The concept of 'fact' in German physics around 1900: a comparison between Ernst Mach and Albert Einstein

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THE CONCEPT OF ‘FACT’

IN GERMAN PHYSICS

AROUND 1900

A comparison between Ernst Mach and Albert Einstein

By Elske de Waal

Report Bachelor Project Physics and Astronomy

Supervisor: Prof. Dr. J.A.E.F. van Dongen

Second assessor: Prof. Dr. B. Nienhuis

Daily supervisor: S.L. ten Hagen, MSc

Institute of Theoretical Physics

Faculty of Science, University of Amsterdam

March 2018

Student number: 10632301

conducted between 01-11-2017 and 23-03-2018

Size 15 EC

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Abstracts

Abstract

The ‘fact’ has a history, and in this thesis I study this history by comparing the use of the concept of two prominent German physicists, Ernst Mach (1838-1916) and Albert Einstein (1879-1955). The comparison is set in the context of the shift from the physics of the nineteenth century to the ‘new’ physics of the twentieth century. Einstein is said to have been influenced by Mach, especially in the early years of his career. In this thesis, I show that this influence is not seen in Einstein’s definition of fact, which in the early years is already more conceptual than Mach’s fact, and only drifts further away from what Mach defined as ‘fact.’ The role of experience in science is also diminished in Einstein’s work, compared to Mach’s.

Samenvatting

Het begrip ‘feit’ lijkt op het eerste gezicht een vanzelfsprekendheid met zich mee te dragen, maar bij nadere bestudering blijkt dat zelfs natuurkundigen er heel ver-schillende definities aan toekennen. Uit historisch onderzoek blijkt dat het feit een roerige geschiedenis heeft, wat een verklaring zou kunnen zijn voor de huidige ambiguïteit. In deze scriptie ligt de focus op het gebruik van het ‘feit’ van twee Duitse natuurkundigen, Ernst Mach (1838-1916) en Albert Einstein (1879-1955). Door de definities van beide natuurkundigen te vergelijken ontstaat het beeld dat Einstein een heel ander begrip had van het ‘feit’ dan Mach. Ook de rol die het ‘feit’ speelt in natuurkunde is bij de twee wetenschappers verschillend.

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Introduction

The ambiguity of the ‘fact’

The word ‘fact’ has a feeling of self-evidence around it, and most people probably never second guess the meaning of the word. However, a first indication that this feeling of certainty may be somewhat unwarranted arises when looking up the word ‘fact’ in the Oxford English Dictionary (OED). This dictionary lists ten separate entries for ‘fact,’ not counting subtle differences in the entries and idioms. The definitions range from “the sum of circumstances and incidents of a case, looked at apart from their legal bearing” to “that which is known (or firmly believed) to be real or true.” The OED discerns two categories in the definitions of the word fact: relating primarily to action, and relating primarily to truth.1_{In the former category,}

we see a hint of the historical origin of the word ‘fact,’ to which I return in a mo-ment.

Looking at the OED, we see various definitions of the word ‘fact,’ but still they all seem to have a connection with something true, or something that hap-pened. However, a discussion about the absoluteness of facts, about their trust-worthiness, seems to become ever more present. A clear example is the coining of the phrase ‘alternative facts.’2_{Earlier, in 1979, Bruno Latour and Steve Woolgar}

famously claimed that the scientific fact is a social construction.3

Statements of two contemporary physicists also raise questions on the definition of the ‘fact.’4_{When asked what a fact was according to him, particle}

physicist Auke Pieter Colijn answered that it was “the peak that you see in certain spectra” when measuring something. Thus, the observation, enabled by measuring devices, is the fact. However, when questioned further, Colijn commented on the discovery of the Higgs-boson, stating that it was an hypothesis, until it was meas-ured, then “it became a fact.” A little later, he even came to speak of ‘faith’ in com-bination with a ‘fact.’ This shows that even though the statements independent of

1_{Oxford English Dictionary. (n.d.). Retrieved March 14, 2018 from}

http://www.oed.com/view/Entry/67478?rskey=N8HKaV&result=1#eid

2_{Blake, A. (2017, January 22). Kellyanne Conway says Donald Trump’s team has ‘alternative}

facts.’ Which pretty much says it all. The Washington Post. Retrieved from

https://www.washingtonpost.com/news/the-fix/wp/2017/01/22/kellyanne-conway-says-

donald-trumps-team-has-alternate-facts-which-pretty-much-says-it-all/?utm_term=.f151ed28d592

3_{Latour, B., & Woolgar, S. (1979). Laboratory life: The construction of scientific facts.}

Prince-ton, NJ: Princeton University Press.

4_{For transcripts of interviews with A.P. Colijn and Ivo van Vulpen (in Dutch), see appendix.}

The interviews were conducted in January 2018 at Nikhef. Both physicists are experimental physicist at the Nikhef and the University of Amsterdam.

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each other seem clear enough, when analysing them thoroughly, we stumble upon (apparent) contradictions.

Another experimental physicist, Ivo van Vulpen, stated that the constancy of the velocity of light “is an experimental fact.” When asked what the reason for this was, he explained that by assuming the constancy of the velocity of light, “we can account for experimental observations.” Thus here, an experimental fact is seen as an explanation for certain observations, instead of the observations them-selves.

This illustrates that, even though these physicists attach importance to facts, their wavering use of the word raises questions on the exact definition of the concept. Variations in the definition and use of the ‘fact’ across national borders and disciplines, can be, at least partly, explained by looking at the history of the ‘fact.’ As Mary Poovey has said, many histories of the fact can and should be told.5

As both its definition and its place in science have changed throughout the previous centuries, there are indeed plenty of histories to be told. In this thesis, I address the history of the fact around 1900 in Germany. Before I go into that, I will give a short overview of the histories that have already been told by others.

A (very short) history of the fact until 1850

The origin of the ‘fact’ lies in sixteenth century England, as Barbara Shapiro has shown.6_{From the context of law, it was transferred to the study of nature by}

Baco-nian natural historians.Then, the concept evolved and was transferred to France quite quickly,7_{but German adoption of the concept was considerably late. In 1756,}

‘matter of fact’ was first translated in German with ‘Thatsache.’8_{At that time, it}

was used in theological discussions, denoting historical acts, actions and deeds related to the divine.9_{The exact mechanisms through which the term transferred}

to German Wissenschaft have remained largely hidden from view, but at the turn

5_{Poovey, M. (1998). A history of the modern fact: Problems of knowledge in the sciences of}

wealth and society. Chicago, Ill: University of Chicago Press. There xiii

6_{Shapiro, B. J. (2003). A culture of fact: England, 1550-1720. Ithaca, NY: Cornell University}

Press.

7_{On the history of the fact in France, see for instance Pia Donato, M. (2017). A Science of}

Facts? Classifying and Using Records in the French Imperial Archives under Napoleon. History

of Humanities, 2(1), 79-100.

8_{Ritter, J. & Gründer, K. (Eds.) (1998). Historisches Wörterbuch der Philosophie, 10, 910-916}

(‘Tatsache’). Basel, Switzerland: Schwabe Verlag. The ‘h’ in Thatsache got dropped around 1900.

9_{Staats, R. (1973). Der theologiegeschichtliche Hintergrund des Begriffes “Tatsache.”}

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of the 19th_{century, Thatsache}10_{became widely used in natural history and}

philoso-phy in Germany. However, the meaning and use of the concept was definitely not set in stone. Many philosophers used the term in different ways in their writings. The focus on facts was not yet such that scientists and philosophers were called out on their loose dealing with the term.

At the end of the eighteenth century, Georg Lichtenberg (1742-1799)11

ar-gued that facts were the theory-free units that physics should be based upon. He differentiated between facts and theories and hypotheses, where the latter were merely of heuristic value.12_{This division between facts and theory was}

representa-tive for the time. Historians of science Christa Jungnickel and Russell McCormmach note that in the early decades of the nineteenth century, German physicists13_felt

the need to distance themselves from Naturphilosophie.14_{This philosophy adhered}

to the idea that a ‘completeness of theory’ was more important than direct obser-vation. Jungnickel and McCormmach see the increased use of the ‘fact’ as well as its contraposition to theory, as a symptom of a broader movement against this theorising.

Around the same time, physicists were confronted with factors that made clear that the ideal of a progressing science without transformation could not hold ground. As Lorraine Daston notes, scientists were suddenly faced with scientific

10_{Alongside Thatsache, also Factum or Faktum were used in Germany around this time. The}

different terms had similar meanings. See for instance Holland, J. (2016), Facts are What One Makes of Them: Constructing the Faktum in the Enlightenment and Early German Romanti-cism. In Lehleiter, C. (Ed.), Fact and Fiction: Literary and Scientific Cultures in Germany and

Britain, (33-49). Toronto, Canada: University of Toronto Press.

11_{Lichtenberg was an important figure in this period. He became professor of physics in the}

1770s and taught influential German scientists such as Alexander Humboldt (1769-1859) and Carl Friedrich Gauss (1777-1855).

12_{Ten Hagen, S. (forthcoming). The concept of ‘fact’ and the formation of the disciplinary}

system.

13_{Physics at that time was not a clearly established field. As historian of science Frank van}

Lunteren notes, it could refer to natural history, natural philosophy (not to be confused with

Naturphilosophie), applied mathematics (angewandte Mathematik), or the experimental

physics that focused on phenomena that could be demonstrated or examined with physical apparatus such as the airpump. Thus, in the early nineteenth century, physics was still close-ly related to both chemistry and mathematics. However, by the end of the century, physics had become a full-fledged discipline. See van Lunteren, F. (2013). Het ontstaan van het systeem van bètadisciplines: de natuurkunde. Studium, 6(2), 91-112.

14_{Jungnickel, C., & McCormmach, R. (1990). Intellectual Mastery of Nature. Theoretical}

Physics from Ohm to Einstein, Volume 1: The Torch of Mathematics, 1800 to 1870 (Vol. 1).

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progress that did indeed call for transformation. 15_{If theories were no longer the}

eternal, steadfast products of science, there was a gap to be filled. According to Daston, “only facts deemed to hold out the hope of definitive achievement in sci-ence, (…) scientific facts not only hardened but grew more precious to scientists in the nineteenth century.”16

This forming of the conception of the ‘fact’ runs parallel to another pro-cess; the forming of the distinct disciplines. Historian of Science Sjang ten Hagen shows that the ‘fact’ played a determining role in this process.17_{The concept came}

to have varying definitions for the varying disciplines. The field of physics was based mainly on empiricism and experiment at the time, with no distinct place for rationalism. In this context it is quite understandable that by the 1850s, the fact was placed in opposition of theory in German physics.

The question now remains, what happened after this period? Did the fact indeed remain completely the opposite of theory, and did they remain the ‘eternal’ products of science? Furthermore, the fact underwent several distinct changes in the first hundred years of its use in Germany, had it become stable by the 1850s? To find an answer to these questions, I will study and compare the interpretation of the ‘fact’ of two prominent German physicists, Ernst Mach (1838-1916) and Albert Einstein (1879-1955).

The fact after 1850

In this thesis, I will focus on the history of the ‘fact’ in German physics in the dec-ades around 1900, by focusing on Ernst Mach and Albert Einstein, an experimental and a theoretical physicist. These labels deserve some extra attention, and I will elaborate on that chapter 2. Einstein was, as historian of science Gerald Holton puts it, “a man who, only a century ago, started to overturn the scientific Weltbild of the time.”18_{Einstein, in turn, credits Ernst Mach with shaking his “dogmatic}

faith” in “mechanics as the final basis of all physics.”19_{In chapter 2, I will return to}

the influence of Ernst Mach’s thinking on Einstein, but it is clear that the main pro-tagonists of this story were both central to a shift in physical thinking.

15_{For instance when in the 1830s the Newtonian emission theory of light was contradicted}

by experiments and the wave theory. See Daston, L. (1998), Fear and Loathing of the Imagi-nation in Science. Daedalus, 127(1), 73-95.

16_{Daston (1998). There 90.} 17_{Ten Hagen (forthcoming).}

18_{Holton, G. (2008). Who was Einstein? Why is he still so alive? In P. Galison, G. Holton, & S.}

Schweber (Ed.), Einstein for the 21st century: His legacy in science, art, and modern culture (3-15). Princeton, NJ: Princeton University Press. There 3.

19_{Einstein, A. (1949). Autobiographical notes. In P. Schlipp (Ed.), Albert Einstein:}

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The category of 'fact' is an interesting point of comparison between Ein-stein and Mach, but it has been largely neglected by others. Holton does touch on it in his 1968 article on the influence of Mach on Einstein.20_{Here, he refers to a}

letter Einstein wrote in 1918, in which he lists some of the things he calls ‘fact.’ Holton concludes that “none of these would have been called ‘facts of experience’ by Mach,”21_{and uses this as an argument to show that Einstein was moving away}

from Mach. In this thesis, I elaborate on this conclusion of Holton. Did Einstein indeed have a different conception of the ‘fact’ than Mach? First, I discuss Mach’s definition of a ‘fact’ and the role ‘facts’ played in his physics. Was this indeed the same as the above sketched mid-nineteenth century ‘fact’? Then, I come to Ein-stein’s ‘facts’; what did he see as ‘facts’ and what role did they play, and how does that compare to Mach? Or did the new era come with new definitions of the ‘fact’? In this manner, I will investigate if Mach and Einstein did indeed have different definitions of facts. Furthermore, I will relate their interpretation of the fact to their general epistemology, and to the discussion in the literature about the influence of Mach on Einstein.

20_{Holton, G. (1968). Mach, Einstein, and the Search for Reality. Daedalus, 97(2), 636-673.} 21_{Holton (1968). There 646.}

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Chapter 1 Ernst Mach’s ‘fact’: ‘what’ is nature?

Physicist with a broad interest

Ernst Mach (figure 1) studied physics in Vienna, where he received his doctorate in 1860.22_{After a short professorship in Graz, he took on a position in Prague, as a}

professor of physics in 1867. Here, he remained for almost three decades, before returning to Vienna.23_{In Prague, Mach produced, among other works, a textbook}

of physics24_{and Die Mechanik in ihrer Entwickelung. In his Prague-period, Mach}

also conducted the experiments on shockwaves he is, possibly, most famous for (figure 2).25

Mach was an experimental physicist, which showed in the physics books he wrote, where he explained theories (almost) always by examples of little exper-iments or observations, and rarely used mathematics to prove something.26

22_{Pittenger, H. (1965). Ernst Mach: Biographical Notes. Science, New series, Vol. 150,}

No.3700, 1120-1122

23_{For a complete overview of Mach’s time in Prague, see Hoffman, D. (1992). Ernst Mach in}

Prague. In J. Blackmore (Ed.), Ernst Mach; a Deeper Look (29-46). Dordrecht, the Nether-lands: Springer.

24_{Mach was invested in the teaching of science, both to students and the general public.}

Examples of this are his physics textbooks, e.g. Mach, E. (1891a). Leitfaden der Physik für

Studierende, 2nd ed. Vienna, Austria: Tempsky.; but also his lectures, bundled in the Popular Scientific Lectures; Mach, E. (1895). Popular Scientific Lectures. 1st_{edition. Chicago, Ill: Open}

court publishing company. In the foreword to this bundle, Mach says: “It is only necessary to set forth the attractive and the alluring features of a problem, and to show what broad domains of fact can be illuminated by the light radiating from the solution of a single and ofttimes unobtrusive point.” For scholarship on the influence of Mach on the teaching of mechanics see Assis, A. & Zylbersztajn, A. (2001). The influence of Ernst Mach in the Teach-ing of Mechanics. Science & Education, 10(1-2), 137-144.

25_{Mach was the first to document shockwaves, by using Schlieren photography. The}

tech-nique was already invented by Töppler in 1864, but Mach perfected it, thus proving Rie-mann’s theory of nonlinear waves that could travel faster than sound. Mach’s efforts in this process are said to illustrate his experimental mindset. Mach’s contributions in the field have led to the naming of several phenomena after him, such as the Mach number and the Mach angle. For a detailed account of Mach’s experiments on shockwaves, see Seeger R.J. (1970). On Mach’s Curiosity about Shockwaves. In R. Cohen & R. Seeger (Eds.), Ernst Mach: Physicist

and Philosopher (60-68). Dordrecht, The Netherlands: Springer.

26_{See for instance Mach, E. (1960). The Science of Mechanics: A Critical and Historical}

Ac-count of Its Development. Translated by T. McCormack. 6th_{edition. La Salle, Ill: Open court}

publishing Company. There 376-395, Mach elaborates on “the laws of the conservation of momentum, of the conservation of gravity and of the conservation of areas.” To do so, he

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ever, Mach did not concern himself with just physics. He was also interested in human physiology and psychology,27_{and he wrote books such as The Analysis of}

Sensations28_{and held lectures entitled On the Fibres of Corti and On the Causes of}

Harmony. Furthermore, lectures like On the Part played by Accident in Invention and Discovery29_{and the fact that from 1896 to 1901, Mach occupied the chair for}

History and Philosophy of the Inductive Sciences,30_{betray his inclination towards}

philosophy. However, in the introduction of the Analysis of Sensations, Mach says “I make no pretension to the title of philosopher. I only seek to adopt in physics a point of view that need not be changed immediately on glancing over into the domain of another science; for, ultimately, all must form one whole.”31_{Hence, his}

philosophical remarks are all in service of his scientific work, which means that they are always connected to scientific practise, albeit sometimes an idealised from of that practice.32

This means, that although in this chapter I focus on Mach’s work in phys-ics, I also made use of his more philosophical work. In the following sections, I first show what Mach’s understanding of a ‘fact’ is, then I elaborate on the role of ‘facts’ in science, as opposed to ‘theory,’ ‘concept’ and ‘principle.’ To study this, I have used several of Mach’s physical works, such as his Science of Mechanics (1883),

included several drawings of experimental setups that would generate the necessary meas-urements.

27_{Mach was very interested in human physiology and psychology. He was of the opinion that}

psychology could be studied as a natural science, but for that goal to be attained, one had to find a new scientific method for this field of research. In this view, Mach was probably in-spired by Gustav Fechner’s Psychophysik, as it came out around the time Mach received his doctorate.

28_{Mach, E. (1959). The Analysis of Sensations, and the Relation of the Physical to the}

Psychi-cal. Translated by C.M. Williams. 1st_{Dover edition, from the 5}th_{German edition. New York,}

NY: Dover Publications, Inc.

29_{This lecture was Mach’s inaugural lecture for his chair of History and Philosophy of the}

Inductive Sciences. The lecture was included in later editions of the Popular Scientific

lec-tures.

30_{This chair has been denoted in different terms. This one is from Hoffman (1992).}

Alterna-tively, Pittenger has called it “the chair of theory of inductive sciences.” See Pittenger, H. (1965). The chair was created especially for Mach, and it was the first of its kind in the world. It would later become the centre of the Wiener Kreis, to which I will return at the end of this chapter.

31_{Mach (1959). There 30}

32_{Mach is now often remembered as a philosopher of science, where his philosophical work}

was nurtured by his science. However, Christoph Hoffmann and Alexandre Métraux argue that this contemporary image does not do justice to the historical reality. They show that Mach should be seen as a natural philosopher, and that his philosophy and science were inseparably linked. Hoffmann, C. & Métraux, A. (2016). Working with Instruments: Ernst Mach as Material Epistemologist, a Short Introduction. Science in Context, 29(4), 429-433.

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which also contains statements on the value of concepts, hypotheses and facts. Another source for Mach’s work is the bundle of lectures he held on several topics; the Popular Scientific Lectures (1895). The topics of these lectures ranged from the technical “The velocity of light” and “The fundamental concepts of electrostatics” to the more philosophical “On Transformation and Adaptation in Scientific Thought” and “The economical nature of physical inquiry.”33_{A last great source for}

Mach’s epistemological ideas is the introduction to the Analysis of Sensations (1886). The rest of the book is focused on physiology and psychology, but the in-troduction is titled: Introductory remarks: Antimetaphiscal.34_{In it he explores the}

relation between the physical, physiological and the psychological, and he empha-sises the role of observation in science.

In order to be able to compare Einstein’s conception of the ‘fact’ to Mach’s, in this chapter I give an overview of Mach’s attitude towards the ‘fact.’ In the following sections I first ask what the word and concept ‘fact’ mean to Mach. Then I go into their role in physics and their relation to terms such as ‘concept,’ ‘theory,’ ‘principle’ or ‘law.’ At the end of the chapter, I see if the focus on Mach’s ‘facts’ can shine new light on a discussion around the question if Mach was an anti-realist. Then in the next chapter, I compare what I have found in this chapter to Einstein’s conception of the ‘fact.’

33_{Mach (1895)} 34_{Mach (1959). There 1}

Figure 1 : Ernst Mach in 1902, published in Zeitschrift für Physikalische Chemie. Source: https://commons.wikimedia.or g/wiki/File:Ernst_Mach_01.jpg Retrieved on 23 March 2018

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Mach’s definition of ‘fact’

In this section I look into what Mach means when he uses the word ‘fact’

(Tatsa-che). In his lecture On the Economical Nature of Physical Inquiry Mach states that

”the goal which [physical science] has set itself is the simplest and most economical expression of facts.”35_{This raises two questions: What are facts? And how do we}

express them in the most economical way? Mach himself never stated his own definition of fact, thus, I give my own definition of what he means when using the word fact. This is the focus of the next section.

To Mach, a physical fact is what ‘is,’ or happens in nature, of which we ob-tain knowledge through experience. One could call these ‘natural phenomena,’ but that might suggest that observation or sensation is intrinsic to facts. The facts exist without observation, however, we cannot know about them without it. In the same lecture as above, Mach states that experience ‘exhibits’ facts.36_{However, Mach}

also uses terms like ‘facts of experience’ and ‘sensory facts. At the end of this chap-ter, I will elaborate on the ambiguity in Mach’s written work and the misrepresen-tations it has caused.

The next question is then: what ‘is or happens in nature’? An illustration of this is given by Mach in an essay titled Sensations and the elements of reality. In it, Mach compares the “motions of atoms” to the “green of trees.” “In the latter” he says, “I see a (sensory) fact, in the former a ‘Gedankending,’ a thing of thought.” 37

Thus the theoretical explanation, the motions of atoms, was a thing of thought, while the green of the trees, that which makes us see the trees as green, that is a fact. Again, the sensation is not the fact, but merely ‘caused’ by the fact. Another illustration of this is an example Mach gives in the introduction of the Analysis of

Sensations. He uses it to illustrate the ambiguousness of the words ‘real’ and

‘ap-pearance,’ but we can also use it to get a clear image of what he calls facts. Consid-er a pencil, held in front of us in the air. This pencil is seen as straight. Then, Mach continues, imagine this pencil halfway immersed in water, “and we see it crooked.” According to Mach, “in both cases we have to do with facts which present us with different combinations of the elements.”38_{In the case of the pencil in water, the}

35_{Mach (1895). There 207.} 36_{Mach (1895). There 210}

37_{Mach, E. (1891b). Some Questions of Psycho-Physics. Sensations and the Elements of}

Reality. The Monist, 393-400. There 396

38_{Mach (1959). There 10. Interesting to note from this quote is that Mach uses the word}

‘elements’ here. Elements to Mach were the building blocks of nature, but they were not the chemical elements that we know today. According to Mach, the world, both the ‘outer’ and ‘inner’ world was built up of elements. They could be for instance ‘colour’ or ‘sound,’ but also memories of colours, or the feeling one gets when touching something. The elements were ‘physical’ when they were ‘outside’ of us and ‘psychological’ when they were ‘inside.’

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rays of light are refracted by the water. This is a fact. That the pencil is ‘in reality’ straight, has nothing to do with the facts; the rays of light we observe. To say something about ‘reality,’ we have to take multiple facts into account. In the case of the pencil, for instance, “it is tactually and metrically straight.”39_This

combina-tion of facts and extraccombina-tion of informacombina-tion from them, is exactly what physical in-quiry is, according to Mach. Individual facts can contradict each other, this does not mean that one fact is ‘less true’ than the other.

To sum up, physical facts to Mach are what ‘is’ or ‘happens’ in nature. We obtain knowledge of the facts, and thus nature, through experience. Observations and sensations are not the physical facts themselves, but merely representations. Now that we know what ‘facts’ are to Mach, in the next section I discuss what “the simplest and most economical expression” 40_{of them entails.}

The combinations of elements were presented by facts, thus ‘psychological facts’ presented combinations of ‘psychological elements.’ This is why Mach says, a little later in the introduc-tion of the Analysis of Sensaintroduc-tions that “the wildest dream [is] a fact as much as any other.” If we differentiate Mach’s ‘physical’ facts from his ‘psychological,’ we can assume that Mach’s (physical) facts ‘are in nature,’ independent from our observation of them. For more on Mach’s elements, see Banks, E. (2003). Ernst Mach’s world elements. Dordrecht, The Nether-lands: Springer.

39_{Mach (1959). There 10} 40_{Mach (1895). There 207.}

Figure 2: Photograph of a bullet in

supersonic flight, published by Ernst Mach in 1887

Source: .John D. Anderson, Jr. "Research in Supersonic Flight and the Breaking of the Sound Barrier -- Chapter

3". history.nasa.gov. p. 65. Retrieved 3 March 2018.

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Ordering the ‘facts’

A requirement for the communication of facts, is that they “must be so described that individuals in all places and at all times can, from a few easily obtained ele-ments, put the facts accurately together in thought, and reproduce them from the description.”41_{In practice, principles, concepts and natural laws are examples of}

economical representation of facts.

Sharing knowledge about nature is easier when this knowledge is present-ed in a compact manner.42_{For instance, all individual cases of refraction are}

impos-sible to comprehend. “But knowing the index of refraction for the two media pre-sented, and the familiar law of the sines, we can easily reproduce or fill out in thought every conceivable case of refraction.”43_{By representing the facts, the}

indi-vidual instances of refracted light rays, in a law, with the help of the index of refrac-tion, one can communicate knowledge about breaking of light, without having to recall every single fact observed. Furthermore, one can make predictions about nature, about how the light will break when passing from one medium to anoth-er.44

Apart from facilitating the communication of knowledge, the economical representation of facts has another advantage. It is also “a means of discovering the interdependence of phenomena.”45_{As this economical ordering requires the}

highlighting of certain aspects of facts, which means they can then be more easily

41_{Mach (1895). 108}

42_{According to Mach, the necessity for ordering knowledge of facts economically has an}

evolutionary origin. He argues that the survival and prospering of the human species is de-pendent on the sharing of knowledge. Darwin’s Origin came out around the time Mach earned his doctorate. Mach references Darwin on several occasions, see for instance Mach, (1895), pp 186-213.

43_{Mach (1895). There 193}

44_{According to Mach, making predictions about nature is quintessential to human nature.}

Man acquires knowledge of nature “half-consciously and automatically, from an instinctive habit of mimicking and forecasting facts in his thought.” Mach considers these habits to be “rooted in the economy of our organism not less firmly than (…) motion and digestion.” Mach then continues to describe the arising need for communication of knowledge. (Mach (1895). There 190) In order for man to continue the accumulation of knowledge, it had to be shared. One person can only experience a limited amount of facts. “By communication, the experience of many persons individually acquired at first, is collected in one.”44

Communica-tion, then, required knowledge to be put in a simple form. “The communication of knowledge and the necessity which everyone feels of managing his stock of experience with the least expenditure of thought, compel us to put our knowledge in economical forms.”44

(Mach (1895). There 97)

45_{Mach, E. (1970). The guiding principles of my scientific theory of knowledge and its}

recep-tion by my contemporaries. In S. Toulmin (Ed.), Physical Reality (44-53). New York City, NY: Harper. There 32

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compared to other, already known facts. This means the new fact can be recog-nized more clearly, when it can be placed in a ‘province’ of other, similar facts.46

However, it is necessary to remember that to Mach, this is always the order in which scientists should operate. First, experience has to exhibit the facts, then science should ‘marshal’ them in economic and perspicuous order. Once this has been done, “there is no doubt we shall understand47_{[the facts]. For other}

under-standing than a mental mastery of facts never existed. Science does not create facts from facts, but simply orders known facts.”48

For all their scientific and economic value, principles and concepts have a downside, compared to direct observation. Principles, concepts and laws will only reproduce part of a fact. “Our physical concepts, however close they come to the facts, must not be regarded as complete and final expression of these facts.”49_{In a}

fact, there is much more contained than the aspect which is represented by the principle. If again we take the refraction of light as an example, we see that the law of the sines allows us to calculate the exact refraction of an incoming ray of light, given that we know the two media concerned. However, it does not give any in-formation about the intensity of the incoming ray of light. In this case, the law of the sines does not contain any use for us. To take on as many facts as possible in a single concept or law, the facts are reduced to only the necessary features, and “in reality, the law always contains less than the fact itself, because it does not repro-duce the fact as a whole, but only in that aspect of it which is important to us, the rest being either intentionally or from necessity omitted.”50

On the role of theory in Mach’s science

This downside of the economical tools (concepts, theories, hypotheses) is an im-portant one to Mach, it could serve as the explanation for his fixation on facts, on experience and experiment. As he illustrates in the lecture On the Economical

Na-ture of Physics:

“In the economical schematism of science lie both its strength and its weakness. Facts are always represented at a sacrifice of com-pleteness and never with greater precision than fits the needs of

46_{Mach (1895). There 194}

47_{By understanding Mach did not mean ‘to know the underlying causes’ or something}

simi-lar. Understanding for Mach meant having a clear, ordered overview of the facts. In a similar way, Mach also used the word ‘explained’ quite often. See Bradley, J. (1971). Mach’s

Philos-ophy of Science. London, UK: Athlone Press, 190-204, for more on Mach and his

‘understand-ing’ and ‘explaining.’

48_{Mach (1895). There 210-211}

49_{Mach (1970). There 43} 50_{Mach (1895). There 193}

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the moment. The incongruence between thought and experience, therefore, will continue to subsist as long as the two pursue their course side by side; but will continually be diminished.”51

As we can see, Mach did appoint a role to theory (thought) in science, side by side with experience. As we have seen in the introduction, the debate on the valuation of theory and facts was a theme around 1850. Mach addresses this issue in his popular lecture On the Principle of Comparison in Physics.52_{A theoretical}

idea, as Mach puts it, “occupies a higher place in our judgement than the mere holding fast to a fact or observation.”53_{However, this higher appreciation of theory}

is entirely quantitative, meaning that a theory can describe (aspects of) multiple facts at once. However, as with any economical tool, not all aspects of the facts can be described by the theory. As we combine facts and observations into theories, we can compare new facts to ones already known, in an easier manner. Further-more, theory helps us to recognise features of a fact that are not directly observa-ble. “[The theoretical idea] can extend the fact, and enrich it with features which we are first induced to seek from suggestion, and which are often actually found.”54

Here, Mach does emphasize that it is always necessary to study the fact(s) further and see if the suggested features are indeed present in them.

This place of theory, as a quantitative tool to order facts, and not as a means to discover new ‘truths,’ is an indication of Mach’s program in science. To Mach, the question was ‘what is there in nature,’ or ‘what happens in nature?’ Mach nev-er sought the undnev-erlying ‘reasons’ or ‘causes’ of nature. In the next chaptnev-er, I show that this is entirely different in Einstein’s case.

Thus, (physical) facts are more easily communicated when put in economical form. This is done with the help of e.g. concepts, principles and theories. The high-er appreciation theory holds in our thinking is thhigh-erefore purely due to its ability to express a set of facts in an instant. However, not all aspects of the facts are con-tained in the economical tool. Now that we know what Mach means when he uses the word ‘fact’ and what place it has in relation to the economical tools, I want to take a look at a discussion in the literature about Mach, and what I can contribute to this discussion based on Mach’s understanding of ‘facts.’

51_{Mach (1895). There 206}

52_{An address delivered before the General Session of the German Association of Naturalists}

and Physicians, at Vienna, September 24, 1894. In Mach (1895), 236-258.

53_{Mach (1895). There 241} 54_{Mach (1895). There 241}

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Was Mach an anti-realist?

Mach has been described with a lot of -isms; positivism, solipsism,55_{empiricism etc.}

At this point, I want to focus on just one of them: anti-realism; due to his emphasis on observation and sensations, Mach is often seen as having an instrumentalist worldview, even denying a world known to us, other than the world of our own observations. Perhaps the best known example of such an accusation is from the pen of Max Planck. The Mach-Planck polemics spanned from 1908 to 1913 and were based on Mach’s denial of the existence of atoms. Planck describes Mach’s view as follows: “[It] holds that there are no other realities than one’s own percep-tions (…) The essential and only elements of the world are perceppercep-tions.”56_Here,

Planck accuses Mach of denying that there is anything besides our own percep-tions, which he finds problematic, because he considers this to be the reason why Mach denied the existence of atoms. However, as we have seen, Mach does indeed accept realities that are not our perceptions: facts. Facts are observable through sensations, we gain knowledge of them by experience, but physical facts are not the same thing as our observations. Hence, Mach cannot be said to be an anti-realist in the way here described by Planck. For Mach, the atoms could not be con-sidered ontological entities, for there was, according to him, no empirical necessity to assume them. As a concept or hypothesis, they could serve science, but Mach was not convinced that they were physical entities.57_{In this distinction, we see the}

above described difference between ‘facts’ and ‘economical tools.’ According to Mach, atoms were not ‘facts,’ at most, they were a ‘conception’ or ‘hypothesis.’

55_{Due to his emphasis on observation and sensations, Mach’s epistemology might seem to}

lead to ‘solipsism.’ In stating that observation is the basis of knowledge, Mach risks the accusation of denying a general truth, a ‘real,’ external world apart from the sensing ego. Philosopher of science Robert Cohen notes that Mach rules out solipsism a priori, by stating that the sensed data are shared. Mach called his science neither subjective or objective, but impersonal.55_{Another way Mach tries to avoid solipsism, is by denying the existence of the}

ontological ego altogether. Sensations do not give any reason for us to believe in an ego, and for Mach, the ego is just as much a metaphysical object as a thing-in-itself. Instead of the one ego, Mach considers a functional whole. All science is a collection of all observations and sensations all of mankind has had and will have. This is his, somewhat metaphorical still, answer to the accusation of solipsism. See Cohen, R. S. (1968). Ernst Mach: Physics, Percep-tion and the Philosophy of Science. Synthese, 18(2-3), 132-170. There 133-134

56_{Planck, M. (1909). Die Einheit des physikalischen Weltbildes. Physikalische Zeitschrift, 10,}

62-75. Translation from Blackmore, J. (2012). Ernst Mach—A deeper look: Documents and

new perspectives (Vol. 143) (127-132). Dordrecht, The Netherlands: Springer. There 130

57_{For a discussion of Mach’s stance on the reality of atoms, see for instance, Hiebert, E.}

(1970). The genesis of Mach’s early views on atomism. In R. Cohen & R. Seeger (Eds.), Ernst

Mach: Physicist and Philosopher (79-106). Dordrecht, The Netherlands: Springer.; Brush, S.

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This view of Mach as an anti-realist can be explained in the context of Mach’s own words. Sentences such as “Even the wildest dream is a fact as much as any other,”58_{indeed paint a picture of a man who believed only in sensations and}

nothing else. However, if we place this statement in the context of Mach’s view on ‘facts,’ the seeming contradiction may be explained as follows: In the sense that someone is ‘observing’ the dream, the dream is the ‘fact’ that the sleeping person is obtaining knowledge of. In this case, the fact is also internal and therefore it is a psychological fact, as opposed to the external physical facts. Of the external physi-cal facts, I have established that Mach indeed did believe in them being a mind-independent reality, and thus he was not anti-realism that caused Mach’s denial of the existence of atoms.

Mach’s Influence in the twentieth century: logical positivism

and Einstein

Now for the last part of this chapter, I want to take a look at the influence Ernst Mach has had on physics and philosophy. As illustrated in the introduction and the beginning of this chapter, Mach was an important scientist at the end of the nine-teenth century, and his philosophy is much discussed. For the history of the fact, it can therefore be interesting to take a look at the ‘fact’ as used by physicists and philosophers who were inspired by Mach. One comparison of this kind I will make in the next chapter, by looking at Einstein’s ‘fact.’ Here, I want to take a short look at Mach’s philosophical influence in the twentieth century.

One group of philosophers (and scientists) that often referred to Mach, was the Wiener Kreis. They name Mach as one of their inspirations and the basis of their logical positivism. The Wiener Kreis,59_{was officially established in 1922, but}

earlier, from 1907 onwards, a group of Viennese scientists regularly came together to “discuss philosophical problems which arose in the foundations of their various disciplines.”60_{One of the members of this ‘early’ group, physicist Philipp Frank, says}

about it: “The European movement had its origin in the ideas of the Austrian

58_{Mach (1959). There 11}

59_{The Wiener Kreis also formed the Verein Ernst Mach. This society had as its goal to help}

spread scientific knowledge and technical literature to the general public. See Stadler, F. (1992). The “Verein Ernst Mach” – What Was It Really? In J. Blackmore (Ed.), Ernst Mach—A

deeper look: Documents and new perspectives (Vol. 143) (363-378). Dordrecht, The

Nether-lands: Springer.

60_{Bell, D. (1997). Logical Positivism. In P. Lamarque (Ed.), Concise Encyclopedia of Philosophy}

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cist Ernst Mach." 61_{However, the character of Mach’s positivism is something that}

should be, and has been, discussed in literature. 62

The first time Mach and positivism were connected, was when Mach oc-cupied the chair for the history and philosophy of the inductive sciences. During this time, positivism was around in many forms, all with their own subtleties and differences.63_{Nowadays, the term is much narrower than when Planck called Mach}

a positivist during the polemics in 1910.64_{To this, Mach replied: “I can only say that}

my ‘Positivism’ has not been rightly judged if it is viewed as a reaction to the fail-ures of atomistic speculation.” It is the only time Mach referred to positivism in relation to his thinking, and he does not seem to accept the term eagerly. Dr. John Bradley gives his definition of Mach’s positivism in the following manner: “[What is positive about Mach’s philosophy,] is that science is no more that the direct or indirect description of natural phenomena and facts."65_{Mach did not think science}

should search for reasons behind the facts. But this did not mean that Mach did not believe in anything else than the sensations. For the facts are in nature, not in our minds or sensations.

In the polemics, Planck seems to have established this view of Mach being a positivist. The Wiener Kreis then took on this view of Mach as a positivist, and built on it, but from an admirer’s perspective. This group of scientists and philoso-phers formed around Mach’s successors occupying the chair of history and philos-ophy of inductive sciences, to which Moritz Schlick was appointed in 1922.66_Schlick

was a student of Mach and greatly influenced by him. The Wiener Kreis took Mach’s, as they saw them, positivist ideas and developed them into logical positiv-ism, by combining them with the ideas of for instance Hume, Poincaré, Frege and Russell.67_{The question then remains, to what extent did the logical positivists of}

61_{Frank, P. (1941). Between physics and philosophy. Harvard University Press.; Cambridge.}

There 6

62_{For a discussion on the extent and form of Mach’s positivism, see for instance Banks, E.}

(2013). Metaphysics for Positivists: Mach versus the Vienna Circle. Discipline Filosophiche, 23(1), 57-77; Noé, K. (1992). Mach’s Relativism vs. Apriorism and the Mechanistic World View. In J. Blackmore (Ed.), Ernst Mach—A deeper look: Documents and new

perspec-tives (Vol. 143) (229-242). Dordrecht, the Netherlands: Springer.

63_{Howard, D. (2004). Fisica e filosofia della scienza all’alba del XX secolo. Enciclopedia}

Italia-na di Storia della Scienza, 8. Translation Howard, D. Physics and philosophy of science at turn

of 20th_{century downloaded on 13-01-18 from}

https://www3.nd.edu/~dhoward1/Phil-Phys-1900.pdf

64_{In 1909 and 1910, the polemic between Mach and Planck was based upon Mach’s denial}

of atoms. Planck was the first to call Mach a positivist, a name that has stuck with him throughout the twentieth century. See Chapter 6 in Blackmore (2012).

65_{Bradley (1971). There 206-207} 66_{Stadler (1992).}

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the Wiener Kreis adopt Mach’s definition of the ‘fact’? Was it indeed a ‘positivistic’ definition? If the Wiener Kreis did adhere to Mach’s definition of the ‘fact,’ it could mean that through their philosophical work, it has had a great influence in twenti-eth century philosophy. These questions should be the objectives of further en-quiry into both the history of the ‘fact’ in general, and the influence of Mach’s ‘fact’ in philosophy specifically.

Now, I return to the main issue of this thesis. Part of Mach’s influence on (the philosophy of) science can be traced through arguably the greatest scientist of the twentieth century: Albert Einstein. In a letter to Moritz Schlick on 14 December 1915, Einstein says:

“Your representations that the theory of [relativity] suggests itself in positivism, yet without requiring it. In this also you saw correctly that this line of thought had a great influence on my efforts, and more specifically, E. Mach, and even more so Hume, whose

Trea-tise of Human Nature I had studied avidly and with admiration

shortly before discovering the theory of relativity. It is very possi-ble that without these philosophical studies I would not have ar-rived at the solution.”

Einstein stressed the importance of philosophy for his science, and with it credits both Hume and Mach as the greatest influences on his thinking. In the next chapter, I will further explore the influence Mach had on Einstein by com-paring their conceptions of the ‘fact.’

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Chapter 2 Albert Einstein’s fact: ‘why’ is nature?

Albert Einstein and the ‘new’ physics

At this point, we turn to the second protagonist of this story: Albert Einstein (figure 3). Einstein’s 1905 paper On the Electrodynamics of Moving Bodies, the paper that formed the basis for relativity theory, became the best known physics paper of the 20th_century.68_{Another paper from the same year contained his quantization}

hy-pothesis,69_{which proved essential for quantum theory and for which he received}

the Nobel Prize in 1921.70_{Apart from his contributions to physics, Einstein also}

wrote a lot on epistemology. He saw, as was common for physicists of the time, the history and philosophy as “an integral, critical part of the larger project of phys-ics.”71_{The method of science, especially of physics, was a returning subject for}

Einstein, in personal communication, lectures and articles.72_{Historian of science}

Don Howard notes that “Einstein was (…) one of the most important, active, con-structive contributors to the development of a new empiricism in the 1910s and 1920s.”73_{It is interesting to see how the most influential physicist of recent times}

viewed and used the concept of ‘fact.’

In the introduction, I called Einstein a theoretical physicist. This is probably how most physicists would describe him now, in fact, he used the term himself.74

However, at the beginning of the twentieth century, theoretical physics as a full-fledged discipline was quite new. In the 1870s and 1880s, German universities instituted extraordinary professorships in theoretical physics. These positions were then stepping-stones for young physicists, to ultimately climb up to the position of ordinary professor of experimental physics. Theoretical physics as such was not yet

68_{Galison, P. (2000). Einstein's clocks: The place of time. Critical Inquiry, 26(2), 355-389.}

There 356.

69_{Einstein, A. (1905a). Über einen die Erzeugung und Verwandlung des Lichtes betreffenden}

heuristischen Gesichtspunkt. Annalen der physik, 322(6), 132-148.

70_{Stachel, J. J. (2005). Einstein's miraculous year: five papers that changed the face of}

phys-ics. Princeton, NJ: Princeton University Press.

71_{Howard (2004) There 8}

72_{A good source for Einstein material is the Collected Papers of Albert Einstein (hereafter}

CPAE). Accessible online at http://einsteinpapers.press.princeton.edu/

73_{Howard (2004) There 3}

74_{E.g. in 1914 in his inaugural lecture for his appointment to the Prussian Academy of}

Sci-ences, Einstein refers to his field of work as “theoretical physics.” Doc. 3 in CPAE, Vol 6, There 16.

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established as a sub-discipline of physics.75_{At the turn of the century, Max Planck,}

who became somewhat of a ‘scientific mentor’ for Einstein,76_{was director of one of}

the (very) few institutes of theoretical physics. During his career, he laboured to get theoretical physics at a same level as experimental physics. At the same time, he did not want to split physics in the two separate disciplines. Ironically, his work on quantum theory helped theoretical physics to claim its separate place next to the experimental division.77

Another development in physics around the turn of the twentieth century, was the abandonment of Newtonian Mechanics as the basis of physical science. This did not happen overnight, of course. Mach had criticized Newton’s notions of absolute space and time in his Science of Mechanics, sections of which Einstein quotes in the eulogy he wrote for Mach in 1916.78_{Furthermore, as mentioned in}

the introduction, according to Einstein, it was Mach who made him second-guess his belief in Newtonian mechanics as the basis of physics. Moreover, Einstein used what he called Mach’s Principle in the development of general relativity.79_{With the}

formulation of the relativity theory, Einstein definitively discarded Newtonian me-chanics as the basis of all science.

Thus, the discipline of physics was in turmoil in the first decades of the twentieth century. It seems likely that this tumultuous context and the changing nature of physics coincided with a changing interpretation of the ‘fact.’ In this chapter, I look at what one of the most important physicists of that turbulent time had to say about the ‘fact.’ First, I briefly go into the influence of Mach on Einstein’s general epistemology, then I look at what Einstein called ‘facts’ and compare this to Mach’s definition of fact. Later, I discuss if Einstein’s appreciation for experience, that which gives us knowledge of the facts, according to Mach, was similar to Mach’s.

75_{Jungnickel, C., & McCormmach, R. (1990). Intellectual Mastery of Nature. Theoretical}

Physics from Ohm to Einstein, Volume 2: The Now Mighty Theoretical Physics, 1870-1925,

(vol.2). Chicago, Ill: University of Chicago Press. There 33–43.

76_{Planck was the editor of the Annalen der Physik when he received Einstein’s first relativity}

paper. Upon receiving it, he held a review seminar on the paper. For more on this relation-ship, see Holton (1968).

77_{Van Lunteren (2013). There 107}

78_{Einstein, A. (1916). Ernst Mach. Physikalische Zeitschrift, 17. English translation from J.}

Blackmore (Ed.), Ernst Mach—A deeper look: Documents and new perspectives (Vol. 143) (154-158). Dordrecht, The Netherlands: Springer.

79_{See for instance Von Borzeszkowski, H., & Wahsner, R. (1995). Mach’s Criticism of Newton}

and Einstein’s Reading of Mach: The stimulating Role of Two Misunderstandings. And Hoefer, C. (1995). Einstein’s Formulations of Mach’s Principle. Both in J. Barbour & H. Pfister (Eds.), Mach’s Principle, From Newton’s Bucket to Quantum Gravity (58-90). Boston, MA: Birkhäuser.

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Einstein and Mach

There is quite some literature on the influence of Mach on Einstein.80_Most

histori-ans agree that Einstein was indeed influenced by Mach. However, the exact degree of this influence has been a matter of debate. Holton, for instance, maintains that Einstein accepted the main features of Mach's doctrine in his early career, but as he developed, he moved away from it significantly.81_{Don Howard, on the other}

hand, argues that, although Mach did indeed have an effect on Einstein's thinking, his general epistemology was much closer to Duhem's conventionalism.82

One example of Mach’s influence on Einstein I have already touched upon; the critical stance towards Newtonian mechanics. However, Mach’s influence on Einstein was not only in regard to physics. As Einstein says in his Autobiographical

Notes, in his younger years “Mach’s epistemological position also influenced [him]

very greatly, a position which today appears to me to be essentially untenable.”83

80_{E.g.: Blackmore, J. T. (1972). Ernst Mach, His Work, Life, and Influence (247-285).}

Universi-ty of California Press.; Wolters, G. (1987). Mach I, Mach II, Einstein und die

Relativitätstheo-rie: Eine Fälschung und ihre Folgen. Berlin, Germany: Walter de Gruyter.; Holton, G. (1979).

Constructing a theory: Einstein's model. The American Scholar, 309-340.; Howard, D. (2005). Einstein as a Philosopher of Science. Physics today, 58(12), 34-40.

81_{Holton (1968).}

82_{Howard, D. (1990). Einstein and Duhem. Synthese, 83(3), 363-384.} 83_{Einstein (1949). There 21}

Figure 3: Albert Einstein during a lecture in Vienna in 1921. Source: https://nl.wikipedia.org/wiki/Al bert_Einstein#/media/File:Einst ein1921_by_F_Schmutzer_2.jpg retrieved on 3 March 2018

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Einstein says here that he was influenced greatly by Mach’s epistemology, but only in his younger years. Later, Mach’s epistemological position even seems “untena-ble.” Why did Einstein come to regard Mach’s views as untenable, and more im-portantly, can we see this change in a shifting role of ‘facts’?

‘Facts’ in the 1918 letter

As mentioned in the introduction, Holton argues that in 1918, Einstein called things ‘fact’, that Mach would never consider. He states this after quoting a letter Einstein wrote in 1918, to his lifelong friend Michele Besso. Besso had apparently expressed his concern on the theory of relativity being derived from mathematical thinking only, without having much basis in experience. Einstein replies to this with the objection:

“Dear Michele, On rereading your last letter, I discovered some-thing that downright annoys me: speculation allegedly had re-vealed itself to be superior to empiricism. In this regard you are thinking of the development of the theory of relativity. But I find that this development teaches something different that is almost the opposite, namely, that in order to be reliable, a theory must be built upon generalizable facts.”84

In this paragraph, Einstein seems genuinely upset that his friend accuses him of developing a theory in which “speculation appeared to be superior to empiri-cism,” a theory not based on “generalizable facts.” As we shall see later on, Ein-stein’s view on this will change in the following years. Einstein continues his letter by listing examples of theories and the facts they are built upon:

“[The m]ain theorems of thermodynamics [are based] on the im-possibility of the perpetuum mobile. Mechanics on the empirically explored law of inertia. Kin[etic] gas theory on the equivalency of heat and mech[anical] energy (also historically). Special relativity on the constancy of the velocity of light & Maxwell’s equations for the vacuum, which on their part are based on empirical founda-tions. Relativity with regard to unif[orm] translation is an observed

fact. General relativity: Equivalency of inertial and gravitational mass.”85

Here Einstein gives some examples of what he counts as ‘facts.’ If we com-pare this to Mach’s definition of facts, we see that Einstein had a much more

84_{Einstein to Michele Besso, 28 August 1918, CPAE, Vol 8 (English translations supplement),}

Doc 607. (emphasis in original)

85_{Einstein to Michele Besso, 28 August 1918, CPAE, Vol 8 (English translations supplement),}

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broadly conceived view of what a fact is. To begin with the first example Einstein gives; the impossibility of the perpetuum mobile. Mach addresses the impossibility always as the ‘principle of impossibility of perpetual motion.’86_{Thus we need to}

know what place a ‘principle’ held in Mach’s epistemology, in comparison to a ‘fact.’ In the Science of Mechanics, Mach addresses this issue. Principles of mechan-ics are “experimental knowledge” about bodies, and “no one is warranted in ex-tending these principles beyond the boundaries of experience.” 87_{Thus, a principle}

is the expression of experimental knowledge. If we now go back to Mach’s defini-tion of ‘fact’: something that ‘is’ or ‘happens’ in nature, of which we can obtain knowledge through experience. Hence, ‘knowledge of a fact’ is not the same as ‘a fact.’ As Mach states in a different section of the Science of Mechanics, a principle is the “ascertainment and establishment of a fact.”88_{A principle is an economical}

tool, like a theory or concept, which contains knowledge about facts. Hence, in calling the impossibility of perpetual motion a ‘fact’ Einstein called something a ‘fact’ that Mach called a ‘principle’ and in Mach’s view, they are not the same thing.

Mach was weary of calling principles, concepts or other things that were not immediately given by experience facts. Facts do not need further investigation into their reality. Anything derived from facts, theories, concepts, and principles, needs to be constantly tested and improved by comparing them to new facts. With this in mind, we turn to another example of Einstein’s ‘facts.’ In the letter to Besso, Einstein also notes the ‘constancy of the velocity of light’ as a fact. This is remarka-ble, for Einstein postulates this phenomenon as a principle in 1905. 89_{In moving}

from ‘principle’ to ‘fact,’ Einstein does something that Mach had warned against multiple times, even specifically in relation to the theory of relativity. In the Guiding

Principles Mach states that “matte, time and space are still problems, to which,

incidentally, the physicists (Lorentz, Einstein, Minkowski) are also slowly approach-ing.”90_{Mach did not consider the problem of time and space solved, the special}

theory of relativity had been a step towards the answer, but by no means the solu-tion. Facts, according to Mach, do not need further investigation into their reality. Anything derived from facts, theories, concepts, and principles, need to be con-stantly tested and improved by comparing them to new facts, and most important-ly, economical tools can never ‘become’ facts.

86_{See for instance Mach, E. (1906). Erkenntnis und Irrtum: Skizzen zur Psychologie der}

For-schung. 2nd_{edition. Leipzig, Germany: JA Barth. There 457-458; or Mach’s lecture On the}

Principle of the Conservation of Energy, in Mach E. (1895), 137-185.

87_{Mach (1960). There 280}

88_{Mach (1960). There 86}

89_{“Das Prinzip der Konstanz der Lichtgeschwindigkeit” Einstein, A. (1905b) Zur}

Elektrodyna-mik bewegter Körper. Annalen der Physik, 17, 891-921. There 895

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Thus we see that in 1918, in writing this letter, Einstein does seem to give ‘facts’ a similar importance over speculation, as Mach would. However, as Holton correctly states, Einstein does have a different idea of what a ‘fact’ is, than Mach. It seems that Einstein’s definition of fact in 1918 allows for more speculation, or the-ory. As we have seen, in Mach’s facts, no theory or other economical tool, is the same as a ‘fact.’

Moving further away from Mach

As Einstein himself said, Mach’s epistemology influenced him greatly in his younger years. Although he had a broader definition of ‘facts’ in 1918, it does seem that he gives them similar importance in his science as Mach. However, if we look at later publications of Einstein, we see a clear shift in definition and appreciation of ‘facts’ with Einstein.91_{An early indication of this shift is given by the comparison of the}

eulogy Einstein wrote for Mach in 1916, and some remarks he made in 1922, when Einstein visited Paris and discussed his theory of relativity.92_{Just before this, in}

1921, Mach’s last book Optics had just been published posthumously with an in-troduction he had written around 1913, in which he distances himself from Ein-stein’s relativity.93 _{It appears that the Einstein’s work had become too}

mathemati-cal and conceptual for Mach’s taste. Until the publication of the Optics, Mach had

91_{In the literature, Einstein is often said to have gone from an empiricist view of science,}

inspired by Mach and Hume, to a form of realism in his later work. This shift was, of course, a gradual one, and Holton has shown that even though in his early work, his empiricism was greatly motivated by Mach, Einstein did already have realist inclinations. However, Jeroen van Dongen has demonstrated that Einstein can be seen as an experimentalist in his early career, but by the 1930s, his general epistemic views had changed into a kind of ‘scientific realism.’ Van Dongen argues that Einstein’s epistemological views were influenced in a ma-jor way by the changing nature of his science. As Einstein progressed towards more and more mathematical and theoretical physics in his unification programme, he tended to stress the importance of rationality over experience. Thus, this was a means to justify his own scientific work, but also showed his attitude towards quantum physics. See for a discus-sion of the shift in Einstein’s work: Holton (1968).; Van Dongen, J. (2010). Einstein’s

Unifica-tion. Cambridge, United Kingdom: Cambridge University Press. And Hentschel, K. (1992).

Einstein's attitude towards experiments: Testing relativity theory 1907–1927. Studies in

History and Philosophy of Science Part A, 23(4), 593-624. For a critique of this view, see

Howard, D. (1993). Was Einstein really a realist?. Perspectives on Science, 1(2). and Howard (2004)

92_{For a discussion of Einstein’s time in Paris, see for instance CPAE, Vol. 13, There xlvi-li; or}

Canales, J. (2015). The Physicist and the Philosopher. Princeton, NJ: Princeton University Press.

93_{Mach, E. (1921). Die Prinzipien der physikalischen Optik: historisch und}

The concept of 'fact' in German physics around 1900: a comparison between Ernst Mach and Albert Einstein