and that the sun is fixed;
the Inquisition said that the earth is fixed and the sun moves; and
Newtonian astronomers, adopting an absolute theory of space, said that
both the sun and the earth move. But now we say that any one of these
three statements is equally true, provided that you have fixed your
sense of ‘rest’ and ‘motion’ in the way required by the statement
adopted. At the date of Galileo’s controversy with the Inquisition,
Galileo’s way of stating the facts was, beyond question, the fruitful
procedure for the sake of scientific research. But in itself it was not
more true than the formulation of the Inquisition. But at that time the
modern concepts of relative motion were in nobody’s mind; so that the
statements were made in ignorance of the qualifications required for
their more perfect truth. Yet this question of the motions of the earth
and the sun expresses a real fact in the universe; and all sides had got
hold of important truths concerning it. But with the knowledge of those
times, the truths appeared to be inconsistent.

Again I will give you another example taken from the state of modern
physical science. Since the time of Newton and Huyghens in the
seventeenth century there have been two theories as to the physical
nature of light. Newton’s theory was that a beam of light consists of a
stream of very minute particles, or corpuscles, and that we have the
sensation of light when these corpuscles strike the retinas of our eyes.
Huyghens’ theory was that light consists of very minute waves of
trembling in an all-pervading ether, and that these waves are travelling
along a beam of light. The two theories are contradictory. In the
eighteenth century Newton’s theory was believed, in the nineteenth
century Huyghens’ theory was believed. To-day there is one large group
of phenomena which can be explained only on the wave theory, and another
large group which can be explained only on the corpuscular theory.
Scientists have to leave it at that, and wait for the future, in the
hope of attaining some wider vision which reconciles both.

We should apply these same principles to the questions in which there is
a variance between science and religion. We would believe nothing in
either sphere of thought which does not appear to us to be certified by
solid reasons based upon the critical research either of ourselves or of
competent authorities. But granting that we have honestly taken this
precaution, a clash between the two on points of detail where they
overlap should not lead us hastily to abandon doctrines for which we
have solid evidence. It may be that we are more interested in one set of
doctrines than in the other. But, if we have any sense of perspective
and of the history of thought, we shall wait and refrain from mutual
anathemas.

We should wait: but we should not wait passively, or in despair. The
clash is a sign that there are wider truths and finer perspectives
within which a reconciliation of a deeper religion and a more subtle
science will be found.

In one sense, therefore, the conflict between science and religion is a
slight matter which has been unduly emphasised. A mere logical
contradiction cannot in itself point to more than the necessity of some
readjustments, possibly of a very minor character on both sides.
Remember the widely different aspects of events which are dealt with in
science and in religion respectively. Science is concerned with the
general conditions which are observed to regulate physical phenomena;
whereas religion is wholly wrapped up in the contemplation of moral and
aesthetic values. On the one side there is the law of gravitation, and
on the other the contemplation of the beauty of holiness. What one side
sees, the other misses; and vice versa.

Consider, for example, the lives of John Wesley and of Saint Francis of
Assisi. For physical science you have in these lives merely ordinary
examples of the operation of the principles of physiological chemistry,
and of the dynamics of nervous reactions: for religion you have lives of
the most profound significance in the history of the world. Can you be
surprised that, in the absence of a perfect and complete phrasing of the
principles of science and of the principles of religion which apply to
these specific cases, the accounts of these lives from these divergent
standpoints should involve discrepancies? It would be a miracle if it
were not so.

It would, however, be missing the point to think that we need not
trouble ourselves about the conflict between science and religion. In an
intellectual age there can be no active interest which puts aside all
hope of a vision of the harmony of truth. To acquiesce in discrepancy is
destructive of candour, and of moral cleanliness. It belongs to the
self-respect of intellect to pursue every tangle of thought to its final
unravelment. If you check that impulse, you will get no religion and no
science from an awakened thoughtfulness. The important question is, In
what spirit are we going to face the issue? There we come to something
absolutely vital.

A clash of doctrines is not a disaster—it is an opportunity. I will
explain my meaning by some illustrations from science. The weight of an
atom of nitrogen was well known. Also it was an established scientific
doctrine that the average weight of such atoms in any considerable mass
will be always the same. Two experimenters, the late Lord Rayleigh and
the late Sir William Ramsay, found that if they obtained nitrogen by two
different methods, each equally effective for that purpose, they always
observed a persistent slight difference between the average weights of
the atoms in the two cases. Now I ask you, would it have been rational
of these men to have despaired because of this conflict between chemical
theory and scientific observation? Suppose that for some reason the
chemical doctrine had been highly prized throughout some district as the
foundation of its social order:—would it have been wise, would it have
been candid, would it have been moral, to forbid the disclosure of the
fact that the experiments produced discordant results? Or, on the other
hand, should Sir William Ramsay and Lord Rayleigh have proclaimed that
chemical theory was now a detected delusion? We see at once that either
of these ways would have been a method of facing the issue in an
entirely wrong spirit. What Rayleigh and Ramsay did do was this: They at
once perceived that they had hit upon a line of investigation which
would disclose some subtlety of chemical theory that had hitherto eluded
observation. The discrepancy was not a disaster: it was an opportunity
to increase the sweep of chemical knowledge. You all know the end of the
story: finally argon was discovered, a new chemical element which had
lurked undetected, mixed with the nitrogen. But the story has a sequel
which forms my second illustration. This discovery drew attention to the
importance of observing accurately minute differences in chemical
substances as obtained by different methods. Further researches of the
most careful accuracy were undertaken. Finally another physicist, F. W.
Aston, working in the Cavendish Laboratory at Cambridge in England,
discovered that even the same element might assume two or more distinct
forms, termed _isotopes_, and that the law of the constancy of average
atomic weight holds for each of these forms, but as between the
different isotopes differs slightly. The research has effected a great
stride in the power of chemical theory, far transcending in importance
the discovery of argon from which it originated. The moral of these
stories lies on the surface, and I will leave to you their application
to the case of religion and science.

In formal logic, a contradiction is the signal of a defeat: but in the
evolution of real knowledge it marks the first step in progress towards
a victory. This is one great reason for the utmost toleration of variety
of opinion. Once and forever, this duty of toleration has been summed up
in the words, ‘Let both grow together until the harvest.’ The failure of
Christians to act up to this precept, of the highest authority, is one
of the curiosities of religious history. But we have not yet exhausted
the discussion of the moral temper required for the pursuit of truth.
There are short cuts leading merely to an illusory success. It is easy
enough to find a theory, logically harmonious and with important
applications in the region of fact, provided that you are content to
disregard half your evidence. Every age produces people with clear
logical intellects, and with the most praiseworthy grasp of the
importance of some sphere of human experience, who have elaborated, or
inherited, a scheme of thought which exactly fits those experiences
which claim their interest. Such people are apt resolutely to ignore, or
to explain away, all evidence which confuses their scheme with
contradictory instances. What they cannot fit in is for them nonsense.
An unflinching determination to take the whole evidence into account is
the only method of preservation against the fluctuating extremes of
fashionable opinion. This advice seems so easy, and is in fact so
difficult to follow.

One reason for this difficulty is that we cannot think first and act
afterwards. From the moment of birth we are immersed in action, and can
only fitfully guide it by taking thought. We have, therefore, in various
spheres of experience to adopt those ideas which seem to work within
those spheres. It is absolutely necessary to trust to ideas which are
generally adequate, even though we know that there are subtleties and
distinctions beyond our ken. Also apart from the necessities of action,
we cannot even keep before our minds the whole evidence except under the
guise of doctrines which are incompletely harmonised. We cannot think in
terms of an indefinite multiplicity of detail; our evidence can acquire
its proper importance only if it comes before us marshalled by general
ideas. These ideas we inherit—they form the tradition of our
civilisation. Such traditional ideas are never static. They are either
fading into meaningless formulae, or are gaining power by the new lights
thrown by a more delicate apprehension. They are transformed by the urge
of critical reason, by the vivid evidence of emotional experience, and
by the cold certainties of scientific perception. One fact is certain,
you cannot keep them still. No generation can merely reproduce its
ancestors. You may preserve the life in a flux of form, or preserve the
form amid an ebb of life. But you cannot permanently enclose the same
life in the same mould.

The present state of religion among the European races illustrates the
statements which I have been making. The phenomena are mixed. There have
been reactions and revivals. But on the whole, during many generations,
there has been a gradual decay of religious influence in European
civilisation. Each revival touches a lower peak than its predecessor,
and each period of slackness a lower depth. The average curve marks a
steady fall in religious tone. In some countries the interest in
religion is higher than in others. But in those countries where the
interest is relatively high, it still falls as the generations pass.
Religion is tending to degenerate into a decent formula wherewith to
embellish a comfortable life. A great historical movement on this scale
results from the convergence of many causes. I wish to suggest two of
them which lie within the scope of this chapter for consideration.

In the first place for over two centuries religion has been on the
defensive, and on a weak defensive. The period has been one of
unprecedented intellectual progress. In this way a series of novel
situations have been produced for thought. Each such occasion has found
the religious thinkers unprepared. Something, which has been proclaimed
to be vital, has finally, after struggle, distress, and anathema, been
modified and otherwise interpreted. The next generation of religious
apologists then congratulates the religious world on the deeper insight
which has been gained. The result of the continued repetition of this
undignified retreat, during many generations, has at last almost
entirely destroyed the intellectual authority of religious thinkers.
Consider this contrast: when Darwin or Einstein proclaim theories which
modify our ideas, it is a triumph for science. We do not go about saying
that there is another defeat for science, because its old ideas have
been abandoned. We know that another step of scientific insight has been
gained.

Religion will not regain its old power until it can face change in the
same spirit as does science. Its principles may be eternal, but the
expression of those principles requires continual development. This
evolution of religion is in the main a disengagement of its own proper
ideas from the adventitious notions which have crept into it by reason
of the expression of its own ideas in terms of the imaginative picture
of the world entertained in previous ages. Such a release of religion
from the bonds of imperfect science is all to the good. It stresses its
own genuine message. The great point to be kept in mind is that normally
an advance in science will show that statements of various religious
beliefs require some sort of modification. It may be that they have to
be expanded or explained, or indeed entirely restated. If the religion
is a sound expression of truth, this modification will only exhibit more
adequately the exact point which is of importance. This process is a
gain. In so far, therefore, as any religion has any contact with
physical facts, it is to be expected that the point of view of those
facts must be continually modified as scientific knowledge advances. In
this way, the exact relevance of these facts for religious thought will
grow more and more clear. The progress of science must result in the
unceasing modification of religious thought, to the great advantage of
religion.

The religious controversies of the sixteenth and seventeenth centuries
put theologians into a most unfortunate state of mind. They were always
attacking and defending. They pictured themselves as the garrison of a
fort surrounded by hostile forces. All such pictures express
half-truths. That is why they are so popular. But they are dangerous.
This particular picture fostered a pugnacious party spirit which really
expresses an ultimate lack of faith. They dared not modify, because they
shirked the task of disengaging their spiritual message from the
associations of a particular imagery.

Let me explain myself by an example. In the early medieval times, Heaven
was in the sky, and Hell was underground; volcanoes were the jaws of
Hell. I do not assert that these beliefs entered into the official
formulations: but they did enter into the popular understanding of the
general doctrines of Heaven and Hell. These notions were what everyone
thought to be implied by the doctrine of the future state. They entered
into the explanations of the most influential exponents of Christian
belief. For example, they occur in the _Dialogues_ of Pope Gregory,[18]
the Great, a man whose high official position is surpassed only by the
magnitude of his services to humanity. I am not saying what we ought to
believe about the future state. But whatever be the right doctrine, in
this instance the clash between religion and science, which has
relegated the earth to the position of a second-rate planet attached to
a second-rate sun, has been greatly to the benefit of the spirituality
of religion by dispersing these medieval fancies.

Footnote 18:

  _Cf._ Gregorovius’ _History of Rome in the Middle Ages_, Book III, Ch.
  III, Vol. II, English Trans.

Another way of looking at this question of the evolution of religious
thought is to note that any verbal form of statement which has been
before the world for some time discloses ambiguities; and that often
such ambiguities strike at the very heart of the meaning. The effective
sense in which a doctrine has been held in the past cannot be determined
by the mere logical analysis of verbal statements, made in ignorance of
the logical trap. You have to take into account the whole reaction of
human nature to the scheme of thought. This reaction is of a mixed
character, including elements of emotion derived from our lower natures.
It is here that the impersonal criticism of science and of philosophy
comes to the aid of religious evolution. Example after example can be
given of this motive force in development. For example, the logical
difficulties inherent in the doctrine of the moral cleansing of human
nature by the power of religion rent Christianity in the days of
Pelagius and Augustine—that is to say, at the beginning of the fifth
century. Echoes of that controversy still linger in theology.

So far, my point has been this: that religion is the expression of one
type of fundamental experiences of mankind: that religious thought
develops into an increasing accuracy of expression, disengaged from
adventitious imagery: that the interaction between religion and science
is one great factor in promoting this development.

I now come to my second reason for the modern fading of interest in
religion. This involves the ultimate question which I stated in my
opening sentences. We have to know what we mean by religion. The
churches, in their presentation of their answers to this query, have put
forward aspects of religion which are expressed in terms either suited
to the emotional reactions of bygone times or directed to excite modern
emotional interests of a nonreligious character. What I mean under the
first heading is that religious appeal is directed partly to excite that
instinctive fear of the wrath of a tyrant which was inbred in the
unhappy populations of the arbitrary empires of the ancient world, and
in particular to excite that fear of an all-powerful arbitrary tyrant
behind the unknown forces of nature. This appeal to the ready instinct
of brute fear is losing its force. It lacks any directness of response,
because modern science and modern conditions of life have taught us to
meet occasions of apprehension by a critical analysis of their causes
and conditions. Religion is the reaction of human nature to its search
for God. The presentation of God under the aspect of power awakens every
modern instinct of critical reaction. This is fatal; for religion
collapses unless its main positions command immediacy of assent. In this
respect the old phraseology is at variance with the psychology of modern
civilisations. This change in psychology is largely due to science, and
is one of the chief ways in which the advance of science has weakened
the hold of the old religious forms of expression. The nonreligious
motive which has entered into modern religious thought is the desire for
a comfortable organisation of modern society. Religion has been
presented as valuable for the ordering of life. Its claims have been
rested upon its function as a sanction to right conduct. Also the
purpose of right conduct quickly degenerates into the formation of
pleasing social relations. We have here a subtle degradation of
religious ideas, following upon their gradual purification under the
influence of keener ethical intuitions. Conduct is a by-product of
religion—an inevitable by-product, but not the main point. Every great
religious teacher has revolted against the presentation of religion as a
mere sanction of rules of conduct. Saint Paul denounced the Law, and
Puritan divines spoke of the filthy rags of righteousness. The
insistence upon rules of conduct marks the ebb of religious fervour.
Above and beyond all things, the religious life is not a research after
comfort. I must now state, in all diffidence, what I conceive to be the
essential character of the religious spirit.

Religion is the vision of something which stands beyond, behind, and
within, the passing flux of immediate things; something which is real,
and yet waiting to be realised; something which is a remote possibility,
and yet the greatest of present facts; something that gives meaning to
all that passes, and yet eludes apprehension; something whose possession
is the final good, and yet is beyond all reach; something which is the
ultimate ideal, and the hopeless quest.

The immediate reaction of human nature to the religious vision is
worship. Religion has emerged into human experience mixed with the
crudest fancies of barbaric imagination. Gradually, slowly, steadily the
vision recurs in history under nobler form and with clearer expression.
It is the one element in human experience which persistently shows an
upward trend. It fades and then recurs. But when it renews its force, it
recurs with an added richness and purity of content. The fact of the
religious vision, and its history of persistent expansion, is our one
ground for optimism. Apart from it, human life is a flash of occasional
enjoyments lighting up a mass of pain and misery, a bagatelle of
transient experience.

The vision claims nothing but worship; and worship is a surrender to the
claim for assimilation, urged with the motive force of mutual love. The
vision never overrules. It is always there, and it has the power of love
presenting the one purpose whose fulfilment is eternal harmony. Such
order as we find in nature is never force—it presents itself as the one
harmonious adjustment of complex detail. Evil is the brute motive force
of fragmentary purpose, disregarding the eternal vision. Evil is
overruling, retarding, hurting. The power of God is the worship He
inspires. That religion is strong which in its ritual and its modes of
thought evokes an apprehension of the commanding vision. The worship of
God is not a rule of safety—it is an adventure of the spirit, a flight
after the unattainable. The death of religion comes with the repression
of the high hope of adventure.




                              CHAPTER XIII

                     REQUISITES FOR SOCIAL PROGRESS


It has been the purpose of these lectures to analyse the reactions of
science in forming that background of instinctive ideas which control
the activities of successive generations. Such a background takes the
form of a certain vague philosophy as to the last word about things,
when all is said. The three centuries, which form the epoch of modern
science, have revolved round the ideas of _God_, _mind_, _matter_, and
also of _space_ and _time_ in their characters of expressing _simple
location_ for matter. Philosophy has on the whole emphasised _mind_, and
has thus been out of touch with science during the two latter centuries.
But it is creeping back into its old importance owing to the rise of
psychology and its alliance with physiology. Also, this rehabilitation
of philosophy has been facilitated by the recent breakdown of the
seventeenth century settlement of the principles of physical science.
But, until that collapse, science seated itself securely upon the
concepts of matter, space, time, and latterly, of energy. Also there
were arbitrary laws of nature determining locomotion. They were
empirically observed, but for some obscure reason were known to be
universal. Anyone who in practice or theory disregarded them was
denounced with unsparing vigour. This position on the part of scientists
was pure bluff, if one may credit them with believing their own
statements. For their current philosophy completely failed to justify
the assumption that the immediate knowledge inherent in any present
occasion throws any light either on its past, or its future.

I have also sketched an alternative philosophy of science in which
_organism_ takes the place of _matter_. For this purpose, the mind
involved in the materialist theory dissolves into a function of
organism. The psychological field then exhibits what an event is in
itself. Our bodily event is an unusually complex type of organism and
consequently includes cognition. Further, space and time, in their most
concrete signification, become the locus of events. An organism is the
realisation of a definite shape of value. The emergence of some actual
value depends on limitation which excludes neutralising cross-lights.
Thus an event is a matter of fact which by reason of its limitation is a
value for itself; but by reason of its very nature it also requires the
whole universe in order to be itself.

Importance depends on endurance. Endurance is the retention through time
of an achievement of value. What endures is identity of pattern,
self-inherited. Endurance requires the favourable environment. The whole
of science revolves round this question of enduring organisms.

The general influence of science at the present moment can be analysed
under the headings: General Conceptions Respecting the Universe,
Technological Applications, Professionalism in Knowledge, Influence of
Biological Doctrines on the Motives of Conduct. I have endeavoured in
the preceding lectures to give a glimpse of these points. It lies within
the scope of this concluding lecture to consider the reaction of science
upon some problems confronting civilised societies.

The general conceptions introduced by science into modern thought cannot
be separated from the philosophical situation as expressed by Descartes.
I mean the assumption of bodies and minds as independent individual
substances, each existing in its own right apart from any necessary
reference to each other. Such a conception was very concordant with the
individualism which had issued from the moral discipline of the Middle
Ages. But, though the easy reception of the idea is thus explained, the
derivation in itself rests upon a confusion, very natural but none the
less unfortunate. The moral discipline had emphasized the intrinsic
value of the individual entity. This emphasis had put the notions of the
individual and of its experiences into the foreground of thought. At
this point the confusion commences. The emergent individual value of
each entity is transformed into the independent substantial existence of
each entity, which is a very different notion.

I do not mean to say that Descartes made this logical, or rather
illogical, transition, in the form of explicit reasoning. Far from it.
What he did, was first to concentrate upon his own conscious
experiences, as being facts within the independent world of his own
mentality. He was led to speculate in this way by the current emphasis
upon the individual value of his total self. He implicitly transformed
this emergent individual value, inherent in the very fact of his own
reality, into a private world of passions, or modes, of independent
substance.

Also the independence ascribed to bodily substances carried them away
from the realm of values altogether. They degenerated into a mechanism
entirely valueless, except as suggestive of an external ingenuity. The
heavens had lost the glory of God. This state of mind is illustrated in
the recoil of Protestantism from aesthetic effects dependent upon a
material medium. It was taken to lead to an ascription of value to what
is in itself valueless. This recoil was already in full strength
antecedently to Descartes. Accordingly, the Cartesian scientific
doctrine of bits of matter, bare of intrinsic value, was merely a
formulation, in explicit terms, of a doctrine which was current before
its entrance into scientific thought or Cartesian philosophy. Probably
this doctrine was latent in the scholastic philosophy, but it did not
lead to its consequences till it met with the mentality of northern
Europe in the sixteenth century. But science, as equipped by Descartes,
gave stability and intellectual status to a point of view which has had
very mixed effects upon the moral presuppositions of modern communities.
Its good effects arose from its efficiency as a method for scientific
researches within those limited regions which were then best suited for
exploration. The result was a general clearing of the European mind away
from the stains left upon it by the hysteria of remote barbaric ages.
This was all to the good, and was most completely exemplified in the
eighteenth century.

But in the nineteenth century, when society was undergoing
transformation into the manufacturing system, the bad effects of these
doctrines have been very fatal. The doctrine of minds, as independent
substances, leads directly not merely to private worlds of experience,
but also to private worlds of morals. The moral intuitions can be held
to apply only to the strictly private world of psychological experience.
Accordingly, self-respect, and the making the most of your own
individual opportunities, together constituted the efficient morality of
the leaders among the industrialists of that period. The western world
is now suffering from the limited moral outlook of the three previous
generations.

Also the assumption of the bare valuelessness of mere matter led to a
lack of reverence in the treatment of natural or artistic beauty. Just
when the urbanisation of the western world was entering upon its state
of rapid development, and when the most delicate, anxious consideration
of the aesthetic qualities of the new material environment was
requisite, the doctrine of the irrelevance of such ideas was at its
height. In the most advanced industrial countries, art was treated as a
frivolity. A striking example of this state of mind in the middle of the
nineteenth century is to be seen in London where the marvellous beauty
of the estuary of the Thames, as it curves through the city, is wantonly
defaced by the Charing Cross railway bridge, constructed apart from any
reference to aesthetic values.

The two evils are: one, the ignoration of the true relation of each
organism to its environment; and the other, the habit of ignoring the
intrinsic worth of the environment which must be allowed its weight in
any consideration of final ends.

Another great fact confronting the modern world is the discovery of the
method of training professionals, who specialise in particular regions
of thought and thereby progressively add to the sum of knowledge within
their respective limitations of subject. In consequence of the success
of this professionalising of knowledge, there are two points to be kept
in mind, which differentiate our present age from the past. In the first
place, the rate of progress is such that an individual human being, of
ordinary length of life, will be called upon to face novel situations
which find no parallel in his past. The fixed person for the fixed
duties, who in older societies was such a godsend, in the future will be
a public danger. In the second place, the modern professionalism in
knowledge works in the opposite direction so far as the intellectual
sphere is concerned. The modern chemist is likely to be weak in zoology,
weaker still in his general knowledge of the Elizabethan drama, and
completely ignorant of the principles of rhythm in English
versification. It is probably safe to ignore his knowledge of ancient
history. Of course I am speaking of general tendencies; for chemists are
no worse than engineers, or mathematicians, or classical scholars.
Effective knowledge is professionalised knowledge, supported by a
restricted acquaintance with useful subjects subservient to it.

This situation has its dangers. It produces minds in a groove. Each
profession makes progress, but it is progress in its own groove. Now to
be mentally in a groove is to live in contemplating a given set of
abstractions. The groove prevents straying across country, and the
abstraction abstracts from something to which no further attention is
paid. But there is no groove of abstractions which is adequate for the
comprehension of human life. Thus in the modern world, the celibacy of
the medieval learned class has been replaced by a celibacy of the
intellect which is divorced from the concrete contemplation of the
complete facts. Of course, no one is merely a mathematician, or merely a
lawyer. People have lives outside their professions or their businesses.
But the point is the restraint of serious thought within a groove. The
remainder of life is treated superficially, with the imperfect
categories of thought derived from one profession.

The dangers arising from this aspect of professionalism are great,
particularly in our democratic societies. The directive force of reason
is weakened. The leading intellects lack balance. They see this set of
circumstances, or that set; but not both sets together. The task of
coördination is left to those who lack either the force or the character
to succeed in some definite career. In short, the specialised functions
of the community are performed better and more progressively, but the
generalised direction lacks vision. The progressiveness in detail only
adds to the danger produced by the feebleness of coördination.

This criticism of modern life applies throughout, in whatever sense you
construe the meaning of a community. It holds if you apply it to a
nation, a city, a district, an institution, a family, or even to an
individual. There is a development of particular abstractions, and a
contraction of concrete appreciation. The whole is lost in one of its
aspects. It is not necessary for my point that I should maintain that
our directive wisdom, either as individuals or as communities, is less
now than in the past. Perhaps it has slightly improved. But the novel
pace of progress requires a greater force of direction if disasters are
to be avoided. The point is that the discoveries of the nineteenth
century were in the direction of professionalism, so that we are left
with no expansion of wisdom and with greater need of it.

Wisdom is the fruit of a balanced development. It is this balanced
growth of individuality which it should be the aim of education to
secure. The most useful discoveries for the immediate future would
concern the furtherance of this aim without detriment to the necessary
intellectual professionalism.

My own criticism of our traditional educational methods is that they are
far too much occupied with intellectual analysis, and with the
acquirement of formularised information. What I mean is, that we neglect
to strengthen habits of concrete appreciation of the individual facts in
their full interplay of emergent values, and that we merely emphasise
abstract formulations which ignore this aspect of the interplay of
diverse values.

In every country the problem of the balance of the general and
specialist education is under consideration. I cannot speak with
first-hand knowledge of any country but my own. I know that there, among
practical educationalists, there is considerable dissatisfaction with
the existing practice. Also, the adaptation of the whole system to the
needs of a democratic community is very far from being solved. I do not
think that the secret of the solution lies in terms of the antithesis
between thoroughness in special knowledge and general knowledge of a
slighter character. The make-weight which balances the thoroughness of
the specialist intellectual training should be of a radically different
kind from purely intellectual analytical knowledge. At present our
education combines a thorough study of a few abstractions, with a
slighter study of a larger number of abstractions. We are too
exclusively bookish in our scholastic routine. The general training
should aim at eliciting our concrete apprehensions, and should satisfy
the itch of youth to be doing something. There should be some analysis
even here, but only just enough to illustrate the ways of thinking in
diverse spheres. In the Garden of Eden Adam saw the animals before he
named them: in the traditional system, children named the animals before
they saw them.

There is no easy single solution of the practical difficulties of
education. We can, however, guide ourselves by a certain simplicity in
its general theory. The student should concentrate within a limited
field. Such concentration should include all practical and intellectual
acquirements requisite for that concentration. This is the ordinary
procedure; and, in respect to it, I should be inclined even to increase
the facilities for concentration rather than to diminish them. With the
concentration there are associated certain subsidiary studies, such as
languages for science. Such a scheme of professional training should be
directed to a clear end congenial to the student. It is not necessary to
elaborate the qualifications of these statements. Such a training must,
of course, have the width requisite for its end. But its design should
not be complicated by the consideration of other ends. This professional
training can only touch one side of education. Its centre of gravity
lies in the intellect, and its chief tool is the printed book. The
centre of gravity of the other side of training should lie in intuition
without an analytical divorce from the total environment. Its object is
immediate apprehension with the minimum of eviscerating analysis. The
type of generality, which above all is wanted, is the appreciation of
variety of value. I mean an aesthetic growth. There is something between
the gross specialised values of the mere practical man, and the thin
specialised values of the mere scholar. Both types have missed
something; and if you add together the two sets of values, you do not
obtain the missing elements. What is wanted is an appreciation of the
infinite variety of vivid values achieved by an organism in its proper
environment. When you understand all about the sun and all about the
atmosphere and all about the rotation of the earth, you may still miss
the radiance of the sunset. There is no substitute for the direct
perception of the concrete achievement of a thing in its actuality. We
want concrete fact with a high light thrown on what is relevant to its
preciousness.

What I mean is art and aesthetic education. It is, however, art in such
a general sense of the term that I hardly like to call it by that name.
Art is a special example. What we want is to draw out habits of
aesthetic apprehension. According to the metaphysical doctrine which I
have been developing, to do so is to increase the depth of
individuality. The analysis of reality indicates the two factors,
activity emerging into individualised aesthetic value. Also the emergent
value is the measure of the individualisation of the activity. We must
foster the creative initiative towards the maintenance of objective
values. You will not obtain the apprehension without the initiative, or
the initiative without the apprehension. As soon as you get towards the
concrete, you cannot exclude action. Sensitiveness without impulse
spells decadence, and impulse without sensitiveness spells brutality. I
am using the word “sensitiveness” in its most general signification, so
as to include apprehension of what lies beyond oneself; that is to say,
sensitiveness to all the facts of the case. Thus “art” in the general
sense which I require is any selection by which the concrete facts are
so arranged as to elicit attention to particular values which are
realisable by them. For example, the mere disposing of the human body
and the eyesight so as to get a good view of a sunset is a simple form
of artistic selection. The habit of art is the habit of enjoying vivid
values.

But, in this sense, art concerns more than sunsets. A factory, with its
machinery, its community of operatives, its social service to the
general population, its dependence upon organising and designing genius,
its potentialities as a source of wealth to the holders of its stock is
an organism exhibiting a variety of vivid values. What we want to train
is the habit of apprehending such an organism in its completeness. It is
very arguable that the science of political economy, as studied in its
first period after the death of Adam Smith (1790), did more harm than
good. It destroyed many economic fallacies, and taught how to think
about the economic revolution then in progress. But it riveted on men a
certain set of abstractions which were disastrous in their influence on
modern mentality. It de-humanised industry. This is only one example of
a general danger inherent in modern science. Its methodological
procedure is exclusive and intolerant, and rightly so. It fixes
attention on a definite group of abstractions, neglects everything else,
and elicits every scrap of information and theory which is relevant to
what it has retained. This method is triumphant, provided that the
abstractions are judicious. But, however triumphant, the triumph is
within limits. The neglect of these limits leads to disastrous
oversights. The anti-rationalism of science is partly justified, as a
preservation of its useful methodology; it is partly mere irrational
prejudice. Modern professionalism is the training of minds to conform to
the methodology. The historical revolt of the seventeenth century, and
the earlier reaction towards naturalism, were examples of transcending
the abstractions which fascinated educated society in the Middle Ages.
These early ages had an ideal of rationalism, but they failed in its
pursuit. For they neglected to note that the methodology of reasoning
requires the limitations involved in the abstract. Accordingly, the true
rationalism must always transcend itself by recurrence to the concrete
in search of inspiration. A self-satisfied rationalism is in effect a
form of anti-rationalism. It means an arbitrary halt at a particular set
of abstractions. This was the case with science.

There are two principles inherent in the very nature of things,
recurring in some particular embodiments whatever field we explore—the
spirit of change, and the spirit of conservation. There can be nothing
real without both. Mere change without conservation is a passage from
nothing to nothing. Its final integration yields mere transient
non-entity. Mere conservation without change cannot conserve. For after
all, there is a flux of circumstance, and the freshness of being
evaporates under mere repetition. The character of existent reality is
composed of organisms enduring through the flux of things. The low type
of organisms have achieved a self-identity dominating their whole
physical life. Electrons, molecules, crystals, belong to this type. They
exhibit a massive and complete sameness. In the higher types, where life
appears, there is greater complexity. Thus, though there is a complex,
enduring pattern, it has retreated into deeper recesses of the total
fact. In a sense, the self-identity of a human being is more abstract
than that of a crystal. It is the life of the spirit. It relates rather
to the individualisation of the creative activity; so that the changing
circumstances received from the environment, are differentiated from the
living personality, and are thought of as forming its perceived field.
In truth, the field of perception and the perceiving mind are
abstractions which, in the concrete, combine into the successive bodily
events. The psychological field, as restricted to sense-objects and
passing emotions, is the minor permanence, barely rescued from the
nonentity of mere change; and the mind is the major permanence,
permeating that complete field, whose endurance is the living soul. But
the soul would wither without fertilisation from its transient
experiences. The secret of the higher organisms lies in their two grades
of permanences. By this means the freshness of the environment is
absorbed into the permanence of the soul. The changing environment is no
longer, by reason of its variety, an enemy to the endurance of the
organism. The pattern of the higher organism has retreated into the
recesses of the individualised activity. It has become a uniform way of
dealing with circumstances; and this way is only strengthened by having
a proper variety of circumstances to deal with.

This fertilisation of the soul is the reason for the necessity of art. A
static value, however serious and important, becomes unendurable by its
appalling monotony of endurance. The soul cries aloud for release into
change. It suffers the agonies of claustrophobia. The transitions of
humour, wit, irreverence, play, sleep, and—above all—of art are
necessary for it. Great art is the arrangement of the environment so as
to provide for the soul vivid, but transient, values. Human beings
require something which absorbs them for a time, something out of the
routine which they can stare at. But you cannot subdivide life, except
in the abstract analysis of thought. Accordingly, the great art is more
than a transient refreshment. It is something which adds to the
permanent richness of the soul’s self-attainment. It justifies itself
both by its immediate enjoyment, and also by its discipline of the
inmost being. Its discipline is not distinct from enjoyment, but by
reason of it. It transforms the soul into the permanent realisation of
values extending beyond its former self. This element of transition in
art is shown by the restlessness exhibited in its history. An epoch gets
saturated by the masterpieces of any one style. Something new must be
discovered. The human being wanders on. Yet there is a balance in
things. Mere change before the attainment of adequacy of achievement,
either in quality or output, is destructive of greatness. But the
importance of a living art, which moves on and yet leaves its permanent
mark, can hardly be exaggerated.

In regard to the aesthetic needs of civilised society the reactions of
science have so far been unfortunate. Its materialistic basis has
directed attention to _things_ as opposed to _values_. The antithesis is
a false one, if taken in a concrete sense. But it is valid at the
abstract level of ordinary thought. This misplaced emphasis coalesced
with the abstractions of political economy, which are in fact the
abstractions in terms of which commercial affairs are carried on. Thus
all thought concerned with social organisation expressed itself in terms
of material things and of capital. Ultimate values were excluded. They
were politely bowed to, and then handed over to the clergy to be kept
for Sundays. A creed of competitive business morality was evolved, in
some respects curiously high; but entirely devoid of consideration for
the value of human life. The workmen were conceived as mere hands, drawn
from the pool of labour. To God’s question, men gave the answer of
Cain—“Am I my brother’s keeper?”; and they incurred Cain’s guilt. This
was the atmosphere in which the industrial revolution was accomplished
in England, and to a large extent elsewhere. The internal history of
England during the last half century has been an endeavour slowly and
painfully to undo the evils wrought in the first stage of the new epoch.
It may be that civilisation will never recover from the bad climate
which enveloped the introduction of machinery. This climate pervaded the
whole commercial system of the progressive northern European races. It
was partly the result of the aesthetic errors of Protestantism and
partly the result of scientific materialism, and partly the result of
the natural greed of mankind, and partly the result of the abstractions
of political economy. An illustration of my point is to be found in
Macaulay’s Essay criticising Southey’s _Colloquies on Society_. It was
written in 1830. Now Macaulay was a very favourable example of men
living at that date, or at any date. He had genius; he was kind-hearted,
honourable, and a reformer. This is the extract:—“We are told, that our
age has invented atrocities beyond the imagination of our fathers; that
society has been brought into a state compared with which extermination
would be a blessing; and all because the dwellings of cotton-spinners
are naked and rectangular. Mr. Southey has found out a way he tells us,
in which the effects of manufactures and agriculture may be compared.
And what is this way? To stand on a hill, to look at a cottage and a
factory, and to see which is the prettier.”

Southey seems to have said many silly things in his book; but, so far as
this extract is concerned, he could make a good case for himself if he
returned to earth after the lapse of nearly a century. The evils of the
early industrial system are now a commonplace of knowledge. The point
which I am insisting on is the stone-blind eye with which even the best
men of that time regarded the importance of aesthetics in a nation’s
life. I do not believe that we have as yet nearly achieved the right
estimate. A contributory cause, of substantial efficacy to produce this
disastrous error, was the scientific creed that matter in motion is the
one concrete reality in nature; so that aesthetic values form an
adventitious, irrelevant addition.

There is another side to this picture of the possibilities of decadence.
At the present moment a discussion is raging as to the future of
civilisation in the novel circumstances of rapid scientific and
technological advance. The evils of the future have been diagnosed in
various ways, the loss of religious faith, the malignant use of material
power, the degradation attending a differential birth rate favouring the
lower types of humanity, the suppression of aesthetic creativeness.
Without doubt, these are all evils, dangerous and threatening. But they
are not new. From the dawn of history, mankind has always been losing
its religious faith, has always suffered from the malignant use of
material power, has always suffered from the infertility of its best
intellectual types, has always witnessed the periodical decadence of
art. In the reign of the Egyptian king, Tutankhamen, there was raging a
desperate religious struggle between Modernists and Fundamentalists; the
cave pictures exhibit a phase of delicate aesthetic achievement as
superseded by a period of comparative vulgarity; the religious leaders,
the great thinkers, the great poets and authors, the whole clerical
caste in the Middle Ages, have been notably infertile; finally, if we
attend to what actually has happened in the past, and disregard romantic
visions of democracies, aristocracies, kings, generals, armies, and
merchants, material power has generally been wielded with blindness,
obstinacy and selfishness, often with brutal malignancy. And yet,
mankind has progressed. Even if you take a tiny oasis of peculiar
excellence, the type of modern man who would have most chance of
happiness in ancient Greece at its best period is probably (as now) an
average professional heavy-weight boxer, and not an average Greek
scholar from Oxford or Germany. Indeed, the main use of the Oxford
scholar would have been his capability of writing an ode in
glorification of the boxer. Nothing does more harm in unnerving men for
their duties in the present, than the attention devoted to the points of
excellence in the past as compared with the average failure of the
present day.

But, after all, there have been real periods of decadence; and at the
present time, as at other epochs, society is decaying, and there is need
for preservative action. Professionals are not new to the world. But in
the past, professionals have formed unprogressive castes. The point is
that professionalism has now been mated with progress. The world is now
faced with a self-evolving system, which it cannot stop. There are
dangers and advantages in this situation. It is obvious that the gain in
material power affords opportunity for social betterment. If mankind can
rise to the occasion, there lies in front a golden age of beneficent
creativeness. But material power in itself is ethically neutral. It can
equally well work in the wrong direction. The problem is not how to
produce great men, but how to produce great societies. The great society
will put up the men for the occasions. The materialistic philosophy
emphasised the given quantity of material, and thence derivatively the
given nature of the environment. It thus operated most unfortunately
upon the social conscience of mankind. For it directed almost exclusive
attention to the aspect of struggle for existence in a fixed
environment. To a large extent the environment is fixed, and to this
extent there is a struggle for existence. It is folly to look at the
universe through rose-tinted spectacles. We must admit the struggle. The
question is, who is to be eliminated. In so far as we are educators, we
have to have clear ideas upon that point; for it settles the type to be
produced and the practical ethics to be inculcated.

But during the last three generations, the exclusive direction of
attention to this aspect of things has been a disaster of the first
magnitude. The watchwords of the nineteenth century have been, struggle
for existence, competition, class warfare, commercial antagonism between
nations, military warfare. The struggle for existence has been construed
into the gospel of hate. The full conclusion to be drawn from a
philosophy of evolution is fortunately of a more balanced character.
Successful organisms modify their environment. Those organisms are
successful which modify their environments so as to assist each other.
This law is exemplified in nature on a vast scale. For example, the
North American Indians accepted their environment, with the result that
a scanty population barely succeeded in maintaining themselves over the
whole continent. The European races when they arrived in the same
continent pursued an opposite policy. They at once coöperated in
modifying their environment. The result is that a population more than
twenty times that of the Indian population now occupies the same
territory, and the continent is not yet full. Again, there are
associations of different species which mutually coöperate. This
differentiation of species is exhibited in the simplest physical
entities, such as the association between electrons and positive nuclei,
and in the whole realm of animate nature. The trees in a Brazilian
forest depend upon the association of various species of organisms, each
of which is mutually dependent on the other species. A single tree by
itself is dependent upon all the adverse chances of shifting
circumstances. The wind stunts it: the variations in temperature check
its foliage: the rains denude its soil: its leaves are blown away and
are lost for the purpose of fertilisation. You may obtain individual
specimens of fine trees either in exceptional circumstances, or where
human cultivation has intervened. But in nature the normal way in which
trees flourish is by their association in a forest. Each tree may lose
something of its individual perfection of growth, but they mutually
assist each other in preserving the conditions for survival. The soil is
preserved and shaded; and the microbes necessary for its fertility are
neither scorched, nor frozen, nor washed away. A forest is the triumph
of the organisation of mutually dependent species. Further a species of
microbes which kills the forest, also exterminates itself. Again the two
sexes exhibit the same advantage of differentiation. In the history of
the world, the prize has not gone to those species which specialised in
methods of violence, or even in defensive armour. In fact, nature began
with producing animals encased in hard shells for defence against the
ills of life. It also experimented in size. But smaller animals, without
external armour, warm-blooded, sensitive, and alert, have cleared these
monsters off the face of the earth. Also, the lions and tigers are not
the successful species. There is something in the ready use of force
which defeats its own object. Its main defect is that it bars
coöperation. Every organism requires an environment of friends, partly
to shield it from violent changes, and partly to supply it with its
wants. The Gospel of Force is incompatible with a social life. By
_force_, I mean _antagonism_ in its most general sense.

Almost equally dangerous is the Gospel of Uniformity. The differences
between the nations and races of mankind are required to preserve the
conditions under which higher development is possible. One main factor
in the upward trend of animal life has been the power of wandering.
Perhaps this is why the armour-plated monsters fared badly. They could
not wander. Animals wander into new conditions. They have to adapt
themselves or die. Mankind has wandered from the trees to the plains,
from the plains to the seacoast, from climate to climate, from continent
to continent, and from habit of life to habit of life. When man ceases
to wander, he will cease to ascend in the scale of being. Physical
wandering is still important, but greater still is the power of man’s
spiritual adventures—adventures of thought, adventures of passionate
feeling, adventures of aesthetic experience. A diversification among
human communities is essential for the provision of the incentive and
material for the Odyssey of the human spirit. Other nations of different
habits are not enemies: they are godsends. Men require of their
neighbours something sufficiently akin to be understood, something
sufficiently different to provoke attention, and something great enough
to command admiration. We must not expect, however, all the virtues. We
should even be satisfied if there is something odd enough to be
interesting.

Modern science has imposed on humanity the necessity for wandering. Its
progressive thought and its progressive technology make the transition
through time, from generation to generation, a true migration into
uncharted seas of adventure. The very benefit of wandering is that it is
dangerous and needs skill to avert evils. We must expect, therefore,
that the future will disclose dangers. It is the business of the future
to be dangerous; and it is among the merits of science that it equips
the future for its duties. The prosperous middle classes, who ruled the
nineteenth century, placed an excessive value upon placidity of
existence. They refused to face the necessities for social reform
imposed by the new industrial system, and they are now refusing to face
the necessities for intellectual reform imposed by the new knowledge.
The middle class pessimism over the future of the world comes from a
confusion between civilisation and security. In the immediate future
there will be less security than in the immediate past, less stability.
It must be admitted that there is a degree of instability which is
inconsistent with civilisation. But, on the whole, the great ages have
been unstable ages.

I have endeavoured in these lectures to give a record of a great
adventure in the region of thought. It was shared in by all the races of
western Europe. It developed with the slowness of a mass movement. Half
a century is its unit of time. The tale is the epic of an episode in the
manifestation of reason. It tells how a particular direction of reason
emerges in a race by the long preparation of antecedent epochs, how
after its birth its subject-matter gradually unfolds itself, how it
attains its triumphs, how its influence moulds the very springs of
action of mankind, and finally how at its moment of supreme success its
limitations disclose themselves and call for a renewed exercise of the
creative imagination. The moral of the tale is the power of reason, its
decisive influence on the life of humanity. The great conquerors, from
Alexander to Caesar, and from Caesar to Napoleon, influenced profoundly
the lives of subsequent generations. But the total effect of this
influence shrinks to insignificance, if compared to the entire
transformation of human habits and human mentality produced by the long
line of men of thought from Thales to the present day, men individually
powerless, but ultimately the rulers of the world.




                                 INDEX

The numbers refer to pages; and ‘_e.s._’ stands for ‘_et seqq._’, where
the reference is to the succeeding pages of the chapter in question.

 Abruptness (in Ingression), 239.
 Absolute, The, 129.
 Abstract, 221.
 Abstraction, 233, _e.s._
 Abstraction (in Mathematics), 28, _e.s._
 Abstractive Hierarchy, 234, _e.s._
 Acceleration, 66.
 Actualisation, 222.
 Adam Smith, 280.
 Aeschylus, 14.
 Alexander, S., _preface_.
 Algebra, 42, 44.
 Alva, 2.
 Ampère, 139.
 Analytical Character (Eternal Objects), 228.
 Anselm, St., 80.
 ‘Any,’ 229.
 Aquinas, Thomas, 12, 13, 205.
 Arabic Arithmetical Notation, 42.
 Archimedes, 7, 8, 9, 10.
 Arguments (of functions), 44.
 Aristotle, 7, _e.s._; 41, 42; 64, _e.s._; 180, 187; 236, _e.s._
 Arnold, Matthew, 115.
 Art, 279, _e.s._
 Art, Medieval, 18, _e.s._
 Aspect, 98; 146, _e.s._
 Associated Hierarchy, 237.
 Aston, F. W., 260.
 Atom, 140, 144.
 Augustine, Saint, 266.

 Bacon, Francis, 11; 56, _e.s._; 92, 136.
 Bacon, Roger, 7.
 Base of Abstractive Hierarchy, 235.
 Being, 227.
 Belisarius, 19.
 Benedict, Saint, 21.
 Bergson, 72; 202, _e.s._
 Berkeley, George, 93, _e.s._; 105, 120, 198.
 Bichât, 141.
 Biology, 58, 88, 144.
 Bonaventure, Saint, 12.
 Boyle, Robert, 57.
 Brown University, _Preface_.
 Bruno, Giordano, 1.
 Byzantine Empire, 19.

 Carlyle, 85.
 Cervantes, 56.
 Change, 121.
 Chaucer, 22.
 China, 8, 106.
 Clairaut, 85, 193.
 Classification, 41, _e.s._
 Clough, A. H., 115.
 Cognition, 97.
 Coleridge, 115, 116.
 Columbus, 22, 49.
 Complex Eternal Objects, 232.
 Components, 232.
 Conic Sections, 42.
 Connexity (of a Hierarchy), 235.
 Connectedness (of an occasion), 237.
 Conservation of Energy, 142, _e.s._
 Continuity, 140.
 Copernicus, 1, 22, 56, 184.
 Cosmas, 254.
 Cromwell, Oliver, 23.

 D’Alembert, 80, 85.
 Dalton, John, 140, 141.
 Da Vinci, Leonardo, 60.
 Darwin, 263.
 Democritus, 140.
 Demos, R., _Preface_.
 Density, 70, 189.
 Desargues, 78.
 Descartes, 25; 43, _e.s._; 56, 57; 104; 115; 195, _e.s._; 272.
 Determinism, 110.
 Differential Calculus, 78.
 Discontinuous Existence, 51; 190, _e.s._
 Distance, 173.
 Divinity, Scholastic, 17.
 Divisibility, 177.

 Education, 277, _e.s._
 Egyptians, 20, 43.
 Einstein, 14, 41, 86, 88; 173, _e.s._; 263.
 Electron, 50, _e.s._; 111, _e.s._; 185, _e.s._
 Empty Events, 214.
 Endurance, 121; 147, _e.s._; 169, _e.s._; 186, _e.s._; 212.
 Endurance, Vibratory, 51.
 Energy, Physical, 51, _e.s._
 Environment, 155, _e.s._
 Envisagement, 148, _e.s._
 Epochs, 177.
 Epochal Durations, 192.
 Essence, 175.
 Eternal Objects, 121, _e.s._; 146, _e.s._; 221, _e.s._
 Ether, 184.
 Euripides, 14.
 Event, 102; 168, _e.s._
 Evolution, 130; 142, _e.s._
 Exhaustion, Method of, 42.
 Extension, 177.
 Extensive Quantity, 178.
 External Relations, 223, _e.s._
 Extrinsic Reality, 146.

 Fallacy of Misplaced Concreteness, 72, _e.s._; 82.
 Faraday, 139.
 Fate, 14.
 Fermat, 78.
 Finite Abstractive Hierarchy, 235.
 Form, 230.
 Force, 64, _e.s._
 Fourier, 85.
 Francis of Assisi, 258.
 Frederick, the Great, 89.
 Frequency, 181, _e.s._
 Fresnel, 139.
 Frost, Robert, 22.
 Future, 245, _e.s._

 Galileo, 2, _e.s._; 43, 45; 56, _e.s._; 88, 162, 187; 255, _e.s._
 Galvani, 88.
 Gauss, 86, 88.
 Geometry, 31, _e.s._
 George II, 93.
 Germany, 57.
 Gibson, 206.
 God, 17, 86, 129; 242, _e.s._
 Gradation of Envisagement, 247.
 Gravitation, 65, 172.
 Greece, 8, _e.s._
 Gregorovius, 265.
 Giotto, 22.
 Gregory, The Great, 21, 265.

 Harvey, 56, 57.
 Heath, Sir T. L., 180.
 Hegel, 40.
 Herz, 86, 88.
 Historical Revolt, 11, _e.s._; 55, 150.
 Hooker, Richard, 13.
 Hume, 5, 47, 61, 73; 80, _e.s._; 107, 198.
 Huyghens, 45; 57, _e.s._; 256.

 Idealism, 89; 127, _e.s._
 Immediate Occasion, 36, _e.s._; 62.
 Individual Essence, 222, _e.s._
 Induction, 34; 60, _e.s._
 Infinite Abstractive Hierarchy, 235.
 Ingression, 99, _e.s._; 222.
 Integral Calculus, 42.
 Internal Relations, 175; 223, _e.s._
 Intrinsic Reality, 146.
 Invention, 136, _e.s._
 Ionian Philosophers, 9.
 Irresistible Grace, 105.
 Isolated Systems, 66.
 Isolation of Eternal Objects, 230.
 Isotopes, 260.
 Italy, 57.

 James, Henry, 3.
 James, William, 3; 199, _e.s._
 Joseph, Hapsburgh Emperor, 89.
 Justinian, 19, 20.

 Kant, 47; 93, _e.s._; 116, 142, 178; 193, _e.s._
 Kepler, 9, 45, 57, 67.

 Lagrange, 84, _e.s._
 Laplace, 85, 142.
 Lavoisier, 84, 146.
 Law, Roman, 16.
 Laws of Nature, 45, 150.
 Least Action, 87, 150.
 Lecky, 15, 16, 254.
 Leibniz, 43, 44, 48, 57, 92, 115; 198, _e.s._
 Life, 58.
 Limitation, 225, _e.s._
 Lloyd Morgan, _Preface_.
 Location, Simple, 69, _e.s._; 81, _e.s._; 95.
 Locke, John, 43, 47; 57, _e.s._; 89, 94, 115, 198.
 Locomotion, Vibratory, 184, _e.s._
 Logic, Abstract, 37, _e.s._
 Logic, Scholastic, 17.
 Lucretius, 140.

 Macaulay, 285.
 Milton, 108, _e.s._
 Mind, 79.
 Mass, 64, _e.s._; 144.
 Mathematics, 10, 23; 28, _e.s._
 Mathematics, Applied, 34, _e.s._
 Matter, 24, 94, 58, 144.
 Matter (philosophical), 231.
 Maupertuis, 85, _e.s._
 Max Müller, 178.
 Maxwell, Clerk, 85, _e.s._; 139, _e.s._; 161.
 Mechanical Explanation, 23.
 Mechanism, 107, _e.s._
 Mechanistic Theory, 71.
 Memory, 73.
 Mersenne, 46.
 Michelson, 162, _e.s._
 Mill, John Stuart, 110.
 Modal Character of Space, 90, _e.s._
 Modal Limitation, 248, _e.s._
 Mode, 99.
 Moral Responsibility, 109, _e.s._
 Motion, Laws of, 65, _e.s._
 Müller, Johannes, 141.

 Narses, 19.
 Natural Selection, 158.
 Naturalism in Art, 22.
 Newman, John Henry, 115, 255.
 Newton, 8, 9, 15; 43, _e.s._; 58, _e.s._; 84, _e.s._; 161; 255, _e.s._
 Not-Being, 227.

 Objectivism, 124, _e.s._
 Occasions, Community of, 63.
 Occupied Events, 215.
 Oersted, 139.
 Order of Nature, 5, _e.s._; 39, _e.s._; 55.
 Organic Mechanism, 112, 151.
 Organism, 51, _e.s._; 58, 90; 105, _e.s._; 111, _e.s._; 145; 185,
    _e.s._; 209.

 Padua, University of, 57, 58.
 Paley, 107.
 Papacy, 13, 20.
 Pascal, 57, 78.
 Past, 245, _e.s._
 Pasteur, Louis, 141, _e.s._
 Pelagius, 266.
 Perception, 101.
 Periodic Law (Mendeleëf), 141.
 Periodicity, 45, _e.s._
 Perspective, 98.
 Petavius, 255.
 Philosophy, 122.
 Physical Field, 138.
 Physics, 57.
 Plato, 10; 41, _e.s._; 180.
 Pope, Alexander, 108, _e.s._
 Possibility, 223.
 Prehension, 97, _e.s._; 207.
 Prehensive Character of Space, 90, _e.s._
 Present, 245, _e.s._
 Primary Qualities, 76.
 Primate, 185, _e.s._
 Prime Mover, 242, _e.s._
 Primordial Element, 51, _e.s._
 Process, 102.
 Professionalism, 271, _e.s._
 Proton, 51, _e.s._; 185, _e.s._
 Psychology, 88, 103.
 Pusey, 115.
 Pythagoras, 39, _e.s._; 240.

 Quality, 73, _e.s._
 Quantum Theory, 50; 181, _e.s._

 Rationalism, 12, _e.s._; 55.
 Ramsay, Sir William, 259.
 Rawley, Dr., 58.
 Rayleigh, Lord, 259.
 Realism, 127, _e.s._
 Reformation, 11.
 Reiteration, 147; 186, _e.s._
 Relational Essence, 223, _e.s._
 Relativity, 68; 165, _e.s._
 Retention, 147.
 Riemann, 86, 88.
 Romans, 8.
 Roman Law, 20.
 Rome, 21.
 Rousseau, 50, 93, 135.
 Royal Society, 43, 73.
 Russell, Bertrand, 216.

 Sarpi, Paul, 12, 26.
 Schleiden, 141.
 Schwann, 141.
 Scientific Materialism, 24, 25.
 Scientific Movement, 11.
 Secondary Qualities, 76, 127.
 Seneca, 15.
 Sense-Object, 99.
 Separative Character of Space, 90, _e.s._
 Shakespeare, 56.
 Shape, 92.
 Shelley, 116, _e.s._
 Sidgwick, Henry, 197.
 Simple Eternal Objects, 232.
 Simple Location, 69, _e.s._; 81, _e.s._; 95; 127, _e.s._; 217.
 Simultaneity, 174.
 ‘Some,’ 229.
 Southey, 285.
 Space, Physical, 32.
 Spatialisation, 72, 175, 206.
 Specious Present, 148.
 Spinoza, 43, 57, 99, 115, 116, 175, 198, 248.
 Sophocles, 14.
 Standpoint, 99, _e.s._
 Stoicism, 16.
 Struggle for Existence, 158.
 Subjectivism, 123, _e.s._
 Substance, 73, _e.s._; 175.
 Substantial Activity, 152, 174, 231.
 Superject, 230.
 Synthetic Prehension, 224, _e.s._

 Technology, 135, _e.s._
 Temporalisation, 179.
 Tennyson, 108, _e.s._
 Time, 169, _e.s._
 Tragedy, 15.
 Translucency of Realisation, 240.
 Trent, Council of, 12.
 Trigonometry, 42.
 True Propositions, 224.

 Unknowns (in Mathematics), 44.
 Universals, 221.
 Untrue Propositions, 221.

 Value, 123, _e.s._; 226, 249.
 Variable, The, 37, _e.s._; 229.
 Vasco da Gama, 22.
 Velocity, 64, _e.s._; 165, _e.s._
 Vertex of Abstractive Hierarchy, 236.
 Vesalius, 1.
 Vibration, 186, _e.s._
 Vibratory Organic Deformation, 184, _e.s._
 Virtual Work, 88.
 Vitalism, 111, _e.s._; 145.
 Volta, 88.
 Voltaire, 57; 80, _e.s._; 143.

 Walpole, 89.
 Washington, George, 89.
 Watt, James, 135.
 Wesley, John, 93.
 Whitman, Walt, 22.
 Wordsworth, 22; 108, _e.s._

 Young, Thomas, 139.

 Zeno, 178, 179, 192.

------------------------------------------------------------------------

                           Transcriber’s Note

The printer employed the diaeresis in words like ‘coördination’ or
‘coöperation’. On p. 157, the first syllable of ‘coöperating’ fell on
the line break, and the word was hyphenated as ‘co-operating’, since the
diaeresis was not needed. The word has been joined here and the
diaeresis employed as ‘coöperating’.

The following words appear both with and without a hyphen: to-day,
non-entity, half-way, inter-connected, non-entity.

Errors deemed most likely to be the printer’s have been corrected, and
are noted here. The references are to the page and line in the original.

 20.10  restraining g[i/o]vernment.                        Replaced.
 21.31  is kept in contact w[ti/it]h                       Transposed.
 57.30  Now the scientific philosop[h]y                    Inserted.
 69.9   no other way of putting[s] things                  Removed.
 77.6   these relationships constitute[s] nature.          Added.
 157.20 societies of c[o-/ö]perating organisms.            Replaced.
 160.8  These divis[i]ons are                              Inserted.
 176.3  extends beyond[s] the spatio-temporal continuum    Removed.
 177.6  by the reali[z/s]ation of pattern                  Consistency.
 177.25 character of spatio-temporal [of ]extension        Removed.
 183.5  radiate its energy i[s/n] an integral number       Replaced.
 195.4  history of the Christi[o/a]n Church                Replaced.
 195.7  apocalyptic forecast[e]s                           Removed.
 202.21 This divis[i]on of territory                       Inserted.
 213.10 what anything is in i[t]self.                      Inserted.
 245.27 even [al]though any such discrimination            Removed.
 274.14 its sta[k/t]e of rapid development                 Replaced.
 276.17 The task of coö[r]dination is left                 Inserted.
 279.22 What I mean is art [(]and aesthetic education.     Removed.
 288.33 mutually coö[o]perate.                             Removed.
 290.3  it bars coö[o]peration.                            Removed.