The Concept of Nature — the Tarner Lectures, 1920

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. subarticles 3-3 to 3-8 and i6-i, 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 1 Camb. Univ. Press, 1920.

13—3p. 198 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 \pr an], ii

Abraham, 105

Absolute position, 105, 106, 114,

188
Abstraction, 33, 37, 168, ryi, 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, loi
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, 8g, go, 113,
191; intrinsic, 80, 82,90, 113, 191

Charge, 160

Closure of nature, 4

Coefficient of drag, 133

Coefficients of impetus, 183

Cogredience, no, i88

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,

i8i, 182, 183, 184, 191
Electromagnetic field, 179
Electron, 30, 146, 158, 171
Element, 17; abstractive, 84
Elliptical phraseology, 7

p. 200

liMJJlA

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, loi

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

INDEX

20 1

Minkowski, viii, 131

Molecule, 32, 171

Moment, 57, 60, 88

Momenta! 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, loi

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

Parallslogram, 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