The second chapter of this book lays down the first principle to be guarded in framing our physical concept. We must avoid vicious bifurcation. Nature is nothing else than the deliverance of sense-awareness. We have no principles whatever to tell us what could stimulate mind towards sense-awareness. Our sole task is to exhibit in one system the characters and inter-relations of all that is observed. Our attitude towards nature is purely ‘behaviouristic,’ so far as concerns the formulation of physical concepts.

Our knowledge of nature is an experience of activity (or passage). The things previously observed are active entities, the ‘events.’ They are chunks in the life of nature. These events have to each other relations which in our knowledge differentiate themselves into space-relations and time-relations. But this differentiation between space and time, though inherent in nature, is comparatively superficial; and space and time are each partial expressions of one fundamental relation between events which is neither spatial nor temporal. This relation I call ‘extension.’ The relation of ‘extending over’ is the relation of ‘including,’ either in a spatial or in a temporal sense, or in both. But the mere ‘inclusion’ is more fundamental than either alternative and does not require any spatio-temporal differentiation. In respect to extension two events are mutually related so that either (i) one includes the other, or (ii) one overlaps the other without complete inclusion, or (iii) they are entirely separate. But great care is required in the definition of spatial and temporal elements from this basis in order to avoid tacit limitations really depending on undefined relations and properties.

Such fallacies can be avoided by taking account of two elements in our experience, namely, (i) our observational ‘present,’ and (ii) our ‘percipient event.’

Our observational ‘present’ is what I call a ‘duration.’ It is the whole of nature apprehended in our immediate observation. It has therefore the nature of an event, but possesses a peculiar completeness which marks out such durations as a special type of events inherent in nature. A duration is not instantaneous. It is all that there is of nature with certain temporal limitations. In contradistinction to other events a duration will be called infinite and the other events are finite[10]. In our knowledge of a duration we distinguish (i) certain included events which are particularly discriminated as to their peculiar individualities, and (ii) the remaining included events which are only known as necessarily in being by reason of their relations to the discriminated events and to the whole duration. The duration as a whole is signified[11] by that quality of relatedness (in respect to extension) possessed by the part which is immediately under observation; namely, by the fact that there is essentially a beyond to whatever is observed. I mean by this that every event is known as being related to other events which it does not include. This fact, that every event is known as possessing the quality of exclusion, shows that exclusion is as positive a relation as inclusion. There are of course no merely negative relations in nature, and exclusion is not the mere negative of inclusion, though the two relations are contraries. Both relations are concerned solely with events, and exclusion is capable of logical definition in terms of inclusion.

Perhaps the most obvious exhibition of significance is to be found in our knowledge of the geometrical character of events inside an opaque material object. For example we know that an opaque sphere has a centre. This knowledge has nothing to do with the material; the sphere may be a solid uniform billiard ball or a hollow lawn-tennis ball. Such knowledge is essentially the product of significance, since the general character of the external discriminated events has informed us that there are events within the sphere and has also informed us of their geometrical structure.

Some criticisms on ‘The Principles of Natural Knowledge’ show that difficulty has been found in apprehending durations as real stratifications of nature. I think that this hesitation arises from the unconscious influence of the vicious principle of bifurcation, so deeply embedded in modern philosophical thought. We observe nature as extended in an immediate present which is simultaneous but not instantaneous, and therefore the whole which is immediately discerned or signified as an inter-related system forms a stratification of nature which is a physical fact. This conclusion immediately follows unless we admit bifurcation in the form of the principle of psychic additions, here rejected.

Our ‘percipient event’ is that event included in our observational present which we distinguish as being in some peculiar way our standpoint for perception. It is roughly speaking that event which is our bodily life within the present duration. The theory of perception as evolved by medical psychology is based on significance. The distant situation of a perceived object is merely known to us as signified by our bodily state, i.e. by our percipient event. In fact perception requires sense-awareness of the significations of our percipient event together with sense-awareness of a peculiar relation (situation) between certain objects and the events thus signified. Our percipient event is saved by being the whole of nature by this fact of its significations. This is the meaning of calling the percipient event our standpoint for perception. The course of a ray of light is only derivatively connected with perception. What we do perceive are objects as related to events signified by the bodily states excited by the ray. These signified events (as is the case of images seen behind a mirror) may have very little to do with the actual course of the ray. In the course of evolution those animals have survived whose sense-awareness is concentrated on those significations of their bodily states which are on the average important for their welfare. The whole world of events is signified, but there are some which exact the death penalty for inattention.

The percipient event is always here and now in the associated present duration. It has, what may be called, an absolute position in that duration. Thus one definite duration is associated with a definite percipient event, and we are thus aware of a peculiar relation which finite events can bear to durations. I call this relation ‘cogredience.’ The notion of rest is derivative from that of cogredience, and the notion of motion is derivative from that of inclusion within a duration without cogredience with it. In fact motion is a relation (of varying character) between an observed event and an observed duration, and cogredience is the most simple character or subspecies of motion. To sum up, a duration and a percipient event are essentially involved in the general character of each observation of nature, and the percipient event is cogredient with the duration.

Our knowledge of the peculiar characters of different events depends upon our power of comparison. I call the exercise of this factor in our knowledge ‘recognition,’ and the requisite sense-awareness of the comparable characters I call ‘sense-recognition.’ Recognition and abstraction essentially involve each other. Each of them exhibits an entity for knowledge which is less than the concrete fact, but is a real factor in that fact. The most concrete fact capable of separate discrimination is the event. We cannot abstract without recognition, and we cannot recognise without abstraction. Perception involves apprehension of the event and recognition of the factors of its character.

The things recognised are what I call ‘objects.’ In this general sense of the term the relation of extension is itself an object. In practice however I restrict the term to those objects which can in some sense or other be said to have a situation in an event; namely, in the phrase ‘There it is again’ I restrict the ‘there’ to be the indication of a special event which is the situation of the object. Even so, there are different types of objects, and statements which are true of objects of one type are not in general true of objects of other types. The objects with which we are here concerned in the formulation of physical laws are material objects, such as bits of matter, molecules and electrons. An object of one of these types has relations to events other than those belonging to the stream of its situations. The fact of its situations within this stream has impressed on all other events certain modifications of their characters. In truth the object in its completeness may be conceived as a specific set of correlated modifications of the characters of all events, with the property that these modifications attain to a certain focal property for those events which belong to the stream of its situations. The total assemblage of the modifications of the characters of events due to the existence of an object in a stream of situations is what I call the ‘physical field’ due to the object. But the object cannot really be separated from its field. The object is in fact nothing else than the systematically adjusted set of modifications of the field. The conventional limitation of the object to the focal stream of events in which it is said to be ‘situated’ is convenient for some purposes, but it obscures the ultimate fact of nature. From this point of view the antithesis between action at a distance and action by transmission is meaningless. The doctrine of this paragraph is nothing else than another way of expressing the unresolvable multiple relation of an object to events.

A complete time-system is formed by any one family of parallel durations. Two durations are parallel if either (i) one includes the other, or (ii) they overlap so as to include a third duration common to both, or (iii) are entirely separate. The excluded case is that of two durations overlapping so as to include in common an aggregate of finite events but including in common no other complete duration. The recognition of the fact of an indefinite number of families of parallel durations is what differentiates the concept of nature here put forward from the older orthodox concept of the essentially unique time-systems. Its divergence from Einstein’s concept of nature will be briefly indicated later.

The instantaneous spaces of a given time-system are the ideal (non-existent) durations of zero temporal thickness indicated by routes of approximation along series formed by durations of the associated family. Each such instantaneous space represents the ideal of nature at an instant and is also a moment of time. Each time-system thus possesses an aggregate of moments belonging to it alone. Each event-particle lies in one and only one moment of a given time-system. An event-particle has three characters[12]: (i) its extrinsic character which is its character as a definite route of convergence among events, (ii) its intrinsic character which is the peculiar quality of nature in its neighbourhood, namely, the character of the physical field in the neighbourhood, and (iii) its position.

The position of an event-particle arises from the aggregate of moments (no two of the same family) in which it lies. We fix our attention on one of these moments which is approximated to by the short duration of our immediate experience, and we express position as the position in this moment. But the event-particle receives its position in moment M in virtue of the whole aggregate of other moments M, M, etc., in which it also lies. The differentiation of M into a geometry of event-particles (instantaneous points) expresses the differentiation of M by its intersections with moments of alien time-systems. In this way planes and straight lines and event-particles themselves find their being. Also the parallelism of planes and straight lines arises from the parallelism of the moments of one and the same time-system intersecting M. Similarly the order of parallel planes and of event-particles on straight lines arises from the time-order of these intersecting moments. The explanation is not given here[13]. It is sufficient now merely to mention the sources from which the whole of geometry receives its physical explanation.

The correlation of the various momentary spaces of one time-system is achieved by the relation of cogredience. Evidently motion in an instantaneous space is unmeaning. Motion expresses a comparison between position in one instantaneous space with positions in other instantaneous spaces of the same time-system. Cogredience yields the simplest outcome of such comparison, namely, rest.

Motion and rest are immediately observed facts. They are relative in the sense that they depend on the time-system which is fundamental for the observation. A string of event-particles whose successive occupation means rest in the given time-system forms a timeless point in the timeless space of that time-system. In this way each time-system possesses its own permanent timeless space peculiar to it alone, and each such space is composed of timeless points which belong to that time-system and to no other. The paradoxes of relativity arise from neglecting the fact that different assumptions as to rest involve the expression of the facts of physical science in terms of radically different spaces and times, in which points and moments have different meanings.

The source of order has already been indicated and that of congruence is now found. It depends on motion. From cogredience, perpendicularity arises; and from perpendicularity in conjunction with the reciprocal symmetry between the relations of any two time-systems congruence both in time and space is completely defined (cf. loc. cit.).

The resulting formulae are those for the electromagnetic theory of relativity, or, as it is now termed, the restricted theory. But there is this vital difference: the critical velocity c which occurs in these formulae has now no connexion whatever with light or with any other fact of the physical field (in distinction from the extensional structure of events). It simply marks the fact that our congruence determination embraces both times and spaces in one universal system, and therefore if two arbitrary units are chosen, one for all spaces and one for all times, their ratio will be a velocity which is a fundamental property of nature expressing the fact that times and spaces are really comparable.

The physical properties of nature are expressed in terms of material objects (electrons, etc.). The physical character of an event arises from the fact that it belongs to the field of the whole complex of such objects. From another point of view we can say that these objects are nothing else than our way of expressing the mutual correlation of the physical characters of events.

The spatio-temporal measurableness of nature arises from (i) the relation of extension between events, and (ii) the stratified character of nature arising from each of the alternative time-systems, and (iii) rest and motion, as exhibited in the relations of finite events to time-systems. None of these sources of measurement depend on the physical characters of finite events as exhibited by the situated objects. They are completely signified for events whose physical characters are unknown. Thus the spatio-temporal measurements are independent of the objectival physical characters. Furthermore the character of our knowledge of a whole duration, which is essentially derived from the significance of the part within the immediate field of discrimination, constructs it for us as a uniform whole independent, so far as its extension is concerned, of the unobserved characters of remote events. Namely, there is a definite whole of nature, simultaneously now present, whatever may be the character of its remote events. This consideration reinforces the previous conclusion. This conclusion leads to the assertion of the essential uniformity of the momentary spaces of the various time-systems, and thence to the uniformity of the timeless spaces of which there is one to each time-system.

The analysis of the general character of observed nature set forth above affords explanations of various fundamental observational facts: (α) It explains the differentiation of the one quality of extension into time and space. (β) It gives a meaning to the observed facts of geometrical and temporal position, of geometrical and temporal order, and of geometrical straightness and planeness. (γ) It selects one definite system of congruence embracing both space and time, and thus explains the concordance as to measurement which is in practice attained. (δ) It explains (consistently with the theory of relativity) the observed phenomena of rotation, e.g. Foucault’s pendulum, the equatorial bulge of the earth, the fixed senses of rotation of cyclones and anticyclones, and the gyro-compass. It does this by its admission of definite stratifications of nature which are disclosed by the very character of our knowledge of it. (ε) Its explanations of motion are more fundamental than those expressed in (δ); for it explains what is meant by motion itself. The observed motion of an extended object is the relation of its various situations to the stratification of nature expressed by the time-system fundamental to the observation. This motion expresses a real relation of the object to the rest of nature. The quantitative expression of this relation will vary according to the time-system selected for its expression.

This theory accords no peculiar character to light beyond that accorded to other physical phenomena such as sound. There is no ground for such a differentiation. Some objects we know by sight only, and other objects we know by sound only, and other objects we observe neither by light nor by sound but by touch or smell or otherwise. The velocity of light varies according to its medium and so does that of sound. Light moves in curved paths under certain conditions and so does sound. Both light and sound are waves of disturbance in the physical characters of events; and (as has been stated above, p.188) the actual course of the light is of no more importance for perception than is the actual course of the sound. To base the whole philosophy of nature upon light is a baseless assumption. The Michelson-Morley and analogous experiments show that within the limits of our inexactitude of observation the velocity of light is an approximation to the critical velocity ‘c’ which expresses the relation between our space and time units. It is provable that the assumption as to light by which these experiments and the influence of the gravitational field on the light-rays are explained is deducible as an approximation from the equations of the electromagnetic field. This completely disposes of any necessity for differentiating light from other physical phenomena as possessing any peculiar fundamental character.

It is to be observed that the measurement of extended nature by means of extended objects is meaningless apart from some observed fact of simultaneity inherent in nature and not merely a play of thought. Otherwise there is no meaning to the concept of one presentation of your extended measuring rod AB. Why not AB where B is the end B five minutes later? Measurement presupposes for its possibility nature as a simultaneity, and an observed object present then and present now. In other words, measurement of extended nature requires some inherent character in nature affording a rule of presentation of events. Furthermore congruence cannot be defined by the permanence of the measuring rod. The permanence is itself meaningless apart from some immediate judgment of self-congruence. Otherwise how is an elastic string differentiated from a rigid measuring rod? Each remains the same self-identical object. Why is one a possible measuring rod and the other not so? The meaning of congruence lies beyond the self-identity of the object. In other words measurement presupposes the measurable, and the theory of the measurable is the theory of congruence.

Furthermore the admission of stratifications of nature bears on the formulation of the laws of nature. It has been laid down that these laws are to be expressed in differential equations which, as expressed in any general system of measurement, should bear no reference to any other particular measure-system. This requirement is purely arbitrary. For a measure-system measures something inherent in nature; otherwise it has no connexion with nature at all. And that something which is measured by a particular measure-system may have a special relation to the phenomenon whose law is being formulated. For example the gravitational field due to a material object at rest in a certain time-system may be expected to exhibit in its formulation particular reference to spatial and temporal quantities of that time-system. The field can of course be expressed in any measure-systems, but the particular reference will remain as the simple physical explanation.

NOTE: ON THE GREEK CONCEPT OF A POINT

The preceding pages had been passed for press before I had the pleasure of seeing Sir T.L. Heath’s Euclid in Greek[14]. In the original Euclid’s first definition is

σημειον εστιν, ου μερος ουθεν.

I have quoted it on p.86 in the expanded form taught to me in childhood, ‘without parts and without magnitude.’ I should have consulted Heath’s English edition—a classic from the moment of its issue—before committing myself to a statement about Euclid. This is however a trivial correction not affecting sense and not worth a note. I wish here to draw attention to Heath’s own note to this definition in his Euclid in Greek. He summarises Greek thought on the nature of a point, from the Pythagoreans, through Plato and Aristotle, to Euclid. My analysis of the requisite character of a point on pp.89 and 90 is in complete agreement with the outcome of the Greek discussion.

NOTE: ON SIGNIFICANCE AND INFINITE EVENTS

The theory of significance has been expanded and made more definite in the present volume. It had already been introduced in the Principles of Natural Knowledge (cf. subarticles3.3 to 3.8 and 16.1, 16.2, 19.4, and articles20, 21). In reading over the proofs of the present volume, I come to the conclusion that in the light of this development my limitation of infinite events to durations is untenable. This limitation is stated in article33 of the Principles and at the beginning of ChapterIV (p.74) of this book. There is not only a significance of the discerned events embracing the whole present duration, but there is a significance of a cogredient event involving its extension through a whole time-system backwards and forwards. In other words the essential ‘beyond’ in nature is a definite beyond in time as well as in space [cf. pp.53, 194]. This follows from my whole thesis as to the assimilation of time and space and their origin in extension. It also has the same basis in the analysis of the character of our knowledge of nature. It follows from this admission that it is possible to define point-tracks [i.e. the points of timeless spaces] as abstractive elements. This is a great improvement as restoring the balance between moments and points. I still hold however to the statement in subarticle35.4 of the Principles that the intersection of a pair of non-parallel durations does not present itself to us as one event. This correction does not affect any of the subsequent reasoning in the two books.

I may take this opportunity of pointing out that the ‘stationary events’ of article57 of the Principles are merely cogredient events got at from an abstract mathematical point of view.

---

f their present, to catch the advancing omens of their future.

Indeed, if anything of France is to be explained in English and to people reading English, I could not desire a better alliance than yours and mine.

But if you ask me why the Renaissance especially--or why in the Renaissance these six poets alone--should have formed the subject of my first endeavour, I can only tell you that in so vast a province, whereof the most ample leisure could not in a lifetime exhaust a tithe, Chance, that happy Goddess, led me at random to their groves.

Whether it will be possible to continue such interpretation I do not know, but if it be so possible, I know still less what next may be put into my hands: Racine, perhaps, may call me, or those forgotten men who urged the Revolution with phrases of fire.

H. BELLOC.
CHELSEA, January, 1904.