Mach’s Philosophy of Science 9781472556561, 9781472511010

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Preface

My interest in Mach arose out of a lecture on the lever given to freshmen at Cambridge in 1927 by the late Alexander Wood. He advised his students to read Mach, and I have been doing so ever since. This book is confined to one aspect of Mach's work, his occasional comments on the philosophy of physical science. These comments amount to a fairly complete elementary introduction to the philosophy of science, although Mach failed to include any discussion of questions of probability. Mach takes a rioh sensuous experience as the basis of science; to him theoretical systematisation is secondary. I believe that Mach's assessment of science is an important one. The beginner may find the book a useful introduction. Mach wrote three admirable textbooks. I n the course of this account of Mach's philosophy, I have found it necessary to set out the foundations of dynamics and thermodynamics in Mach's own style. These summaries could be useful to the young student of physics. If they direct the more mature reader to Maoh's texts, they will have been worth while. There is no Mach Principle in the writings of Mach. Indeed, the so-called principle was not formulated until some years after Mach's death in 1916. Here I have traced out the evolution of this affair in a simple factual manner. This may be of some interest to physicists and philosophers. The most important part of the book, in my view, is the classification of metrical concepts according to their relative 'closeness to' and 'remoteness from' sense-perception. This is Mach's own idea, but I have extended it somewhat. Professor H. Dingle has been a constant inspiration and guide since about 1950. It is a pleasure to acknowledge the debt I

Sense-perceptions

1 . Descartes and Mach

Descartes' first principle is man's duty to doubt everything that can be doubted, before the principles of philosophy are established. It is necessary for a man t o pass beyond this condition of doubt, but i t is also necessary for him t o pass through it.l This a t any rate, thought Mach, is an admirable start: The maxim of doubting cverytlrirlg that has hitherto passcd for establislled truth cannot bc rated too high; although i t was more observed and exploited by his followers than by himself." After a remarkable alialytical discussion, thc details of which need not concern us here, Descartes is left with two orders of substance, extended substance and thinking substance, which he regards as distinct and separate., and concerning the being of which he can entertain no doubt. Mach, who refers t o himself as a monist,3 rejects this Cartesian dualism, although it is certainly not evidently true that body or extended substance is ideiztioal wit11 mind or thinking substance. Followiilg G a l i l e ~ Descartes ,~ considers that extended substance bears two main kinds of quality, the so-called primary and secondary qualities. Thc primary qualities are objective, they are out there in nature. I n Descartes' form of the doctrine of qualities, the primary ones are exclusively mathematical and R. Descartes, Descc~rtesSelectior~s,etl. R. M . Saton, Ncw York: 1027, p. 1%. M., p. 362. A., p. 14. A. N. Whitehead, h'ssays in Science und Philosophy, London: 1948, pp. 1734.

Metrical concepts

1 . The ordinal test Although all the metrical concepts of physical scienoo draw their power from sensuous sources, the character of the relationship between sense-perception and concept may vary radically. This is the plain meaning of Mach's distinction between 'force' which is a matter of fact (eilze Tatsache), and 'quantity of electricity' which is "a supplement to this fact" (cine Zutat). It is possible to develop this distinction of Mach,l and in the present work I have attempted to derive from it a classification of the metrical concepts. Let us take as initial examples the five metrical concepts: force, temperature, mass, heat and quantity of electricity. Specific values of these typcs of quantity are derived from experiments which may include measurements and calculations. There is however a certain difference in tho relationship between these concepts and the experience, some of it qualitative, which gives rise to them. 'Behind' the metrical concepts of 'force' and 'temperature' there lies a group of simple acts of sense-perception, which can, under favourable circumstances and within a rather narrow range of experience, be ordered by the percipient according to felt intensity, in an order which tallies with the metrical values subsequently reached by operations and measurements. The use of 'felt' as an alternative to 'sense-perceived' is found in H ~ m e . ~ This notion of ordinal correspondence is best understood by two simple examples. Suppose there are three baskets of J . Bradley, T h e Ordering of the Concepts of Classical Physics and Chemistry, M.Sc. Dissertation, University of London, 1951, pp. 71-85. a D. Hume, Hume's Enquiries, p. 62.

Mach and dynamics

1 . Introduction Mach's account of the dynamics of Newton sharply focuses his teaching on the two main kinds of metrical concept; for 'force' -which 'sets mechanics off' as Bridgman would put it-is a n '0' concept, whereas 'mass' is a 'non-0' concept quite remote from sensuous experience. The Mechanics is a t once critical and historical; the first phase of Mach's criticism of mechanical theory is within the classical tradition of Newton, but the second phase goes beyond this tradition and approaches-so Einstein judged-relativity physics. These two phases correspond roughly to this chapter and its successor. The discussion of these themes will enable us to extend the treatment of the concept of temperature, and to follow Mach in his critical account of the conservation of energy.

2. The concept of force: the foundations laid by Galileo The sciences of statics and dynamics as they developed in history ". . . contain a double mode of interpretation of 'force' : on the one hand force as a push or pull, on the other hand force as a circumstance determinative of a~celeration."~ The position is logically equivalent to having two concepts of force, which u priori should not be judged to be identical (Bridgman). These two concepts require reconciliation. One example of this reconciliation has been given in connection with the discussion of Hoolre's theory of 'return'. No contradiction arises from assuming that one force on the lump of lead may be judSed statically from the extension of a spiral spring, E., p. 174.

6 The Mach Principle

1 . The relativity of physical knowledge There is no Mach Principle in Mach's writings. His general point of view leads him to recur to the evident relativity of measurement; if I say that the coffee table is 3 feet in length, I can only mean that the foot ruler will fit into the length of the table three times. As physical science is based on measurement -although i t is not true that 'science is measurement'-our physical knowledge must be in some degree 'relative', for the basis of it is acknowledged to be 'relative'. I n the simple example of the length of the coffee table, another wooden object, the foot ruler, 'enters' as i t were into the measured length. According to Mach, the mass of a body is conditioned in exactly the same way, but with additional complications. The mass of the body can only be found by letting i t react with another mass, observing accelerations and then making a calculation. This leads Mach to the idea of mass as a relation; he belittles the notion of the localised mass, that "obscure mysterious lump" which "we seek for in vain outside the mind".l Nevertheless, the notion of the localised mass is of some importance as I have indicated in the previous chapter. Physical time has the same kind of ineradicable relativity. What does g mean ? Simply that when the earth has performed 11864 000 part of its revolution, a body has fallen from rest through a height of 112 g metres towards the earth's centre. Instead of referring events to the earth we may refer them to a clock, . . . Now, because all are connected, and each may be made the measure of the rest, the illusion easily arises that time has significance independently of P., p. 203.

P., pp. 204, 205.

7 The intellectual science element 1. Introduction The intellectual element in science is not something added on after an experiment. Newton's hypotheses nonJingo expresses an important truth, but it would be an absurd error if it were taken to mean that any part of the process of science can take place without the action of the human mind. Before Galileo can begin his investigation on falling bodies, his mind is informed by preconceived opinions or prejudices. Were this not so he would have neither motive to experiment at all nor chance of success : Without some preconceived opinion the experiment is impossible, because its form is determined by the opinion. For how and on what could we experiment if we did not previously have some suspicion of what we were about? . . . The experiment confirms, modifies, or overthrows our suspici0n.l This affirmation by Mach is the more striking because the technical term 'hypothesis' and the philosophical jargon 'hypothetico-deductive method' are avoided. Mach considers it important to trace the metrical concepts of physical science back to sense-perception. The line back may be short (from force, temperature) or long (from energy, entropy) but it is always a line of thought. At the same time, he is aware that the sense-perception by itself requires intellectual interpretation. The mere succession of images on the retina does not enable Galileo to perceive a falling stone. The psychological equation for the simplest experience is this : sensation

+ mind = sense-percepti~n.~

Er~is t Mach: a biographical note'

Ernst Mach was born on 18 February 1838, in Turas, Moravia. His father, Johann Mach, was a teacher, and later a smallholder. His mother, unworldly like her husband, was interested in music and art. I n the main, Ernst was educated a t home by his father. At the age of 15 he entered the grammar school a t Kremsier, Moravia. Two years later, he proceeded to the University of Vienna where he read mathematics and physics. As Privat-Dozent, he taught physics from 1861 to 1864. I n 1864, Mach was called to the chair of mathematics in the University of Graz, Austria. The chair of physics was addcd later. Important papers on the psychology of sense-perceptions began t o appear about this time. Mach's very extensive investigations on this subject are held in high estccm by psychologists, and they constitute the point of departure in his philosophy of physics. Mach became professor of physics a t the German university of Prague in 1867, which was also the year of his marriage t o Ludovica Marrusig. Also in 1867, appeared his important paper O n the D~jinitionof Mass in Carls Rcpertorium. This was reproduced and amplified in the monograph on TTL~ Conservation of Energy (1872). Mach's textbook of mechanics, treatcd as a branch of physics, was published in 1883. It is his best and most important work. His experimental work on the photography of sound waves began in 1884. Mach is known to many through the modern 1 H. Henning: Ernst Mach als Philosoph, Pl~ysikerund Psycholog, Leipzig: 1915, pp. 1-8, pp. xi-xviii. H. Dingler, Die Grundgedanken der Macl~schen Philosophie, Loipzig: 1924, pp. 8-16. F. Ratliff, Mach Bands, San Francisco: 1965, pp. 8-20. K. D. Heller, Ernst Mach, Wien: 1964, pp. 1-22, pp. 96-8, pp. 133-43.

Index of names

More important references are italicised Alexander, P., 213-15 Aliotta, A., 13 Amagat, E. H., 35 Amontons, G., 34 ilnaxirnander, 6 Archimedes, 74, 119-30 Aristotle, 70, 101, 108, 112, 187, 211 Avenarius, It., 2 12 Bergson, II., 149 Berkeley, G., 3-8, 16, 40, 51, 54, 149-58 Black, J., 32, 54, 59-62, 131, 138, 141, 171 Roltzmann, L., 201 Bondi, H., 159-65 Born, M., 201 Boscovich, R. J., 7 Boutroux, E., 48, 115 Boyle, R., 35, 73, 189, 201 Brahe, T., 209 Braithwaite, R. B., 181, 212 Bridgman, P. W., 28, 40, 49, 79, 98, 118, 158-62, 202 Burniston Brown, G., 117-19, 166 Campbell, N. R., 166, 212 C'arnap, IL., 177 Carnot, S., 62, 70, 86, 113, 131-5, 186, 193 Celsius, A., 27, 171 Charles, J . A. C., 35 Clapeyron, E., 138 Clausius, R., 62, 113, 135, 174 Clerk Maxwell, J., 201

Comte, A., 204 Copernicus, N., 101 Coulomb, C. A., 18-21, 55, 173 Coxeter, 13. S. M., 80 D'lllembert, M., 129 Dalton, J., 39 Darwin, C., 206 da Vinci, L., 125 Dawes Hicks, G., 17-18, 24 delle Colombe, L., 101 Democritus, 56, 139, 200 Descartes, H., 1-3, 10, 17, 71, 75, 100, 162, 214 Dingle, lI., 158, 190 Ilulong, I?. L., 35 Eddington, A. S., 87, 151-5, 165 Einstein, A., 40, 157-68, 206, 218 Euclid, 45, 69-73, 79-82, 185-6 Paraday, M., 20, 185 Fourier, J. B. J., 192 Prank, P. G . , 158 Galilei, G., 1, 70, 98-102, 115, 125, 132, 155, 161, 174-6, 183, 211 Gauss, C . P., 80, 118, 124, 130 Gay-Lussac, J. I,., 35 Hahn, O . , 113 Hempel, C. G., 17 Heraclitus, 8 Hirn, G. A., 133 IIooke, R., 14-16, 105, 171, 18990, 209

Index of subjects

&lore inzportnnt

references are italicised

Abstraction, 100 Acceleration, 08, 105, 213 absolute, 161, 165 quotient, 114 relative, 151, 163 Action a t a distance, 168 A d a p t,I.t'1011, ideas/facts, 170 ideeslidcas, 170 Alternative concepts, 170-6 cold/heat, 171-2 electricity, 172-1 forcelenergy, 1744 Analogies, first kind, 101-7 heat/elcctricty, 191, 105- 7 heatlWater, 191, 103-5 hrigl~t/temperature,60, 132 mathematics/pflysics, 73, 186 Ohm's law, 191 pendulum/weight, 190 -1 srcond kind, 197-20 1 timr/tcmperet~~re, 87-9 Analogy, 100, 114, 182 Analytic functioning of laws, 18890 Analytic judgements, 44 12nnihil;~tionof mass, 113 iintl-lropomorphism, I2 Aphorisms, 52-3 Kant, 50, 52-3 Mach, 52-3 Arbitrariness of scales, 37 Area, 68 Arithmetic, 46, 75 Asymmetr~icmolecules, '72

Asymmetry, beat/work, 136 Atoms, 3, 5, 13, 139-40, 197-204 Biograplly of Mach, 217-18 Biology, 170, 206 Body, see Substance Calculus, 102, 132 Categories, see Verstandesbegriffe Causality, 42-4, 48-50, 115-17, 138, 143, 176, 181 Central force, scr b'orce ('entre of gravity, 125 Centre of mass, 125, 157 Chernical change, 49, 57, 113, 203-4 Chemical compound, 180 ('hemica1 equation, 49, 59, 200, 20 t Clocks, 85, 87, 89-91, 91-6, 97 Collision between balls, 42-4, 160I, 186 Common object (table), 7, 12, 40, 199 Commlmication, 207, 213-14 Comparative physics, 170, 193, 209 ('ompletion of experience. 10-12 Cornpound pendulum, 128 c7oncepts, 14, 17, 22-9, 40-1, 188, 216 Conceptualsystem, 184,200-3,210 Conservatioii of electricity, 174 energy, 2, 49, 128 energy-comprehensive, 131-3