Historians have long sought putative connections between different areas of Newton’s scientific work, while recently scholars have argued that there were causal links between even more disparate fields of his intellectual activity. In this paper I take an opposite approach, and attempt to account for certain tensions in Newton’s ‘scientific’ work by examining his great sensitivity to the disciplinary divisions that both conditioned and facilitated his early investigations in science and mathematics. These momentous undertakings, exemplified by research that he wrote (...) up in two separate notebooks, obey strict distinctions between approaches appropriate to both new and old ‘natural philosophy’ and those appropriate to the mixed mathematical sciences. He retained a fairly rigid demarcation between them until the early eighteenth century. At the same time as Newton presented the ‘mathematical principles’ of natural philosophy in his magnum opus of 1687, he remained equally committed to a separate and more private world or ontology that he publicly denigrated as hypothetical or conjectural. This is to say nothing of the worlds implicit in his work on mathematics and alchemy. He did not lurch from one overarching ontological commitment to the next but instead simultaneously—and often radically—developed generically distinct concepts and ontologies that were appropriate to specific settings and locations as well as to relevant styles of argument. Accordingly I argue that the concepts used by Newton throughout his career were intimately bound up with these appropriate generic or quasi-disciplinary ‘structures’. His later efforts to bring together active principles, aethers and voids in various works were not failures that resulted from his ‘confusion’ but were bold attempts to meld together concepts or ontologies that belonged to distinct enquiries. His analysis could not be ‘coherent’ because the structures in which they appeared were fundamentally incompatible.Author Keywords: Connectionism; Incoherence; Appropriateness; Setting; Discipline; Genre; Structure. (shrink)

ABSTRACT Historians of science, inasmuch as they are concerned with knowledges and practices rather than institutions, have tended of late to focus on case studies of common processes such as experiment and publication. In so doing, they tend to treat science as a single category, with various local instantiations. Or, alternatively, they relate cases to their specific local contexts. In neither approach do the cases or their contexts build easily into broader histories, reconstructing changing knowledge practices across time and space. (...) This essay argues that by systematically deconstructing the practices of science and technology and medicine (STM) into common, recurrent elements, we can gain usefully “configurational” views, not just of particular cases and contexts but of synchronic variety and diachronic changes, both short term and long. To this end, we can begin with the customary actors’ disciplines of early modern knowledge (natural philosophy, natural history, mixed mathematics, and experimental philosophy), which can be understood as elemental “ways of knowing and working,” variously combined and disputed. I argue that these same working knowledges, together with a later mode—synthetic experimentation and systematic invention—may also serve for the analysis of STM from the late eighteenth century to the present. The old divisions continued explicitly and importantly after circa 1800, but they were also “built into” an array of new sciences. This historiographic analysis can help clarify a number of common problems: about the multiplicity of the sciences, the importance of various styles in science, and the relations between science and technology and medicine. It suggests new readings of major changes in STM, including the first and second scientific revolutions and the transformations of biomedicine from the later twentieth century. It offers ways of recasting both microhistories and macrohistories, so reducing the apparent distance between them. And it may thus facilitate both more constructive uses of case studies and more innovative and acceptable longer histories. (shrink)

The ArgumentThis paper, an attempt at an institutional history of ideas, compares patterns of reproduction of scientific knowledge in Catholic and Protestant educational institutions. Franciscus Eschinardus'Cursus Physico-Mathematicusand Jean-Robert Chouet'sSyntagma Physicumare examined for the strategies which allow for accommodation of new contents and new practices within traditional institutional frameworks. The texts manifest two different styles of inquiry about nature, each adapted to the peculiar constraints implied by its environment. The interpretative drive of Eschinardus and a whole group of “modern astronomers” is (...) here seen as pushing beyond the traditional task of “saving the phenomena,” towards celestial hermeneutics which is thoroughly experimental and mathematical. In spite of the insistence on physical interpretation of celestial phenomena, Eschinardus' astronomical discourse is yet constrained by a complex game of intellectual-political considerations. Commitment to the Thomistic organization of knowledge, which sets a boundary between a science of motion and the “geometry of heavens”, suppresses any impulse to ask about the mechanical causes of celestial appearances. The Copernican cosmology is thus rejected qua an attempt to cross this guarded boundary. Chouet in Geneva, by contrast, frees himself from these constraints on the organization of natural knowledge. By strictly separating philosophy from theology, he can combine physics and astronomy, favor a Copernican cosmology and adopt a Cartesian mechanistic worldview. Moreover, unlike the Jesuit Eschinardus, Chouet seeks toexplainnatural phenomena in terms of causes, rather than justinterpretthem. Yet he does so within a philosophical discourse largely scholastic in nature, which best suits the conservative institutional framework in which he teaches. Whereas the Jesuit Eschinardus employs a new type of discourse without severing his links with the traditional Thomistic worldview, the Calvinist Chouet adopts a new Cartesian worldview and adapts it to a largely traditional type of discourse. (shrink)

This article examines a set of letters and observational reports that passed between Ludwig of Württemberg and Wilhelm of Hesse in response to the nova of 1572. Discussing the terminology used in this debate, it demonstrates that the terms “star” and “comet” were not unambiguous for sixteenth-century authors. A consideration of the relationship between accuracy of observation and the accuracy of the conclusions drawn from them, judged in the terms of twentieth-century astronomy, shows that those observers with the best instruments (...) did not always have the best understanding of what they had observed. Finally, the role played by theology in facilitating interpretations that did not accord with Aristotelian physics is highlighted. (shrink)

This paper argues that Kepler considered his work in optics as part of natural philosophy and that, consequently, he aimed at change within natural philosophy. Back-to-back with John Schuster’s claim that Descartes’ optics should be considered as a natural philosophical appropriation of innovative results in the tradition of practical and mixed mathematics the central claim of my paper is that Kepler’s theory of optical imagery, developed in his Paralipomena ad Vitellionem (1604), was the result of a move similar to Descartes’ (...) by Kepler. My argument consists of three parts. First, Kepler borrowed a geometrical model and experiment of optical imagery from the mélange of mixed and practical mathematics provided in the works of the sixteenth-century mathematicians Ettore Ausonio and Giovanni Battista Della Porta. Second, Kepler criticized the Aristotelian theory of light and he developed his own alternative metaphysics. Third, Kepler used his natural philosophical assumptions about the nature of light to re-interpret the model of image formation taken from Della Porta’s work. Taken together, I portray Kepler’s theory of optical imagery as a natural philosophical appropriation of an innovative model of image formation developed in a sixteenth-century practical and mixed mathematical tradition which was not interested in questioning philosophical assumptions on the nature of light. (shrink)

It is argued that the disciplinary identity of anatomy and physiology before 1800 are unknown to us due to the subsequent creation, success and historiographical dominance of a different discipline-experimental physiology. The first of these two papers deals with the identity of physiology from its revival in the 1530s, and demonstrates that it was a theoretical, not an experimental, discipline, achieved with the mind and the pen, not the hand and the knife. The physiological work of Jean Fernel, Albrecht von (...) Haller and others is explored to prove this point. In conclusion this old physiological tradition is compared to the new experimental physiology, as practised by Francois Magendie and Pierre Flourens. (shrink)

Following the exploration of the disciplinary identity of physiology before 1800 in the previous paper of this pair, the present paper seeks to recover the complementary identity of the discipline of anatomy before 1800. The manual, artisanal character of anatomy is explored via some of its practitioners, with special attention being given to William Harvey and Albrecht von Haller. Attention is particularly drawn to the important role of experiment in anatomical research and practice-which has been misread by historians as physiological (...) experiment. Although scientific status was claimed by some practitioners for the discipline, the knife remained the tool of the discipline. Finally the differences between the teleological assumptions underlying anatomy, and the 'argument from design' or natural theology are explored. (shrink)

Why did Copernicus's research programme supersede Ptolemy's?’, Lakatos and Zahar argued that, on Zahar's criterion for ‘novel fact’, Copernican theory was objectively scientifically superior to Ptolemaic theory. They are mistaken, Lakatos and Zahar applied Zahar's criterion to ‘a historical thought-experiment’—fictional rather than real history. Further, in their fictional history, they compared Copernicus to Eudoxus rather than Ptolemy, ignored Tycho Brahe, and did not consider facts that would be novel for geostatic theories. When Zahar's criterion is applied to real history, the (...) results are distinctly different. Finally, most of the historical and conceptual problems in applying Zahar's criterion to the Copernican Revolution primarily arise from a deep difficulty in Lakatos's programme: the necessity of individuating research programmes and identifying their originators. 1 Working closely with David Dahl was crucial in developing this paper. Robert Westman's valiant effort to keep me on the historical straight and narrow drastically limited my tendency to a priori historical pronouncements. The Vassar Philosophy Department, John Tompsich, and Jean Sterling were also helpful. (shrink)

: Marin Mersenne was central to the new mathematical approach to nature in Paris in the 1630s and 1640s. Intellectually, he was one of the most enthusiastic practitioners of that program, and published a number of influential books in those important decades. But Mersenne started his career in a rather different way. In the early 1620s, Mersenne was known in Paris primarily as a writer on religious topics, and a staunch defender of Aristotle against attacks by those who would replace (...) him by a new philosophy. In this essay, I would like to examine Mersenne's changing attitude toward Galileo. In the early 1620s, Mersenne lists Galileo among the innovators in natural philosophy whose views should be rejected. However, by the early 1630s, less than a decade later, Mersenne has become one of Galileo's most ardent supporters. How, then, did Mersenne learn to love Galileo? (shrink)

: We question the claim, common since Duhem, that sixteenth century astronomy, and especially the Wittenberg interpretation of Copernicus, was instrumentalistic rather than realistic. We identify a previously unrecognized Wittenberg astronomer, Edo Hildericus (Hilderich von Varel), who presents a detailed exposition of Copernicus's cosmology that is incompatible with instrumentalism. Quotations from other sixteenth century astronomers show that knowledge of the real configuration of the heavens was unattainable practically, rather than in principle. Astronomy was limited to quia demonstrations, although demonstration propter (...) quid remained the ideal. We suggest that Osiander's notorious preface to Copernicus expresses these sixteenth century commonplaces rather than twentieth century instrumentalism, and that neither `realism', nor `instrumentalism', in their modern meanings, apply to sixteenth century astronomy. (shrink)

The ArgumentThe Doctor of Philosophy, a nonmedieval academic figure who spread throughout the globe in the Modern Era, and who emblemized the transformation of academic knowledge into the “pursuit of research,” emerged through a long and tortuous path in the early modern Germanies. The emergence and recognition of the Doctor of Philosophy would be correlative with the nineteenth-century professionalization of the arts and sciences. Throughout the Early Modern Era, the earlier Doctors and older “professional” faculties from the medieval university — (...) Theology, Law, and Medicine — opposed recognition of the Doctor of Philosophy. In Saxony, the forces of “medievalism” were able to block recognition of the Doctor of Philosophy, and they retained the degraded Master of Arts or Philosophy as the highest degree in arts and sciences. Forces of “modernism” prevailed, however, in Austria and Prussia in the late eighteenth and early nineteenth centuries. In Austria, the Doctor of Philosophy arrived as a wholly modern figure, the creation of a nice dossier and a civil service examination: the medieval “juridical” persona became a modern “bureaucratic” persona. Between this bureaucratic modernism of the Austrians and corporatist medievalism of the Saxons, the Prussians pursued a via media. Unlike the Saxons, they recognized the Doctor of Philosophy; but unlike the Austrians, they did not completely bureaucratize the candidate's persona. The Prussians demanded from the candidate a “work of research,” a doctoral dissertation, which exhibited the aesthetic qualities of the Romantic artist: originality and personality. (shrink)

I argue that Copernicus accepted the reality of celestial spheres on the grounds that the equant problem is unintelligible except as a problem about real spheres. The same considerations point to a number of generally unnoticed liabilities of Copernican astronomy, especially gaps between the spheres, and the failure of some spheres to obey the principle that their natural motion is to rotate. These difficulties may be additional reasons for Copernicus's reluctance to publish, and also stand in the way of strict (...) realism as applied to De Revolutionibus, although a realistic astronomy may be envisioned as a goal for Copernicus's research program. (shrink)

: To honor Bernard Goldstein, this article highlights in the "Defense of Theon against George of Trebizond" by Regiomontanus (1436-1476) themes that resonate with leading strands of Goldstein's scholarship. I argue that, in this poorly-known work, Regiomontanus's mastery of Ptolemy's mathematical astronomy, his interest in making astronomy physical, and his homocentric ideals stand in unresolved tension. Each of these themes resonates with Gold- stein's fundamental work on the Almagest, the Planetary Hypotheses, and al-Bitruji's Principles of Astronomy. I flesh out these (...) tensions with an intriguing interpretation of the history of astronomy, in which Regiomontanus contrasts the two-dimensional "eccentric astronomy" attributed to the Almagest and the Arabs with the three-dimensional spheres of the "later" astronomers. A similar contrast reappears when Regiomontanus portrays as a "fictitious art" an astronomy that does not go beyond the accommodation of computations to the appearances. To conclude, I use Regiomontanus's expression to reinstate (pace Goldstein and Barker in this journal, 1998) fictionalism as an actor's category in Osiander and sixteenth-century astronomy. (shrink)

The upheavals of late eighteenth century Europe encouraged people to demand greater liberties, including the freedom to explore the natural world, individually or as part of investigative associations. The Moravian Agricultural and Natural Science Society, organized by Christian Carl André, was one such group of keen practitioners of theoretical and applied scientific disciplines. Headquartered in the “Moravian Manchester” Brünn, the centre of the textile industry, society members debated the improvement of sheep wool to fulfil the needs of the Habsburg armies (...) fighting in the Napoleonic Wars. Wool, as the raw material of soldiers' clothing, could influence the war’s outcome. During the early nineteenth century, wool united politics, economics, and science in Brno, where breeders and natural scientists investigated the possibilities of increasing wool production. They regularly discussed how “climate” or “seed” characteristics influenced wool quality and quantity. Breeders and academics put their knowledge into immediate practice to create sheep with better wool traits through consanguineous matching of animals and artificial selection. This apparent disregard for the incest taboo, however, was viewed as violating natural laws and cultural norms. The debate intensified between 1817 and 1820, when a Hungarian veteran soldier, sheep breeder, and self-taught natural scientist, Imre Festetics, displayed his inbred Mimush sheep, which yielded wool extremely well suited for the fabrication of light but strong garments. Members of the Society questioned whether such “bastard sheep” would be prone to climatic degeneration, should be regarded as freaks of nature, or could be explained by natural laws. The exploration of inbreeding in sheep began to be distilled into hereditary principles that culminated in 1819 with Festetics’s “laws of organic functions” and “genetic laws of nature,” four decades before Gregor Johann Mendel’s seminal work on heredity in peas. (shrink)

The production of big pictures is arguably the most significant sign of the intellectual maturity of a field. It suggests both that the field's broad contours, refined over several generations of scholarship, enjoy the approval of practitioners, and that audiences exist with an interest in or need for overviews. The situation is somewhat more complicated in the history of science, since the existence of big historical pictures precedes that of a well-defined scholarly field by about two centuries. Broadly conceived histories (...) of science and medicine were being written in the eighteenth century, when such an all-encompassing vision was central to the claims about the progress of knowledge upon which Enlightenment ideologues set such store. The Plato to Nato style histories, characteristic of the earlier twentieth century, were written largely by isolated pioneers, and while these were used in teaching as the field was becoming professionalized, recent scholars have preferred to concentrate on a monographic style of research. Despite the existence of the series started by Wiley, and now published by Cambridge University Press, it is only in the last ten years or so that more conscious attempts have been made to generate a big-picture literature informed by new scholarship. It is noteworthy that most of this is addressed to students and general readers, although there is no logical reason why it should not tackle major theoretical issues of concern to scholars. My point about maturity still holds, then, since as a designated discipline the history of science is rather new; it is still feeling out its relationship with cognate disciplines. Big-picture histories have an important role to play in these explorations since they make findings and ideas widely available and thereby offer material through which ambitious interpretations can be debated, modified and transformed. (shrink)

We will examine Kepler's use of a relation between velocity and distance from a centre of circular motion. This relation plays an essential role, through a derivation in chapter 40 of the Astronomia Nova, in the presentation of the Area Law of planetary motion. Kepler transcends ancient and contemporary applications of the distance-velocity relation by connecting it with his metaphysical commitment to the causal role of the Sun. His second main innovation is to replace the astronomical models of his predecessors (...) with an account that derives trajectories from physical principles. In this paper we restrict our attention primarily to the first 40 chapters of Kepler's Astronomia Nova. Hence, we do not discuss Kepler's discovery of elliptical planetary orbits. (shrink)

General discussions of the appropriate relations between history and philosophy of science must be complemented by examinations of particular studies involving both fields. Martin Curd's attempt to illuminate the rationality of theory change through analysis of the Copernican Revolution is such a study; his work is undercut by serious flaws and actually displays an ahistorical approach. The result misleads both about the Copernican Revolution and the general problem of theory change in science. The study does illustrate several types of failing (...) that can vitiate efforts to bring historical considerations into philosophical discussion, namely, pitfalls in the characterization of theories, arguments, range of choices, and criteria. (shrink)

The increased popularity of the label "cultural" within science studies, especially in relation to "cultural studies, " invites consideration of how it is and can be used in historical work. A lot more seems now to be invested in the notion of "cultural history. " This article examines some recent historiography of science as a means of considering what counts as cultural history in that domain and attempts to coordinate it with the sociologically informed studies of the past ten orfifteen (...) years. The label "sociocultural" seems a more useful term by which to capture recent developments. (shrink)

ABSTRACT Looking in particular at the Scientific Revolution, this essay argues that, for all their differences, positivist commentators on science and contextualist historians of science ought to be committed to the view that counterfactual changes in the history of science would have made no significant difference to its historical development. Assumptions about the history of science as an inexorable march toward the truth commit the positivist to the view that, even if things had been different, scientific knowledge would still have (...) ended up where it is. Perhaps surprisingly, the move away from “great man” history and the increasing emphasis among contextualist historians on the broad cultural influences on scientific thought and practice also imply that changes of a restricted or specific nature ought to have no significant effect on general outcomes. Unlike the positivist, however, the contextualist is willing to concede that things might have been different if the entire cultural background had been different. But in such cases the effect of such sweeping changes would be impossible to conceive and so deprive counterfactual history of any useful insights it might be supposed to offer. (shrink)

ArgumentDuring the two decades before the turning point in Copernicus's personal and scientific development in 1510, he had experience of political activity which has been largely ignored by the existing Copernicus literature but part of which is reconstructed in outline in this paper. Given the close linkage between politics and astrology, Copernicus's likely reaction to astrology is re-examined here. This reconstruction also suggests that the turning point in 1510, when Copernicus left his post as secretary to his uncle Lucas Watzenrode (...) the prince-bishop of Warmia, was not only linked to Copernicus's first version of his heliocentric theory in theCommentariolus, but also to major political setbacks being experienced by Watzenrode during these years, and with the publication of Copernicus's translation of theLettersof Theophylactus Simocatta. Some of these considerations contribute to maintaining the view that Copernicus and his work were in several respects exceptional. (shrink)

This paper examines the correspondence and contacts between Galileo and a number of French intellectuals. It demonstrates that exchanges between Galileo and those Frenchmen did much to stimulate an interest in new scientific ideas in France, especially in astronomy; for example, Galileo provided a number of good telescopic lenses that did much to establish observational astronomy in France. The Frenchmen for their part provided Galileo with considerable useful information. Several were very active in his support after the condemnation of 1633 (...) and in publishing his later works. The paper further demonstrates the extent of the network of intellectuals who corresponded with Galileo and each other across Europe in the early seventeenth century. (shrink)

Summary A new culture of mathematics was developed in sixteenth-century England, the culture of ?the mathematicalls?. Its representatives were the self-styled mathematical practitioners who presented their art as a practical and worldly activity. The careers of two practitioners, Thomas Bedwell and Thomas Hood, are used as case studies to examine the establishment of this culture of the mathematicalls. Both practitioners self-consciously used mathematical instruments as key resources in negotiating their own roles. Bedwell defined his role in contrast to mechanicians and (...) he secured patronage in military engineering and the service of the commonwealth; Hood worked in the commercial setting of London as a teacher, author, chartmaker, and retailer. Working in new contexts and dealing with new audiences of gentlemen and mechanicians, Bedwell and Hood used instruments to construct a public consensus on the status and aims of mathematics. (shrink)

This paper offers a caution that emphasis upon the importance of mathematics in recent historiography is in danger of obscuring the historical fact that, for the most part, mathematics was not seen as important in the pre-modern period. The paper proceeds by following a single case study, and in so doing offers the first account of the mathematical writings of Jean Fernel (1497–1558), better known as a leading medical innovator of the 16th century. After establishing Fernel's early commitment to mathematics, (...) and attempt to forge a career as a cosmographer, it goes on to explain his abandonment of mathematics for a career in medicine. The ‘mathematization of the world picture’ is usually explained in terms of the perceived usefulness of mathematics, but Fernel's case shows that for many pre-modern thinkers mathematics was not regarded as a useful pursuit. The paper should serve as a reminder, therefore, that the take-up of mathematics by natural philosophers was by no means inevitable, but had to be carefully managed by early modern mathematical practitioners. The case of Fernel indicates that perhaps he was not the only would-be mathematical practitioner to abandon mathematics in favour of a calling that was more appreciated by contemporaries. (shrink)

The ArgumentOne of the earliest arguments for Copernicanism was a widely accepted fact: that on a horizontal plane a body subject to no external resistance can be set in motion by the smallest of all possible forces. This fact was contrary to Aristotelian physics; but it was a physical argument (by abduction) for the possibility of the Copernican world system. For it would be explained if that system was true or at least possible.Galileo argued: only nonviolent motions can be caused (...) by the smallest of all possible forces; hence resistance-free horizontal motions are nonviolent; this confirms Copernicanism insofar as it designates the rotations of celestial spheres (being resistance-free horizontal motions) as nonviolent.Galileo's argument was compatible with (and supportive of) the specific Copernican version of impetus mechanics; but it was also compatible with a (somewhat qualified) principle of inertia. Thus it promoted decisively the transition from impetus mechanics to classical inertial mechanics. (shrink)

In setting forth a new theory of the growth of scientific knowledge, Larry Laudan shows that any account of scientific change has consequences for the relationship between the history, philosophy and sociology of science. It is a laudable feature of his work that he does not treat any of these disciplines as undifferentiated monoliths. In fact, one of his main goals is to show that his account of progress requires specific ways of doing and relating these three disciplines. As an (...) historian invited to speak at the Philosophy of Science Association, it seemed appropriate for me to appraise the function of history of science in Laudan’s program. Without going into unnecessary detail, let me begin by examining some of his main claims.The focus of Laudan’s argument is on science construed as a form of problem-solving activity and on progress and rationality as appraisals of problem-solving capabilities. (shrink)

The ArgumentThe publication of Johannes Kepler's brilliant and revolutionary Astronomia nova has hitherto been viewed as somehow inevitable. This paper argues that, on the contrary, the book's very existence and a measure of its unusual form and content are in fact highly contingent, and derive from a legal dispute between Kepler and Tycho's heirs over the right to capitalize on his astronomical legacy. On Tycho's death, Kepler rather accidentally found himself in charge of Tycho's posthumous astronomical publications, especially the highly (...) prestigious Rudol phine Tables. Tycho's legal heirs, not having been paid by the emperor for Tycho's astronomical assets and feigning Kepler's unworthiness as his successor, wrested this mandate back. Ordered in turn to justify his employment, Kepler contrived the Astronomia nova as an interim announcement of the fruits of his astronomical research. In an effort to block Kepler's continuing exploitation of Tycho's observations, the heirs obtained the legal right to censor his publications, which severely threatened his philosophical freedom. The threat of editorial interference was responsible in part for Astronomia nova's unusual narrative form. (shrink)

ArgumentThe subject of the paper is the shift from an astrology-oriented astronomy towards an allegedly more objective, mathematically grounded approach to astronomy. This shift is illustrated through a close reading of Tycho Brahe's scientific development and the contemporaneous changes in his communicational strategies. Basing the argument on a substantial array of original sources it is claimed that the Danish astronomer developed a new astronomical discourse in pursuit of credibility, giving priority to observational astronomy and natural philosophical questions. The abandonment of (...) astrology in public discourse is primarily explained by Tycho's social position and greater sensibility to controversial issues. Tycho's example suggests that the changes in rhetorical strategies regarding astrology (which happened earlier than changes in astrological belief) should be given more recognition in the history of astronomy. (shrink)

Reading Galileo: Scribal Technologies and The Two New Sciences, by Renée Raphael, Baltimore, Johns Hopkins University Press, 2017, ix + 265 pp., figs., bibl., index, £40.50 (cloth), ISBN 9781421421...

Generally speaking, virtual displacement or work concerns to a timely idea according to which a motion of a certain body is not the unique possible motion. The process of reducing this motion to a particular magnitude and concept, eventually minimizing as a hypothesis, can be traced back to the Aristotelian school. In the history and philosophy of science one finds various enunciations of the Principle of Virtual Laws and its virtual displacement or work applications, i.e., from Aristotle to Leibniz’s vis (...) viva, from Maupertuis’ least action to Euler and Lagrange with calculus of variations to Lazare Carnot’s mechanics. In this case study, I will demonstrate that a particular approach used by Lazare Carnot is original by explaining within the historical context of rival approaches such as the development of the Principle of virtual Laws. I will also discuss Carnot’s geometric motion as one of the possible but invertible movements applied to virtual displacement as employed in his theories of machines and collisions. I will then go on to explore how the originality of an invertible motion within his mechanical and, in general, mathematical research program permitted Carnot to introduce a new way of structuring a scientific theory and making mechanics, with respect to the Newtonian paradigm, to scholars and his students of the École polytechnique de Paris. (shrink)

William Harvey's famous quantitative argument fromDe motu cordis about the circulation of blood explained how a small amount of blood could recirculate and nourish the entire body, upending the Galenic conception of the blood's motion. This paper argues that the quantitative argument drew on the calculative and rhetorical skills of merchants, including Harvey's own brothers. Modern translations ofDe motu cordisobscure the language of accountancy that Harvey himself used. Like a merchant accounting for credits and debits, intake and output, goods and (...) moneys, Harvey treated venous and arterial blood as essentially commensurate, quantifiable and fungible. For Harvey, the circulation of blood was an arithmetical necessity. The development of Harvey's circulatory model followed shifts in the epistemic value of mercantile forms of knowledge, including accounting and arithmetic, also drawing on an Aristotelian language of reciprocity and balance that Harvey shared with mercantile advisers to the royal court. This paper places Harvey's calculations in a previously underappreciated context of economic crisis, whose debates focused largely on questions of circulation. (shrink)