THE ULTIMATE PHYSICAL CONCEPTS
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.
[10] Cf. note on 'significance,' pp. 197, 198.
[11] Cf. Ch. III, pp. 51 et seq.
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.
[12] Cf. pp. 82 et seq.
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.
[13] Cf. _Principles of Natural Knowledge_, and previous chapters of the
present work.
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:
({alpha}) It explains the differentiation of the one quality of
extension into time and space. ({beta}) It gives a meaning to the
observed facts of geometrical and temporal position, of geometrical and
temporal order, and of geometrical straightness and planeness. ({gamma})
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. ({delta}) 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. ({epsilon}) Its
explanations of motion are more fundamental than those expressed in
({delta}); 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
semeion estin, ou meros outhen.
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.
[14] Camb. Univ. Press, 1920.
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. subarticles 3.3 to 3.8 and 16.1, 16.2, 19.4, and
articles 20, 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 article 33 of the _Principles_ and at the beginning of
Chapter IV (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 subarticle 35.4 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 article 57 of the _Principles_ are merely cogredient events got at
from an abstract mathematical point of view.
INDEX
_In the case of terms of frequent occurrence, only those occurrences are
indexed which are of peculiar importance for the elucidation of
meaning._
A [_or_ an], 11
Abraham, 105
Absolute position, 105, 106, 114, 188
Abstraction, 33, 37, 168, 171, 173;
extensive, 65, 79, 85
Abstractive element, 84;
set, 61, 79
Action at a distance, 159, 190
Action by transmission, 159, 190
Active conditions, 158
Activity, field of, 170, 181
Adjunction, 101
Aggregate, 23
Alexander, Prof., viii
Alexandria, 71
Alfred the Great, 137
Anticipation, 69
Anti-prime, 88
Apparent nature, 31, 39
Area, 99;
momental, 103;
vagrant, 103
Aristotelian logic, 150
Aristotle, 16, 17, 18, 24, 197
Associate-potential, 183
Atom, 17
Attribute, 21, 26, 150
Awareness, 3
Axiom, 36, 121
Axioms of congruence, 128 et seqq.
Bacon, Francis, 78
Behaviouristic, 185
Bergson, 54
Berkeley, 28
Between, 64
Beyond, 186, 198
Bifurcation, vi, 30, 185, 187
Boundary, 100;
moment, 63;
particle, 100
Broad, C. D., viii
Calculation, formula of, 45, 158
Cambridge, 97
Causal nature, 31, 39
Causation, 31, 146
Centrifugal force, 138
Change, uniformity of, 140
Character, extrinsic, 82, 89, 90, 113, 191;
intrinsic, 80, 82, 90, 113, 191
Charge, 160
Closure of nature, 4
Coefficient of drag, 133
Coefficients of impetus, 183
Cogredience, 110, 188
Coherence, 29
Comparison, 124, 125, 143, 189
Complex, 13
Conceptual nature, 45;
space, 96
Concrete facts, 167, 171, 189
Conditioning events, 152
Conditions, active, 158
Congruence, 65, 96, 118, 120, 127, 196
Continuity, 157;
Dedekindian, 102;
of events, 76;
of nature, 59, 76
Convention, 121
Convergence, 62, 79;
law of, 82
Conveyance, 154, 155
Co-present, 177
Covering, 83
Creative advance, 178
Critical velocity, 193, 195
Curvature of space-time, 182
Cyclone, 194
Dedekindian continuity, 102
Definite, 53, 194, 198
Delusions, 31, 38
Delusive perceptual object, 153
Demarcation of events, 144
Demonstrative phrase, 6
Descriptive phrase, 6, 10
Differential equations, 196
Discrimination, 14, 50, 144
Diversification of nature, 15
Duddington, Mrs, 47
Duration, 37, 53, 55, 186
Durations, families of, 59, 73, 190
Dynamical axes, 138
Einstein, vii, 102, 131, 164, 165, 181, 182, 183, 184, 191
Electromagnetic field, 179
Electron, 30, 146, 158, 171
Element, 17;
abstractive, 84
Elliptical phraseology, 7
Empty space, 145
Entity, 5, 13
Equal in abstractive force, 83
Error, 68
Ether, 18, 78, 160;
material, 78;
of events, 78
Euclid, 85, 94, 197
Euler, 140
Event, 15, 52, 75, 165;
percipient, 107, 152, 186
Event-particle, 86, 93, 94, 172, 191
Events, conditioning, 152;
continuity of, 76;
demarcation of, 144;
ether of, 78;
infinite, 197, 198;
limited, 74;
passage of, 34;
signified, 52;
stationary, 198;
stream of, 167;
structure of, 52, 166
Exclusion, 186
Explanation, 97, 141
Extended nature, 196
Extension, 22, 58, 75, 185
Extensive abstraction, 65, 79, 85
Extrinsic character, 82, 89, 90, 113, 191;
properties, 62
Fact, 12, 13
Factors, 12, 13, 15
Facts, concrete, 167, 171
Family of durations, 59, 63, 73;
of moments, 63
Faraday, 146
Field, gravitational, 197;
of activity, 170, 181;
physical, 190
Finite truths, 12
Fitzgerald, 133
Formula of calculation, 45, 158
Foucault, 138, 194
Four-dimensional manifold, 86
Fresnel, 133
Future, the, 72, 177
Galileo, 139
Geometrical order, 194
Geometry, 36;
metrical, 129
Gravitation, 179 et seqq.
Gravitational field, 197
Greek philosophy, 16;
thought, 197
Gyro-compass, 194
Heath, Sir T. L., 197
Here, 107
Idealists, 70
Immediacy, 52;
of perception, 72
Impetus, 181, 182;
coefficients of, 183;
integral, 183
Inclusion, 186
Individuality, 13
Infinite events, 197, 198
Inge, Dr, 48
Ingredient, 14
Ingression, 144, 145, 148, 152
Inherence, 83
Inside, 106
Instant, 33, 35, 57
Instantaneous plane, 91;
present, 72;
spaces, 86, 90, 177
Instantaneousness, 56, 57
Intersection, locus of, 90
Intrinsic character, 80, 82, 90, 113, 191;
properties, 62
Ionian thinkers, 19
Irrelevance, infinitude of, 12
Irrevocableness, 35, 37
It, 8
Julius Caesar, 36
Junction, 76, 101
Kinetic energy, 105;
symmetry, 129
Knowledge, 28, 32
Lagrange, 140
Larmor, 131
Law of convergence, 82
Laws of motion, 137, 139;
of nature, 196
Leibnizian monadology, 150
Level, 91, 92
Light, 195;
ray of, 188;
velocity of, 131
Limit, 57
Limited events, 74
Location, 160, 161
Locke, 27
Locus, 102;
of intersection, 90
London, 97
Lorentz, H. A., 131, 133
Lossky, 47
Manifold, four-dimensional, 86;
space-time, 173
Material ether, 78;
object, 169
Materialism, 43, 70
Matrix, 116
Matter, 16, 17, 19, 20, 26
Maxwell, 131, 133
Measurableness, 196;
of nature, 193
Measurement, 96, 120, 174, 196;
of time, 65, 140
Measure-system, 196
Memory, 68
Metaphysics, 28, 32
Metrical geometry, 129
Michelson-Morley, 195
Milton, 35
Mind, 27, 28
Minkowski, viii, 131
Molecule, 32, 171
Moment, 57, 60, 88
Momental area, 103;
route, 103
Momentum, 105
Motion, 105, 114, 117, 127, 188, 192
Multiplicity, 22
Natural philosophy, 29, 30
Natural science, philosophy of, 46
Nature, 3;
apparent, 31, 39;
causal, 31, 39;
conceptual, 45;
continuity of, 59, 76;
discrimination of, 144;
extended, 196;
laws of, 196;
passage of, 54;
stratification of, 194, 196;
system of, 146
Newton, 27, 136, 139, 140
Object, 77, 125, 143, 169, 189;
delusive perceptual, 155;
material, 169;
perceptual, 153;
physical, 155, 157;
scientific, 158, 169;
uniform, 162
Occupation, 22, 34, 36, 100, 101
Order, source of, 192;
spatial, 95, 194;
temporal, 64, 95, 194
Organisation of thought, 79
Outside, 63, 100
Paradox, 192
Parallel, 63, 127;
durations, 190
Parallelism, 95, 191
Parallelogram, 127
Paris, 87, 138
Parliament, 120
Part, 14, 15, 58
Passage of events, 34;
of nature, 54
Past, the, 72, 177
Perception, 3
Perceptual objects, 149, 153
Percipience, 28
Percipient event, 107, 152, 186, 187
Period of time, 51
Permanence, 144
Perpendicularity, 117, 127, 193
Philosophy, 1;
natural, 29, 30;
of natural science, 46;
of the sciences, 2
Physical field, 190;
object, 155, 156, 157
Physics, speculative, 30
Place, 51
Plane, 191;
instantaneous, 91
Plato, 16, 17, 18, 24, 197
Poincare, 121, 122, 123
Point, 35, 89, 91, 114, 173, 176
Point-flash, 172, 173
Point of space, 85
Point, timeless, 192
Point-track, 113, 198
Pompey, 36
Position, 89, 90, 92, 93, 99, 113, 191;
absolute, 105, 106, 114, 188
Potential, 183;
associate-, 183
Predicate, 18
Predication, 18
Present, the, 69, 72, 177;
instantaneous, 72;
observational, 186
Primary qualities, 27
Prime, 88
Process, 53, 54;
of nature, 54
Psychic additions, 29, 187
Punct, 92, 93, 94
Pythagoreans, 197
Quality, 27
Quantum of time, 162
Quantum theory, 162
Ray of light, 188
Reality, 30;
of durations, 55, 187
Recognition, 124, 143, 189
Rect, 91, 92
Recurrence, 35
Relative motion, 117;
velocity, 130
Relativity, 169;
restricted theory of, 193
Rest, 105, 114, 188, 192
Rotation, 138, 194
Route, 99;
momental, 103;
straight, 103
Russell, Bertrand, 11, 122, 123
Schelling, 47
Science, 2;
metaphysical, 32
Scientific objects, 149, 158, 169
Secondary qualities, 27
Self-congruence, 196
Self-containedness of nature, 4
Sense-awareness, 3, 67
Sense-object, 149, 170
Sense-perception, 3, 14
Sense-recognition, 143, 189
Series, temporal, 66, 70, 85, 178
Set, abstractive, 61, 79
Significance, 51, 186, 187, 188, 194, 197, 198
Signified events, 52
Simplicity, 163, 173
Simultaneity, 53, 56, 196
Situation, 15, 78, 147, 148, 152, 160, 189
Solid, 99, 101, 102;
vagrant, 101
Sound, 195
Space, 16, 17, 31, 33, 79;
empty, 145;
timeless, 86, 106, 114;
uniformity of, 194
Spaces, instantaneous, 86, 90
Space-system, 179
Space-time manifold, 173
Spatial-order, 95
Spatio-temporal structure, 173
Speculative demonstration, 6
Speculative physics, 30
Standpoint for perception, 107, 188
Station, 103, 104, 113
Stationary events, 198
Straight line, 91, 114, 191;
route, 103
Stratification of nature, 187, 194, 196
Stream of events, 167
Structure of events, 52, 166
Structure, spatio-temporal, 173
Subject, 18
Substance, 16, 18, 19, 150
Substratum, 16, 18, 21
Symmetry, 118, 126;
kinetic, 129
System of nature, 146
System, time-, 192
Tarner, Edward, v, 1
Temporal order, 64, 95, 194
Temporal series, 66, 70, 85
Tensor, 182
Terminus, 4
The, 11
Theory, quantum, 162
There, 110, 189
This, 11
Thought, 3, 14
Timaeus, the, 17, 20, 24
Time, 16, 17, 31, 33, 49, 79;
measurement of, 140;
quantum of, 162;
transcendence of, 39
Time-series, 178, also cf. Temporal series
Time-system, see Time-series, also 91, 97, 104, 179, 192
Timeless point, 192;
space, 86, 106, 114, 177
Totality, 89
Transcendence of time, 39
Transmission, 26, 28;
action by, 159, 190
Tubes of force, 146
Unexhaustiveness, 50
Uniform object, 162
Uniformity of change, 140;
of space, 194
Vagrant area, 103;
solid, 101
Veblen and Young, 36
Velocity, critical, 193, 195;
of light, 131, 195;
relative, 130
Volume, 92, 101
When, 107
Where, 107
Whole, 58
Within, 63
Young, Veblen and, 36
End of Project Gutenberg's The Concept of Nature, by Alfred North Whitehead