ANNALS OF SCIENCE, Vol. 63, No. 4, October 2006, 471 481
Edward Milne’s Influence on Modern Cosmology
THOMAS LEPELTIER Christ Church, University of Oxford, Oxford OX1 1DP, UK
Received 25 October 2005. Revised paper accepted 23 March 2006
Summary During the 1930 and 1940s, the small world of cosmologists was buzzing with philosophical and methodological questions. The debate was stirred by Edward Milne’s cosmological model, which was deduced from general principles that had no link with observation. Milne’s approach was to have an important impact on the development of modern cosmology. But this article shows that it is an exaggeration to intimate, as some authors have done recently, that Milne’s rationalism went on to infiltrate the discipline.
Contents 1. Introduction...... 471 2. Methodological and philosophical questions ...... 473 3. The outcome of the debate ...... 476
1. Introduction In a series of articles, Niall Shanks, John Urani, and above all George Gale1 have analysed the debate stirred by Edward Milne’s cosmological model.2 Milne was a physicist we can define, at a philosophical level, as an ‘operationalist’, a ‘rationalist’ and a ‘hypothetico-deductivist’.3 The first term means that Milne considered only the observable entities of a theory to be real; this led him to reject the notions of curved space or space in expansion. The second term means that Milne tried to construct a
1 When we mention these authors without speaking of one in particular, we will use the expression ‘Gale and co.’ 2 George Gale, ‘Rationalist Programmes in Early Modern Cosmology’, The Astronomy Quarterly,8 (1991), 193 218. George Gale, ‘Philosophical Aspects of the Origin of Modern Cosmology’ in Encyclopedia of Cosmology, edited by Norris S. Herherington (London, 1993), 481 495. George Gale and John Urani, ‘Philosophical midwifery and the birthpangs of modern cosmology’, American Journal of Physcis, 61 (1993), 66 73. John Urani and George Gale, ‘E. A. Milne and the Origins of Modern Cosmology: An Essential Presence’, in The Attraction of Gravitation: New Studies in the History of General Relativity (Einstein Studies, vol. 5), edited by John Earman, Michel Janssen and John D. Norton (Boston, 1993), 390 419. George Gale and Niall Shanks, ‘Methodology and the Birth of Modern Cosmological Inquiry’, Studies in History and Philosophy of Modern Physics, 27 (1996), 279 296. George Gale and John Urani, ‘Milne, Bondi and the ‘Second Way’ to Cosmology’, in The Expanding Worlds of General Relativity (Einstein Studies, vol. 7), edited by H. Goenner, J. Renn, J. Ritter and T. Sauer (Boston, 1999), 343 375. George Gale, 2002, ‘Cosmology: Methodological Debates in the 1930s and 1940s’, in The Stanford Encyclopedia of Philosophy (Summer 2002 Edition), edited by Edward N. Zalta (http://plato.stanford.edu/ archives/sum2002/entries/cosmology-30s/), 2002), 1 18. 3 See, in particular, George Gale and John Urani, 1993 (note 2).
Annals of Science ISSN 0003-3790 print/ISSN 1464-505X online # 2006 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/00033790600718578 472 Thomas Lepeltier physics that was not reliant on observation, thus countering the empirical conception in which scientific knowledge begins with observation. Finally, the third term characterized the fact that Milne tried to deduce the laws of physics from general principles in the hope that they would concord with observation. It is from these philosophical and methodological positions that from 1932 onwards, Milne developed a cosmological model to rival the relativistic models.4 While cosmologists had so far applied the laws of physics to the largest object, the Universe, Milne developed a cosmological theory ignoring these laws and relying on a priori hypotheses about the Universe. To put it differently, while the other cosmologists extrapolated the laws of physics to the Universe, Milne deduced these laws from general principles concerning the Universe. This alternative model*which was to inspire Hermann Bondi and Thomas Gold in 1948 in their invention of the steady- state theory5 *did not go unnoticed. It was startling to see a cosmological model, independent of the general theory of relativity, capable of accounting for astronom- ical observations, in particular for the apparent recession of galaxies. However, some researchers judged that Milne’s approach went against scientific method. Milne thus found himself in the middle of an epistemological debate that created a stir in the small world of cosmologists, and even beyond. Because of his atypical position and the extent of his work*Milne sought to reorganize not just cosmology but the whole of physics*his research programme could, according to some commentators, have triggered a scientific revolution if it had been more successful.6 It was not to be the case: Milne’s cosmology had no posterity after his death. This failure does not mean that Milne has not had an influence on modern cosmology. Indeed, as Gale and co. have shown,7 the Robertson Walker metric was developed according to the operational methodology that Milne advocated. However, these authors go further and intimate that Milne played an essential role in the development of modern cosmology and that his rationalism has infiltrated the discipline. For example, they assert that ‘the establishment of the Robertson Walker metric [...], without Milne’s outspoken commitment to a minority philosophical view (i.e. operationalism), would never have come about’.8 Similarly, they claim that the debates sparked by Milne’s work have led to the following outcomes: (1) ‘a pruning of the existential extravagances of ‘‘curved space’’, ‘‘expanding space’’, and [...] conceptual excesses of all sorts, had been accomplished’, as Milne wanted; (2) ‘the hypothetico-deductive methodology [advocated by Milne] had been legitimated’; (3) ‘the rationalist position [of Milne] had been so well grounded that it was available for specific and explicit use by Bondi at the end of the next decade’.9 Calling the approach developed by relativistic models the ‘First Way’, they also write that in ‘the end Milne’s Second Way won legitimacy’.10
4 Edward Arthur Milne, ‘World Structure and the Expansion of the Universe’, Nature, 130 (1932), 9 10. 5 Hermann Bondi and Thomas Gold, ‘The Steady-State Theory of the Expanding Universe’, Monthly Notices of the Royal Astronomical Society, 108 (1948), 252 270. 6 Allen J. Harder, ‘E. A. Milne, Scientific Revolutions and the Growth of Knowledge’, Annals of Science, 31 (1974), 351 363. 7 In particular, in John Urani and George Gale (note 2). 8 George Gale, 1993 (note 2), 492. 9 George Gale and John Urani, 1993 (note 2), 72. 10 George Gale and Niall Shanks (note 2), 291. Edward Milne’s influence on modern cosmology 473
Milne was without doubt a brilliant astrophysicist, and his cosmological model, at the time it was invented, was recognized as original and sophisticated. Having fallen into oblivion since, its rehabilitation by Gale and co. is welcome. However, as the quotations above show, these authors describe Milne as the victorious champion of the hypothetico-deductive method and of rationalism in physics. This conclusion is exaggerated and leads to confusion. The hypothetico-deductive method is now an integral part of cosmology, but Milne does not seem to bear any responsibility for it. As for his rationalism, it is far from having entered the discipline. The misunder- standing comes, in our opinion, from the fact that the difference between these two methodological positions has not been clearly established. Some physicists can recognize the merits of the hypothetico-deductive method, without necessarily being rationalist or, at least, without adopting physical models that have no link with observation. That is what this article intends to show by going back over the debates sparked by Milne’s approach to cosmology.
2. Methodological and philosophical questions Milne saw his cosmological model as utterly deductive and as deeply different from relativistic cosmology. As he says, there are: two separate ways of attacking the structure of the universe: the one to make use of every available piece of empirical knowledge known to be valid on the small scale; the other to begin with the situation actually presented to us by the totality of things without supposing ourselves to know anything.11 It is this second way that he had chosen, i.e. while relativistic cosmology extrapolated empirical knowledge locally established to devise the structure of the whole, Milne tried to deduce local physics from what he claimed were the inherent principles of that whole. As soon as 1933 (after the first long presentation of his theory12), this approach was sharply criticized by Herbert Dingle.13 The latter thought that ‘its fundamental viewpoint is inconsistent with the general principle of scientific thought’.14 For Dingle, the core of the problem was Milne’s aim to deduce his model from the cosmological principle, which he was still calling ‘the extended principle of relativity’. Dingle argued that this principle is only acceptable if it is interpreted as a hypothesis about the homogeneity of the Universe, that is a revisable hypothesis that depends on observation and not as an axiom.15 For Dingle, scientific method consists in starting from observation and not from a priori hypotheses. All science, the theory of relativity included, is constructed in this way: ‘The spirit of relativity is simply a re-affirmation of Newton’s principle of induction from phenomena. Its fruits*the principle of relativity itself*are the product of countless experiments and observations’.16 In contrast, ‘Milne approaches the problems of physics in precisely the opposite way. He starts, not with phenomena, but with a
11 Edward Arthur Milne, ‘Cosmological Theories’, The Astrophysical Journal, 91 (1940), 129 158, 133. 12 Edward Arthur Milne, ‘World-Structure and the Expansion of the Universe’, Zeitschrift fu¨ r Astrophysik, 6 (1933), 1 95. 13 Herbert Dingle, ‘On E. A. Milne’s Theory of World Structure and the Expansion of the Universe’, Zeitschrift fu¨ r Astrophysik, 6 (1933), 167 179. 14 Herbert Dingle (note 13), 167. 15 Herbert Dingle (note 13), 179. 16 Herbert Dingle (note 13), 178. 474 Thomas Lepeltier hypothetical smoothed-out universe which must obey an arbitrary principle’.17 Dingle’s conclusion is unambiguous: ‘the general course of Milne’s theory is at variance with the fundamental principles of scientific method’.18 Dingle’s opposition did not weaken in the following years. It reached a peak in an article whose title ‘Modern Aristotelianism’ underlined its approach.19 Dingle attacked not only Milne but also Paul Dirac and Arthur Eddington for not respecting ‘the fundamental principles of scientific method’. In their works on cosmology, Dirac and Eddington had adopted an approach that resembled Milne’s, in trying to develop physical theories from general considerations. As Milne had said: ‘It is [...] possible to derive the laws of dynamics rationally [...] without recourse to experience’.20 For Dingle, this sentence symbolized the three researchers’ approach to such an extent that he quoted it at the beginning of his article. For him, science had to rely on observation and not on free invention: ‘the first step in the study of Nature should be sense observation, no general principles being admitted which are not derived by induction therefrom’.21 Dingle justified his analysis by the supposed opposition between Aristotle and Galileo’s methods: To the Aristotelian the human mind had super-sensory knowledge of the principles which Nature obeyed, or alternatively reason could, apart from sense, dictate the course of experience; to Galileo, Nature was independent, and the mind could watch and try to describe in general terms her processes, or alternatively reason could seek to correlate sense observations into a logical system.22 To go back to Aristotle was for Dingle a crime against the principles of the scientific method supposedly defined since Galileo. This explains the offensive style Dingle adopted against those he called scourges of science. For example, he called their method a ‘pseudoscience of invertebrate cosmythology’, or a ‘skin disease’, while they were ‘traitors’, guilty of ‘something so rotten’ that it put the whole scientific enterprise in danger.23 This attack sparked such reactions from the scientific community that, a few weeks later, the journal Nature published a supplement entirely devoted to the issue.24 Milne, Dingle’s principal target, opened it.25 Dingle, the instigator of the controversy, closed it.26 Of the fourteen participants in the debate, a majority took a stance against Dingle. Different kinds of argument were used in what was a highly animated debate. For example, William McCrea tried to show that Dingle had made the very mistake he was denouncing:
17 Herbert Dingle (note 13), 178. 18 Herbert Dingle (note 13), 179. 19 Herbert Dingle, ‘Modern Aristotelianism’, Nature, 139 (1937a), 784 786. 20 Edward Arthur Milne, ‘Kinematics, Dynamics, and the Scale of Time’, Proceedings of the Royal Society of London, A, 158 (1937a), 329. 21 Herbert Dingle (note 19), 784. 22 Herbert Dingle (note 19), 784. 23 Herbert Dingle (note 19), 786. 24 Arthur Stanley Eddington et al., ‘Physical Science and Philosophy’, Nature, 139 (1937), 1000 1010. 25 Edward Arthur Milne, ‘On the Origin of Laws of Nature’, Nature, 139 (1937b), 997 999. 26 Herbert Dingle, ‘Deductive and Inductive Methods in Science: A Reply’, Nature, 139 (1937b), 1011 1012. Edward Milne’s influence on modern cosmology 475
Dingle’s objection to ‘modern Aristotelianism’ seems to be itself what he would call Aristotelian rather than Galilean. For a truly Galilean point of view would be to observe whether Eddington, or Milne, or anyone else, can in fact deduce properties of the physical world [from a priori arguments]. Should it turn out that such a deduction is possible, the fact would be a new and exceedingly important experimental result, throwing fresh light upon the relation of the ‘physical world’ to the human mind, and worthy of the attention of all true Galileans.27 The reference to Aristotle was not to be to everyone’s liking. For some participants in the debate, Aristotle was not the rationalist that Dingle supposed and, therefore, the opposition between Galileans and Aristotelians was not as clear-cut as he meant. Nevertheless, this problem was secondary for Dingle. As he wrote in his contribution to the debate, if he has chosen to call the physicists he criticized ‘Aristotelians’, it is ‘because they have revived the fallacy maintained by those whom Galileo and Newton called Aristotelians’28 and not a reference to Aristotle’s real philosophy. To avoid any ambiguity, he agreed to put Aristotle’s name ‘in quotation marks’ henceforth.29 But the question of whether Milne’s approach was in agreement with the evolution of science was more fundamental than a mere debate about terminology of this kind. Gerald Whitrow, Norman Cambell, and William McCrea put it at the core of their argument. In particular, McCrea began by observing that the value of a theory is judged on one hand by the fewness and simplicity of its hypotheses, and on the other by the closeness of the agreement of its predictions with the results of observation, and also the number of phenomena which it can so predict from the one set of hypotheses.30 For this reason, he asserted that it was up to the theories to reduce the number of their hypotheses and that this attitude corresponded to the historical development of physics. Admitting that Milne’s theory ‘is still too new for a consensus of scientific opinion to have been expressed’, he thought that it was ‘in harmony with the historic evolution of mathematical physics’.31 This intervention shows clearly that the hypothetico-deductive dimension of Milne’s theory was recognized as legitimate. McCrea even considers that scientific theories tend to rely on a smaller and smaller number of axioms and that, in this sense, Milne’s theory fits very well into the progress of science. However, McCrea did not consider the problem of the origins of hypotheses that was the crucial point of Dingle’s critics. Indeed, Dingle did not criticize the reduction in the number of hypotheses in a theory. He only required that these hypotheses come from observation. Why? Because otherwise one cannot be sure the theory is not a free construction of the mind, even when the theory’s deductions are in agreement with observations. Two participants in this debate, W. Peddie and L. Filon, tackled this problem of the origins of hypotheses by
27 Arthur Stanley Eddington et al. (note 24), 1002. 28 Herbert Dingle (note 26), 1011. 29 Herbert Dingle (note 26), 1011. 30 Arthur Stanley Eddington et al. (note 24), 1002. 31 Arthur Stanley Eddington et al. (note 24), 1003. 476 Thomas Lepeltier criticizing researchers who start from a mathematical intuition instead of observation on the ground that, as the second writes, what they ‘are really doing is not to explain Nature, but to explore the possibilities of the human mind’.32 Nevertheless, there was only one participant to the debate to conjointly tackle both problems: on the one hand the origins of hypotheses and on the other the confrontation between what was deduced from these hypotheses and observation. The mathematician Harold Jeffreys started by recalling that the value of a deduction relies on the value of the premises, and in experimental sciences the latter can only be obtained by induction. Besides, as he says on a sarcastic note, ‘without using induction, Milne and Eddington could not order their lives for a day’.33 Following his argument, Jeffreys observed that even when it seems fruitful to deduce laws of physics from general hypotheses, it is necessary to resort to some verifications using inductive processes to validate the latter. To give some weight to his argument, Jeffreys took an example in which he had himself just played a part. Considering that the general theory of relativity arose from a rationalist approach*Milne did not agree with this, but that is not important here*Jeffreys recalled that the mere observation of the bending of light near the Sun as it had been foreseen by Einstein could not be seen as making the success of such an approach. Indeed, Jeffreys recalled that he had himself looked for an alternative explanation and had reached the conclusion that the one proposed by the general theory of relativity was the most likely. For him, this last information was necessary to validate the general theory of relativity: without it, the fact that the deduction of the general theory of relativity agreed with observation was not sufficient to warrant the pertinence of this theory, because nothing says whether another theory would not ensure a better agreement. This was, according to him, something the rationalists had not understood. It could also explain why they never mention his own work, because it would lead them to accept ‘that the postulates of the theory are not a priori certain’.34 Jeffreys explains this attitude by an over-confidence in the capacity of mathematics to reflect reality. In any case, it brought to the fore what can be considered as the crucial point of the debate: the question was not whether the laws of physics could be deduced from general principles*despite the fact that this was what some of Milne’s defenders had perceived in Dingle’s attack*but to know how to obtain these hypotheses. It is thus not Milne’s hypothetico-deductive stance that was at the core of the debate as Gale and co. suggest, but his rationalism.
3. The outcome of the debate This exchange of arguments did not put an end to the controversy, with everyone sticking to their positions. Given the trend of cosmological debates over the following years, however, in particular their relative appeasement, Gale and co. suggest that Milne’s argument won over Dingle’s. As we have mentioned, we consider Milne’s success to be overstated. Certainly, the operational methodology advocated by Milne was picked up by Robertson and Walker, and allowed the establishment of the metric that now bears their names (see also the favourable analysis of this method in an
32 Arthur Stanley Eddington et al. (note 24), 1006. 33 Arthur Stanley Eddington et al. (note 24), 1004. 34 Arthur Stanley Eddington et al. (note 24), 1005. Edward Milne’s influence on modern cosmology 477 article by George Temple reviewing cosmological theories35). However, there is no reason to believe that ‘the establishment of the Robertson Walker metric which, without Milne’s outspoken commitment to a minority philosophical view, would never have come about’.36 Similarly, the assertion that the debate led to ‘a pruning of the existential extravagances of ‘‘curved space’’, ‘‘expanding space’’’ is strange, since these notions are still part of cosmology. To assert that the hypothetico-deductive method has been justified is correct but, as Jeffreys underlines, the core of the controversy between Milne and Dingle was not about this method but about the origins of hypotheses in any theory. Indeed, Dingle had nothing against this method as long as the fundamental hypotheses on which a theory is built are linked with observation. As everybody accepted the idea of making deductions from hypotheses, the controversy was not between pure inductivists and hypothetico-deductivists, but between empiricists and rationalists, and even in such an opposition it is hard to speak of pure empiricists or pure rationalists. For example, Milne grounds his approach to cosmology on at least one indubitable empirical fact: our internal sense of time. In any case, Milne is less the champion of the hypothetico-deductive method than of rationalism. This does not necessarily make him a successful champion. Milne tried to found his cosmological model on a purely deductive mode, from axioms independent of observation, like the cosmological principle. Some researchers have expressed doubts about the supposed absence of links between these axioms and observation. For example, the biologist John Haldane, one of the participants in the debate published in Nature, considered that if Milne had tried to obtain ‘the laws of dynamics rationally*without recourse to experience’, he would have deserved Dingle’s critics. However, for Haldane, this was not the case since the cosmological principle came from observation. Haldane added that this principle is so linked to the current state of observation that it would have been judged absurd in Aristotle’s time.37 Other researchers also thought that Milne, without being aware of it, relied on observational information.38 Nevertheless, the status that Milne confers to this principle is different from the hypothesis of homogeneity and isotropy of the Universe as expressed in relativistic cosmology. As Robertson wrote: It must be said [...] that there exists an essential distinction in the metaphysical status of the uniformity postulate in the two theories: whereas in relativistic cosmology it is set up as an extrapolation of observation for the purpose of determining a suitable ideal structural background for the actual world, it is used in Milne’s theory as an a priori principle which may even be applied to the construction of a theory of gravitation.39 Instead of being a mere conjecture about the Universe, Milne’s cosmological principle is a kind of ‘transcendental’ hypothesis in Kantian terms: it is a condition of the possibility of any knowledge of the Universe. As Milne wrote: ‘If the universe is not homogeneous (in our extended usage of the word), then [...] there will be no
35 George Temple, ‘Relativistic cosmology’, The Proceedings of the Physical Society, 51 (1939), 465 478. 36 George Gale, 1993 (note 2), 492. 37 Arthur Stanley Eddington et al. (note 24), 1003. 38 For example, Hermann Bondi, Cosmology (Cambridge, 1960 [1952]), 123 124. 39 Percy Howard Robertson, ‘On E. A. Milne’s Theory of World-Structure’, Zeitschrift fu¨ r Astrophysik, 6 (1933), 158. 478 Thomas Lepeltier world-wide dynamics possible’.40 To put it succinctly: no cosmology without a cosmological principle. Therefore, it is not important, in this article, to ask if this principle could be linked to observation; only the fact that Milne considered it as a priori principle has to be taken into account. It is in this sense that he can be defined as a rationalist, and it is on this point that we have to see if he convinced cosmologists. It is important to note, first of all, that Milne was not the first physicist to be rationalist. To take a famous example, Albert Einstein was explicitly in favour of a rationalist approach. He asserts, in 1933, ‘that any attempt logically to derive the basic concepts and law of mechanics from the ultimate data of experience is doomed to failure’.41 He does then pose the question of the credibility of a physics detached from observation: ‘If then it is the case that the axiomatic basic of theoretical physics cannot be an inference from experience, but must be free invention, have we any right to hope that we shall find the correct way?’42 But his answer is unambiguous: Our experience up to date justifies us in feeling sure that in Nature is actualized the ideal of mathematical simplicity. It is my conviction that pure mathematical construction enables us to discover the concepts and the laws connecting them which give us the key to the understanding of the phenomena of Nature.43 He adds further: ‘I hold it to be true that pure thought is competent to comprehend the real, as the ancients dreamed’.44 This shows clearly that Einstein was a rationalist. His rationalism, however, owes nothing to Milne’s influence. Nor was he Milne’s ally on questions of cosmology. Speaking about Milne, he wrote in 1949: ‘From my point of view one cannot arrive, by way of theory, at any at least somewhat reliable results in the field of cosmology, if one makes no use of the principle of general relativity’.45 But according to Milne’s own approach, relativistic cosmology is not the product of a rationalist approach. One should not minimize the difference between the two approaches as, for example, Bondi recalled it in 1948: One can approach the problem [of cosmology] either by extrapolating from laboratory physics to form a comprehensive mathematical theory of relativity first and consider its cosmological implications only afterwards or, alterna- tively, one may try to postulate a rigorous cosmological principle and attempt to derive the corresponding theory of relativity and gravitation afterwards. The first procedure was adopted by the school of general relativity, the second by Milne and his followers in kinematical relativity.46 Thus, despite the fact that Einstein strove for a rationalist approach to physics, his approach to cosmology*which is still dominant among cosmologists*was distinct from Milne’s and does not reflect any influence of the latter’s rationalism on modern cosmology.
40 Edward Arthur Milne (note 11), 151. 41 Albert Einstein, ‘On the Method of Theoretical Physics’, Philosophy of Science, 1 (1934), 166. 42 Albert Einstein (note 41), 167. 43 Albert Einstein (note 41), 167. 44 Albert Einstein (note 41), 167. 45 Albert Einstein, ‘Remarks to the Essays Appearing in this Collective Volume’, in Albert Einstein: Philosopher-Scientist, edited by Paul Arthur Schilpp (Evanston, IL, 1949), 684. 46 Hermann Bondi, ‘Review of Cosmology’, Monthly Notices of the Royal Astronomical Society, 108 (1948), 107. Edward Milne’s influence on modern cosmology 479
Another difficulty in assessing Milne’s influence comes from the fact that hypothetico-deductivists are often open-minded about rationalism. Gale and co. underline this point.47 Nevertheless, the fact that cosmologists turn to the hypothetico-deductivist approach does not mean that they are adopting a rationalist approach to cosmology as defined by Milne. Indeed, a clear distinction has to be made between an attraction towards a highly axiomatized theory, such as the general theory of relativity, and an attraction towards a theory deduced from general principles that have no link with observation, such as kinematic relativity. Unfortunately, such a distinction is missing in Gale and co.’s analysis of three articles that supposedly illustrate Milne’s success.48 (1) For example, they present American cosmologist Richard Tolman’s 1932 stance as an example of Milne’s success. Concerning the principles on which a cosmological theory relies, Tolman said that they could be obtained in two ways: either ‘as immediate generalizations of experimental findings’ or ‘as desiderata for the inner harmony and simplicity of the theoretical structure he is attempting to build’.49 However, this second way does not correspond to Milne’s rationalism. In rationalism, the Universe has to be analysed ‘without appealing to any small-scale experiments or to knowledge derived from small-scale experiments’.50 This is not the same as the search for harmony and simplicity in an already-established theoretical corpus. Besides, in order to justify looking for principles in this fashion, Tolman mentioned the general theory of relativity, which has been criticized by Milne because it is a theory which relies on ‘small-scale experiments’. Thus, even if cosmologists have adopted Tolman’s position, it does not necessarily reflect the success of Milne’s rationalism. (2) Gale and co. also refer to an article by William McCrea in which he analyses the evolution of theories of space time, including Milne’s.51 McCrea is positive about the latter, arguing that ‘each theory leaves us in a position in which the succeeding one appears as a perfectly natural next step in the development of ideas’.52 He considers Milne’s theory to show the same hypothetico-deductive aspect as other theories: in spite of superficial differences in character, the theories all necessarily possess the same general structure constituted by the presence of hypotheses, from which certain general mathematical relations are deduced, which in their turn are used to predict relations between observable quantities.53 It is through this comparison with observational data that McCrea saw the ultimate means to assess theories: ‘the ultimate reason for belief in the ‘‘truth’’ of Newton’s, or Einstein’s, or Milne’s laws of dynamics must be the same, namely agreement of the consequences of one theory or another, as a whole, with observation’.54 However, in opposition to Milne, he did not think that the laws of dynamics had to be the
47 George Gale, 1991 (note 2), 215. George Gale and John Urani (note 2), 68. 48 George Gale, 1993 (note 2), 493. George Gale and John Urani (note 2), 72. George Gale and Niall Shanks (note 2), 291. George Gale and John Urani, 1993 (note 2), 345 347. 49 Richard Tolman, ‘Models of the Physical Universe’, Science, 75 (1932), 373. 50 Edward Arthur Milne (note 11), 132. 51 William Hunter McCrea, ‘The Evolution of Theories of Space Time and Mechanics’, Philosophy of Science, 6 (1939), 137 162. 52 William Hunter McCrea (note 51), p. 137. 53 William Hunter McCrea (note 51), p. 137. 54 William Hunter McCrea (note 51), p. 154. 480 Thomas Lepeltier
‘consequences of inescapable postulates’.55 McCrea does not adopt Dingle’s stance, in which hypotheses have necessarily to arise from observation, but neither does he adopt Milne’s rationalism. McCrea is a hypothetico-deductivist, and it is this dimension of Milne’s model that he defend, not his rationalism. (3) Finally, as a testimony to Milne’s victory, Gale and co. mention a paper by Edmund Whittaker, at the Royal Society of Edinburgh in 1941, in which he went back over the controversy sparked by Milne and Eddington. Via a short survey of the history of physics, he comes to the most important problem ‘of Natural Philosophy’: ‘What is the minimum set of observational data which is sufficient to form a basis for the whole edifice of physical theory?’.56 At first sight, he seems in favour of rationalism: We may [...] conjecturally look forward to a time in the future when a treatise on any branch of physics could, if so desired, be written in the same style as Euclid’s Elements of Geometry, beginning with some a priori principles, namely, postulates of impotence, and then deriving everything else from them by syllogistic reasoning.57 What he called a ‘postulate of impotence’ is a principle that expresses an impossibility, such as the principle of special relativity, which stipulates that it is ‘impossible to detect a uniform translatory motion, which is possessed by a system as a whole, by observations of phenomena taking place wholly within the system’.58 These ‘postulates of impotence’ do not correspond to a ‘set of observational data’. However, they are not principles without any link to observation. Whittaker is explicit on this point: ‘the postulates of impotence are generalizations from experiment’.59 Thus, for Whittaker, the progress of science corresponds to an increase in axiomatization, but he does not consider it possible to discover the laws of physics by a purely a priori process. When he recognizes that Milne’s work is part of the progress of science since, what he is doing is ‘essentially to assume a postulate of impotence [the cosmological principle] and then deduce its logical consequences’,60 Whittaker again takes into account only one aspect of Milne’s work, the importance of the axiomatization of physics, and not his rationalist stance. Even if these three examples of Gale and co. had clearly shown an acceptance of a rationalist approach to physics, that would not have been enough to affirm the victory of Milne’s rationalism: a small number of cases does not represent a general orientation. In any case, as we have seen, these three cases are far from embodying such a victory. Moreover, Milne’s project to construct a physics ‘without appealing to any small scale experiments’ does not seem to have many followers: the great majority of cosmologists are still working in the framework of the general theory of relativity. There is of course the exception of Hermann Bondi. Bondi was, with Thomas Gold, the inventor of the steady-state theory that stipulates that globally the Universe does not evolve through time.61 (Fred Hoyle also developed such a model from 1948, but
55 William Hunter McCrea (note 51), p. 154. 56 Edmund Taylor Whittaker, ‘Some Disputed Questions in the Philosophy of the Physical Sciences’, Proceedings of the Royal Society of Edinburgh A, 61 (1943), 166. 57 Edmund Taylor Whittaker (note 56), 169. 58 Edmund Taylor Whittaker (note 56), 169. 59 Edmund Taylor Whittaker (note 56), 172. 60 Edmund Taylor Whittaker (note 56), 169. 61 Hermann Bondi and Thomas Gold (note 5). Edward Milne’s influence on modern cosmology 481 from other principles.) Bondi never disguised the fact that Milne was a source of inspiration for him (see Bondi’s book on cosmology,62 and the convincing analysis by Gale and co.63 Nevertheless, this influence is not at all representative of what happened in the cosmological community. One could again mention Dingle who, as with Milne’s model, was sharply critical of the steady-state theory and did not hesitate to write that with such a model ‘the elementary principles of science are being [...] openly outraged’.64 One could also mention George McVittie, who criticized this model for its rationalist approach.65 Beyond these critical judgements, the steady-state theory, although it seduced some researchers, was often looked at with suspicion. Moreover, this cosmological model, which Bondi stopped defending in the middle of the 1960s, now belongs to the past.66 So, it is difficult to see Milne’s influence on Bondi as a victory of his rationalism. One could also mention the influence of Milne on Paul Dirac.67 But Dirac’s cosmological model, like Bondi’s, has had few followers. In these conditions, it is difficult to speak of a victory of Milne. Outside his role in the establishment of the Robertson Walker metric, his rationalist approach is far from having an influence on cosmology. Posterity’s judgement has even sometimes been harsh. In 1952, for example, the philosopher Milton Munitz spoke of Milne’s ‘rationalist fallacy’68 and concluded his analysis of his cosmology by saying that ‘it is an illusion to expect that by some wholly intuitive device one can derive a quantitative theory without appealing explicitly or tacitly to some selected quantitative data’.69 Less polemical, in a tribute to Milne, Chandrasekhar recognized that if ‘Milne did not succeed in completing his program, it is probable that the program is an inherently impossible one’.70 Nevertheless, Milne’s work was very interesting. It is fascinating that he was able to construct such an elaborate physics from a few general principles. He deserves to be raised out of the general oblivion into which he has fallen, but instead of speaking of his victory, it would be better to speak of his honourable failure.
Acknowledgements I would like to thank Danny Yee and Jennifer Yee for help with my English.
62 Hermann Bondi (note 38). 63 In particular, in George Gale and John Urani, 1999 (note 2). 64 Herbert Dingle, ‘On Science and Modern Cosmology’, Monthly Notices of the Royal Astronomical Society, 113 (1953), 403. 65 George Cunliffe McVittie, ‘Rationalism Versus Empiricism in Cosmology’, Science, 133 (1961), 1231 1236. 66 Helge Kragh, Cosmology and Controversy: The Historical Development of Two Theories of the Universe (Princeton, NJ, 1996). 67 Helge Kragh, ‘Cosmo-Physics in the Thirties: Towards a History of Dirac Cosmology’, Historical Studies in the Physical Sciences, 13 (1982), 69 108. 68 Milton Munitz, ‘Scientific Method in Cosmology’, Philosophy of Science, 19 (1952), 108 130. 69 Milton Munitz (note 68), 118. 70 Subrahmanyan Chandrasekhar,‘Edward Arthur Milne: His Part in the Development of Modern Astrophysics’, Quarterly Journal of the Royal Astronomical Society, 21 (1980), 103.