The Concept Of Reduction

This volume investigates the notion of reduction. Building on the idea that philosophers employ the term ‘reduction’ to reconcile diversity and directionality with unity, without relying on elimination, the book offers a powerful explication of an “ontological”, notion of reduction the extension of which is (primarily) formed by properties, kinds, individuals, or processes. It argues that related notions of reduction, such as theory-reduction and functional reduction, should be defined in terms of this explication. Thereby, the book offers a coherent framework, which sheds light on the history of the various reduction debates in the philosophy of science and in the philosophy of mind, and on related topics such as reduction and unification, the notion of a scientific level, and physicalism. The book takes its point of departure in the examination of a puzzle about reduction. To illustrate, the book takes as an example the reduction of water. If water reduces to H2O, then water is identical to H2O – thus we get unity. Unity does not come at the price of elimination – claiming that water reduces to H2O, we do not thereby claim that there is no water. But what about diversity and directionality? Intuitively, there should be a difference between water and H2O, such that we get diversity. This is required for there to be directionality: in a sense, if water reduces to H2O, then H2O is prior to, or more basic than water. At least, if water reduces to H2O, then H2O does not reduce to water. But how can this be, if water is identical to H2O? The book shows that the application of current models of reduction does not solve this puzzle, and proposes a new coherent definition, according to which unity is tied to identity, diversity is descriptive in nature, and directionality is the directionality of explanation.

Grand debates over reduction and emergence are playing out across the sciences, but these debates have reached a stalemate, with both sides declaring victory on empirical grounds. In this book, Carl Gillett provides new theoretical frameworks with which to understand these debates, illuminating both the novel positions of scientific reductionists and emergentists and the recent empirical advances that drive these new views. Gillett also highlights the flaws in existing philosophical frameworks and reorients the discussion to reflect the new scientific advances and issues, including the nature of 'parts' and 'wholes', the character of aggregation, and thus the continuity of nature itself. Most importantly, Gillett shows how disputes about concrete scientific cases are empirically resolvable and hence how we can break the scientific stalemate. Including a detailed glossary of key terms, this volume will be valuable for researchers and advanced students of the philosophy of science and metaphysics, and scientific researchers working in the area.

This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity; fast evaluation of representations of general linear groups; and complexity of immanants.

Oxidizing and Reducing Agents S. D. Burke University of Wisconsin at Madison, USA R. L. Danheiser Massachusetts Institute of Technology, Cambridge, USA Recognising the critical need for bringing a handy reference work that deals with the most popular reagents in synthesis to the laboratory of practising organic chemists, the Editors of the acclaimed Encyclopedia of Reagents for Organic Synthesis (EROS) have selected the most important and useful reagents employed in contemporary organic synthesis. Handbook of Reagents for Organic Synthesis: Oxidizing and Reducing Agents, provides the synthetic chemist with a convenient compendium of information concentrating on the most important and frequently employed reagents for the oxidation and reduction of organic compounds, extracted and updated from EROS. The inclusion of a bibliography of reviews and monographs, a compilation of Organic Syntheses procedures with tested experimental details and references to oxidizing and reducing agents will ensure that this handbook is both comprehensive and convenient.

Using simple physical examples, this work by Erhard Scheibe presents an important and powerful approach to the reduction of physical theories. Novel to the approach is that it is not based, as usual, on a single reduction concept that is fixed once and for all, but on a series of recursively constructed reductions, with which all reductions appear as combinations of very specific elementary reductions. This leaves the general notion of theory reduction initially open and is beneficial for the treatment of the difficult cases of reduction from the fields of special and general relativity, thermodynamics, statistical mechanics,and quantum mechanics, which are treated in the second volume. The book is systematically organized and intended for readers interested in philosophy of science as well as physicists without deep philosophical knowledge.

Build a solid foundation in the area of arithmetic groups and explore its inherent geometric and number-theoretical components.

The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.

The Messianic Reduction is a groundbreaking study of Walter Benjamin's thought. Fenves places Benjamin's early writings in the context of contemporaneous philosophy, with particular attention to the work of Bergson, Cohen, Husserl, Frege, and Heidegger. By concentrating on a neglected dimension of Benjamin's friendship with Gershom Scholem, who was a student of mathematics before he became a scholar of Jewish mysticism, Fenves shows how mathematical research informs Benjamin's reflections on the problem of historical time. In order to capture the character of Benjamin's "entrance" into the phenomenological school, the book includes a thorough analysis of two early texts he wrote under the title of "The Rainbow," translated here for the first time. In its final chapters, the book works out Benjamin's deep and abiding engagement with Kantian critique, including Benjamin's discovery of the political counterpart to the categorical imperative in the idea of "pure violence."