The Analysis of Matter

not common sense, but solipsism and phenomenalism. Solipsism, as an epistemologically serious theory, must mean the view that from the events which I experience there is no valid method of inferring the character, or even the existence, of events which I do not experience. If inference is taken in the sense of strict deductive logic, there is, so far as I can see, no escape from the solipsist position. And it should be observed that this position cannot admit unconscious events in me, any more than events outside me: its basis is epistemological, and therefore, for it, the important distinction is between what I experience and what I do not experience, not between what is mine and what is not mine in some metaphysical or physical sense. We cannot escape from the solipsist position without bringing in induction and causality, which are still subject to the doubts resulting from Hume's sceptical criticism. Since, however, all science rests upon induction and causality, it seems justifiable, at least pragmatically, to assume that, when properly employed, they can give at least a probability. In the present work, I have made this assumption baldly,[Pg 399] without attempting to justify it; I have done this because I do not believe that a justification could be much briefer than Mr Keynes's Treatise on Probability, and also because, while I am convinced that a justification is possible, I am not satisfied with those put forward by others or with any that I have been able to invent myself. It seemed best, therefore, to make the assumption as stark as possible, without any attempt at artificial plausibility. Intermediate between solipsism and the ordinary scientific view, there is a half-way house called "phenomenalism." This admits events other than those which I experience, but holds that all of them are percepts or other mental events. Practically, it means, when advocated by scientific men, that they will accept the testimony of other observers as to what they have actually experienced, but that they will not infer thence anything which no observer has experienced. It may be said, in justification of this position, that, while it employs analogy and induction, it refrains from assuming causality. But it may be doubted whether it can really abstain from causality. Phenomenalists appear to take testimony for granted, i.e. to assume that the words which they see and hear express what they themselves would express if they used them. But this involves causality, and involves it in the form in which the cause is in one person and the effect in another. There does not seem, therefore, to be any substantial justification for this half-way house. We therefore assume, though with less than demonstrative certainty, that percepts have causes which may be not percepts, and, in particular, that when a number of people have similar percepts simultaneously, there is what may be called a "field" of causally connected events, which, it is found, have relations that often enable us to arrange them in a spherical order about a centre. We thus arrive at a space-time order of events, which is found to be the same whichever of many[Pg 400] possible methods of arriving at it we adopt; in this order, a percept is located in the head of the percipient. In drawing inferences from percepts to their causes, we assume that the stimulus must possess whatever structure is possessed by the percept, though it may also have structural properties not possessed by the percept. The assumption that the structural properties of the percept must exist in the stimulus follows from the maxim "same cause, same effect" in the inverted form "different effects, different causes," from which it follows that if, e.g., we see red and green side by side, there is some difference between the stimulus to the red percept and the stimulus to the green percept. The structural features possessed by the stimulus but not by the percept, when they can be inferred, are inferred by means of general laws—e.g. when two objects look similar to the naked eye but dissimilar under the microscope, we assume that there are differences in the stimuli to the naked-eye percepts which produce either no differences, or no perceptible differences, in the corresponding percepts. These principles enable us to infer a great deal as to the structure of the physical world, but not as to its intrinsic character. They put percepts in their place as occurrences analogous to and connected with other events in the physical world, and they enable us to regard a dictaphone or a photographic plate as having something which, from the standpoint of physics, is not very dissimilar from perception. We no longer have to contend with what used to seem mysterious in the causal theory of perception: a series of light-waves or sound-waves or what not suddenly producing a mental event apparently totally different from themselves in character. As to intrinsic character, we do not know enough about it in the physical world to have a right to say that it is very different from that of percepts; while as to structure we have reason to hold that it is similar in the stimulus and the percept. This has become possible owing to the facts that "matter" can be[Pg 401] regarded as a system of events, not as part of the stuff of the world, and that space-time, as it occurs in physics, has been found to be much more different from perceptual space than was formerly imagined. This brings us to Part III., in which we endeavour to discover a possible structure of the physical world which shall at once justify physics and take account of the connection with perception demanded by the necessity for an empirical basis for physics. Here we are concerned first with the construction of points as systems of events which overlap, or are "co-punctual," in space-time, and then with the purely ordinal properties of space-time. The method employed is very general, and can be adapted to a discrete or to a continuous order; it is proved that , events are sufficient to generate a continuum of points, given certain laws as to the manner of their overlapping. The whole of this theory, however, aims only at constructing such properties of space-time as belong to analysis situs; everything appertaining to intervals and metrics is omitted at this stage, since causal considerations are required for the theory of intervals. The conception of one unit of matter—say one electron—as a "substance," i.e. a single simple entity persisting through time, is not one which we are justified in adopting, since we have no evidence whatever as to whether it is false or true. We define a single material unit as a "causal line," i.e. as a series of events connected with each other by an intrinsic differential causal law which determines first-order changes, leaving second-order changes to be determined by extrinsic causal laws. (In this we are for the moment ignoring quantum phenomena.) If there are light-quanta, these will more or less fulfil this definition of matter, and we shall have returned to a corpuscular theory of light; but this is at present an open question. The whole conception of matter is less fundamental to physics than it used to be, since energy has more and more[Pg 402] taken its place. We find that under terrestrial conditions electrons and protons persist, but there is nothing in theoretical physics to lead us to expect this, and physicists are quite prepared to find that matter can be annihilated. This view is even, put forward to account for the energy of the stars. The question of interval presents great difficulties, when we attempt to construct a picture of the world which shall make its importance seem not surprising. The same may be said of the quantum. I have endeavoured, not, I fear, with much success, to suggest hypotheses which would link these two curious facts into one whole. I suggest that the world consists of steady events accompanied by rhythms, like a long note on the violin while arpeggios are played on the piano, or of rhythms alone. Steady events are of various sorts, and many sorts have their appropriate rhythmic accompaniments. Quantum changes consist of "transactions," i.e. of the substitution, suddenly, of one rhythm for another. When two events have a time-like interval, if space-time is discrete, this interval is the greatest number of transitions on any causal route leading from the one event to the other. The definition of space-like intervals is derived from that of time-like intervals. The whole process of nature may, so far as present evidence goes, be conceived as discontinuous; even the periodic rhythms may consist of a finite number of events per period. The periodic rhythms are required in order to give an account of the uses of the quantum principle. A percept, at any rate when it is visual, will be a steady event, or system of steady events, following upon a transaction. Percepts are the only part of the physical world that we know otherwise than abstractly. As regards the world in general, both physical and mental, everything that we know of its intrinsic character is derived from the mental side, and almost everything that we know of its causal laws is derived from the physical side. But from the standpoint of philosophy the distinction between physical and mental is superficial and unreal. [Pg 403] INDEX A priori and empirical knowledge: 173 Abstract geometry: 76 Acceleration: 231, 368 „ absolute: 18, 67 Accuracy: 99 Action: 36, 341, 379, 394 „ at a distance: 18, 108, 162, 327, 356, 359, 374, 380 Action, principle of least: 19 Adjectives: 242 Æther: 19, 121, 276, 355 Analogy: 399 Analysis: 4 „ logical: 2 Analysis situs: 55, 113, 114, 295, 298, 303, 311, 401 Analytic and synthetic propositions: 169 Ancestor: 373, 378 Apes: 148 Aristotle: 161 Arithmetic: 4, 276 Aspects: 347 Astronomy: 163, 234, 317, 397 Atom: 24, 234 „ Heisenberg's: 42 „ nucleus of: 25 „ Rutherford-Bohr: 24, 27, 42 Atomic number: 234 „ weight: 234 Atomism, spatial: 22 Axioms: 2 Bach: 392 Beauty: 392 Behaviourism: 142 Beliefs: 142, 174, 178 Bergson: 101, 279, 387 Berkeley: 6, 7, 136, 156, 159, 192, 213 Between: 305 Bifurcation of nature: 257 Biography: 212 Black-body radiation: 30 Bohr: 32, 33, 35, 133, 134, 195, 286, 360 Bolyai: 20, 103 Born: 42, 343 Boscovitch: 13 Bradley: 387 Brain: 382 Braithwaite: 167 Broad: 197, 259, 260, 286 Camera: 209, 265 Cantor, Georg: 14 Cantorian continuum: 58, 279 Cartesianism: 160 Category: 238, 243 Causal ancestor: 314 „ chain: 285, 314, 320, 371 „ laws: 107, 121, 168, 191, 200, 214, 245, 285, 340, 355, 366, 381 „ „ extrinsic: 324 „ lines: 313, 401 „ relation: 367 „ route: 379 „ unit: 315 Causality: 313, 367, 381, 398, 399 Causation: 108, 383 „ at a distance: 214 Cause: 150, 159 Cause-and-effect: 346 Change: 281, 362 Chuang-Tze: 180 Clarke: 14 Classes: 116, 387 Collinear: 306 Collinearity: 308 Colour: 288 Colour-similarity: 288 Colours: 253 Common sense: 141, 156 Comparison: 278 Compresent: 294, 336, 349, 356, 372, 374, 376, 378, 383, 385 Conjunctions: 242 Constants: 172, 251 Continuity: 24, 71, 168, 214, 217, 231, 279, 322, 362 „ perceptual: 280 „ qualitative: 81 Continuous, space-time is: 42, 311 Continuum: 401 „ mathematical: 280 Contravariant: 65 Co-ordinates: 56, 57, 60, 63, 71, [Pg 404]110, 334, 337, 397 Co-punctual: 307, 314, 321, 373, 401 „ events: 315 Co-punctuality: 299, 376, 386 Co-regional: 311 Correlation: 188, 204, 205 Correspondence: 239 Co-superficial: 311 Co-variant: 65 „ derivative: 96 Curve of pursuit: 101 Data: 141, 187, 189 De Broglie: 46 Debye: 32 Descartes: 6, 9, 19, 71, 156, 160, 205 Determinism: 390 „ physical: 214 Dictaphone: 209, 265, 400 Differential equations: 231 „ law: 245 „ „ intrinsic: 323 Diffraction: 395 Dimensions: 312, 341 Dirac: 42, 43 Discontinuity: 24, 395 Distance: 166, 303, 350 Diversity: 386 Doppler effect: 165 Dreams: 205, 222 Eddington: 57, 64, 75, 78, 82, 84, 91, 96, 97, 103, 106, 110, 117, 122, 129, 131, 136, 168, 341, 377, 395 Einstein: 13, 32, 42, 52, 75, 77, 129, 161, 187, 233, 323, 395 Electromagnetism: 328 Electrons: 9, 24, 80, 90, 135, 153, 168, 234, 244, 276, 287, 319, 320, 325, 347, 386, 394 Ellis: 123, 125, 126 Emergent: 286 Empirical: 141, 176 Empiricists: 169 Enclosure-series: 291 Energy: 84, 122, 234, 318, 345, 360, 362, 394, 401 „ kinetic: 123 „ radiant: 365 Entities, unperceived: 191, 206 „ unperceivable: 216 Epistemology: 179 Error: 183, 184, 186 Euclid: 61, 70, 71, 103 Euclid's first axiom: 94, 99 Euler's diagrams: 387 Events: 9, 243, 247, 275, 284, 286, 345, 356, 377, 384 Events: group of: 244 „ luminous: 352, 333, 354, 369, 371, 373 „ maximum: 293 „ minimum: 292 „ persistent: 347 „ steady: 355, 356, 363, 368, 402 Evidence, empirical: 6 Existents, unperceived: 213, 226 Expectations: 181, 182, 183, 189 Experience: 173 Facts: 239 Fallacy of simple location: 340 Faraday: 20 Fijians: 102 FitzGerald contraction: 50, 100 Force: 18, 19, 76, 161 Form: 172 Foucault's pendulum: 358 Fowler: 33, 42 Franck: 38 Freewill: 38 Frege: 4, 242 Frequency: 357, 364 Galileo: 6, 13, 101, 161, 395 Gauge-system: 97, 98 Gauss: 58, 59, 113 Geodesics: 55, 62, 69, 72, 313, 327, 371, 372, 379, 396 Geometry: 2, 3, 21, 102, 117, 174, 227 „ abstract: 76 „ affine: 98 „ descriptive: 210 „ Euclidean, 77 „ natural: 76 „ non-Euclidean: 20, 59, 396 „ projective: 103, 109 Gestalt-psychologie: 345 Gramophone: 205, 249 Gravitation: 17, 52, 60, 74, 77, 85, 89, 163, 176, 187, 324, 326, 371 Group, ideal: 212 : 30, 33, 45, 317, 330, 341, 343, 360, 364, 365, 368, 394 Habit: 184, 191 Haldane, J. B.: 233 Hallucinations: 222 Hand-eye co-ordination: 143, 147 185 Hausdorff: 296, 297, 303, 312 Hearing: 316 Hegel: 55, 199 Heisenberg: 24, 27, 42, 43, 45, 246, 283, 321, 322, 326, 332, 343, 338, [Pg 405]360, 361 Helium: 24, 26 Helmholtz: 138 Heraclitus: 62, 176 Hertz: 19, 20, 22 Holt: 10 Hume: 159, 190, 398 Hydrogen: 25 „ spectrum: 32 Hypothesis: 194 Idealism: 7, 28, 215, 382, 387, 388 Idealists: 215 Impenetrable: 385 Implication, strict: 199 Indestructible: 385 Indistinguishability: 282 Individuals: 387 Induction: 153, 154, 167, 175, 194, 230, 233, 398 „ mathematical: 71 Inference: 150, 187, 190 „ physiological: 150, 190 Infinite divisibility: 279 Infinitesimals: 104, 107 Instants: 294 Integers, finite: 3 Interference: 352, 395 Interpenetration, logical: 386 „ spatio-temporal: 386 Interpretation: 4, 88, 137, 141, 188, 225, 288 Interval: 51, 58, 69, 70, 88, 110, 117, 129, 314, 327, 330, 354, 367, 377, 396, 397, 402 „ discontinuous: 367 „ time-like; space-like: 51 Introspection: 173 Invariants: 82, 84 Jeans: 31, 32, 123, 129, 341, 381, 386 Jeremiah: 240 Johnson, Dr.: 136 Jordan, P.: 38, 42, 343 Kant: 14, 20, 55, 78, 157, 159, 160, 169, 171, 174, 175, 279 Keynes: 167, 233, 399 Kinematics: 361 King, L. V.: 47, 129 Kirchoff: 19 Knowledge: 174, 178 „ subjective factor in: 334 Köhler: 148 Kropotkin: 74 Language: 152, 239 Laws, causal: 101 Laws: differential: 101 „ general: 229 „ of contradiction: 171 „ of motion, first: 323 „ simple: 232, 236 „ scientific: 388 „ statistical: 231, 235, 236 Learned reactions: 154 Leibniz: 8, 14, 17, 18, 156, 157, 160, 200, 238, 328 Leonardo: 161 Lewis, G. I.: 199 „ G. N.: 125, 126, 134, 164 Light: 123, 131, 132, 155, 163, 216, 235, 244, 267, 276, 314, 317, 328, 339, 345, 351, 364, 369, 373, 395 „ frequency of: 353 Light-quantum: 124, 268, 316, 318, 395, 401 Light-ray: 70 Limit: 309 Limitation of variety: 233 Limits: 71, 117 Line: 306 „ spectra: 32 „ "straight": 61 Lobatchevsky: 20, 103 Location: 258, 320 Locke: 132, 159, 257, 339 Logic: 2, 9, 171, 239, 247, 250, 387 „ mathematical: 2, 9, 71, 107, 138, 350 „ traditional: 387 Logical property: 251 „ symbols: 289 Lorentz: 124 „ transformation: 49, 54 Mach: 15, 19 Mass: 53, 86, 122, 163, 284, 318, 386 „ gravitational: 341 „ invariant: 122 „ relative: 122 Material energy-tensor: 86 Materialism: 7, 162, 383, 387, 388 Materialists: 215 Mathematics: 174, 176 „ applied: 5 Matrices: 44, 46 Matter: 131, 134, 156, 160, 182, 192, 215, 243, 321, 324, 355, 372, 379, 384, 392, 401 „ atomicity of: 30 „ indestructibility of: 168 „ unperceived: 232 Matters of fact: 176, 178[Pg 406] Maxwell, Clerk: 15, 20, 22 Maxwell's equations: 49, 54, 97, 121, 258, 359 Meaning: 240, 243 Measurement: 90, 97, 99, 107, 109, 337, 377, 397 Memory: 186, 266, 267, 389 Mendelians: 233 Menger, Karl: 312 Mental states: 320, 322 Mercury: 40 Metre: 91 Mill, J. S.: 21, 101, 171 Mind: 156, 160, 192, 336, 382, 387 Minkowski: 15, 135, 395 Mnemic phenomena: 265, 315 Modality: 169 Momentum: 36, 84, 86, 156, 162 Monad: 157 Moore, G. E.: 210 Motion: 244, 246, 278, 317, 326, 355 „ absolute: 356, 358 „ continuous: 380 „ percept of: 279 „ periodic: 344, 348 „ relative: 359, 378 Motor habits: 148 Muscular physics: 160 Naive realism: 155, 218, 262, 398 Names: 152 Napoleon: 186 Necessary and contingent propositions: 169 Neighbourhoods: 295 ff., 303, 312 Neutral monism: 382 „ stuff: 10 Newman, M. H. A.: 290 Newton: 13, 18, 161, 356, 358, 395 Nicod: 167 Nisbet: 167 Nucleus: 347 Numbers: 4 „ ordinal: 250 „ real: 290 Object: 142, 181, 182, 186, 204, 207, 218