Hermann Grassmann's Ausdehnungslehre of 1844 and his Lehrbuch der Arithmetik of 1861 are landmark works in mathematics; the former not only developed new mathematical fields but also both contributed to the setting of modern standards of rigor. Their very modernity, however, may obscure features of Grassmann's view of the foundations of mathematics that were not adopted since. Grassmann gave a key role to the learning of mathematics that affected his method of presentation, including his emphasis on making initial assumptions explicit. (...) In order to better understand this less well-known aspect of his work it will help to examine why some commentators have overlooked his theme of unifying logic, pedagogy and foundations, while others have recognised it. (shrink)

Hermann Grassmann's ideas on the nature and foundations of mathematics were published as an integral part of his mathematical treatise, the Ausdehnungslehre, in 1844. In spite of its notoriously obscure style we can better understand the work if we view it as an expression of the dialectical philosophy of his mentor, the theologian F. Schleiermacher. The relation to Schleiermacher is presented here through an analysis of the principal ideas of the Ausdehnungslehre.

The 1896-1899 papers, few of which were published in Russell's lifetime, concentrate primarily on physics, arithmetic and the concept of quantity. Several views that later became well-known in his The Principles of Mathematics actually originate in his earlier work, and though incomplete, An Analysis of Mathematical Reasoning , forms a centrepiece of the volume.

During the First World War, Bertrand Russell was political commentator for _The Tribunal_, the official weekly publication of the No-Conscription Fellowship, of which Russell was Action Chairman. This volume contains many short papers from that period, which reflect Russell's immediate reponses to developments in the conflict. These documents bear witness to Russell's growing commitment to pacifism, and reveal the development of the patterns of political argument, rhetoric and activism which were to characterise his work throughout his life.

First published in 1994. Routledge is an imprint of Taylor & Francis, an informa company.

This is the diary of an observant mathematician who documented the drama of the resolution of Fermat's Last Theorem as it unfolded around him from 1993 to 1995. Pierre Fermat claimed around 1637, in the most famous marginalia in the history of mathematics, to have a proof of the theorem that xn + yn = zn has no whole number solutions for n greater than 2. The other principal figure is the British mathematician Andrew Wiles, who emigrated to Princeton University (...) in the 1980s and who in 1993, at what for mathematicians is the relatively advanced age of forty, announced a proof of FLT. In the course of Wiles's initial exposition to mathematicians, before a full‐fledged proof could be published, a gap was discovered. This was too late to forestall announcements in the world press of an imminent proof. What had been an almost secretive devotion to the task by Wiles now became a rather more public and pressurized effort over the course of nearly a year. Wiles wondered at times if success could be achieved, but with the help of other mathematicians the gap was filled in and the full formal proof published in 1995.The statement of the theorem is likely to be the only part of the 1990s story that a nonspecialist can immediately appreciate, and the author has not especially addressed his book to the nonspecialist. Rather, this account is analogous to a well‐illustrated exhibition guidebook that serves as a memento and record to those who visited in person but that is not intended fully to inform those who did not experience it. For a broader account of the historical and mathematical background a reader can consult the three principal books published previously on the same topic by Amir Aczel, Simon Singh, and Alfred J. van der Poorten. The author knew many of the main players, attended most of the key talks, took notes, made recordings, and photographed. A major part of the book is a selection of sixty‐two photographs from the total of three thousand made by the author. He asked questions of Wiles and others and recorded both formal and informal reactions that he observed around him during the many public and nonpublic presentations that were made. Also, in keeping with the journal nature of his work, he has recorded his own reactions. Appendixes include an excerpt from Wiles's 1995 Annals of Mathematics publication and a synopsis by Ram Murty of the key results by Gerhard Frey, Jean‐Pierre Serre, and Kenneth Ribet that formed a basis for Wiles's work.It may interest historians and archivists to learn of the extent to which the primary sources for this story include e‐mail, web pages, photographs, and newspaper and television interviews. Though we recognize this reality of contemporary science, a diary account probably brings the issue home more directly than would studies by professional historians, who might feel obligated to do more of their own interviews, for example, rather than rely on the media. Mathematics has rarely had such a public spotlight turned on it—the proof of the four‐color theorem in 1976 is the only comparable event that comes to mind. Consequently, it has opened an unusual window into how mathematicians do mathematics. (shrink)

In a recent paper, David Albert has suggested that no quantum theory can yield a description of the world unfolding in Minkowski spacetime. This conclusion is premature; a natural extension of Stein's notion of becoming in Minkowski spacetime to accommodate the demands of quantum nonseparability yields such an account, an account that is in accord with a proposal which was made by Aharonov and Albert but which is dismissed by Albert as a ‘mere trick’. The nature of (...) such an account is clarified by an extension to a relativistic quantum context of David Lewis' picture of objective chances evolving in time. 1 Introduction 2 Classical relativistic becoming 3 Relativistic quantum becoming, without collapse 4 Relativistic quantum becoming, with collapse 5 Objective chance, conditional probability, and definite properties 6 The nature of the wave function 7 Conclusion. (shrink)

C. S. Lewis sets out to persuade his audience of the importance and relevance of universal values such as courage and honor in contemporary society.

C. S. Lewis' article addresses a critically important issue on which Howard Ahmanson comments. Professor Oliver O'Donovan addresses the same issue in a sermon in Christ Church Oxford on Trinity Sunday 1997. We publish the three articles together in the year of the fiftieth anniversary of the independence of India and Pakistan and invite correspondence on the issues at stake. Eds.

C. S. Lewis sets out to disentangle this knotty issue but wisely adds that in the end no intellectual solution can dispense with the necessity for patience and ...

On the occasion of the 50th anniversary of C. S. Lewis’s death, a special annotated edition of his Christian classic, The Screwtape Letters, with notes and excerpts from his other works that help illuminate this diabolical masterpiece. Since its publication in 1942, The Screwtape Letters has sold millions of copies worldwide and is recognized as a milestone in the history of popular theology. A masterpiece of satire, it offers a sly and ironic portrayal of human life and foibles from (...) the vantage point of Screwtape, a highly placed assistant to “Our Father Below.” At once wildly comic, deadly serious, and strikingly original, The Screwtape Letters comprises the correspondence of the worldly-wise devil Screwtape and his nephew Wormwood, a novice demon in charge of securing the damnation of an ordinary young man. For the first time, The Screwtape Letters will be presented in full-text accompanied by helpful annotations in a striking two-color format. These annotations will give fans a deeper, more nuanced understanding of the popular book, providing background information, explanations of terms, historical significance, and excerpts from Lewis’s other works that more fully explain the ideas in this volume. For both expert Lewis fans and casual readers, The Screwtape Letters: Annotated Edition will be a beautiful and insightful guide to a beloved classic. (shrink)

A repackaged edition of the revered author's classic work that examines the four types of human love: affection, friendship, erotic love, and the love of God—part of the C. S. Lewis Signature Classics series. C.S. Lewis—the great British writer, scholar, lay theologian, broadcaster, Christian apologist, and bestselling author of Mere Christianity, The Screwtape Letters, The Great Divorce, The Chronicles of Narnia, and many other beloved classics—contemplates the essence of love and how it works in our daily lives in (...) one of his most famous works of nonfiction. Lewis examines four varieties of human love: affection, the most basic form; friendship, the rarest and perhaps most insightful; Eros, passionate love; charity, the greatest and least selfish. Throughout this compassionate and reasoned study, he encourages readers to open themselves to all forms of love—the key to understanding that brings us closer to God. (shrink)

C. S. Lewis takes us on a profound journey through both heaven and hell in this engaging allegorical tale. Using his extraordinary descriptive powers, Lewis introduces us to supernatural beings who will change the way we think about good and evil.

C. Lewy; VI—Entailment and Propositional Identity, Proceedings of the Aristotelian Society, Volume 64, Issue 1, 1 June 1964, Pages 107–122, https://doi.org/10.1.