Du grand ingénieur et mathématicien Simon Stevin (Bruges 1548 - La Haye ? 1620), l'histoire a retenu avant tout l'œuvre scientifique, marquante par sa diversité et sa vocation à constituer des manuels pratiques.

Many pioneers of the Scientific Revolution such as Galileo, Kepler, Stevin, Descartes, Mersenne, and others, wrote extensively about musical theory. This was not a chance interest of a few individual scientists. Rather, it reflects a continuing concern of scientists from Pythagorean times onwards to solve certain quantifiable problems in musical theory. One of the issues involved was technically known as ‘the division of the octave’, the problem, that is, of which notes to make music with. Simon Stevin's (...) contribution to this issue, in his treatise Vande Spiegheling der Singconst , is usually conceived of as a remarkably early plea for equal temperament, which is the tuning system we nowadays all take for granted. In this paper I show that, even though it is true that Stevin calculated the figures for what is now known as equal temperament, in fact the subject of temperament has almost nothing to do with his accompanying considerations, and that, therefore, his calculations served another purpose. A careful analysis of the problem situation in the science of music around 1600, reveals that Stevin's treatise highlights a particular stage in the history of what has always been the core issue of the science of music, namely, the problem of consonance. This is the search for an explanation, on scientific principles, of Pythagoras' law: ‘Why is it that those few musical intervals which affect our ear in a sweet and pleasing manner, correspond to the ratios of the first few integers?’ Through an analysis of the source material available we find that Stevin's theory, which makes no sense if interpreted as an early stage in the ‘evolution’ of equal temperament, was meant as a solution—as freshly original as it was wrongheaded—to this perennial problem of consonance, which has continued to baffle some of the best scientific minds from the very beginning of science to the present day. (shrink)

This paper offers a reassesment of Simon Stevin’s mechanics, by focusing on how Stevin tries to anchor his mathematical demonstrations in the behavior of material instruments. It is shown how his views on the relation between spiegheling and daet are crucial to correctly understand his famous proof of the law of the inclined plane and his experimental test of the Aristotelian law of free fall. The distance separating spiegheling and daet is reproduced in that between instruments at (...) rest and instruments in motion, because of Stevin’s claim that impediments to motion are “inseperable accidents” of all moving objects. (shrink)

This paper explores Simon Stevin’s l’Arithmétique of 1585, where we find a novel understanding of the concept of number. I will discuss the dynamics between his practice and philosophy of mathematics, and put it in the context of his general epistemological attitude. Subsequently, I will take a close look at his justificational concerns, and at how these are reflected in his inductive, a postiori and structuralist approach to investigating the numerical field. I will argue that Stevin’s renewed (...) conceptualisation of the notion of number is a sort of “existential closure” of the numerical domain, founded upon the practice of his predecessors and contemporaries. Accordingly, I want to make clear that l’Aritmetique have to be read not as an ontological analysis or exploration of the numerical field, but as an explication of a mathematical ethos. In this sense, this article also intends to make a specific contribution to the broader issue of the “ethics of geometry.”. (shrink)

Résumé Les arts libéraux tiennent un rôle particulier dans la pensée de Simon Stevin (1548-1620). Grâce à eux, ce savant peut dévoiler dans son épistémologie d’une part ce que sont les dispositions innées de l’esprit (distinguer le vrai du faux, parler, compter) et d’autre part les fondements des objets de la Nature (le nom, le nombre, la mesure et le poids). Un art de penser associe alors l’âme et la Création et permet de codifier les différents arts et (...) l’action vertueuse. Dans cet article, nous voulons montrer le rôle que jouent la dialectique et l’arithmétique dans l’art de penser de ce mathématicien et ingénieur flamand. Nous expliciterons alors les liens entre ces deux disciplines et la mise en place grâce à eux d’outils communs comme la proportion et la méthode dans la réalisation d’un projet encyclopédique. (shrink)

We explore the potential of Simon Stevin’s numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.2 (2003) 276-277 [Access article in PDF] Wiep Van Bunge. From Stevin to Spinoza: An Essay on Philosophy in the Seventeenth-Century Dutch Republic. Leiden: Brill, 2001. Pp. xii + 217. Cloth, $80.00 By 1660 there were probably more followers of Descartes in the Dutch Republic, population 1.4 million, than in France, population 20 million. Protestantism and prosperity encouraged high rates of literacy (...) and the universities of Leiden and Utrecht were among the liveliest in the world. This vibrancy infused the metaphors that Descartes put into his great Discours de la methode published first in Leiden in 1637. In it he spoke about the beauty of cities that looked as if they had been built by a single architect and of the freedom to be found among people so busy with their business as to leave thinkers to their pursuits. Indirectly he spoke about his adopted homeland where he found many followers—some more eager than loyal. By the 1640s disputes raged in the Republic and the anti-Cartesian forces were led by the Aristotelian and anti-Copernican Gisbertus Voetius. What has been missing in our scholarship up to now has been any convincing account as to why these disputes occurred, and how they resonated within the Dutch context. Wiep Van Bunge's book takes a big step toward closing that knowledge gap.Van Bunge convincingly argues that the vibrancy of the stadtholder-less period up to 1672 produced a willingness to entertain new ideas. It also did not hurt to have Descartes on the scene and active on behalf of his mechanical philosophy, even to the point of addressing the Utrecht magistrates publicly and asking that his critics be chastised. What is remarkable—especially given the resistance to Descartes seen at Oxford and Cambridge—was the speed with which Cartesian ideas entered the Dutch classrooms where as many as a third of the students came from abroad. Again Van Bunge provides context when he starts with the Dutch engineer Simon Stevin and demonstrates the vitality of mathematics for a commercial society but also for a militant one. (The Netherlands was at war with Spain up to 1609.) A recent exhibition at the J. Paul Getty Museum in Los Angeles, April to July 2002, also illustrates another aspect of mathematics in the Republic. Precisely in the 1630s when Descartes was putting the finishing touches on his Discours, Pieter Saenredam applied geometry to the interiors of the elegant Utrecht churches so as to give his paintings a regularity and precision worthy of the Cartesian dream of order and clarity. The Dutch commitment to discipline and order also made their army one of the most accomplished in the world. It was perhaps over-determined that Descartes, who had trained with it, would find such a sympathetic audience in the Republic.One of the more fascinating aspects of Van Bunge's detailed study, first of Cartesianism and then of Spinozism in the Republic, concerns the political and ideological meanings to be extracted from the new philosophy. Hobbes also finds a place in the narrative, surprisingly taken up by republicans eager to construct a state that could control the passions. Abraham van Berkel, who put Hobbes's Leviathan into Dutch in 1667, gave the allegiance of his text and himself to Jan de Witt and the cause of the regents and the estates. We can only wonder what Hobbes would have made of the association. The republican affiliations of the mechanical philosophy in the Republic provide a distinctively Dutch context to the [End Page 276] political writings of Spinoza, the most famous and outrageous Cartesian of the century. Van Bunge is especially deft in finding Spinozists and providing far more evidence than I could back in 1981 when I argued for a radical enlightenment within the late seventeenth-century Dutch context (see The Radical Enlightenment. Pantheists, Freemasons and Republicans [London: 1981]). None of these positions with their deeply heretical implications could be taken lightly or without danger. Men lost... (shrink)

This monograph investigates the development of hydrostatics as a science. In the process, it sheds new light on the nature of science and its origins in the Scientific Revolution. Readers will come to see that the history of hydrostatics reveals subtle ways in which the science of the seventeenth century differed from previous periods. The key, the author argues, is the new insights into the concept of pressure that emerged during the Scientific Revolution. This came about due to contributions from (...) such figures as Simon Stevin, Pascal, Boyle and Newton. The author compares their work with Galileo and Descartes, neither of whom grasped the need for a new conception of pressure. As a result, their contributions to hydrostatics were unproductive. The story ends with Newton insofar as his version of hydrostatics set the subject on its modern course. He articulated a technical notion of pressure that was up to the task. Newton compared the mathematical way in hydrostatics and the experimental way, and sided with the former. The subtleties that lie behind Newton's position throws light on the way in which developments in seventeenth-century science simultaneously involved mathematization and experimentation. This book serves as an example of the degree of conceptual change that new sciences often require. It will be of interest to those involved in the study of history and philosophy of science. It will also appeal to physicists as well as interested general readers. (shrink)

Simon Critchley's first book, The Ethics of Deconstruction, was originally published to great acclaim in 1992. This edition contains three new appendices and a new preface where Critchley reflects upon the origins, motivation and reception of The Ethics of Deconstruction.

Gilles Deleuze’s engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges provide an opportunity to reconfigure particular philosophical problems – for example, the problem of individuation – and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction of Deleuze’s philosophy, (...) as well as addressing the undervalued and often neglected question of the mathematical thinkers who influenced his work. -/- In the wake of Alain Badiou’s recent and seemingly devastating attack on the way the relation between mathematics and philosophy is configured in Deleuze’s work, Simon Duffy offers a robust defence of the structure of Deleuze’s philosophy and, in particular, the adequacy of the mathematical problems used in its construction. By reconciling Badiou and Deleuze’s seeming incompatible engagements with mathematics, Duffy succeeds in presenting a solid foundation for Deleuze’s philosophy, rebuffing the recent challenges against it. -/- Simon B. Duffy is a Senior Lecturer in Philosophy at Yale-NUS College, Singapore, and Honorary Research Associate in the Department of Philosophy at the University of Sydney, Australia. He is the author of The Logic of Expression: Quality, Quantity, and Intensity in Spinoza, Hegel and Deleuze (2006). (shrink)

This bestselling dictionary is written by one of the leading philosophers of our time, and it is widely recognized as the best dictionary of its kind. Comprehensive and authoritative, it covers every aspect of philosophy from Aristotle to Zen. With clear and concise definitions, it provides lively and accessible coverage of not only Western philosophical traditions, but also themes from Chinese, Indian, Islamic, and Jewish philosophy. New entries on philosophy of economics, social theory, neuroscience, philosophy of the mind, and moral (...) conceptions, bring this authoritative third edition up to date. It is the ideal introduction to philosophy for anyone with an interest in the subject, and it is an indispensable work of reference for students and teachers. (shrink)

I intend to argue that good friendship sometimes requires epistemic irresponsibility. To put it another way, it is not always possible to be both a good friend and a diligent believer.

The return to religion has perhaps become the dominant cliche of contemporary theory, which rarely offers anything more than an exaggerated echo of a political reality dominated by religious war. Somehow, the secular age seems to have been replaced by a new era, where political action flows directly from metaphysical conflict. The Faith of the Faithless asks how we might respond. Following Critchley's Infinitely Demanding, this new book builds on its philosophical and political framework, also venturing into the questions of (...) faith, love, religion and violence. Should we defend a version of secularism and quietly accept the slide into a form of theism--or is there another way? From Rousseau's politics and religion to the return to St. Paul in Taubes, Agamben and Badiou, via explorations of politics and original sin in the work of Schmitt and John Gray, Critchley examines whether there can be a faith of the faithless, a belief for unbelievers. Expanding on his debate with Slavoj Zizek, Critchley concludes with a meditation on the question of violence, and the limits of non-violence. (shrink)

It is shown that the Hilbert-Bernays-Quine principle of identity of indiscernibles applies uniformly to all the contentious cases of symmetries in physics, including permutation symmetry in classical and quantum mechanics. It follows that there is no special problem with the notion of objecthood in physics. Leibniz's principle of sufficient reason is considered as well; this too applies uniformly. But given the new principle of identity, it no longer implies that space, or atoms, are unreal.

In considering the debate about the meaning of ‘disease’, the positions are generally presented as falling into two categories: naturalist, e.g., Boorse, and normativist, e.g., Engelhardt and many others. This division is too coarse, and obscures much of what is going on in this debate. I therefore propose that accounts of the meaning of ‘disease’ be assessed according to Hare’s (1997) taxonomy of evaluative terms. Such an analysis will allow us to better understand both individual positions and their inter-relationships. Most (...) importantly, it will show that it is unlikely that there is a single unique disease-concept at issue. Rather, different authors are, for the most part, considering different concepts. (shrink)

But this picture of a ‘block universe’, composed of a timeless web of ‘world-lines’ in a four-dimensional space, however strongly suggested by the theory of relativity, is a piece of gratuitous metaphysics. Since the concept of change, of something happening, is an inseparable component of the common-sense concept of time and a necessary component of the scientist's view of reality, it is quite out of the question that theoretical physics should require us to hold the Eleatic view that nothing happens (...) in ‘the objective world’. Here, as so often in the philosophy of science, a useful limitation in the form of representation is mistaken for a deficiency of the universe. (shrink)

This paper considers John Doris, Stephen Stich, Alexandra Plakias, and colleagues’ recent attempts to utilize empirical studies of cross-cultural variation in moral judgment to support a version of the argument from disagreement against moral realism. Crucially, Doris et al. claim that the moral disagreements highlighted by these studies are not susceptible to the standard ‘diffusing’ explanations realists have developed in response to earlier versions of the argument. I argue that plausible hypotheses about the cognitive processes underlying ordinary moral judgment and (...) the acquisition of moral norms, when combined with a popular philosophical account of moral inquiry—the method of reflective equilibrium—undercut the anti-realist force of the moral disagreements that Doris et al. describe. I also show that Stich's recent attempt to provide further theoretical support for Doris et al.'s case is unsuccessful. (shrink)

This book, designed for high-level undergraduates, postgraduates and fellow researchers, introduces the reader to the main areas of metaethical work today. As we as introducing familiar positions and arguments, Kirchin argues clearly and engagingly for a set of distinctive and arresting views.

Kerngedachten uit de nagelaten manuscripten van deze jong gestorven schrijfster, doordrongen van een mystiek, die zich richt zowel op de schoonheid van de schepping als op de goddelijke volmaaktheid, en van medeleven met de lijdende mensheid.

If science fiction is a genre, then attempts to think about the nature of science fiction will be affected by one’s understanding of what genres are. I shall examine two approaches to genre, one dominant but inadequate, the other better, but only occasionally making itself seen. I shall then discuss several important, interrelated issues, focusing particularly on science fiction : what it is for a work to belong to a genre, the semantics of genre names, the validity of attempts to (...) define genres, and the connections between genre and normativity. One important but neglected clue to the nature of genres lies in the kinds of disagreements they generate over the assignment of works to genres. I conclude by explaining why these disagreements tell us something about the nature of genres, and discussing in some detail two famous cases of disagreement about whether some work or works are science fiction. (shrink)

Philosophers have traditionally used thought-experiments in their endeavours to find a satisfactory account of the self and personal identity. Yet there are considerations from empirical psychology as well as related ones from philosophy itself that appear to completely undermine the method of thought-experiment. This paper focuses on both sets of considerations and attempts a defence of the method.

Minds, Brains and Biology -- A Body of Knowledge -- Towards an Aesthetics of Behavior.

Pierre Bourdieu is widely regarded as one of the most influential sociologists of his generation, and yet the reception of his work in different cultural contexts and academic disciplines has been varied and uneven. This volume maps out the legacy of Pierre Bourdieu in contemporary social and political thought from the standpoint of classical European sociology and from the broader perspective of transatlantic social science. It brings together contributions from prominent scholars in the field, providing a range of perspectives on (...) the continuing relevance of Bourdieu's oeuvre to substantive problems in social and political analysis. (shrink)

Ethical discussions about Artificial Intelligence (AI) often overlook its potentially large impact on nonhuman animals. In a recent commentary on our paper about AI’s possible harms, Leonie Bossert argues for a focus not just on the possible negative impacts but also the possible beneficial outcomes of AI for animals. We welcome this call to increase awareness of AI that helps animals: developing and using AI to improve animal wellbeing and promote positive dimensions in animal lives should be a vital ethical (...) goal. Nonetheless, we argue that there is some value in focusing on technology-based harms in the context of AI ethics and policy discourses. A harms framework for AI can inform some of our strongest duties to animals and inform regulation and risk assessment impacts designed to prevent serious harms to humans, the environment, and animals. (shrink)