AN ENQUIRY CONCERNING THE PRINCIPLES OF NATURAL KNOWLEDGE

A. N. WHITEHEAD, Sc.D., F.R.S.

Fellow of Trinity College, Cambridge, Professor of Philosophy in Harvard University, and sometime Professor of Applied Mathematics in the Imperial College of Science and Technology

"PHILONOUS. I am not for imposing any sense on your words: you are at liberty to explain them as you please. Only, I beseech you, make me understand something by them."

BERKELEY,

The First Dialogue between
Hylas and Philonous.

CAMBRIDGE
AT THE UNIVERSITY PRESS
1925

TO
ERIC ALFRED WHITEHEAD
ROYAL FLYING CORPS
November 27, 1898 to March 13, 1918

Killed in action over the Forêt de Gobain giving himself that the city of his vision may not perish.

The music of his life was without discord, perfect in its beauty.

First Edition 1919
Second Edition 1925

PRINTED IN GREAT BRITAIN

PREFACE

THERE are three main streams of thought which are relevant to the theme of this enquiry; they may, with sufficient accuracy, be termed the scientific, the mathematical, and the philosophical movements.

Modern speculative physics with its revolutionary theories concerning the natures of matter and of electricity has made urgent the question, What are the ultimate data of science? It is in accordance with the nature of things that mankind should find itself acting and should then proceed to discuss the rationale of its activities. Thus the creation of science precedes the analysis of its data and can even be accompanied by the acceptance of faulty analyses, though such errors end by warping scientific imagination.

The contributions of mathematics to natural science consist in the elaboration of the general art of deductive reasoning, the theory of quantitative measurement by the use of number, the theory of serial order, of geometry, of the exact measurement of time, and of rates of change. The critical studies of the nineteenth century and after have thrown light on the nature of mathematics and in particular on the foundations of geometry. We now know many alternative sets of axioms from which geometry can be deduced by the strictest deductive reasoning. But these investigations concern geometry as an abstract science deduced from hypothetical premisses. In this enquiry we are concerned with geometry as a physical science. How is space rooted in experience?

The modern theory of relativity has opened the possibility of a new answer to this question. The successive labours of Larmor, Lorentz, Einstein, and Minkovski have opened a new world of thought as to the relations of space and time to the ultimate data of perceptual knowledge. The present work is largely concerned with providing a physical basis for the more modern views which have thus emerged. The whole investigation is based on the principle that the scientific concepts of space and time are the first outcome of the simplest generalisations from experience, and that they are not to be looked for at the tail end of a welter of differential equations. This position does not mean that Einstein's recent theory of general relativity and of gravitation is to be rejected. The divergence is purely a question of interpretation. Our time and space measurements may in practice result in elaborate combinations of the primary methods of measurement which are explained in this work. For example, the theory of gravitational matter may involve the theory of 'vagrant solids' which is pointed out as a subject for investigation in [article 39], but not developed. It has certainly resulted from Einstein's investigations that a modification of the gravitational law, of an order of magnitude which is

of the main effect [

being the velocity of the matter and

that of light], will account for the more striking outstanding difficulties otherwise unexplained by the law of gravitation. This is a remarkable discovery for which the utmost credit is due to the author. Now that the fact is known, it is easy to see that it is the sort of modification which on the simple electromagnetic theory of relativity is likely to be required for this law. I have however been anxious to disentangle the consideration of the main positions of this enquiry from theories designed to explain special laws of nature. Also at the date of writing the evidence for some of the consequences of Einstein's theory is ambiguous and even adverse. In connection with the theory of relativity I have received suggestive stimulus from Dr L. Silberstein's Theory of Relativity, and from an important Memoir [1] by Profs. E. B. Wilson and G. N. Lewis.

The discussion of the deduction of scientific concepts from the simplest elements of our perceptual knowledge at once brings us to philosophical theory. Berkeley, Hume, Kant, Mill, Huxley, Bertrand Russell and Bergson, among others, have initiated and sustained relevant discussions. But this enquiry is touched by only one side of the philosophical debate. We are concerned only with Nature, that is, with the object of perceptual knowledge, and not with the synthesis of the knower with the known. This distinction is exactly that which separates natural philosophy from metaphysics. Accordingly none of our perplexities as to Nature will be solved by having recourse to the consideration that there is a mind knowing it. Our theme is the coherence of the known, and the perplexity which we are unravelling is as to what it is that is known. In matters philosophic the obligations of an author to others usually arise from schools of debate rather than from schools of agreement. Also such schools are the more important in proportion as assertion and retort do not have to wait for the infrequent opportunities of formal publication, hampered by the formidable permanence of the printed word. At the present moment England is fortunate in this respect. London, Oxford and Cambridge are within easy reach of each other, and provide a common school of debate which rivals schools of the ancient and medieval worlds. Accordingly I have heavy obligations to acknowledge to Bertrand Russell, Wildon Carr, F. C. Schiller, T. P. Nunn, Dawes Hicks, McTaggart, James Ward, and many others who, amid their divergencies of opinion, are united in the candid zeal of their quest for truth.

It is quite unnecessary to draw attention to the incompleteness of this investigation. The book is merely an enquiry. It raises more difficulties than those which it professes to settle. This is inevitable in any philosophical work, however complete. All that one can hope to do is to settle the right sort of difficulties and to raise the right sort of ulterior questions, and thus to accomplish one short step further into the unfathomable mystery.

Memories are short, and perhaps it is not inapt to put on record circumstances common to the life of all England during years of war. The book is the product of intervals of leisure amid pressing occupation, a refuge from immediate fact. It has been thought out and written amid the sound of guns—guns of Kitchener's army training on Salisbury Plain, guns on the Somme faintly echoing across the Sussex coast: some few parts composed to pass times of expectation during air-raids over London, punctuated by the sound of bombs and the answer of artillery, with argument clipped by the whirr of aeroplanes. And through the land anxiety, and at last the anguish which is the price of victory.

A. N. W.

April 20, 1919

[1]'The Space-Time Manifold of Relativity.' Proc. of the Amer. Acad. of Arts and Sciences, vol. XLVIII, 1912.

PREFACE TO SECOND EDITION

Since the publication of the first edition of this book in 1919, the various topics contained in it have been also considered by me in The Concept of Nature (Camb. Univ. Press, 1920) and in The Principle of Relativity (Camb. Univ. Press, 1922). I hope in the immediate future to embody the standpoint of these volumes in a more complete metaphysical study.

A few notes have been appended to this edition to elucidate obscurities, and a few slips in the text have been corrected.

A.N.W.

TRINITY COLLEGE,
CAMBRIDGE
August, 1924

[PART I] THE TRADITIONS OF SCIENCE
[CHAPTER I.] MEANING
ARTS. 1. [Traditional Scientific Concepts]
2. [Philosophic Relativity]
3. [Perception]
[CHAPTER II.] THE FOUNDATIONS OF DYNAMICAL PHYSICS
4. [Newton's Laws of Motion]
5. [The Ether]
6. [Maxwell's Equations]
Appendix I : [Newton's Laws of Motion]
Appendix II: [Clerk Maxwell's Equations of the
Electromagnetic Field]
[CHAPTER III.] SCIENTIFIC RELATIVITY
7. [Consentient Sets]
8. [Kinematic Relations]
9. [Motion through the Ether]
10. [Formulae for Relative Motion]
Appendix: [Mathematical Formulae]
[CHAPTER IV.] CONGRUENCE
11. [Simultaneity]
12. [Congruence and Recognition]
[PART II] THE DATA OF SCIENCE
[CHAPTER V.] THE NATURAL ELEMENTS
13. [The Diversification of Nature]
14. [Events]
15. [Objects]
[CHAPTER VI.] EVENTS
16. [Apprehension of Events]
17. [The Constants of Externality]
18. [Extension]
19. [Absolute Position]
20. [The Community of Nature]
21. [Characters of Events]
[CHAPTER VII.] OBJECTS
22. [Types of Objects]
23. [Sense-Objects]
24. [Perceptual Objects]
25. [Scientific Objects]
26. [Duality of Nature]
[PART III] THE METHOD OF EXTENSIVE ABSTRACTION
[CHAPTER VIII.] PRINCIPLES OF THE METHOD OF EXTENSIVE ABSTRACTION
27. [The Relation of Extension, Fundamental Properties]
28. [Intersection, Separation and Dissection]
29. [The Junction of Events]
30. [Abstractive Classes]
31. [Primes and Antiprimes]
32. [Abstractive Elements]
[CHAPTER IX.] DURATIONS, MOMENTS AND TIME-SYSTEMS
33. [Antiprimes, Durations and Moments]
34. [Parallelism and Time-Systems]
35. [Levels, Rects, and Puncts]
36. [Parallelism and Order]
[CHAPTER X.] FINITE ABSTRACTIVE ELEMENTS
37. [Absolute Primes and Event-Particles]
38. [Routes]
39. [Solids]
40. [Volumes]
[CHAPTER XI.] POINTS AND STRAIGHT LINES
41. [Stations]
42. [Point-Tracks and Points]
43. [Parallelism]
44. [Matrices]
45. [Null-Tracks]
46. [Straight Lines]
[CHAPTER XII.] NORMALITY AND CONGRUENCE
47. [Normality]
48. [Congruence]
[CHAPTER XIII.] MOTION
49. [Analytic Geometry]
50. [The Principle of Kinematic Symmetry]
51. [Transitivity of Congruence]
52. [The Three Types of Kinematics]
[PART IV] THE THEORY OF OBJECTS
[CHAPTER XIV.] THE LOCATION OF OBJECTS
53. [Location]
54. [Uniform Objects]
55. [Components of Objects]
[CHAPTER XV.] MATERIAL OBJECTS
56. [Material Objects]
57. [Stationary Events]
58. [Motion of Objects]
59. [Extensive Magnitude]
[CHAPTER XVI.] CAUSAL COMPONENTS
60. [Apparent and Causal Components]
61. [Transition from Appearance to Cause]
[CHAPTER XVII.] FIGURES
62. [Sense-Figures]
63. [Geometrical Figures]
[CHAPTER XVIII.] RHYTHMS
64. [Rhythms]
[Notes]

[PART I]
THE TRADITIONS OF SCIENCE

[CHAPTER I]
MEANING

[1. Traditional Scientific Concepts]. 1.1 What is a physical explanation? The answer to this question, even when merely implicit in the scientific imagination, must profoundly affect the development of every science, and in an especial degree that of speculative physics. During the modern period the orthodox answer has invariably been couched in terms of Time (flowing equably in measurable lapses) and of Space (timeless, void of activity, euclidean), and of Material in space (such as matter, ether, or electricity).

The governing principle underlying this scheme is that extension, namely extension in time or extension in space, expresses disconnection. This principle issues in the assumptions that causal action between entities separated in time or in space is impossible and that extension in space and unity of being are inconsistent. Thus the extended material (on this view) is essentially a multiplicity of entities which, as extended, are diverse and disconnected. This governing principle has to be limited in respect to extension in time. The same material exists at different times. This concession introduces the many perplexities centering round the notion of change which is derived from the comparison of various states of self-identical material at different times.

[1.2] The ultimate fact embracing all nature is (in this traditional point of view) a distribution of material throughout all space at a durationless instant of time, and another such ultimate fact will be another distribution of the same material throughout the same space at another durationless instant of time. The difficulties of this extreme statement are evident and were pointed out even in classical times when the concept first took shape. Some modification is evidently necessary. No room has been left for velocity, acceleration, momentum, and kinetic energy, which certainly are essential physical quantities.

We must therefore in the ultimate fact, beyond which science ceases to analyse, include the notion of a state of change. But a state of change at a durationless instant is a very difficult conception. It is impossible to define velocity without some reference to the past and the future. Thus change is essentially the importation of the past and of the future into the immediate fact embodied in the durationless present instant.

This conclusion is destructive of the fundamental assumption that the ultimate facts for science are to be found at durationless instants of time.

1.3 The reciprocal causal action between materials

and

is the fact that their states of change are partly dependent on their relative locations and natures. The disconnection involved in spatial separation leads to reduction of such causal action to the transmission of stress across the bounding surface of contiguous materials. But what is contact? No two points are in contact. Thus the stress across a surface necessarily acts on some bulk of the material enclosed inside. To say that the stress acts on the immediately contiguous material is to assert infinitely small volumes. But there are no such things, only smaller and smaller volumes. Yet (with this point of view) it cannot be meant that the surface acts on the interior.

Certainly stress has the same claim to be regarded as an essential physical quantity as have momentum and kinetic energy. But no intelligible account of its meaning is to be extracted from the concept of the continuous distribution of diverse (because extended) entities through space as an ultimate scientific fact. At some stage in our account of stress we are driven to the concept of any extended quantity of material as a single unity whose nature is partly explicable in terms of its surface stress.

1.4 In biology the concept of an organism cannot be expressed in terms of a material distribution at an instant. The essence of an organism is that it is one thing which functions and is spread through space. Now functioning takes time. Thus a biological organism is a unity with a spatio-temporal extension which is of the essence of its being. This biological conception is obviously incompatible with the traditional ideas. This argument does not in any way depend on the assumption that biological phenomena belong to a different category to other physical phenomena. The essential point of the criticism on traditional concepts which has occupied us so far is that the concept of unities, functioning and with spatio-temporal extensions, cannot be extruded from physical concepts. The only reason for the introduction of biology is that in these sciences the same necessity becomes more clear.

1.5 The fundamental assumption to be elaborated in the course of this enquiry is that the ultimate facts of nature, in terms of which all physical and biological explanation must be expressed, are events connected by their spatio-temporal relations, and that these relations are in the main reducible to the property of events that they can contain (or extend over) other events which are parts of them. In other words, in the place of emphasising space and time in their capacity of disconnecting, we shall build up an account of their complex essences as derivative from the ultimate ways in which those things, ultimate in science, are interconnected. In this way the data of science, those concepts in terms of which all scientific explanation must be expressed, will be more clearly apprehended. But before proceeding to our constructive task, some further realisation of the perplexities introduced by the traditional concepts is necessary.

[2. Philosophic Relativity]. 2.1 The philosophical principle of the relativity of space means that the properties of space are merely a way of expressing relations between things ordinarily said to be 'in space.' Namely, when two things are said to be 'both in space' what is meant is that they are mutually related in a certain definite way which is termed 'spatial.' It is an immediate consequence of this theory that all spatial entities such as points, straight lines and planes are merely complexes of relations between things or of possible relations between things.

For consider the meaning of saying that a particle

is at a point

. This statement conveys substantial information and must therefore convey something more than the barren assertion of self-identity '

.' Thus what must be meant is that

has certain relations to other particles

′,

″, etc., and that the abstract possibility of this group of relations is what is meant by the point

The extremely valuable work on the foundations of geometry produced during the nineteenth century has proceeded from the assumption of points as ultimate given entities. This assumption, for the logical purpose of mathematicians, is entirely justified. Namely the mathematicians ask, What is the logical description of relations between points from which all geometrical theorems respecting such relations can be deduced? The answer to this question is now practically complete; and if the old theory of absolute space be true, there is nothing more to be said. For points are ultimate simple existents, with mutual relations disclosed by our perceptions of nature.

But if we adopt the principle of relativity, these investigations do not solve the question of the foundations of geometry. An investigation into the foundations of geometry has to explain space as a complex of relations between things. It has to describe what a point is, and has to show how the geometric relations between points issue from the ultimate relations between the ultimate things which are the immediate objects of knowledge. Thus the starting point of a discussion on the foundations of geometry is a discussion of the character of the immediate data of perception. It is not now open to mathematicians to assume sub silentio that points are among these data.

2.2 The traditional concepts were evidently formed round the concept of absolute space, namely the concept of the persistent ultimate material distributed among the persistent ultimate points in successive configurations at successive ultimate instants of time. Here ultimate' means 'not analysable into a complex of simpler entities.' The introduction of the principle of relativity adds to the complexity—or rather, to the perplexity—of this conception of nature. The statement of general character of ultimate fact must now be amended into 'persistent ultimate material with successive mutual ultimate relations at successive ultimate instants of time.'

Space issues from these mutual relations of matter at an instant. The first criticism to be made on such an assertion is that it is shown to be a metaphysical fairy tale by any comparison with our actual perceptual knowledge of nature. Our knowledge of space is based on observations which take time and have to be successive, but the relations which constitute space are instantaneous. The theory demands that there should be an instantaneous space corresponding to each instant, and provides for no correlation between these spaces; while nature has provided us with no apparatus for observing them.

2.3 It is an obvious suggestion that we should amend our statement of ultimate fact, as modified by the acceptance of relativity. The spatial relations must now stretch across time. Thus if

′,

″, etc. be material particles, there are definite spatial relations connecting

′,

″, etc. at time

with

′,

″, etc. at time

, as well as such relations between

and

′ and

″, etc. at time

and such relations between

and

′ and

″, etc. at time

. This should mean that

at time

has a definite position in the spatial configuration constituted by the relations between

′,

″, etc. at time

. For example, the sun at a certain instant on Jan. 1st, 1900 had a definite position in the instantaneous space constituted by the mutual relations between the sun and the other stars at a definite instant on Jan. 1st, 1800. Such a statement is only understandable (assuming the traditional concept) by recurring to absolute space and thus abandoning relativity; for otherwise it denies the completeness of the instantaneous fact which is the essence of the concept. Another way out of the difficulty is to deny that space is constituted by the relations of

′,

″, etc., at an instant, and to assert that it results from their relations throughout a duration of time, which as thus prolonged in time are observable.

As a matter of fact it is obvious that our knowledge of space does result from such observations. But we are asking the theory to provide us with actual relations to be observed. This last emendation is either only a muddled way of admitting that 'nature at an instant' is not the ultimate scientific fact, or else it is a yet more muddled plea that, although there is no possibility of correlations between distinct instantaneous spaces, yet within durations which are short enough such non-existent correlations enter into experience.

2.4 The persistence of the material lacks any observational guarantee when the relativity of space is admitted into the traditional concept. For at one instant there is instantaneous material in its instantaneous space as constituted by its instantaneous relations, and at another instant there is instantaneous material in its instantaneous space. How do we know that the two cargoes of material which load the two instants are identical? The answer is that we do not perceive isolated instantaneous facts, but a continuity of existence, and that it is this observed continuity of existence which guarantees the persistence of material. Exactly so; but this gives away the whole traditional concept. For a 'continuity of existence' must mean an unbroken duration of existence. Accordingly it is admitted that the ultimate fact for observational knowledge is perception through a duration; namely, that the content of a specious present, and not that of a durationless instant, is an ultimate datum for science.

2.5 It is evident that the conception of the instant of time as an ultimate entity is the source of all our difficulties of explanation. If there are such ultimate entities, instantaneous nature is an ultimate fact.

Our perception of time is as a duration, and these instants have only been introduced by reason of a supposed necessity of thought. In fact absolute time is just as much a metaphysical monstrosity as absolute space. The way out of the perplexities, as to the ultimate data of science in terms of which physical explanation is ultimately to be expressed, is to express the essential scientific concepts of time, space and material as issuing from fundamental relations between events and from recognitions of the characters of events. These relations of events are those immediate deliverances of observation which are referred to when we say that events are spread through time and space.

[3. Perception]. 3.1 The conception of one universal nature embracing the fragmentary perceptions of events by one percipient and the many perceptions by diverse percipients is surrounded with difficulties. In the first place there is what we will call the 'Berkeleyan Dilemma' which crudely and shortly may be stated thus: Perceptions are in the mind and universal nature is out of the mind, and thus the conception of universal nature can have no relevance to our perceptual life. This is not how Berkeley stated his criticism of materialism; he was thinking of substance and matter. But this variation is a detail and his criticism is fatal to any of the traditional types of 'mind-watching-things' philosophy, even if those things be events and not substance or material. His criticisms range through every type of sense-perception, though in particular he concentrates on Vision.

3.2 "Euphranor.[2] Tell me, Alciphron, can you discern the doors, windows, 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?

Alc. I cannot deny it.

Euph. Tell me, is not the visible appearance alone the proper object of sight?

Alc. It is.

What think you now (said Euphranor, pointing towards the heavens) of the visible appearance of yonder planet? Is it not a round luminous flat, no bigger than a six-pence?

Alc. What then?

Euph. Tell me then, what you think of the planet itself? Do you not conceive it to be a vast opaque globe, with several unequal risings and valleys?

Alc. I do.

Euph. How can you therefore conclude that the proper object of your sight exists at a distance?

Alc. I confess I do not know.

Euph. For your further conviction, do but consider that crimson cloud. Think you that, if you were in the very place where it is, you would perceive anything like what you now see?

Alc. By no means. I should perceive only a dark mist.

Euph. 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?"

3.3 Now the difficulty to be faced is just this. We may not lightly abandon the castle, the planet, and the crimson cloud, and hope to retain the eye, its retina, and the brain. Such a philosophy is too simple-minded—or at least might be thought so, except for its wide diffusion.

Suppose we make a clean sweep. Science then becomes a formula for calculating mental 'phenomena' or 'impressions.' But where is science? In books? But the castle and the planet took their libraries with them.

No, science is in the minds of men. But men sleep and forget, and at their best in any one moment of insight entertain but scanty thoughts. Science therefore is nothing but a confident expectation that relevant thoughts will occasionally occur. But by the bye, what has happened to time and space? They must have gone after the other things. No, we must distinguish: space has gone, of course; but time remains as relating the succession of phenomena. Yet this won't do; for this succession is only known by recollection, and recollection is subject to the same criticism as that applied by Berkeley to the castle, the planet, and the cloud. So after all, time does evaporate with space, and in their departure 'you' also have accompanied them; and I am left solitary in the character of a void of experience without significance.

3.4 At this point in the argument we may break off, having formed a short catalogue of the sort of considerations which lead from the Berkeleyan dilemma to a complete scepticism which was not in Berkeley's own thought.

There are two types of answer to this sceptical descent. One is Dr Johnson's. He stamped his foot on a paving-stone, and went on his way satisfied with its reality. A scrutiny of modern philosophy will, if I am not mistaken, show that more philosophers should own Dr Johnson as their master than would be willing to acknowledge their indebtedness.

The other type of answer was first given by Kant. We must distinguish between the general way he set about constructing his answer to Hume, and the details of his system which in many respects are highly disputable. The essential point of his method is the assumption that 'significance' is an essential element in concrete experience. The Berkeleyan dilemma starts with tacitly ignoring this aspect of experience, and thus with putting forward, as expressing experience, conceptions of it which have no relevance to fact. In the light of Kant's procedure, Johnson's answer falls into its place; it is the assertion that Berkeley has not correctly expounded what experience in fact is.

Berkeley himself insists that experience is significant, indeed three-quarters of his writings are devoted to enforcing this position. But Kant's position is the converse of Berkeley's, namely that significance is experience. Berkeley first analyses experience, and then expounds his view of its significance, namely that it is God conversing with us. For Berkeley the significance is detachable from the experience. It is here that Hume came in. He accepted Berkeley's assumption that experience is something given, an impression, without essential reference to significance, and exhibited it in its bare insignificance. Berkeley's conversation with God then becomes a fairy tale.

3.5 What is 'significance'? Evidently this is a fundamental question for the philosophy of natural knowledge, which cannot move a step until it has made up its mind as to what is meant by this 'significance' which is experience.

'Significance' is the relatedness of things. To say that significance is experience, is to affirm that perceptual knowledge is nothing else than an apprehension of the relatedness of things, namely of things in their relations and as related. Certainly if we commence with a knowledge of things, and then look around for their relations we shall not find them. 'Causal connection' is merely one typical instance of the universal ruin of relatedness. But then we are quite mistaken in thinking that there is a possible knowledge of things as unrelated. It is thus out of the question to start with a knowledge of things antecedent to a knowledge of their relations. The so-called properties of things can always be expressed as their relatedness to other things unspecified, and natural knowledge is exclusively concerned with relatedness.

3.6 The relatedness which is the subject of natural knowledge cannot be understood without reference to the general characteristics of perception. Our perception of natural events and natural objects is a perception from within nature, and is not an awareness contemplating all nature impartially from without. When Dr Johnson 'surveyed mankind from China to Peru,' he did it from Pump Court in London at a certain date. Even Pump Court was too wide for his peculiar locus standi; he was really merely conscious of the relations of his bodily events to the simultaneous events throughout the rest of the universe. Thus perception involves a percipient object, a percipient event, the complete event which is all nature simultaneous with the percipient event, and the particular events which are perceived as parts of the complete event. This general analysis of perception will be elaborated in [Part II]. The point here to be emphasised is that natural knowledge is a knowledge from within nature, a knowledge 'here within nature' and 'now within nature,' and is an awareness of the natural relations of one element in nature (namely, the percipient event) to the rest of nature. Also what is known is not barely the things but the relations of things, and not the relations in the abstract but specifically those things as related.

Thus Alciphron's vision of the planet is his perception of his relatedness (i.e. the relatedness of his percipient event) to some other elements of nature which as thus related he calls the planet. He admits in the dialogue that certain other specified relations of those elements are possible for other percipient events. In this he may be right or wrong. What he directly knows is his relation to some other elements of the universe namely, I, Alciphron, am located in my percipient event 'here and now' and the immediately perceived appearance of the planet is for me a characteristic of another event 'there and now.' In fact perceptual knowledge is always a knowledge of the relationship of the percipient event to something else in nature. This doctrine is in entire agreement with Dr Johnson's stamp of the foot by which he realised the otherness of the paving-stone.

3.7 The conception of knowledge as passive contemplation is too inadequate to meet the facts. Nature is ever originating its own development, and the sense of action is the direct knowledge of the percipient event as having its very being in the formation of its natural relations. Knowledge issues from this reciprocal insistence between this event and the rest of nature, namely relations are perceived in the making and because of the making. For this reason perception is always at the utmost point of creation. We cannot put ourselves back to the Crusades and know their events while they were happening. We essentially perceive our relations with nature because they are in the making. The sense of action is that essential factor in natural knowledge which exhibits it as a self-knowledge enjoyed by an element of nature respecting its active relations with the whole of nature in its various aspects. Natural knowledge is merely the other side of action. The forward moving time exhibits this characteristic of experience, that it is essentially action. This passage of nature—or, in other words, its creative advance—is its fundamental characteristic; the traditional concept is an attempt to catch nature without its passage.

3.8 Thus science leads to an entirely incoherent philosophy of perception in so far as it restricts itself to the ultimate datum of material in time and space, the spatio-temporal configuration of such material being the object of perception. This conclusion is no news to philosophy, but it has not led to any explicit reorganisation of the concepts actually employed in science. Implicitly, scientific theory is shot through and through with notions which are frankly inconsistent with its explicit fundamental data.

This confusion cannot be avoided by any kind of theory in which nature is conceived simply as a complex of one kind of inter-related elements such as either persistent things, or events, or sense-data. A more elaborate view is required of which an explanation will be attempted in the sequel. It will suffice here to say that it issues in the assertion that all nature can (in many diverse ways) be analysed as a complex of things; thus all nature can be analysed as a complex of events, and all nature can be analysed as a complex of sense-data. The elements which result from such analyses, events, and sense-data, are aspects of nature of fundamentally different types, and the confusions of scientific theory have arisen from the absence of any clear recognition of the distinction between relations proper to one type of element and relations proper to another type of element. It is of course a commonplace that elements of these types are fundamentally different. What is here to be insisted on is the way in which this commonplace truth is important in yielding an analysis of the ultimate data for science more elaborate than that of its current tradition. We have to remember that while nature is complex with time-less subtlety, human thought issues from the simple-mindedness of beings whose active life is less than half a century.

[2]Alciphron, The Fourth Dialogue, Section 10.

[CHAPTER II]
THE FOUNDATIONS OF DYNAMICAL PHYSICS

[4. Newton's Laws of Motion]. 4.1 The theoretical difficulties in the way of the application of the philosophic doctrine of relativity have never worried practical scientists. They have started with the working assumptions that in some sense the world is in one euclidean space, that the permanent points in such a space have no individual characteristics recognisable by us, except so far as they are occupied by recognisable material or except in so far as they are defined by assigned spatial relations to points which are thus definitely recognisable, and that according to the purpose in hand either the earth can be assumed to be at rest or else astronomical axes which are defined by the aid of the solar system, of the stars, and of dynamical considerations deduced from Newton's laws of motion.

4.2 Newton's laws [3] of motion presuppose the notions of mass and force. Mass arises from the conception of a passive quality of a material body, what it is in itself apart from its relation to other bodies; the notion of 'force' is that of an active agency changing the physical circumstances of the body, and in particular its spatial relations to other bodies. It is fairly obvious that mass and force were introduced into science as the outcome of this antithesis between intrinsic quality and agency, although further reflection may somewhat mar the simplicity of this outlook. Mass and force are measurable quantities, and their numerical expressions are dependent on the units chosen. The mass of a body is constant, so long as the body remains composed of the same self-identical material. Velocity, acceleration and force are vector quantities, namely they have direction as well as magnitude. They are thus representable by straight lines drawn from any arbitrary origin.

4.3 These laws of motion are among the foundations of science; and certainly any alteration in them must be such as to produce effects observable only under very exceptional circumstances. But, as is so often the case in science, a scrutiny of their meaning produces many perplexities.

In the first place we can sweep aside one minor difficulty. In our experience, a finite mass of matter occupies a volume and not a point. Evidently therefore the laws should be stated in an integral form, involving at certain points of the exposition greater elaboration of statement. These forms are stated (with somewhat abbreviated explanation) in dynamical treatises.

Secondly, Lorentz's distinction between macroscopic equations and microscopic equations forces itself on us at once, by reason of the molecular nature of matter and the dynamical nature of heat. A body apparently formed of continuous matter with its intrinsic geometrical relations nearly invariable is in fact composed of agitated molecules. The equations of motion for such a body as used by an engineer or an astronomer are, in Lorentz's nomenclature, macroscopic. In such equations even a differential element of volume is to be supposed to be sufficiently large to average out the diverse agitations of the molecules, and to register only the general unbalanced residuum which to ordinary observation is the motion of the body.

The microscopic equations are those which apply to the individual molecules. It is at once evident that a series of such sets of equations is possible, in which the adjacent sets are macroscopic and microscopic relatively to each other. For example, we may penetrate below the molecule to the electrons and the core which compose it, and thus obtain infra-molecular equations. It is purely a question as to whether there are any observed phenomena which in this way receive their interpretation.

The inductive evidence for the validity of Newton's equations of motion, within the experimental limits of accuracy, is obviously much stronger in the case of the macroscopic equations of the engineer and the astronomer than it is in the case of the microscopic equations of the molecule, and very much stronger than in the case of the infra-microscopic equations of the electron. But there is good evidence that even the infra-microscopic equations conform to Newton's laws as a first approximation. The traces of deviation arise when the velocities are not entirely negligible compared to that of light.

4.4 What do we know about masses and about forces? We obtain our knowledge of forces by having some theory about masses, and our knowledge of masses by having some theory about forces. Our theories about masses enable us in certain circumstances to assign the numerical ratios of the masses of the bodies involved; then the observed motions of these bodies will enable us to register (by the use of Newton's laws of motion) the directions and magnitudes of the forces involved, and thence to frame more extended theories as to the laws regulating the production of force. Our theories about the direction and comparative magnitudes of forces and the observed motions of the bodies will enable us to register (by the use of Newton's laws of motion) the comparative magnitudes of masses. The final results are to be found in engineers' pocket-books in tables of physical constants for physicists, and in astronomical tables. The verification is the concordant results of diverse experiments. One essential part of such theories is the judgment of circumstances which are sufficiently analogous to warrant the assumption of the same mass or the same magnitude of force in assigned diverse cases. Namely the theories depend upon the fact of recognition.

4.5 It has been popular to define force as the product of mass and acceleration. The difficulty to be faced with this definition is that the familiar equation of elementary dynamics, namely,

now becomes

It is not easy to understand how an important science can issue from such premisses. Furthermore the simple balancing of a weight by the tension of the supporting spring receives a very artificial meaning. With equal reason we might start with our theories of force as fundamental, and define mass as force divided by acceleration. Again we should be in equal danger of reducing dynamical equations to such identities as

Also the permanent mass of a bar of iron receives a very artificial meaning.

[5. The Ether]. 5.1 The theory of stress between distant bodies, considered as an ultimate fact, was repudiated by Newton himself, but was adopted by some of his immediate successors. In the nineteenth century the belief in action at a distance has steadily lost ground.

There are four definite scientific reasons for the adoption of the opposite theory of the transmission of stress through an intermediate medium which we will call the 'ether.' These reasons are in addition to the somewhat vague philosophic preferences, based on the disconnection involved in spatial and temporal separation. In the first place, the wave theory of light also postulates an ether, and thus brings concurrent testimony to its existence. Secondly, Clerk Maxwell produced the formulae for the stresses in such an ether which, if they exist, would account for gravitational, electrostatic, and magnetic attractions. No theory of the nature of the ether is thereby produced which in any way explains why such stresses exist; and thus their existence is so far just as much a disconnected assumption as that of the direct stresses between distant bodies. Thirdly, Clerk Maxwell's equations of the electromagnetic field presuppose events and physical properties of apparently empty space. Accordingly there must be something, i.e. an ether, in the empty space to which these properties belong. These equations are now recognised as the foundations of the exact science of electromagnetism, and stand on a level with Newton's equations of motion. Thus another testimony is added to the existence of an ether.

Lastly, Clerk Maxwell's identification of light with electromagnetic waves shows that the same ether is required by the apparently diverse optical and electromagnetic phenomena. The objection is removed that fresh properties have to be ascribed to the ether by each of the distinct lines of thought which postulate it.

It will be observed that gravitation stands outside this unification of scientific theory due to Maxwell's work, except so far that we know the stresses in the ether which would produce it.

5.2 The assumption of the existence of an ether at once raises the question as to its laws of motion. Thus in addition to the hierarchy of macroscopic and microscopic equations, there are the equations of motion for ether in otherwise empty space. The à priori reasons for believing that Newton's laws of motion apply to the ether are very weak, being in fact nothing more than the inductive extension of laws to cases widely dissimilar from those for which they have been verified. It is however a sound scientific procedure to investigate whether the assumed properties of ether are explicable on the assumption that it is behaving like ordinary matter, if only to obtain suggestions by contrast for the formulation of the laws which do express its physical changes.

The best method of procedure is to assume certain large principles deducible from Newton's laws and to interpret certain electromagnetic vectors as displacements and velocities of the ether. In this way Larmor has been successful in deducing Maxwell's equations from the principle of least action after making the necessary assumptions. In this he is only following a long series of previous scientists who during the nineteenth century devoted themselves to the explanation of optical and electromagnetic phenomena. His work completes a century of very notable achievement in this field.

5.3 But it may be doubted whether this procedure is not an inversion of the more fundamental line of thought. It will have been noted that Newton's equations, or any equivalent principles which are substituted for them, are in a sense merely blank forms. They require to be supplemented by hypotheses respecting the nature of the stresses, of the masses, and of the motions, before there can be any possibility of their application. Thus by the time that Newton's equations of motion are applied to the explication of etherial events there is a large accumulation of hypotheses respecting things of which we know very little. What in fact we do know about the ether is summed up in Maxwell's equations, or in recent adaptations of his equations such as those due to Lorentz. The discovery of electromagnetic mass and electromagnetic momentum suggests that, for the ether at least, we gain simpler conceptions of the facts by taking Maxwell's equations, or the Lorentz-Maxwell equations, as fundamental. Such equations would then be the ultimate microscopic equations, at least in the present stage of science, and Newton's equations become macroscopic equations which apply in certain definite circumstances to etherial aggregates. Such a procedure does not prejudge the debated theory of the purely electromagnetic origin of mass.

5.4 The modern theory of the molecule is destructive of the obviousness of the prejudgment in favour of the traditional concepts of ultimate material at an instant. Consider a molecule of iron. It is composed of a central core of positive electricity surrounded by annular clusters of electrons, composed of negative electricity and rotating round the core. No single characteristic property of iron as such can be manifested at an instant. Instantaneously there is simply a distribution of electricity and Maxwell's equations to express our expectations. But iron is not an expectation or even a recollection. It is a fact; and this fact, which is iron, is what happens during a period of time. Iron and a biological organism are on a level in requiring time for functioning. There is no such thing as iron at an instant; to be iron is a character of an event. Every physical constant respecting iron which appears in scientific tables is the register of such a character. What is ultimate in iron, according to the traditional theory, is instantaneous distributions of electricity; and this ultimateness is simply ascribed by reason of a metaphysical theory, and by no reason of observation.

5.5 In truth, when we have once admitted the hierarchy of macroscopic and microscopic equations, the traditional concept is lost. For it is the macroscopic equations which express the facts of immediate observation, and these equations essentially express the integral characters of events. But this hierarchy is necessitated by every concept of modern physics—the molecular theory of matter, the dynamical theory of heat, the wave theory of light, the electromagnetic theory of molecules, the electromagnetic theory of mass.

[6. Maxwell's Equations][4]. [6.1] A discussion of Maxwell's equations would constitute a treatise on electromagnetism. But they exemplify some general considerations on physical laws.

These equations (expressed for an axis-system

involve for each point of space and each instant of time the vector quantities (

), (

) and (

), namely the electric and magnetic 'forces' and the velocity of the charge of electricity. Now a vector involves direction; and direction is not concerned with what is merely at that point. It is impossible to define direction without reference to the rest of space; namely, it involves some relation to the whole of space.

Again the equations involve the spatial differential operators

, which enter through the symbols

; and they also involve the temporal differential operator

. The differential coefficients thus produced essentially express properties in the neighbourhood of the point (

) and of the time

, and not merely properties at (

). For a differential coefficient is a limit, and the limit of a function at a given value of its argument expresses a property of the aggregate of the values of the function corresponding to the aggregate of the values of the argument in the neighbourhood of the given value.

This is essentially the same argument as that expressed above in [1.2] for the particular case of motion. Namely, we cannot express the facts of nature as an aggregate of individual facts at points and at instants.

6.2 In the Lorentz-Maxwell equations [cf. [Appendix II]] there is no reference to the motion of the ether. The velocity (

) which appears in them is the velocity of the electric charge. What then are the equations of motion of the ether? Before we puzzle over this question, a preliminary doubt arises. Does the ether move?

Certainly, if science is to be based on the data included in the Lorentz-Maxwell equations, even if the equations be modified, the motion of the ether does not enter into experience. Accordingly Lorentz assumes a stagnant ether: that is to say, an ether with no motion, which is simply the ultimate entity of which the vectors (

and

) express properties. Such an ether has certainly a very shadowy existence; and yet we cannot assume that it moves, merely for the sake of giving it something to do.

6.3 The ultimate facts contemplated in Maxwell's equations are the occurrences of

(the volume-density of the charge), (

), (

) and (

) at the space-time points in the neighbourhood surrounding the space-time point (

). But this is merely to say that the ultimate facts contemplated by Maxwell's equations are certain events which are occurring throughout all space. The material called ether is merely the outcome of a metaphysical craving. The continuity of nature is the continuity of events; and the doctrine of transmission should be construed as a doctrine of the coextensiveness of events with space and time and of their reciprocal interaction. In this sense an ether can be admitted; but, in view of the existing implication of the term, clearness is gained by a distinction of phraseology. We shall term the traditional ether an 'ether of material' or a 'material ether,' and shall employ the term 'ether of events' to express the assumption of this enquiry, which may be loosely stated as being 'that something is going on everywhere and always.' It is our purpose to express accurately the relations between these events so far as they are disclosed by our perceptual experience, and in particular to consider those relations from which the essential concepts of Time, Space, and persistent material are derived. Thus primarily we must not conceive of events as in a given Time, a given Space, and consisting of changes in given persistent material. Time, Space, and Material are adjuncts of events. On the old theory of relativity, Time and Space are relations between materials; on our theory they are relations between events.

[3]Cf. [Appendix I] to this chapter

[4]Cf. [Appendix II] to this chapter

[APPENDIX I TO CHAPTER II]
NEWTON'S LAWS OF MOTION

Let (

) as in the accompanying figure be rectangular axes at rest; let (

) be the velocity of a material particle

of mass

at (

) relative to these axes, and let (

) be the acceleration of the same particle. Also let (

) be the force on the particle

. The first two of Newton's laws can be compressed into the equations

Fig. 1.

It is unnecessary to trace the elementary consequences of these equations.

The third law of motion considers a fundamental characteristic of force and is founded on the sound principle that all agency is nothing else than relations between those entities which are among the ultimate data of science. The law is, Action and reaction are equal and opposite. This means that there must be particles