Charles W. Curtis is a prominent mathematician who has made important contributions to the field of representation theory. His textbooks in this field have been classics for a long time. In Pioneers of Representation Theory he has set out to present the historical development of the main ideas of the discipline, from the work of Georg Ferdinand Frobenius in the 1890s up to 1960. In addition to Frobenius, the book focuses mainly on three other “pioneers”: William Burnside, Issai (...) Schur, and Richard Brauer.Curtis states that his interest in the history of representation theory arose gradually, and jointly with that of Reiner, in the process of writing their textbooks. Thus, a main aim of the book is to show how the pioneers reached their important results while using only the mathematics then available to them. In order to do so, Curtis presents successive and thorough accounts of the works in which the new and seminal ideas of the pioneers were introduced and then developed. At the same time, however, he simplifies some of the original arguments by translating them into modern terminology.In an attempt to make the book appealing and accessible to a wider circle of potential readers, some of the necessary mathematics is explained. Thus Chapter 1 presents an introduction to the basic ideas and problems of nineteenth‐century algebra and number theory; later on, as the need arises, additional mathematical sections addressed to nonexperts are included. Of course, even this very clear presentation will be accessible only to readers with at least a graduate‐level knowledge of algebra.Curtis also attempts to provide some historical context. He is particularly concerned to clarify the main problems that the work of each of the mathematicians discussed here was originally meant to resolve. In a book of this kind this is surely one of the major benefits that the reader may expect to obtain.There are biographical sketches of the major figures involved, as well as additional information about other participants. Some illuminating documents are quoted, and Curtis supplies brief accounts of the mathematical traditions within which each of the pioneers was educated and worked. He acknowledges, however, that Pioneers of Representation Theory has only a limited claim as a work of historical research. He thus provides references to more historically oriented work that interested readers can consult. In particular, he mentions several articles by Thomas Hawkins; it should be stressed that much of Hawkins's work has recently been published in book form: Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics, 1869–1926 . Curtis's and Hawkins's books complement each other in many important ways, and each should appeal to readers of the other.Charles Curtis has written an impressive, authoritative, and well‐informed book on a difficult subject. Mathematicians and historians of twentieth‐century mathematics with the relevant background will find it difficult but rewarding reading. Along the way, historiographical questions may arise. To what extent is it possible to translate, as Curtis does, the original proofs of the pioneers into more modern terminology and yet remain faithful to the sources? In most cases, however, it will require the technical expertise of the author himself to answer questions like this one properly. We can only hope that the firm starting point this book provides will lead Curtis to further historical research in this and related fields. (shrink)

Name der Zeitschrift: Semiotica Jahrgang: 2015 Heft: 204 Seiten: 121-143.

The Leo Strauss transcript project -- Editor's introduction: Strauss, Nietzsche, and the history of political philosophy -- Editorial headnote -- Introduction: Nietzsche's philosophy, existentialism, and the problem of our age -- Restoring nature as ethical principle: Zarathustra, prologue -- The creative self: Zarathustra, part 1, 1-8 -- The true individual as the highest goal: Zarathustra, part 1, 9-15 -- Postulated nature and final truth: Zarathustra, part 1, 16-22 -- Truth, interpretation, and intelligibility: Zarathustra, part 2, 1-12 -- Will to power (...) and self-overcoming: Zarathustra, part 2, 15-20 -- Summary and review: fusing Plato and the creative self -- Greek philosophy and the Bible; nature and history: Zarathustra, part 2, 20-22 -- Eternal recurrence: Zarathustra, part 2, 21; part 3, 1-13 -- Survey: Nietzsche and political philosophy -- The goodness of the whole, Socratic and Heideggerian critiques: Zarathustra, part 4-12 -- Creative contemplation: Zarathustra, part 3, 13 -- Restoring the sacred and the final question: Zarathustra, part 4. (shrink)

Presents the early published writings of the distinguished political philosopher Leo Strauss, available here for the first time in English. “Zank places at the reader’s disposal the young Strauss’s passionate advocacy of political Zionism and his early confrontations with Spinoza, consideration of whom helped lead Strauss to formulate his teaching on ‘the quarrel between the ancients and the moderns.’” — National Review.

The paper illustrates how organic chemists dramatically altered their practices in the middle part of the twentieth century through the adoption of analytical instrumentation — such as ultraviolet and infrared absorption spectroscopy and nuclear magnetic resonance spectroscopy — through which the difficult process of structure determination for small molecules became routine. Changes in practice were manifested in two ways: in the use of these instruments in the development of ‘rule-based’ theories; and in an increased focus on synthesis, at the expense (...) of chemical analysis. These rule-based theories took the form of generalizations relating structure to chemical and physical properties, as measured by instrumentation. This ‘Instrumental Revolution’ in organic chemistry was two-fold: encompassing an embrace of new tools that provided unprecedented access to structures, and a new way of thinking about molecules and their reactivity in terms of shape and structure. These practices suggest the possibility of a change in the ontological status of chemical structures, brought about by the regular use of instruments. The career of Robert Burns Woodward provides the central historical examples for the paper. Woodward was an organic chemist at Harvard from 1937 until the time of his death. In 1965, he won the Nobel Prize in Chemistry. (shrink)

Maude's excellent translation of Tolstoy's treatise on the emotionalist theory of art was the first unexpurgated version of the work to appear in any language. More than ninety years later this work remains, as Vincent Tomas observed, "one of the most rigorous attacks on formalism and on the doctrine of art for art's sake ever written". Tomas' Introduction makes this the edition of choice for students of aesthetics and anyone with philosophical interests.

I. The function of models in the empirical sciencesII. Structure and purpose: conditions of a structural nature which models should satisfy in order to accomplish their function.III. Generalisation and specialisation of the classical definition of model, in view of the above requirements:the algebraic model conceptthe semantic model conceptthe syntactical model conceptIV. Attempt towards reunification: the concept of model on a pragmatic basis.

Offering an innovative approach to critical thinking, Good Reasoning Matters! identifies the essential structure of good arguments in a variety of contexts and also provides guidelines to help students construct their own effective arguments. In addition to examining the most common features of faulty reasoning--slanting, bias, propaganda, vagueness, ambiguity, and a common failure to consider opposing points of view--the book introduces a variety of argument schemes and rhetorical techniques. This edition adds material on visual arguments and more exercises.

In Homos, he studies the historical, political, and philosophical grounds for the current distrust, within the gay community, of self-identifying moves, for the ...

Media use can empower people, provided that this is accompanied by a deeper understanding of the actors, processes and structures in the media sector – including media policy. It is, however, to be expected that media users’ literacy of media policy is rather limited. This is problematic as the absence of such understanding makes it impossible for citizens to hold the politicians they elected accountable for the media policy they develop. This article explores what media users know about media policy, (...) what they expect to know, and whether they care. We adopted a case-study approach, researching this question for the region of Flanders based on a combination of quantitative (representative survey) and qualitative (49 in-depth interviews) data. While the article focuses on the case of Flanders, its theoretical basis as well as conclusion section are relevant beyond that specific context. (shrink)

Over the last decades we have seen an increased interest in forensic rhetoric in Plato's dialogues, notably in relation to hisApology. However, little interest has been paid to this strain of rhetoric in relation to theGorgias. In this article I focus on one notion, βοήθεια, as it was discussed in Plato'sGorgias. This notion had a wide currency in forensic rhetoric in classical Athens.

Leo Corry tells the story behind the idea of number, from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the mathematics of the 18th to the early 20th century.

Leo Strauss's introductions to ten writings of Moses Mendelssohn -- Preliminary remark by Alexander Altmann -- Introduction to Pope a metaphysician! -- Introduction to "Epistle to Mr. Lessing in Leipzig" -- Introduction to Commentary on Moses Maimonides' "Logical terms" -- Introduction to Treatise on evidence in metaphysical sciences -- Introduction to Phädon -- Introduction to Treatise on the incorporeality of the human soul -- Introduction to "On a handwritten essay of Mr. de Luc's" -- Introduction to The soul -- Introduction (...) to Morning hours and to the friends of Lessing -- Introduction to God's cause, or providence vindicated. (shrink)

Thomas Taylor’s interpretation of Plato’s works in 1804 was condemned as guilty by association immediately after its publication. Taylor’s 1804 and 1809 reviewer thus made a hasty generalisation in which the qualities of Neoplatonism, assumed to be negative, were transferred to Taylor’s own interpretation, which made use of Neoplatonist thinkers. For this reason, Taylor has typically been marginalised as an interpreter of Plato. This article does not deny the association between Taylor and Neoplatonism. Instead, it examines the historical and historiographical (...) reasons for the reviewer’s assumption that Neoplatonic readings of Plato are erroneous by definition. In particular, it argues that the reviewer relied on, and tacitly accepted, ethical and theological premises going back to the historiography of philosophy developed by Jacob Brucker in his Historia critica philosophiae . These premises were an integral part of Brucker’s Lutheran religiosity and thus theologically and ethically biased. If these premises are identified, articulated and discussed critically—which they have not been so far in connection with Taylor’s reception—it becomes less obvious that the reviewer was justified in his assumption that the Neoplatonic reading was erroneous by definition. This, in turn, leaves Taylor’s Plato interpretation in a more respectable position. (shrink)

Volume 28, Issue 3, May 2020, Page 431-441.

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)

This article critically explores the history and nature of a hermeneutic assumption which frequently guided interpretations of Plotinus from the 18th century onwards, namely that Plotinus advanced a system of philosophy. It is argued that this assumption was introduced relatively late, in the 18th and 19th centuries, and that it was primarily made possible by Brucker’s methodology for the history of philosophy, dating from the 1740s, to which the concept of a ‘system of philosophy’ was essential. It is observed that (...) the concept is absent from Ficino’s commentary from the 15th century, and that it remained absent in interpretations produced between the 15th and 18th centuries. It is also argued that the assumption of a ‘system of philosophy’ in Plotinus is historically incorrect—we do not find this concept in Plotinus’ writings, and his own statements about method point in other directions. Eduard Zeller is typically regarded as the first to give a satisfying account of Plotinus’ philosophy as a whole. In this article, on the other hand, Zeller is seen as having finalised a tradition initiated in the 18th century. Very few Plotinus scholars have examined the interpretative development prior to Zeller. Schiavone and Bonetti , for instance, have given little attention to Brucker’s introduction of the concept of a ‘system of philosophy’. The present analysis, then, has value for an understanding of Plotinus’ Enneads. It also explains why “pre-Bruckerian” interpretations of Plotinus appear alien to the modern reader; the analysis may even serve to make some sense of the hermeneutics employed by Renaissance Platonists and commentators, who are often eclipsed from the tradition of Platonism. (shrink)

Contextualizing the emergence of history of philosophy within eighteenth-century German Enlightenment, this book discusses the philosophical nature of the historiographical concept ‘system of philosophy’ and the concept’s influence upon the methods of history of philosophy and history of ideas.

Philosophers often claim that forgiveness is a paradoxical phenomenon. I here examine two of the most widespread ways of dealing with the paradoxical nature of forgiveness. One of these ways, emblematized by Aurel Kolnai, seeks to resolve the paradox by appealing to the idea of repentance. Somehow, if a wrongdoer repents, then forgiving her is no longer paradoxical. I argue that this influential position faces more problems than it solves. The other way to approach the paradox, exemplified here by the (...) work of Jacques Derrida, is just too obscure to be by itself helpful. Yet, I argue that what I take to be its spirit is on the right track. I recommend distinguishing between the definition and the justification of forgiveness, and also between forgiveness understood as a mental phenomenon and an overt, communicative act. These distinctions are not given their due in the specialized literature, and I expose the nefarious consequences of this neglect. By focusing on forgiveness as a mental phenomenon I seek to analyze the root of the talk of paradoxes which surrounds the discussion of forgiveness. Finally, I present an analysis of forgiveness as a pure mental phenomenon, and argue that this analysis is the most important step in understanding forgiveness in any other sense. While my analysis reveals interesting aspects of forgiveness, it reveals, too, that forgiveness is not quite as paradoxical after all. (shrink)

The essays are based on a long and intimate familiarity with the works, but the essay on Aristotle is especially important as one of Strauss's few writings on ...

Methods facilitating noetic ascent -- Contraction as an ontological concept -- Contraction and noesis -- Contraction and memory -- Physiologically induced contraction -- The scholastic tradition of contraction -- Cusanus and the scholastic tradition of contraction.

How common are corporate codes of ethics in the UK and especially among Britain's most admired companies? The author is Wicklander Professor of Professional Ethics at DePaul University, Chicago, and current President of the American Society for Business Ethics.

With a view to the theme of church renewal, this article explores the role of a well-known and popular phrase in the Reformed tradition within Protestantism, that is, ecclesia reformata semper reformanda [‘the reformed church should always be reformed’]. Is this a helpful slogan when considering the possibilities and the limitations of church renewal? Firstly, the historical background of this phrase is described: it is rooted in the Dutch Reformed tradition, and only in the 20th century it was widely recognised (...) in Reformed circles. Against this background the hermeneutical problem, linked with the principle of sola Scriptura, is presented, and put into an ecumenical ecclesiological perspective: the church is grounded in the gospel. Finally, the article focuses on church polity as an important field of renewal, taking into account Karl Barth’s interpretation of this phrase. From this perspective, a balanced and ecumenical approach of church renewal is possible. (shrink)

In this article I argue that Socrates appropriated a traditional discourse characteristic of Athenian law courts and politics keyed to the concept of protection (boētheia). More specifically, I argue that Socrates aimed at protecting the Athenians, though not directly, but indirectly, namely via his life-long endeavour to serve (boēthein) Apollo. I thus read Plato’s Apology as a political text, though not “political” in the sense of Socrates being suspect of overthrowing democracy, as sometimes claimed, but “political” in the sense that (...) Plato’s Socrates latched on to this concept of boēthein in the Apology. (shrink)

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.".

Mr. Brown's paper contains a detailed statement of the industrial situation at the present day, and the part which Scholastic philosophy should naturally take in bettering it. Some of the facts he delineates will come as a surprise to many people; those, for example who expect the workingman to gain redress through the courts will find added interest in this paper.

While it is no doubt a good pedagogical principle to stress the most convincing proof in the first learning of a philosophic thesis, yet a man with any pretence to philosophic effeciency should certainly have at his beck and call several proofs to do service in various situations. Mr. Brown indicates a few subsidiary proofs in connection with the subject of materialsm, a consideration of grave import in the philosophical world today.

It is commonly known that ancient schools of ethics were revived during the Renaissance: The texts pertaining to Platonic, Aristotelian, Stoic and Epicurean ethics were edited, translated and discussed in this period. It is less known that the Renaissance also witnessed a revival of Plotinian ethics, by then perceived as a legitimate form of Platonic ethics. Plotinus' ethics had been transmitted through the Middle Ages through Macrobius' Latin treatise In somnium Scipionis I.8, which relied heavily on Plotinus' student, Porphyry, and (...) his report of Plotinus' ethics. In this article it is argued that the Florentine humanist and philosopher Marsilio Ficino carried on this tradition of Platonic, or rather Plotinian, ethics. He was familiar with Plotinus' Enneads, since he had had access to it through Greek manuscripts from around 1462; his Latin translation of the Enneads was published in 1492. The article argues that in his commentary on Plato's Symposium, completed in 1469, Ficino made use of Plotinian ethi.. (shrink)

This article is currently available as a free download on ingentaconnect.