Leibnizâs correspondence in mathematics, science and technology is being edited and published in Series III of the German Academy Edition of all of his writings and letters.1 The first volume of the third series covering the period of Leibnizâs sojourn in Paris (1672â1676) was edited by Joseph Ehrenfried Hofmann (1900â1973) and published posthumously in 1976, and in a revised form in 1988.2 Hofmann was a scholar â whose specialist interest was the development of Leibnizâs infinitesimal calculus during the Paris period â and the author of Die Entwicklungsgeschichte der Leibnizschen Mathematik während des Aufenthaltes in Paris (1672â1676), published in 1949,3 and of Leibniz in Paris 1672â1676 â his growth to mathematical maturity, published in 1974 and reprinted in 2008.4 The overriding interest in mathematics in the first volume of the series meant that the systematic presentation of Leibnizâs correspondence in science, technology â a term that was used for the first time in the modern sense more than 60 years after Leibnizâs death â and medicine only began with the publication of the second volume in 1987, which covered Leibnizâs first years in Hanover from 1676 to 1679.5 Subsequent volumes of the series then appeared in 1991, 1995, 2003, 2004, 2011 and 2015, covering Leibnizâs life to the year 1701.6
The present work aims to present in English central themes, and central texts, from Leibnizâs correspondence in science, technology and medicine derived mainly from the first eight volumes of Series III of the Academy Edition. Chapter 1 presents key texts published (for the most part) in the first three volumes of the series. Each one of the following five chapters (Chapters 2 to 6) then presents texts published (again for the most part) in a specific volume of the series (volumes 4 to 8). The author of the present work (writing here in the third person) has coedited the texts of (and coauthored the introductions to) the latter five volumes. However, the ideas and interpretations presented here in the introduction, and in the text presentations, are the outcome of the joint editorial âspadeworkâ undertaken in cooperation with a range of former colleagues over a period of twenty six years spent at the âLeibniz-Archivâ, the editorial and research center at the âGottfried Wilhelm Leibniz Bibliothekâ, the State Library of the German federal state of Lower Saxony, in Hanover.
A play on words, a pun around the German word âBandâ (meaning volume), gave rise within the editorial team to the designation âBandleaderâ (bandleader or band leader) for the most senior colleague working on a particular volume. In this vein then, mention must be made here of the âband leadersâ whose ideas and interpretations find expression in the present work (albeit in translation by the author), namely Herbert Breger (Volume 3), Heinz-Jürgen Heà (Volumes 2, 4, 5 and 6), and Charlotte Wahl (Volume 8). The author of the present work then had the honor to act as a âbig band leaderâ for Volume 7 (with more than 1000 printed pages), covering the period of the greatest density of Leibnizâs correspondence in mathematics, science and technology, namely from July 1696 to December 1698. Besides the ideas and interpretations of the âband leadersâ referred to here, those of other former colleagues who worked on the volumes of Series III may possibly also be found in the present work, namely Ralf Krömer and Heike Sefrin-Weis (Volume 7) and Uwe Mayer (Volume 8).
If the play on words, or pun, around the German word âBandâ be applied to the present volume, then the author must surely be seen in his role as a âbroad band leaderâ and architect of a volume in which there is a shift away from a predominance of mathematics, with scientific subject areas now becoming more prevalent. While mathematics retains its pivotal (or pole) position in many respects, nine other scientific or scholarly subject areas have been identified and included alongside mathematics. The present âbroad bandâ represents, as it were, a decathlon of the history of science and technology at the end of the seventeenth century, with the âbroad band leaderâ assuming the role here of an editorial decathlete. The authorâs penchant for a âbroad-bandâ approach is attributable, on the one hand, to a scholarly background in engineering, engineering science and the history of science and technology (rather than mathematics and history of mathematics, or philosophy and history of philosophy) and, on the other hand, to a latitudinal early academic career development (spent for the most part in western Europe along or near the 53rd parallel north, or circle of latitude), specifically at the National University of Ireland, the former University of Manchester Institute of Science and Technology (UMIST), the former âTechnische Hogeschool Delftâ, and the former âInstitut für Social- und Wirtschaftsgeschichteâ, the then center for social and economic history, and history of technology, at the University of Hamburg. Although not primarily concerned with Leibniz or his correspondents, the works of a number of former mentors, influencers and colleagues are cited in the footnotes, and listed in the Bibliography. These include James Dooge (history of fluid mechanics after Galileo), Donald Cardwell (thermodynamics in the early industrial age), Richard Hills (history of power technology), Alan Williams (medieval and early-modern arms and armor), Emrys Evans (Celtic studies), Olaf Pedersen and Maureen Farrell (early physics and astronomy, and the historical interaction between science and religion), Volker Bialas (Kepler Edition), specialists in Christiaan Huygens studies from the years between the Huygens anniversary celebrations in 1979 and 1995 (including Henk Bos, Joella Yoder, Jan van Maanen), and Ulrich Troitzsch (technological thought in the late seventeenth and eighteenth centuries).
Although not intended as a biography of Leibniz, the Introduction and the six chapters present factual and chronological biographical information, which is intended to serve as a frame of reference for his interaction with his correspondents and which in turn may serve as a basis for Leibniz biographical and chronological studies in the future.7 The work Leibniz: A biography of the historian of mathematics and physics, Eric J. Aiton (1920â1991), was for the author of the present work the first real introduction to Leibniz studies.8 Having first encountered the biographer at the University of Manchester in the mid-1970s, it was a pleasure to have discussions with him in Germany at the end of the following decade. However, Aitonâs biography was published at the time when only the first volume of Leibnizâs correspondence in mathematics, science and technology had been published. A further issue is the fact that the sum total of Leibnizâs correspondence covers many more scholarly fields than those scientific areas treated in the present work, as for example the fields of logic, metaphysics, ethics, jurisprudence, political and social philosophy, and history (to name just those alluded to by a peer reviewer of the present work) and which of course are central aspects for biographers of Leibniz like, for example, Maria Rosa Antognazza.9 At all events, the author of the present work would argue that Leibniz, following studies and academic qualification in philosophy and jurisprudence, first became a scientist â an alchemist or chemist,10 who in 1667 was secretary of an alchemical society in Nuremberg,11 and who contemplated at that time editing the works of renowned alchemists â before becoming a jurist, mathematician, engineer, scientist and philosopher. If the years 1672â1676 marked (in the words of Hofmann) Leibnizâs growth to mathematical maturity, the years 1676â1701 surely marked his growth to maturity in a range of scientific disciplines. The raison dâêtre then of the present work is accordingly â following in the footsteps of Eric Aiton â to lay on the foundation of Leibnizâs correspondence the groundwork for a more pronounced scientific dimension in future Leibniz biographical studies. In this sense too, the ten âthesesâ presented in the epilogue â each arising within one of the ten subject areas considered, and each epitomized by a leading quotation, reflecting Leibnizâs ambitions and intentions in that field â should be seen. Leibnizâs correspondence reveals his fundamental standpoint that, although mathematics and the sciences are rooted in metaphysics, or (to use the formulation of the authorâs former colleague at the Leibniz edition, Hartmut Hecht) are within the paradigm of metaphysics,12 one cannot use metaphysics to explain the physical world (or universe) and its laws. In view of the traditional proximity of paradigms and scientific revolutions,13 in the history of science and mathematics,14 the author of the present work suggests an alternative paradigm, or framework, which might be formulated as âGottfried Wilhelm Leibnizâs Correspondence: Science, Technology and Medicine within the paradigm of the Scientific Revolutionâ. Leibnizâs correspondence reveals him not just as a philosopher, but also as a scientist in the tradition of major figures of the Scientific Revolution of the seventeenth century, which saw the replacement of qualitative scholastic Aristotelian natural philosophy by quantitative mechanistic Newtonian mathematical physics and the evolution of âClassical Scienceâ.15 The Scientific Revolution likewise saw the appearance of a group of outstanding scientists and mathematicians, which included Johannes Kepler, Galileo Galilei, René Descartes, Pierre de Fermat, Christiaan Huygens, Isaac Newton,16 and of course Leibniz himself, and which pursued an envisioned goal â that followed from Galileoâs new conception of the task of science and that was in accordance with the explicit statement by Newton of the mathematical principles of natural philosophy (in the title of his magnum opus) â of discovering the mathematical relations that hold for the physical world (or universe).17
As regards philosophy, Leibniz appears at times to be at odds not just with Cartesian philosophy, but with metaphysics as such. Specifically he appears to follow in the footsteps of Galileo as an engineer and proponent of rational thought and experimental science.18 Leibniz even expressed his standpoint (in a letter to Friedrich Hoffmann on November 1, 1701) that, in higher education, a single lesson (or lecture hour) in experimental science had a greater value for him than a hundred corresponding lessons in metaphysics, logic, or ethics. Drawing inspiration from the book Christianity not mysterious (1696) of the Irish âhereticâ John Toland,19 one who, having fallen out with the Catholic Church, subsequently fell foul of the Irish Protestant Ascendancy, before going on to become a âpersona non grataâ in Hanover,20 and with the perception that Leibnizâs standpoint (namely that, although mathematics and the sciences are rooted in metaphysics, one cannot use metaphysics to explain the physical world) mirrors Tolandâs deistic, rationalistic, and controversial standpoint (namely that, although God created the world, there was no subsequent divine interaction with, or direct intervention in, that created world),21 the author of the present work coined the title âScience not metaphysicalâ for an earlier publication on Galileoâs influence on Leibniz, which was also intended as a plea for a research and editorial approach to the edition of Leibnizâs correspondence in mathematics, science and technology, within the framework of the academic field of history of science and technology, and embracing the paradigm of the scientific revolution, rather than that of metaphysics.22
In the history of science and religion, following the triumph of Copernican- Galilean heliocentrism,23 geological, geomorphological, cosmological, and cosmogenic theorizing then served â in the time of Newton and Leibniz â to greatly undermine the strict historical veracity of Biblical narrative.24 And so the interaction between science and religion in the early-modern period led ultimately, in the words of Olaf Pedersen, to a âdivorce of science and religionâ.25 Pedersen has, for example, likewise described Leibnizâs meeting with the Danish physician, geologist, and Catholic theologian Nicola(u)s Steno (Niels Stensen) in Hanover, on December 7, 1677,26 as the meeting of a âScientist and [a] Saintâ, of a âRationalistâ and a âFaithful Observerâ, and which was the overture perhaps to their extensive scientific, philosophical, and theological exchanges.27 In the light of this divorce of science and religion, Leibniz chose, in treating the physical world, to take the low road, as it were, of enlightenment, and of rational thought and scientific rationalism,28 rather than the high road, so to speak, of mysticism, religion and theology.29 In this sense then Leibniz stands apart from contemporaries like Robert Boyle, Isaac Newton, William Whiston, and others, who have been broadly characterized as âscientist-theologiansâ, or as advocates of a physico-theology, and who were inspired by a sense of compatibility of science and religion.30 Accordingly, following the concluding thesis of this work â which underlines Leibnizâs role both in the development of rational scientific thought in the last quarter of the seventeenth century, and in an adherence to the principle of the separation of science and religion â and considering also his autobiographical self-characterization of his tiger-like vivacity and sprightly manners (in his letter to Rudolf Christian von Bodenhausen on December 30, 1693), the last line of the Epilogue may be seen as the unofficial title of this book.
The Academy Edition of all of Leibnizâs writings and letters (A) = G. W. Leibniz, Sämtliche Schriften und Briefe, published by the Prussian, later German, and most recently Berlin- Brandenburg Academy of Sciences, together with the Academy of Sciences in Göttingen, Darmstadt (later Leipzig, most recently Berlin), 1923â; to date (end of 2022) 64 volumes in 7 series (IâIV, VIâVIII) have been published.
A III,1 = Academy Edition, ser. III, vol. 1.
J. E. Hofmann, Die Entwicklungsgeschichte der Leibnizschen Mathematik während des Aufenthaltes in Paris (1672â1676), Munich, 1949.
J. E. Hofmann, Leibniz in Paris 1672â1676 â his growth to mathematical maturity, London and New York, 1974 and 2008 (reprint).
A III,2.
A III,3â8.
Cf., for example, K. Müller, G. Krönert (eds.), Leben und Werk von G. W. Leibniz: Eine Chronik, Frankfurt am Main, 1969.
E. J. Aiton, Leibniz: A biography, Bristol and Boston, 1985 and Gottfried Wilhelm Leibniz: Eine Biographie, Frankfurt am Main, 1991.
M. R. Antognazza, Leibniz: An intellectual biography, New York, 2008.
That is, prior to the denigration of alchemy, an attitude that first began to take hold in the eighteenth century; cf. p. 105 in: N. Guicciardini, Isaac Newton and natural philosophy, London (and Chicago), 2018.
Cf. G. MacDonald Ross, âLeibniz and the Nuremberg alchemical societyâ, Studia Leibnitiana, vol. 6(2), (1974), pp. 222â248.
Cf. H. Hecht, Gottfried Wilhelm Leibniz: Mathematik und Naturwissenschaften im Paradigma der Metaphysik, Stuttgart, Leipzig, 1992. In the context of this âparadigm of metaphysicsâ, see also for example: R. T. W. Arthur, Classic thinkers: Leibniz, Cambridge, UK, and Malden, MA, 2014.
Cf. T. S. Kuhn, The structure of scientific revolutions, Chicago, 1962, 1970, 1996, and 2012; see chap. V (The priority of paradigms); T. S. Kuhn, The Copernican revolution: Planetary astronomy in the development of western thought, Cambridge, MA, 1957 and 1992.
In this context, cf. R. C. Brown, The tangled origins of the Leibnizian calculus: A case study of a mathematical revolution, Singapore, New Jersey, London, 2012; see in particular chap. 1, pp. 1â14 (Evolution or revolution in mathematics: The case of Leibniz), and chap. 11, pp. 231â244 (Some concluding remarks on mathematical change).
Cf. E. J. Dijksterhuis. De mechanisering van het wereldbeeld, Amsterdam, 1950, 1983, 1998, and 2006: E. J. Dijksterhuis (C. Dikshoorn, trans.), The mechanization of the world picture, Oxford, London, New York, 1961, 1969, and Princeton, 1986; see Part IV (The evolution of classical science).
Cf. for example: I. Bernard Cohen, The Newtonian revolution with illustrations of the transformation of scientific ideas, Cambridge and New York, 1980 and 1983; H. F. Cohen, The scientific revolution: A historiographical inquiry, Chicago, 1994; J. Henry, The scientific revolution and the origins of modern science, Basingstoke, New York, 1997; J. C. Boudri (S. McGlinn, trans.), What was mechanical about mechanics: The concept of force between metaphysics and mechanics from Newton to Lagrange, Dordrecht, 2002; see chap. 1, pp. 5â8 (The horizon of the scientific revolution).
Cf. M. Kline, Mathematics in western culture, Oxford, London, New York, 1953 and 1964; see chap. 16 (The Newtonian influence: Science and philosophy), in particular p. 237.
Cf. M. Valleriani, Galileo engineer (Boston Studies in the Philosophy of Science, vol. 269), Dordrecht, Heidelberg, London, New York, 2010.
Cf. J. G. Simms, âJohn Toland (1670â1722), Donegal hereticâ, Irish Historical Studies, vol. 16, no. 63, (March 1969), pp. 304â320; M. Brown, A political biography of John Toland, Oxford, New York, 2012, and in particular chap. 1 (Ireland, 1670â1697), chap. 2 (London, 1697â1700), and chap. 3 (Hanover, 1701â1707).
Cf. N. Gädeke, âMatières dâesprit et de curiosité oder: Warum wurde John Toland in Hannover zur persona non grata?â, pp. 145â166, in: W. Li, S. Noreik (eds.), G.W. Leibniz und der Gelehrtenhabitus: Anonymität, Pseudonymität, Camouflage, Cologne, Weimar, Vienna, 2016.
Cf. J. Toland, Christianity not mysterious, or a treatise shewing, that there is nothing in the Gospel contrary to reason, nor above it, and that no Christian doctrine can properly be callâd a mystery, London, 1696; P. Mc Guinness, A. Harrison, R. Kearney (eds.), John Tolandâs Christianity not mysterious: Text, associated works and critical essays, Dublin, 1997. Regarding Leibnizâs thought on divine creation, see for example N. G. Robertson, âThe doctrine of creation and the enlightenmentâ, pp. 425â439, in: R. D. Crouse, W. Otten, W. Hannam, M. Treschow (eds.), Divine creation in ancient, medieval, and early modern thought, Leiden, Boston, 2007.
Cf. J. G. OâHara, âScience not metaphysical: Leibniz als Naturwissenschaftler in der Nachfolge von Galileiâ, pp. [33]â56 in: M. Kempe (ed.), Der Philosoph im U-Boot: Praktische Wissenschaft und Technik im Kontext von Gottfried Wilhelm Leibniz, Hanover: Gottfried Wilhelm Leibniz Bibliothek, Forschung, vol. 1, 2013.
Cf., for example, O. Pedersen, Early physics and astronomy: A historical introduction, Cambridge, 1974 and 1993, chap. 20 (The reform of astronomy), and in particular pp. 263â282 (Nicolaus Copernicus, and after Copernicus); F. Krafft, âDie Copernicanische Revolutionâ, Antike und Abendland, vol. 40, (1994), pp. 1â30 (Reprinted as pp. 181â214 in: H. Kuester (ed.), Das sechzehnte Jahrhundert: Europäische Renaissance, Regensburg, 1995); M. A. Finocchiaro, Defending Copernicus and Galileo: Critical reasoning in the two affairs (Boston Studies in the Philosophy of Science, vol. 280), Dordrecht, Heidelberg, London, New York, 2010; J. L. Heilbron, Galileo, Oxford, 2010.
Cf. I. Leask, âConstant process: The science of Tolandâs pantheisticonâ, Eighteenth-Century Ireland/ Iris an dá chultúr [Ireland of the two cultures], vol. 34, (2019): pp. 11â27, in particular p. 16.
Cf. O. Pedersen, âThe divorce of science and religion: Historical interaction between science and religionâ, pp. 139â160, in: J. Fennema, I. Paul (eds.), Science and religion: One world â Changing perspectives on reality, Dordrecht, Boston, London, 1990.
Cf. K. Müller, G. Krönert, 1969 (note 7), p. 50.
Cf. A. Vibeke Vad, âPolidore and Théophile: The rationalist and the faithful observerâ, pp. 39â47 (in particular p. 39) in: K. Ascani, H. Kermit, G. Skytte (eds.), Niccolo Stenone (1638â1686): Anatomista, geologo, vescovo, Atti del seminario organizzato da Universitetsbiblioteket i Tromsø e lâAccademia di Danimarca lunedi 23 ottobre 2000 [Proceedings of a Conference on October 23, 2000], (Analecta Romana Instituti Danici, Suppl. XXXI), Rome, 2002; H. Kermit, M. Drake (trans.), Niels Stensen 1638â1686: The scientist who was beatified, Leominster, Herefordshire, UK, 2003; R. Andrault, M. Lærke (eds.), âLeibniz and Steno, 1675â1680â, chap. 3 (pp. 63â84), in: R. Andrault,â M. Lærke (eds.), Steno and the philosophers (Studies in Intellectual History, vol. 276), Leiden, 2018.
Cf. M. Dascal (ed.), Leibniz: What kind of rationalist? Logic, epistemology, and the unity of science, vol. 13, Dordrecht, 2009; see in particular pp. 1â13 (Introduction) and pp. [83]â152 (Part II: Natural sciences and mathematics).
Cf., for example, G. MacDonald Ross, âLeibniz and the origin of thingsâ, Part III (Theology and mysticism), chap. 17 (pp. [241]â257) in: M. Dascal, E. Yakira (eds.), Leibniz and Adam, Tel Aviv, 1993; A. P. Coudert, R. H. Popkin, G. M. Weiner (eds.), Leibniz, mysticism and religion (International archives of the history of ideas, no. 158), Dordrecht, Boston, London, 1998; L. Strickland (ed.), Leibniz on God and religion: A reader, London, 2016.
Cf. R. Jakapi, âEarly modern natural philosophy allied with revealed religion: Boyle and Whistonâ, part IV, chap. 19 (pp. 233â244), in: M. Fuller, D. Evers, A. Runehov, K.-W. Sæther, B. Michollet (eds.), Issues in science and theology: nature and beyond: Transcendence and immanence in science and theology, Cham, Switzerland, 2020; A. Wragge-Morley, Aesthetic science: Representing nature in the Royal Society of London, 1650â1720, Chicago, 2020, in particular Sect.1 (Physico-theology, natural philosophy, and sensory experience).