Abstract
This chapter investigates the histories of sciences put forward in the second half of the nineteenth century on the European continent and the historiographical frameworks that shaped those histories. The authors were mainly scientists and mathematicians with marked historical interests and sometimes with a good philosophical background. More specifically, the chapter focuses on German-speaking and French-speaking scientists-historians and mathematicians-historians. Deep scientific, technological, and social transformations took place in the last decades of the century, together with a process of professionalization and specialization of scientific practices. These scientists undertook meta-theoretical research on the explicit and implicit foundations of sciences, on the development of scientific theories and practices over time, and on aims and methods of sciences. The awareness of the complexity of scientific traditions can be found both in French research from Cournot to Duhem and in German research from Cantor to Mach. The existence of this cultural environment allows us to understand that Mach and Duhem cannot be looked upon as isolated forerunners. They represented the starting point of the subsequent professionalization of meta-theoretical research on science and at the same time the most meaningful outcome of historical research that spread through Europe from the mid-nineteenth century.
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Notes
- 1.
The establishment of definite boundaries between science and philosophy was one of the achievements of scientific practices in the late nineteenth century. As Pickstone pointed out, “the sciences we take for granted – chemistry, physics, biology, and so forth – were chiefly the creations of the nineteenth century.” Moreover, we should distinguish the process of professionalization from the process of institutionalization in the field of the history of sciences. Institutionalization occurred now and then at the end of the century but took place in a systematic way only after World War II (Pickstone 2007, pp. 490 and 492). Professionalization took place at the end of the nineteenth century, when sophisticated historiographies began to spread throughout Europe.
- 2.
Scandinavian historians of mathematics frequently published or re-published their research in German or French.
- 3.
- 4.
According to Iggers, until the early nineteenth century, “there had been two dominant traditions of writing history: one predominantly learned and antiquarian, the other essentially literary.” History was looked upon as history of European élite and its “key institutions, primarily the state, that occupied the central role in the narrative.” There was only one history (Iggers 2005, pp. 23, 52, and 142–43).
- 5.
At the end of the century, a design of international collaboration was put forward by the German mathematician Felix Klein. His Encyklopädie der mathematischen Wissenschaften encompassed both the mathematical body of knowledge and its history. This encyclopedia was published in German and then in French.
- 6.
According to Frederick Beiser, German historicism might be traced back to Herder and to a cultural tradition that merged history with natural history and natural laws. This complex network of influences led to some unexpected philosophical convergences like the provisional alliance between Ranke and positivists (Beiser 2011, pp. 100–105, 167–168, 255, 261, and 323–327).
- 7.
Droysen also blamed “the false alternative between materialism and idealism” (Droysen 1875, p. 11).
- 8.
On the network of philosophical influences on German historicism, see McQuillan (2013, p. 136): “… some of the figures associated with the historicist tradition identified with the enlightenment, while others turned to historicism in reaction against the enlightenment. […] many early historicists saw their work as an extension of enlightenment naturalism and the “science of man”, while later historicists tried to distinguish their methods from those of the natural sciences”.
- 9.
Until the end of the seventeenth century, investigations into the history of mathematics were part of mathematical practice: historical introductions and historical remarks were quite common in mathematical papers and textbooks. At the same time, since ancient mathematics had been surpassed by the modern one, mathematicians thought that old mathematics did not deserve a specific field of research (Peiffer 2002, pp. 4–5).
- 10.
See Nesselmann (1842, p. 1): “Die Geschichte der Mathematik ist, wie es scheint, sehr frühe behandelt worden.”
- 11.
- 12.
Comte had an enduring influence both in French-speaking countries and in England. Going beyond Comte’s sharp scientism, William Whewell delved into the philosophical structures of scientific thought in his The Philosophy of the Inductive Sciences, Founded Upon Their History (Whewell 1847, vol. 1, pp. v–x, 1, 7, and 14; Whewell 1847, vol. 2, pp. 321–322, 324, 326, and 329). An intermediate philosophy between Comte’s and Whewell’s can be found in Mill’s (1848) A System of Logic, Ratiocinative and Inductive. For a wider analysis of French and English positivist environment, see Bordoni (2017b, pp. 21–25).
- 13.
After becoming Dean in Grenoble, in 1838, Cournot was appointed General Inspector of Public Education. In the same year, he published a short book on the mathematical theory of economics, Recherches sur les principes mathématiques de la théorie des richesses, and in 1843, a longer book on statistics and probability, focusing on their philosophical and scientific foundations. In 1851, in the book Essai sur les fondements de nos connaissances et sur les caractères de la critique philosophique, he undertook a sophisticated analysis of scientific practices, just highlighting the role of statistics and probability. For Cournot’s biography, see Moore (1905, pp. 521–543).
- 14.
It is worth stressing that Cournot rejected any reductionism, in particular the reduction of life sciences to chemistry and physics. He restated his anti-reductionism in the 1872 book Considérations sur la marche des idées et des événements dans les temps modernes. His philosophical stance was not shared by many authoritative scientists. For instance, in the same year, the renowned German physiologist Emile Du Bois-Reymond claimed that scientific knowledge consisted in “reducing all transformations taking place in the material world to atomic motions.” A strict reductionism led him to a strict determinism: the universe was ruled by mechanical necessity (Du Bois-Reymond 1872, pp. 441–444 and 446). For more details, see Bordoni (2017a, pp. 64–72).
- 15.
It is worth remarking that, only a century after Cournot’s investigations, in the second half of the twentieth century, scholars inquired extensively into the differences between the two traditions. See Thomas Kuhn’s interpretation of “classical” and “Baconian” sciences (Kuhn 1976, pp. 4–22).
- 16.
Cantor attended Arneth’s lectures in Heidelberg, Gauss and Wilhelm Weber’s lectures in Göttingen, and those of Lejeune Dirichlet in Berlin. He also met Chasles in Paris in 1860 (Lützen and Purkert 1994, pp. 2–3).
- 17.
For the influence of Chasles on Cantor and Zeuthen, see Peiffer (2002, p. 22): “Chasles played a major role in establishing the history of mathematics as a subdiscipline of mathematics. Through his immense reputation, …, Chasles exercised an influence on many mathematicians, French and foreign, including Hieronymus Zeuthen and Moritz Cantor, that is still under-appreciated.”
- 18.
In 1936, the Belgian historian of sciences George Sarton pointed out that Cantor’s account of “ancient and medieval period and oriental mathematics in general” was definitely “insufficient”: his history of mathematics should be “entirely rewritten.” However, many details had already been corrected by the historian of mathematics Gustaf H. Eneström and his collaborators in the journal Bibliotheca Mathematica. With regard to Zeuthen, Sarton remarked that “he was himself a creative mathematician and had a keener sense of mathematical subtleties than Cantor” (Sarton 1936 (1957), pp. 42 and 44).
- 19.
In 1834, after having got his PhD from the University of Berlin, Poggendorff became extraordinary professor of physics in the same university, and there he remained until his death in 1877. For many years, he was in charge as the Annalen der Physik und Chemie’s editor, the best-known and the most authoritative scientific journal in German-speaking countries in the nineteenth century. This was his lifework, the translation of foreign papers included. In 1863, he published an extensive, encyclopedic Handwörterbuch on the history of exact sciences in two volumes, with biographies of many scientists and short accounts of their achievements and publications.
- 20.
We have seen that this historiographical thesis had already been put forward in Cournot (1872, pp. 292–294). See also footnote 15.
- 21.
Mach’s frequent mention of the “economy of thought” has led many historians and philosophers to speaking of Mach’s empiricism. However, even philosophers who lean toward this thesis have acknowledged that “Mach’s empiricism is complicated.” According to Paul Pojman, such empiricism would be mitigated by “the belief that knowledge is a product of evolution, that our senses, minds, and cultures have an evolutionary history.” Mach’s historical research might be looked upon as “archaeologies of science, digging at the past to critically elucidate the present” (Pojman 2020, online Stanford Encyclopedia of Philosophy).
- 22.
See Banks (2021, p. 273): “It is very wrong to say that Mach was sceptical of laws or abstract principle and believed only in economical lists of particulars. His view of economy is much more subtle than that.”
- 23.
Mach’s concept of “economy” has been widely debated by historians and philosophers, and the interpretation of this concept always depends on the philosophical classification of Mach’s thought. When Mach is considered as an empiricist, its “economy” undergoes an empiricist nuance; when Mach becomes a pragmatist, even its “economy” leans toward pragmatism, and so on …. The fact is that “the economical role of science” (“die Oekonomie der Wissenschaft”) made reference to any rational procedure that helps us set the empirical body of knowledge in order. In the context of Mach’s research, the adjective economical and the noun economy essentially mean theoretical systematization. According to Mach, there is no science without rational or theoretical practices (Mach 1883, pp. 452 and 454).
- 24.
In 2004, Erik Banks pointed out Mach’s awareness of the intrinsic tension between the “uniqueness” of individual events and “abstract laws and schemata, however necessary these were for the pursuit of science.” There was a conflict between “his heraclitean view of nature as a limitless non-repeating flux and his commitment as a scientist,” namely, “the view that nature repeats itself with sufficient regularity to frame true laws and symmetries” (Banks 2004, pp. 23, 25, 27, and 29). In other words, science requires “the economy of thought” that leads from individual events to laws and theories. The search for synthesis or economy is the core of scientific practices.
- 25.
During the twentieth century, many philosophical labels were put forward in order to qualify Mach’s intellectual enterprise: phenomenalist, empiricist, instrumentalist, pragmatist, etc. Because of “the increasing tendency to think of science in formal terms,” sometimes, Mach has been looked upon as some kind of “a pre-logical positivist.” Probably “historicist naturalism” is the most reasonable label for qualifying Mach’s stance (Preston 2021, p. 7). It is also reasonable that “Mach’s historicist naturalism be looked upon as an original form of pragmatism” (Uebel 2021, p. 99).
- 26.
Gerland lectured in physics and electrotechnics in a peripheral institution, the Königliche Bergakademie in Klausthal (Royal Institute of Mining Engineering in Clausthal, in Lower Saxony).
- 27.
According to the historian of philosophy Isaac Benrubi, Cournot’s intellectual pathway does not suit “a definite summary and a sharp classification” (Benrubi 1926, pp. 89–90).
- 28.
- 29.
On the influence of German history of philosophy on Tannery and more specifically on the philosophical background of the conception “of history of science as complementary to history of philosophy,” see Catana (2011, pp. 517–523).
- 30.
George Sarton praised Tannery for having early understood the plurality of skills and sensitivities the history of science required More specifically, Tannery combined “a philological precision with a wide and profound scholarship, and a remarkable philosophical awareness” (Sarton 1954, p. 321).
- 31.
On Milhaud’s institutional role in the establishment of a chair of philosophical history of science in France, see Chimisso (2008, pp. 25–26).
- 32.
On Duhem’s design for a generalized mechanics, see Bordoni (2012a, pp. 238–43) and Bordoni (2012b, Chaps. 6–10). Duhem’s generalized mechanics or Energetics should not be identified with Georg Helm and Wilhelm Ostwald’s Energetics, which dealt with the universality of the principle of the conservation of energy and on the replacement of mass with energy as the fundamental physical entity. On the friendship between Duhem and Ostwald, see Brouzeng (1981, vol. 2, pp. 226–228).
- 33.
Mach’s Mechanik was translated into French only in 1904, whereas Mach’s follower Friedrich Adler translated Duhem’s 1906 La théorie physique into German in 1908. Mach himself wrote the introduction.
- 34.
Duhem’s representation of the history of science as a periodical series of dull applications and exciting revolutions was developed 70 years later in a completely different intellectual context. See Kuhn’s “normal” and “revolutionary” stages in the history of sciences (Kuhn 1962 (1996), pp. 10 and 111). In that context, Kuhn did not mention Duhem.
- 35.
At that time, Duhem was “maitre de conférences” at Lille University; for further biographical details, see Brouzeng (1987, p. 54).
- 36.
Duhem’s meta-theoretical design was better unfolded only afterward in a book he published in 1903, L’évolution de la mécanique (Duhem 1903 (1992), pp. 199 and 218–219).
- 37.
The original passage deserves to be quoted: “Ainsi, sous les théories qui ne s’élèvent que pour être abattues; sous les hypothèses qu’un siècle contemple comme le mécanisme secret et le ressort caché de l’Univers, et que le siècle suivant brise comme des jouets d’enfant, se poursuit le progrès lent, mais incessant, de la physique mathématique” (Duhem 1894, p. 125). Stoffel pointed out the striking analogy between Duhem’s passage and one of Pascal’s Pensées on cyclic, historical processes (Pascal 1951, p. 417; Stoffel 2007, pp. 292–293). I point out the analogy with Naville’s passage on the slow, scientific progress underlying the appearance and disappearance of theories (Naville 1883, p. 55).
- 38.
- 39.
For instance, more than 10 years ago, Paul Forman pointed out the markers of “the transition from modernity to postmodernity” in science (Forman 2010, pp. 157–158).
- 40.
It is worth stressing that this network of cultural transformations “was as yet understood, or even observed, by relatively exiguous numbers of men and women in a handful of countries” (Hobsbawm 1989, p. 243). At the same time, the technical and social progress was really enjoyed by large communities, more specifically large cities’ inhabitants. They could actually rely on electric lighting, electric means of transportation, and electric means of communication. See footnote 3.
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Bordoni, S. (2023). The Emergence of a Sophisticated Historiography of Science in Continental Europe in the Late Nineteenth Century. In: Condé, M.L., Salomon, M. (eds) Handbook for the Historiography of Science. Historiographies of Science. Springer, Cham. https://doi.org/10.1007/978-3-030-99498-3_24-1
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