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)

Simone Weil (1909-1943) was a defining figure of the twentieth century; a philosopher, Christian, resistance fighter, anarchist, feminist, labor activist and teacher. She was described by T. S. Eliot as "a woman of genius, of a kind of genius akin to that of the saints," and by Albert Camus as "the only great spirit of our time." Originally published posthumously in two volumes, these newly reissued notebooks, are among the very few unedited personal writings of Weil's that still survive today. (...) Containing her thoughts on art, love, science, God and the meaning of life, they give context and meaning to Weil's famous works, revealing a unique philosophy in development and offering a rare private glimpse of her singular personality. (shrink)

Particle indistinguishability has always been considered a purely quantum mechanical concept. In parallel, indistinguishable particles have been thought to be entities that are not properly speaking objects at all. I argue, to the contrary, that the concept can equally be applied to classical particles, and that in either case particles may (with certain exceptions) be counted as objects even though they are indistinguishable. The exceptions are elementary bosons (for example photons).

The relationship of part to whole is one of the most fundamental there is; this is the first and only full-length study of this concept. This book shows that mereology, the formal theory of part and whole, is essential to ontology. Peter Simons surveys and criticizes previous theories, especially the standard extensional view, and proposes a more adequate account which encompasses both temporal and modal considerations in detail. 'Parts could easily be the standard book on mereology for the next twenty (...) or thirty years.' Timothy Williamson, Grazer Philosophische Studien. (shrink)

We demonstrate that the quantum-mechanical description of composite physical systems of an arbitrary number of similar fermions in all their admissible states, mixed or pure, for all finite-dimensional Hilbert spaces, is not in conflict with Leibniz's Principle of the Identity of Indiscernibles (PII). We discern the fermions by means of physically meaningful, permutation-invariant categorical relations, i.e. relations independent of the quantum-mechanical probabilities. If, indeed, probabilistic relations are permitted as well, we argue that similar bosons can also be discerned in all (...) their admissible states; but their categorical discernibility turns out to be a state-dependent matter. In all demonstrated cases of discernibility, the fermions and the bosons are discerned (i) with only minimal assumptions on the interpretation of quantum mechanics; (ii) without appealing to metaphysical notions, such as Scotusian haecceitas, Lockean substrata, Postian transcendental individuality or Adamsian primitive thisness; and (iii) without revising the general framework of classical elementary predicate logic and standard set theory, thus without revising standard mathematics. This confutes: (a) the currently dominant view that, provided (i) and (ii), the quantum-mechanical description of such composite physical systems always conflicts with PII; and (b) that if PII can be saved at all, the only way to do it is by adopting one or other of the thick metaphysical notions mentioned above. Among the most general and influential arguments for the currently dominant view are those due to Schrodinger, Margenau, Cortes, Dalla Chiara, Di Francia, Redhead, French, Teller, Butterfield, Giuntini, Mittelstaedt, Castellani, Krause and Huggett. We review them succinctly and critically as well as related arguments by van Fraassen and Massimi. (shrink)

Gravity and Grace was the first ever publication by the remarkable thinker and activist, Simone Weil. In it Gustave Thibon, the priest to whom she had entrusted her notebooks before her untimely death, compiled in one remarkable volume a compendium of her writings that have become a source of spiritual guidance and wisdom for countless individuals.

I show that frequentism, as an explanation of probability in classical statistical mechanics, can be extended in a natural way to a decoherent quantum history space, the analogue of a classical phase space. The result is a form of finite frequentism, in which Gibbs’ concept of an infinite ensemble of gases is replaced by the quantum state expressed as a superposition of a finite number of decohering microstates. It is a form of finite and actual frequentism (as opposed to hypothetical (...) frequentism) insofar as all the microstates exist, in keeping with the decoherence-based Everett interpretation, and some versions of pilot-wave theory. (shrink)

The central claim of this article is that post-truth requires a political and socio-economical perspective, rather than a moral or epistemological one. The article consists of two parts. The first part offers a critical examination of the dominant analyses of post-truth in terms of shifting standards of the origin and the evaluation of facts. Moreover, the claim that postmodernism is the cause of post-truth is examined and refuted. In the second part an alternative perspective is developed, centring around the notion (...) of gatekeepers. Rather than linking post-truth to bullshit and postmodernism, it should be understood as a symptom of a contemporary shift in the gatekeepers of truth and knowledge. Knowledge and truth are always mediated in society through the hands of gatekeeping institutions such as journalism or science. Post-truth is a symptom of a broader transformation of the gatekeeping institutions of our current society. It therefore requires a political philosophy of these institutional shifts and the new risks they involve. (shrink)

Into wrestling with that question, Simone Weil put the very substance of her mind and temperament.

"What is required if men and women are to feel at home in society and are to recover their vitality? Into wrestling with that question, Simone Weil put the very substance of her mind and temperament. The apparently solid edifices of our prepossessions fall down before her onslaught like ninepins, and she is as fertile and forthright in her positive suggestions . . . she can be relied upon to toss aside the superficial and to come to grips with the (...) essential and the profound." -- Time Literary Supplement. (shrink)

This is a very short introduction to ethics. It divides into three parts: first, introducing and discussing reasons for skepticism about ethics; second introducing themes of birth, death, happiness, desire and freedom to show how deeply our lives are interwoven with ethics; third, introducing attempts to found ethics, due to Aristotle, Kant, and the contractarian tradition.

One Stoic response to the skeptical indistinguishability argument is that it fails to account for expertise: the Stoics allow that while two similar objects create indistinguishable appearances in the amateur, this is not true of the expert, whose appearances succeed in discriminating the pair. This paper re-examines the motivations for this Stoic response, and argues that it reveals the Stoic claim that, in generating a kataleptic appearance, the perceiver’s mind is active, insofar as it applies concepts matching the perceptual stimulus. (...) I argue that this claim is reflected in the Stoic definition of the kataleptic appearance, and that it respects their more general account of mental representation. I further suggest that, in attributing some activity to the mind in creating each kataleptic appearance, and in claiming that the expert’s mind allows her to form more kataleptic appearances than the amateur, the Stoics draw inspiration from the wax tablet model in Plato’s Theaetetus (190e–196d), where Socrates distinguishes the wise from the ignorant on the basis of how well they match sensory input with its appropriate mental ‘seal’ (σφραγίς). (shrink)

This is a book about the religious life of the Greeks from the eighth century BC to the fifth century AD, looked at in the context of a variety of different cities and periods. Simon Price does not describe some abstract and self-contained system of religion or myths but examines local practices and ideas in the light of general Greek ideas, relating them for example, to gender roles and to cultural and political life (including Attic tragedy and the trial (...) of Socrates). He also lays emphasis on the reactions to Greek religions of ancient thinkers - Greek, Roman, Jewish and Christian. The evidence drawn on is of all kinds: literary texts, which are translated throughout; inscriptions, including an appendix of newly translated Greek inscriptions; and archaeology, which is highlighted in the numerous illustrations. (shrink)