we present a number of findings concerning galileo's major discoveries which question both the methods and the results of dating his achievements by common historiographic criteria. the dating of galileo's discoveries is, however, not our primary concern. this paper is intended to contribute to a critical reexamination of the notion of discovery from the point of view of historical epistemology. we claim that the puzzling course of galileo's discoveries is not an exceptional comedy of errors but rather illustrates the normal (...) way in which scientific progress is achieved. we argue that scientific knowledge generally develops not as a sequence of independent discoveries accumulating to a new body of knowledge but rather as a network of interdependent activities which only as a whole makes the individual steps understandable as meaningful “discoveries.”. (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)

This paper examines the role of mathematical instrument makers in establishing a public culture of precision measurement in early-modern England. I argue that this culture was promoted through trials and demonstrations, in the context of which artisans held a privileged position. The trials described here cover land surveying, the measurement of magnetic variation, and standards of measurement for customs and excise. These trials were decisive moments in the ‘cultural biographies’ of precision instruments. I ask how it was that instrument makers (...) were able to assume positions of authority, and what this means for our understanding of the socio-material system of precision measurement in the early-modern period, and the contemporary rise of ‘experimental’ and ‘philosophical’ trials. Because practical mathematics was a self-consciously economic activity – motivated by trade, commerce, exploration and colonization – direct connections to natural philosophy are significant, a point explored in my conclusion. (shrink)

Sébastien Le Clerc (1637–1714) was the most renowned engraver of Louis XIV's France. For the history of scientific publishing, however, Le Clerc represents a telling paradox. Even though he followed a traditional route based on classic artisanal training, he also published extensively on scientific topics such as cosmology and mathematics. While contemporary scholarship usually stresses the importance of artisanal writing as a direct expression of artisanal experience and know-how, Le Clerc's publications, and specifically the work on cosmology in hisSystème du (...) monde(1706–1708), go far beyond this. By reconstructing the debate between Le Clerc and the professor Mallemant de Messange on the authorship of this ‘system of the world’, this article argues that Le Clerc's involvement in publishing ventures shaped his identity both as an artisan and as a scientific author. Whereas the Scientific Revolution supposedly heralded a change from the world of ‘more or less’ to the ‘world of precision’, this article shows how an artisan could be more ‘precise’ than the learned scholar whose claims he disputed, and points to the importance of the literary field as a useful lens for observing the careers of early modern scientific practitioners. (shrink)

The Kunstkammer of the Electors of Saxony, founded in Dresden around 1560, housed one of the richest collections of tools and scientific instruments in its day. A close analysis of the optical objects in the collection in the decades around 1600 is undertaken here—in particular, their arrangement by a mathematically trained curator, Lucas Brunn, and their use in an ‘experiment’ by a distinguished visitor, Johannes Kepler. It is argued that the selection, display and use of optical objects within this collection (...) reflect a specific, playful image of optics promoted at the Saxon court.Keywords: Court collections; Optics; Instruments; Perspective; Wonder. (shrink)

SummaryThe medical career of Sir John Colbatch illuminates some of the ways in which experimental philosophy, social change, and medical entrepreneurialism together helped bring about the end of the old medical regime in England. Colbatch's career in Augustan England depended very much on a growing public culture in which the well-to-do decided matters of intellectual importance for themselves, becoming increasingly free not only from the clerics but from the physicians. In this new world, debates about the fundamental principles of the (...) new science took place increasingly in public, and in the English language, without the learned men of the university being able to enforce their authority. It gave people like Colbatch a new opportunity to make their way into the medical establishment. (shrink)

The Jesuit C.F. Milliet Dechales, author of one of the most famous early modern mathematical encyclopedias, Cursus seu mundus mathematicus, wrote a hundred-folio-page long treatise devoted to the “progress of mathematics,” which was published in the second, enlarged edition of his encyclopedia. His historical treatise covers the gamut of mixed mathematics—including astronomy, mechanics, optics, music, geography and navigation, ars tignaria, and architecture. The early modern historical narratives about the mathematical sciences, from Regiomontanus’s Oratio onwards, have been aptly characterized by their (...) literary form and goals rather than their historical content. Rhetoric, humanistic topoi, and philosophical filiation turned the histories of mathematics into powerful tools for different purposes. My account of Dechales’ tract on the “progress of mathematics” analyzes the ways in which it dovetails with Jesuit approaches to mathematics, provides legitimation to the mathematical sciences as well as to their authors, and contributes to define the role and boundaries of the discipline, in particular vis-à-vis natural philosophy. (shrink)

The ArgumentWe present a number of findings concerning Galileo's major discoveries which question both the methods and the results of dating his achievements by common historiographic criteria. The dating of Galileo's discoveries is, however, not our primary concern. This paper is intended to contribute to a critical reexamination of the notion of discovery from the point of view of historical epistemology. We claim that the puzzling course of Galileo's discoveries is not an exceptional comedy of errors but rather illustrates the (...) normal way in which scientific progress is achieved. We argue that scientific knowledge generally develops not as a sequence of independent discoveries accumulating to a new body of knowledge but rather as a network of interdependent activities which only as a whole makes the individual steps understandable as meaningful “discoveries.”. (shrink)

In La nova scientia , Niccolò Tartaglia analyses trajectories of cannonballs by means of different forms of reasoning, including ‘physical and geometrical reasoning’, ‘demonstrative geometrical reasoning’, ‘Archimedean reasoning’, and ‘algebraic reasoning’. I consider what he understood by each of these methods and how he used them to render the quick succession of a projectile's positions into a single entity that he could explore and explain. I argue that our understanding of his methods and style is greatly enriched by considering the (...) abacus tradition in which he worked. As a maestro d'abaco in sixteenth-century Venice he had access to a great variety of mathematical and natural-philosophical works. This paper traces how Tartaglia drew elements from a vast spectrum of sources and combined them in an innovative manner. I examine his use of algebra and geometry, consider what he knew about Archimedes and suggest a reading of his enigmatic phrase ‘Archimedean reasoning’, which has eluded satisfactory interpretation. (shrink)

The ArgumentIt is not easy to point to the place of knowledge in our culture. More precisely, it is difficult to locate the production of our most valued forms of knowledge, including those of religion, literature and science. A pervasive topos in Western culture, from the Greeks onward, stipulates that the most authentic intellectual agents are the most solitary. The place of knowledge is nowhere in particular and anywhere at all. I sketch some uses of the theme of the solitary (...) philosopher across a broad sweep of history, giving particular attention to its deployment in and around the scientific culture of seventeenth-century England. I argue that the rhetoric of solitude is strongly implicated in individualistic views of society and empiricist portrayals of scientific knowledge. Solitude is a state that symbolically expresses direct engagement with the sources of knowledge – divine and transcendent or natural and empirical. At the same time, solitude publicly expresses disengagement from society, identified as a set of conventions and concerns which act to corrupt knowledge. Hence, the study of the social uses of solitude adds further support to the notion that problems of knowledge and problems of social order are solved together. (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)

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)

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)

Mathematical practitioners in seventeenth-century London formed a cohesive knowledge community that intersected closely with instrument-makers, printers and booksellers. Many wrote books for an increasingly numerate metropolitan market on topics covering a wide range of mathematical disciplines, ranging from algebra to arithmetic, from merchants’ accounts to the art of surveying. They were also teachers of mathematics like John Kersey or Euclid Speidell who would use their own rooms or the premises of instrument-makers for instruction. There was a high degree of interdependency (...) even beyond their immediate milieu. Authors would cite not only each other, but also practitioners of other professions, especially those artisans with whom they collaborated closely. Practical mathematical books effectively served as an advertising medium for the increasingly self-conscious members of a new emerging professional class. Contemporaries would talk explicitly of ‘the London mathematicians’ in distinction to their academic counterparts at Oxford or Cambridge. The article takes a closer look at this metropolitan knowledge culture during the second half of the century, considering its locations, its meeting places and the mathematical clubs which helped forge the identity of its practitioners. It discusses their backgrounds, teaching practices and relations to the London book trade, which supplied inexpensive practical mathematical books to a seemingly insatiable public. (shrink)

This paper offers a reconstruction of Alessandro Piccolomini's philosophy of mathematics, and reconstructs the role of Themistius and Averroes in the Renaissance debate on Aristotle's theory of proof. It also describes the interpretative context within which Piccolomini was working in order to show that he was not an isolated figure, but rather that he was fully involved in the debate on mathematics and physics of Italian Aristotelians of his time. The ideas of Lodovico Boccadiferro and Sperone Speroni will be analysed. (...) This paper demonstrates that Piccolomini's attack on the certitude of mathematics was a product of discussions between Aristotelians. (shrink)

Summary The reception process of Aristotle's Mechanical Questions during the early modern period began with the publication of the corpus aristotelicum between 1495 and 1498. Between 1581 and 1627, two of the thirty-five arguments discussed in the text, namely Question XIV concerning the resistance to fracture and Question XVI concerning the deformation of objects such as timbers, became central to the work of the commentators. The commentaries of Bernardino Baldi (1581–1582), Giovanni de Benedetti (1585), Giuseppe Biancani (1615) and Giovanni di (...) Guevara (1627) gradually approached the doctrine of proportions of the Renaissance architects, some aspects of which deal with the strength of materials according to the Vitruvian conception of scalar building. These aspects of the doctrine of proportions were integrated into the Aristotelian arguments so that a theory of linear proportionality concerned with the strength of materials could be formulated. This very first theory of strength of materials is the theory to which Galileo critically referred in his Discorsi where he published his own theory of strength of materials. Economic and military constraints are determined as the fundamental reasons for the commentators’ commitment to developing a theory of strength of materials that later linked Galileo's work to the practical knowledge of the architects and machine-builders of his time. (shrink)

Descartes describes in the Discours de la méthode his stay in Germany in winter 1619/20 as decisive for his intellectual development. In Germany he was especially interested in the mathematics of German reckoningmasters and mathematical practitioners. Frustrated from their form of representation, from their mathematical „style”, he began to create his own, which he considered a first step in the development of his method in order to secure true knowledge. Descartes could derive additional confirmation for his task by the mentalities (...) of orthodox and heterodox protestantism. He learned that Johannes Faulhaber one of the leading German mathematicians had strong connections to the rosicrucian movement, a very popular form of heterodox protestantism. The convictions and aims of the supporters of the rosicrucian movement in part agreed with and in part contradicted seriously those of Descartes, whereas the arguments of the orthodox protestants in their fight against the rosicrucian movement interacted positively with the ideas of Descartes. The reaction of Descartes to his encounter with German protestantism offers an important element for the explanation of the strong positive and negative reactions to Cartesianism in protestant countries, especially in the Netherlands. (shrink)