Logic is, and should be, the core subject area of modern mathemat ics. The blueprint for twentieth century mathematical thought, thanks to Hilbert and Bourbaki, is the axiomatic development of the subject. As a result, logic plays a central conceptual role. At the same time, mathematical logic has grown into one of the most recondite areas of mathematics. Most of modern logic is inaccessible to all but the special ist. Yet there is a need for many mathematical scientists-not just those engaged in mathematical research-to become conversant with the key ideas of logic. The Handbook of Mathematical Logic, edited by Jon Bar wise, is in point of fact a handbook written by logicians for other mathe maticians. It was, at the time of its writing, encyclopedic, authoritative, and up-to-the-moment. But it was, and remains, a comprehensive and authoritative book for the cognoscenti. The encyclopedic Handbook of Logic in Computer Science by Abramsky, Gabbay, and Maibaum is a wonderful resource for the professional. But it is overwhelming for the casual user. There is need for a book that introduces important logic terminology and concepts to the working mathematical scientist who has only a passing acquaintance with logic. Thus the present work has a different target audience. The intent of this handbook is to present the elements of modern logic, including many current topics, to the reader having only basic mathe matical literacy.
Artist, psychoanalyst, and feminist theorist Bracha Ettinger presents an original theoretical exploration of shared affect and emergent expression, across the thresholds of identity and memory. Ettinger works through Lacan’s late works, the anti-Oedipal perspectives of Deleuze and Guattari, as well as object-relations theory to critique the phallocentrism of mainstream Lacanian theory and to rethink the masculine-feminine opposition. She replaces the phallic structure with a dimension of emergence, where objects, images, and meanings are glimpsed in their incipiency, before they are differentiated. This is the matrixial realm, a shareable, psychic dimension that underlies the individual unconscious and experience. Concerned with collective trauma and memory, Ettinger’s own experience as an Israeli living with the memory of the Holocaust is a deep source of inspiration for her paintings, several of which are reproduced in the book. The paintings, like the essays, replay the relation between the visible and invisible, the sayable and ineffable; the gaze, the subject, and the other. Bracha Ettinger is a painter and a senior clinical psychologist. She is professor of psychoanalysis and aesthetics at the University of Leeds, England, and Bezalel Academy, Jerusalem. Judith Butler is professor of rhetoric and comparative literature at the University of California, Berkeley. Griselda Pollock is professor of fine arts at the University of Leeds. Brian Massumi is professor of communication at the University of Montreal.
Drawing inspiration from the work of Rene Char, Melissa Kwasny in The Nine Senses presents a new kind of prose poem. Casting aside the narrative-plus-moral formula of old, these experiments make each line equal to the next, challenging the way we read sequentially. Dylan Thomas, Roman water lines, Paul Celan, Shirin Neshat, anti-depressants, Buddhism, William Carlos Williams, Trakl, cancer, Beckett, Pound, Breton, the Iraq War, telekinesis, clairvoyance, Jaune Quick-to-See Smith, and Yeats, among many others, appear side by side in these pages. As if liberating the intellect, the prose poem form invites a wave of vivid, colliding images, and allows a comfortable wordiness and word play that is inherently poetic. Raising the ante even further than Reading Novalis in Montana, this book asks how do we tie ourselves to the world when our minds are always someplace other than where we are? As bromides and aphorisms degrade in this new construct, we are left with the realization that we have been misled by culture and politics, which encourages prevarication. Obliquely touching on the cancer of a friend, her own troubled relationship with her father, and the break-up of a nearly thirty-year partnership, Kwasny also questions mortality, temporality, and eternity. Walking the knife-edge between safety and danger, and marveling over the quickness with which the familiar can end, Kwasny posits a new perception of time, in which the work lives on under new direction. Near the end of the book, Kwasny’s signature abstraction melts away in some very direct poems about her own cancer and diagnosis. With this manuscript, Kwasny achieves a new level of artistry. Although form is consistent throughout, the thematic cycle is rich and varied: abstract, elliptic, collaged, and ultimately evolving toward the end into powerful statements that are some of the most direct ever uttered by this author.
Among the several dozens of symposia held on the occasion of the quincentennial of U ppsala University, there was included one symposium devoted to the theme of 'Philosophy and Grammar'. A selection of the most important papers delivered at this symposium have been collected in this volume. The papers need no introduction, but the inclusion of two of them in this collection requires a brief comment. First, the paper by von Wright, although not directly concerned with the central topic of the symposium, has been included because it was the terminating speech of the six parallel symposia (including the symposium on 'Philosophy and Grammar') held by the Humanities Faculty and moreover, because the raison d'etre of the Humanities is analyzed in this paper by a very prominent Swedish-speaking philosopher. Second, Professor Hintikka was unable to participate. In view of his expertise in the field, we nevertheless requested him to contribute a paper, so to speak, post factum. This he very generously did. We wish to express our sincere appreciation to all who participated and/or helped to carry the sessions through to a successful conclusion. We also wish to extend a special thanks to Professor Roman lakobson of Harvard University, who assumed the responsibility of General Chairman of the symposium.
Computer networks and embedded systems are ubiquitous and critical parts of our daily life. Therefore performance and reliability guarantees for these systems are crucial. To this end, versatile probabilistic modelling and analysis techniques have been developed. However existing probabilistic analysis methods are inherently limited to small systems. This dissertation introduces a new probabilistic analysis method that scales to large and even infinite systems which are far out of reach of previous methods. The key idea is to approximate a given system by a smaller abstraction which is refined automatically until sufficient precision has been achieved. The thesis discusses the various foundational and practical challenges involved in developing this method, as well as its effectiveness in practice.