The essays collected in Persecution and the Art of Writing all deal with one problem--the relation between philosophy and politics. Here, Strauss sets forth the thesis that many philosophers, especially political philosophers, have reacted to the threat of persecution by disguising their most controversial and heterodox ideas.

This uniquely fascinating volume is not merely a learned treatise in historical semantics; it is itself a stupendous display of world harmony as a creed-a vivid demonstration that "all is all.".

In the present article two possible meanings of the term mathematical structure are discussed: a formal and a nonformal one. It is claimed that contemporary mathematics is structural only in the nonformal sense of the term. Bourbaki's definition of structure is presented as one among several attempts to elucidate the meaning of that nonformal idea by developing a formal theory which allegedly accounts for it. It is shown that Bourbaki's concept of structure was, from a mathematical point of view, a (...) superfluous undertaking. This is done by analyzing the role played by the concept, in the first place, within Bourbaki's own mathematical output. Likewise, the interaction between Bourbaki's work and the first stages of category theory is analyzed, on the basis of both published texts and personal documents. (shrink)

The ArgumentRecent studies in the philosophy of mathematics have increasingly stressed the social and historical dimensions of mathematical practice. Although this new emphasis has fathered interesting new perspectives, it has also blurred the distinction between mathematics and other scientific fields. This distinction can be clarified by examining the special interaction of thebodyandimagesof mathematics.Mathematics has an objective, ever-expanding hard core, the growth of which is conditioned by socially and historically determined images of mathematics. Mathematics also has reflexive capacities unlike those of (...) any other exact science. In no other exact science can the standard methodological framework usedwithinthe discipline also be used to study the nature of the discipline itself.Although it has always been present in mathematical research, reflexive thinking has become increasingly central to mathematics over the past century. Many of the images of the discipline have been dictated by the increase in reflexive thinking which has also determined a great portion of the contemporary philosophy and historiography of mathematics. (shrink)

This volume provides an unequaled introduction to the thought of chief contributors to the Western tradition of political philosophy from classical Greek antiquity to the twentieth century. Written by specialists on the various philosophers, this third edition has been expanded significantly to include both new and revised essays.

This article explores the changing relationships between geometric and arithmetic ideas in medieval Europe mathematics, as reflected via the propositions of Book II of Euclid’s Elements. Of particular interest is the way in which some medieval treatises organically incorporated into the body of arithmetic results that were formulated in Book II and originally conceived in a purely geometric context. Eventually, in the Campanus version of the Elements these results were reincorporated into the arithmetic books of the Euclidean treatise. Thus, while (...) most of the Latin versions of the Elements had duly preserved the purely geometric spirit of Euclid’s original, the specific text that played the most prominent role in the initial passage of the Elements from manuscript to print—i.e., Campanus’ version—followed a different approach. On the one hand, Book II itself continued to appear there as a purely geometric text. On the other hand, the first ten results of Book II could now be seen also as possiblytranslatable into arithmetic, and in many cases even as inseparably associated with their arithmetic representation. (shrink)

Natural right and the historical approach -- Natural right and the distinction between facts and values -- The origin of the idea of natural right -- Classic natural right -- Modern natural right : Hobbes ; Locke -- The crisis of modern natural right : Rousseau ; Burke.

The present article discusses the computational tools (both conceptual and material) used in various attempts to deal with individual cases of FLT, as well as the changing historical contexts in which these tools were developed and used, and affected research. It also explores the changing conceptions about the role of computations within the overall disciplinary picture of number theory, how they influenced research on the theorem, and the kinds of general insights thus achieved. After an overview of Kummer’s contributions and (...) its immediate influence, I present work that favored intensive computations of particular cases of FLT as a legitimate, fruitful, and worth-pursuing number-theoretical endeavor, and that were part of a coherent and active, but essentially low-profile tradition within nineteenth century number theory. This work was related to table making activity that was encouraged by institutions and individuals whose motivations came mainly from applied mathematics, astronomy, and engineering, and seldom from number theory proper. A main section of the article is devoted to the fruitful collaboration between Harry S. Vandiver and Emma and Dick Lehmer. I show how their early work led to the hesitant introduction of electronic computers for research related with FLT. Their joint work became a milestone for computer-assisted activity in number theory at large. (shrink)

"Strauss gives us an impressive addition to his life's work—the recovery of the Great Tradition in political philosophy. The problem the book proposes centers formally upon Socrates.

The ArgumentThe belief in the existence of eternal mathematical truth has been part of this science throughout history. Bourbaki, however, introduced an interesting, and rather innovative twist to it, beginning in the mid-1930s. This group of mathematicians advanced the view that mathematics is a science dealing with structures, and that it attains its results through a systematic application of the modern axiomatic method. Like many other mathematicians, past and contemporary, Bourbaki understood the historical development of mathematics as a series of (...) necessary stages inexorably leading to its current state — meaning by this, the specific perspective that Bourbaki had adopted and were promoting. But unlike anyone else, Bourbaki actively put forward the view that their conception of mathematics was not only illuminating and useful for dealing with the current concerns of mathematics, but that this was in fact the ultimate stage in the evolution of mathematics, bound to remain unchanged by any future development of this science. In this way, they were extending in an unprecedented way the domain of validity of the belief in the eternal character of mathematical truths, from the body to the images of mathematical knowledge.Bourbaki were fond of presenting their insistence on the centrality of the modern axiomatic method as a way to ensure the eternal character of mathematical truth as an offshoot of Hilbert's mathematical heritage. A detailed examination of Hilbert's actual conception of the axiomatic method, however, brings to the fore interesting differences between it and Bourbaki's conception, thus underscoring the historically conditioned character of certain, fundamental mathematical beliefs. (shrink)

The present issue of Science in Context comprises a collection of articles dealing with various, specific aspects of the history of mathematics during the last third of the nineteenth century and the first half of the twentieth. Like the September issue of 2003 of this journal, which was devoted to the history of ancient mathematics, this collection originated in the aftermath of a meeting held in Tel-Aviv and Jerusalem in May 2001, under the title: “History of Mathematics in the Last (...) 25 Years: New Departures, New Questions, New Ideas.” Taken together, these two topical issues are meant as a token of appreciation for the work of Sabetai Unguru and his achievements in the history of mathematics. (shrink)

ArgumentThis article gives the background to a public lecture delivered in Hebrew by Edmund Landau at the opening ceremony of the Hebrew University in Jerusalem in 1925. On the surface, the lecture appears to be a slightly awkward attempt by a distinguished German-Jewish mathematician to popularize a few number-theoretical tidbits. However, quite unexpectedly, what emerges here is Landau's personal blend of Zionism, German nationalism, and the proud ethos of pure, rigorous mathematics – against the backdrop of the situation of Germany (...) after World War I. Landau's Jerusalem lecture thus shows how the Zionist cause was inextricably linked to, and determined by political agendas that were taking place in Europe at that time. The lecture stands in various historical contexts - Landau's biography, the history of Jewish scientists in the German Zionist movement, the founding of the Hebrew University in Jerusalem, and the creation of a modern Hebrew mathematical language. This article provides a broad historical introduction to the English translation, with commentary, of the original Hebrew text. (shrink)

A reissue of the 1975 edition, with four added essays, this collection offers a clear introduction to Strauss' views regarding the nature of political ...

The human body is a multifaceted reality. As such, it has become a reference pole for a new positivity. Among the various areas of corporeal expression and recuperation, sport has become the most absorbing and efficient. Sport as a system shapes the human body in all its aspects, and confers on it a new status: the "corps sportif" which is a new paradigm of our civilization.

Le corps humain est une réalité plurielle. En tant que tel, il est devenu un pôle de référence pour une nouvelle positivité. De tous les lieux d'expression et de récupération du corps, le sport est devenu le plus accaparant et le plus efficace. Le système sportif façonne le corps humain dans tous ses aspects et lui confère un statut nouveau, celui de corps sportif, ce nouveau paradigme des temps actuels.The human body is a multifaceted reality. As such, it has become (...) a reference pole for a new positivity. Among the various areas of corporeal expression and recuperation, sport has become the most absorbing and efficient. Sport as a system shapes the human body in all its aspects, and confers on it a new status: the "corps sportif" which is a new paradigm of our civilization. (shrink)

A persistent criticism of Edmund Husserl’s transcendental phenomenology is that it begs the question of its own possibiIity as science. In this essay I propose a reading of Husserl which addresses this question and attempts to show that the phenomenological ideal of freedom from all presuppositions, that is, the ideal of radical methodological autonomy, is not dogmatically assumed as valid but rests on a conception of philosophy which, although not explicitly formulated by Husserl, nevertheless informs his thinking on questions of (...) method and, ultimately, the nature of science. According to this conception, phiIosophy, phenomenological or otherwise, is not sui generis the ground of is own possibiIity but is derived from the logic of experience itself and so is immanent to conscious, intentional life in all of its manifold occupations and interests. That is, experience ultimately fulfills itself not in the accumulation of objective facts but in its continued faithfulness to the idea of a more perfect knowledge. Thus, in the end, I hope to show that the question of the status and possibiIity of phenomenological philosophy is not of interest to phenomenologists alone but addresses the enterprise of philosophy itself. (shrink)