The main purpose of this article is to present new material concerning Leibniz's use of indivisibles and infinitesimals in his early mathematical texts. Most of these texts are contained in hitherto unpublished manuscripts and are soon to be printed in volume VII, 4 of the Academy Edition. They present examples which illustrate how Leibniz operated with concepts such as indivisibles and infinitesimals in that period of his development.

Physics was the leading science of the twentieth century and the book retraces important discoveries, made between 1895 and 2001, in 100 self-contained episodes. Each is a short story of the scientists involved, their time and their work. The book is richly illustrated byabout 600 portraits, photographs, and figures.

"Der geschichtliche Sinn, welcher schon das Altertum auszeichnete, bewahrte sich auch auf unserm Gebiete, und es hat schon in fruher Zeit nicht an Versuchen gefehlt, den Entwicklungsgang des Wissens bis zu einem gewissen Termine zu schildern. Nach Diogenes von Laerte, einem freilich nicht immer vollig zuverlassigen Gewahrsmann, hat schon ein Schuler des Aristoteles, der als Naturforscher bekanntere Theophrast, Geschichtswerke uber Arithmetik, Geometrie und Astronomie verfasst, von denen sich jedoch hochstens insofern eine Spur erhalten hat, als nach den ausgezeichneten Untersuchungen von (...) Diels bei einer ganzen Reihe spatlateinischer und spatgriechischer Autoren Anklange an historische Angaben Theophrasts zu finden sind. Ahnliches gilt von der angeblich geometrischen Schrift des Xenokrates, deren ebenfalls Diogenes Erwahnung tut." [...] Der bedeutende Philosoph und Philosophiehistoriker Dr. Wilhelm Windelband (1848-1915) gilt als Begrunder der sudwestdeutschen Schule (auch Badische Schule ), die eine Richtung des Neukantianismus darstellt. Windelbands Hauptaugenmerk galt der Abgrenzung von Natur- und Kulturwissenschaften. Sein wichtigster Schuler war Heinrich Rickert. Sigmund Gunther lebte von 1848 - 1923 und gilt als einer der wichtigsten Mathematikhistoriker. Er wurde mit der Dissertation "Studien zu theoretischen Photometrie" promoviert. In dem vorliegenden Werk gehen beide Autoren ausfuhrlich auf die geschichtlichen Hintergrunde der Naturwissenschaften und der Philosophie ein. Das Buch erschien ursprunglich als funfter Band im "Handbuch der klassischen Altertums-Wissenschaft" und wurde 1888 erstmals veroffentlicht. Der Verlag der Wissenschaften verlegt historische Literatur bekannter und unbekannter wissenschaftlicher Autoren. Dem interessierten Leser werden so teilweise langst nicht mehr verlegte Werke wieder zugangig gemacht. Das vorliegende Buch ist ein unveranderter Nachdruck der Originalausgabe.". (shrink)

Noise has become an increasingly noticeable and significant symptom of our civilization. Fundamentally an acoustic phenomenon, noise has wider implications. It is the legitimate object of scientific investigations in the fields of psychology and physiology. It can be properly evaluated by its role in music and in general aesthetics. It leads to basic questions of sociology. We shall pursue the implications in these various fields one by one. In this process, as elsewhere, music provides the bridge from facts to commitments (...) . Siegmund Levarie is professor of music at the City University of New York. The author of books on Mozart, Guillaume de Machaut, harmony, and Italian music, he has also collaborated with Ernst Levy on Tone: A Study in Musical Acoustics and the forthcoming A Dictionary of Musical Morphology. (shrink)

The lack of access to gender-affirming surgery represents a significant unmet health care need within the transgender community, frequently resulting in depression and self-destructive behavior. While some transgender people may have access to gender reassignment surgery, an overwhelming majority cannot afford facial feminization surgery. The former may be covered as a “medical necessity,” but FFS is considered “cosmetic” and excluded from insurance coverage. This demarcation between “necessity” and “cosmetic” in transgender health care based on specific body parts is in direct (...) opposition to the scientific community’s understanding of gender dysphoria and professional guidelines for transgender health. GRS affects one’s ability to function in an intimate relationship, while FFS has the same impact on social interactions an, therefore may have a far greater implication for one’s quality of life. FFS is a cost-effective intervention that needs to be covered by insurance policies. The benefits of such coverage far exceed the insignificant costs. (shrink)

Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of (...) the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians. (shrink)

This paper is divided into a surveying and argumentative part and a slightly longer documentary part, which is meant to verify or at least make more plausible claims made in the first part. The first part deals in broad outline with the relationship of Frank and von Mises to the Vienna Circle of Logical Empiricism on the one hand and to the physicists and mathematicians in the German-speaking world on the other. The varying special positions, partly the non-conformity of the (...) two Austrian scientists are emphasized, in particular, their adherence to Ernst Mach’s epistemology and their shared interest in probability theory and applied mathematics. The impact of emigration and the after-effects in the U.S. are discussed. This leads to new insights into the fine structure of the Vienna Circle and the latter’s relationship to German academia within ‘Weimar Culture’. P. Forman’s interpretation (1971) of von Mises’ position is critically discussed. The second, documentary part, uses recently discovered correspondence between Frank and von Mises, and, to a lesser extent, von Mises’ personal diary. It aims at further substantiating some of the introductory theses and will at the same time provide material for a thorough biographical appreciation of the two scholars and friends. (shrink)

Subject: Volume dedicated to the question of how dance, both in its historical and in its contemporary manifestations, is intricately linked to conceptualisations of the political. Whereas in this context the term "policy" means the reproduction of hegemonic power relations within already existing institutional structures, politics refers to those practices which question the space of policy as such by inscribing that into its surface which has had no place before. The art of choreography consists in distributing bodies and their relations (...) in space. It is a distribution of parts that within the field of the visible and the sayable allocates positions to specific bodies. Yet in the confrontation between bodies and their relations, a deframing and dislocating of positions may take place. The essays included in this book are aimed at the multiple connections between politics, community, dance, and globalisation from the perspective of e.g. Dance and Theatre Studies, History, Philosophy, and Sociology. (shrink)

Die Abgrenzung des Designs von der Kunst, welche die ästhetische Theorie im 20. Jahrhundert vornahm, hat uns implizit eine Definition von Design und designerischem Handeln vorgegeben, die diesem nicht in Gänze gerecht wird. Mit der Auszeichnung der Kunst fand eine Abwertung gestalterischen Handelns statt. Die angebliche Distanz des Künstlerischen zum Funktionalen und Ökonomischen steht heute mehr denn je in Frage, wie sich auch bemerken lässt, dass Design seit seiner Entstehung vielfach durch künstlerische Einflüsse geprägt worden ist. Um heute Design adäquat (...) theoretisch zu fassen, muss seine kategoriale Abgrenzung von den. (shrink)

Der Beitrag beschäftigt sich aus philosophischer Perspektive mit der kontroversen öffentlichen Diskussion zur documenta fifteen. Einigen Stellungnahmen in dieser Debatte liegen implizit Prämissen einer kantisch geprägten ästhetischen Theorie zugrunde; ihnen stehen anders situierte Diskussionsstrategien aus außereuropäischen Kontexten gegenüber. Im Text wird der kantische universalistische Gedanke eines ästhetischen Gemeinsinns kritisch im Sinne einer postkolonialen Kritik gelesen. Gibt es andere universale Annäherungen an künstlerisches Arbeiten, die stärker von einer Haltung des Zuhörens geprägt sind? Entsprechend den in diesem Feld möglichen Differenzen variiert auch (...) das Verständnis, was es bedeutet, in einem Künstler:innenkollektiv zu arbeiten. (shrink)

What follows shall provide an introduction to a predominantly philosophical and polemical, but historically revealing, paper on the foundations of the theory of probability. The leading Russian probabilist Aleksandr Yakovlevich Khinchin wrote the paper in the late 1930s, commenting on a slightly older, but still competing approach to probability theory by Richard von Mises. Together with the even more influential Andrey Nikolayevich Kolmogorov, who was nine years his junior, Khinchin had revolutionized probability theory around 1930 by introducing the modern measure-theoretic (...) approach, which is still standard today and which allowed for a sufficiently general treatment of important new notions such as “stochastic processes.” This development had its first culmination in Kolmogorov's booklet, Grundbegriffe der Wahrscheinlichkeitsrechnung, written in German in 1933, which has exerted an enormous influence world wide. (shrink)

The correspondence between Richard von Mises and George Pólya of 1919/20 contains reflections on two well-known articles by von Mises on the foundations of probability in the Mathematische Zeitschrift of 1919, and one paper from the Physikalische Zeitschrift of 1918. The topics touched on in the correspondence are: the proof of the central limit theorem of probability theory, von Mises' notion of randomness, and a statistical criterion for integer-valuedness of physical data. The investigation will hint at both the fruitfulness and (...) the limits of several of von Mises' notions such as ``collective'', ``distribution'' and ``complex adjuncts'' (characteristic functions) for further developments in probability theory and in ``directional statistics''. By pointing to the selectiveness of Pólya's criticism, the historical analysis shows the differing expectations of the two men with respect to the further development of the theory of probability and its applications. The paper thus gives a glimpse of the provisional state of the theory around 1920, before others such as P. Lévy (1886–1971) and A. N. Kolmogorov (1903–1987) stepped in and created a new paradigm for probability theory. (shrink)

Imagine a scenario where you are cooking and suddenly, the contents of the pot start to come out, and the oven bell rings. You would have to stop what you are doing and start responding to the changing demands, switching between different objects, operations and mental sets. This ability is known as cognitive flexibility. Now, add to this scenario a strong emotional atmosphere that invades you as you spontaneously recall a difficult situation you had that morning. How would you behave? (...) Recent studies suggest that emotional states do modulate cognitive flexibility, but these findings are still controversial. Moreover, there is a lack of evidence regarding the underlying brain processes. The purpose of the present study was, therefore, to examine such interaction while monitoring changes in ongoing cortical activity using EEG. In order to answer this question, we used two musical stimuli to induce emotional states (positive/high arousal/open stance and negative/high arousal/closed stance). Twenty-nine participants performed two blocks of the Madrid Card Sorting Task (MCST) in a neutral silence condition and then four blocks while listening to the counterbalanced musical stimuli. To explore this interaction, we used a combination of first-person (micro-phenomenological interview) and third-person (behavior and EEG) approaches. Our results show that compared to the positive stimuli and silence condition, negative stimuli decrease reaction times (RTs) for the shift signal. Our data show that the valance of the first emotional block is determinant in the RTs of the subsequent blocks. Additionally, the analysis of the micro-phenomenological interview and the integration of first- and third-person data show that the emotional disposition generated by the music could facilitate task performance for some participants or hamper it for others, independently of its emotional valence. When the emotional disposition hampered task execution, RTs were slower, and the P300 potential showed a reduced amplitude compared to the facilitated condition. These findings show that the interaction between emotion and cognitive flexibility is more complex than previously thought and points to a new way of understanding the underlying mechanisms by incorporating an in-depth analysis of individual subjective experience. (shrink)

According to both contemporary intuitions and scholarly opinion, autonomy is something specifically modern. It is certainly taken to be incompatible with religions like Islam and Judaism, if these are invested with political power. Both religions are seen as centered on a divine Law (sharî'a, viz., torah) which prescribes what we may and may not do, promising reward for obedience and threatening punishment for disobedience. Not we, but God makes the rules. This picture is in important ways misleading. There is, I (...) argue, a substantive intellectual tradition, going back to Plato's Laws, which takes the purpose of a theocracy—a community governed by God through the intermediary of a divine Law—to be promoting rational autonomy, conceived as (1) the ability to rationally determine what is in one's best interest and (2) having the motivation to live accordingly.Among the most important representatives of this intellectual tradition are medieval Muslim and Jewish philosophers. (shrink)