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Ernst Specker Selecta
Ernst Specker has made decisive contributions towards shaping direc tions in topology, algebra, mathematical logic, combinatorics and algorith mic over the last 40 years. We have derived great pleasure from marking his seventieth birthday by editing the majority of his scientific publications, and thus making his work available in a unified form to the mathematical community. In order to convey an idea of the richness of his personality, we have also included one of his sermons. Of course, the publication of these Selecta can pay tribute only to the writings of Ernst Specker. It cannot adequately express his originality and wisdom as a person nor the fascination he exercises over his student...
Stability, Instability, and Direct Integrals
In this masterful study, the author sets forth a unique treatment of the stability and instability of the periodic equilibria of partial differential equations as they relate to the notion of direct integrals. His results, and to a large extent his methods are new. Although he aims this work at theory rather than applications, once the theoretical framework is built, applications emerge with ease. Readers with some basis in functional analysis-notably semigroups-and measure theory can strengthen their background through its introductory material on direct integrals and its proofs worked out in detail. In Stability, Instability and Direct Integrals, applied and pure mathematicians and theoretical physicists can discover from an acknowledged innovator the most recent results of research in this active and expanding field.
Functional Analysis and Evolution Equations
Gunter Lumer was an outstanding mathematician whose works have great influence on the research community in mathematical analysis and evolution equations. He was at the origin of the breath-taking development the theory of semigroups saw after the pioneering book of Hille and Phillips from 1957. This volume contains invited contributions presenting the state of the art of these topics and reflecting the broad interests of Gunter Lumer.
Le Tractatus de Wittgenstein et l’ Éthique de Spinoza
Wittgenstein et Spinoza construisent, l'un dans le Tractatus, l'autre dans l'Éthique, des systèmes philosophiques réunissant le monde, l'homme et Dieu dans lesquels ils s'opposent sur de nombreux points. C'est ainsi par exemple que, suivant Spinoza, l'homme est assuré que rien ne se produit sans cause alors que Wittgenstein rejette la possibilité de rapports d'ordre causal entre les événements. Le présent travail dissèque dans une première partie l'œuvre de Wittgenstein, il analyse dans une deuxième partie la doctrine de Spinoza, et il compare enfin dans la troisième partie les deux systèmes dont il fait ressortir les points de concordance et de dissemblance dans leurs constructions respectives. Il traite les œuvres philosophiques que sont le Tractatus et l'Éthique comme si elles relevaient de sciences telles que la mécanique, l'astronomie, etc., et utilise des modèles géométriques appropriés à leur interprétation. L'étude comparative du Tractatus et de l'Éthique, qui ne cessent d'exercer leur influence sur la pensée humaine, permet de conclure que le Tractatus, œuvre du XXe siècle, renoue avec le rationalisme du XVIIe siècle exprimé par Spinoza.
Modern Uses of Multiple-Valued Logic
This is a collection of invited papers from the 1975 International Sym posium on Multiple-valued Logic. Also included is an extensive bib liography of works in the field of multiple-valued logic prior to 1975 - this supplements and extends an earlier bibliography of works prior to 1965, by Nicholas Rescher in his book Many-Valued Logic, McGraw-Hill, 1969. There are a number of possible reasons for interest in the present volume. First, the range of various uses covered in this collection of papers may be taken as indicative of a breadth which occurs in the field of multiple-valued logic as a whole - the papers here can do no more than cover a small sample: question-answering systems, analysi...
Fuzzy Logic and Mathematics
The main part of the book is a comprehensive overview of the development of fuzzy logic and its applications in various areas of human affair since its genesis in the mid 1960s. This overview is then employed for assessing the significance of fuzzy logic and mathematics based on fuzzy logic.
Gentzen's Centenary
Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory.
Hypercomputation
This book provides a thorough description of hypercomputation. It covers all attempts at devising conceptual hypermachines and all new promising computational paradigms that may eventually lead to the construction of a hypermachine. Readers will gain a deeper understanding of what computability is, and why the Church-Turing thesis poses an arbitrary limit to what can be actually computed. Hypercomputing is a relatively novel idea. However, the book’s most important features are its description of the various attempts of hypercomputation, from trial-and-error machines to the exploration of the human mind, if we treat it as a computing device.
