history and philosophy of constructive type theory synthese library volume 290

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History And Philosophy Of Constructive Type Theory

Author : Giovanni Sommaruga
ISBN : 9789401593939
Genre : Philosophy
File Size : 72. 86 MB
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A comprehensive survey of Martin-Löf's constructive type theory, considerable parts of which have only been presented by Martin-Löf in lecture form or as part of conference talks. Sommaruga surveys the prehistory of type theory and its highly complex development through eight different stages from 1970 to 1995. He also provides a systematic presentation of the latest version of the theory, as offered by Martin-Löf at Leiden University in Fall 1993. This presentation gives a fuller and updated account of the system. Earlier, brief presentations took no account of the issues related to the type-theoretical approach to logic and the foundations of mathematics, while here they are accorded an entire part of the book. Readership: Comprehensive accounts of the history and philosophy of constructive type theory and a considerable amount of related material. Readers need a solid background in standard logic and a first, basic acquaintance with type theory.

Probability Theory

Author : Vincent F. Hendricks
ISBN : 0792369521
Genre : Mathematics
File Size : 25. 14 MB
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A collection of papers presented at the conference on Probability Theory - Philosophy, Recent History and Relations to Science, University of Roskilde, Denmark, September 16-18, 1998. Since the measure theoretical definition of probability was proposed by Kolmogorov, probability theory has developed into a mature mathematical theory. It is today a fruitful field of mathematics that has important applications in philosophy, science, engineering, and many other areas. The measure theoretical definition of probability and its axioms, however, are not without their problems; some of them even puzzled Kolmogorov. This book sheds light on some recent discussions of the problems in probability theory and their history, analysing their philosophical and mathematical significance, and the role pf mathematical probability theory in other sciences.

Axiomatic Method And Category Theory

Author : Andrei Rodin
ISBN : 9783319004044
Genre : Philosophy
File Size : 42. 96 MB
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This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.

Types And Programming Languages

Author : Benjamin C. Pierce
ISBN : 0262162091
Genre : Computers
File Size : 36. 24 MB
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Mathematical Preliminaries - Untyped Systems - Untyped Arithmetic Expressions - An ML Implementation of Arithmetic Expressions - The Untyped Lambda-Calculus - Nameless Representation of Terms - An ML Implementation of the Lambda-Calculus - Types Arithmetic Expressions - Simply Typed Lambda-Calculus - An ML Implementation of Simple Types - Simple Extensions - Normalization - Exceptions - Subtyping - Metatheory of Subtyping - An ML Implementation of Subtyping - Recursive Types - Metatheory of Recursive Types - Polymorphism - Type Reconstruction - Universal Types - Existential Types - An ML Implementation of System F - Bounded Quantification - Higher-Order Systems - Higher-Order Polymorphism - Higher-Order Subtyping.

The Handbook Of Contemporary Semantic Theory

Author : Shalom Lappin
ISBN : 9780470670736
Genre : Language Arts & Disciplines
File Size : 21. 36 MB
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The second edition of The Handbook of Contemporary Semantic Theory presents a comprehensive introduction to cutting-edge research in contemporary theoretical and computational semantics. Features completely new content from the first edition of The Handbook of Contemporary Semantic Theory Features contributions by leading semanticists, who introduce core areas of contemporary semantic research, while discussing current research Suitable for graduate students for courses in semantic theory and for advanced researchers as an introduction to current theoretical work

Reference Truth And Conceptual Schemes

Author : G. Forrai
ISBN : 9789401728683
Genre : Philosophy
File Size : 29. 88 MB
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1. HISTORICAL BACKGROUND The purpose of the book is to develop internal realism, the metaphysical-episte mological doctrine initiated by Hilary Putnam (Reason, Truth and History, "Introduction", Many Faces). In doing so I shall rely - sometimes quite heavily - on the notion of conceptual scheme. I shall use the notion in a somewhat idiosyncratic way, which, however, has some affinities with the ways the notion has been used during its history. So I shall start by sketching the history of the notion. This will provide some background, and it will also give opportunity to raise some of the most important problems I will have to solve in the later chapters. The story starts with Kant. Kant thought that the world as we know it, the world of tables, chairs and hippopotami, is constituted in part by the human mind. His cen tral argument relied on an analysis of space and time, and presupposed his famous doctrine that knowledge cannot extend beyond all possible experience. It is a central property of experience - he claimed - that it is structured spatially and temporally. However, for various reasons, space and time cannot be features of the world, as it is independently of our experience. So he concluded that they must be the forms of human sensibility, i. e. necessary ingredients of the way things appear to our senses.

Business Language And Asymmetric Perceptions

Author : Jack Douglas Stecher
ISBN : MINN:31951P00787063V
Genre :
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Mathematical Reviews

Author :
ISBN : UVA:X001409606
Genre : Mathematics
File Size : 75. 64 MB
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Eine Kurze Geschichte Der Menschheit

Author : Yuval Noah Harari
ISBN : 9783641104986
Genre : History
File Size : 73. 71 MB
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Krone der Schöpfung? Vor 100 000 Jahren war der Homo sapiens noch ein unbedeutendes Tier, das unauffällig in einem abgelegenen Winkel des afrikanischen Kontinents lebte. Unsere Vorfahren teilten sich den Planeten mit mindestens fünf weiteren menschlichen Spezies, und die Rolle, die sie im Ökosystem spielten, war nicht größer als die von Gorillas, Libellen oder Quallen. Vor 70 000 Jahren dann vollzog sich ein mysteriöser und rascher Wandel mit dem Homo sapiens, und es war vor allem die Beschaffenheit seines Gehirns, die ihn zum Herren des Planeten und zum Schrecken des Ökosystems werden ließ. Bis heute hat sich diese Vorherrschaft stetig zugespitzt: Der Mensch hat die Fähigkeit zu schöpferischem und zu zerstörerischem Handeln wie kein anderes Lebewesen. Anschaulich, unterhaltsam und stellenweise hochkomisch zeichnet Yuval Harari die Geschichte des Menschen nach und zeigt alle großen, aber auch alle ambivalenten Momente unserer Menschwerdung.

Allgemeine Theorie Der Besch Ftigung Des Zinses Und Des Geldes

Author : John Maynard Keynes
ISBN : 9783428529124
Genre : Business & Economics
File Size : 32. 39 MB
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"Die Lektüre von Keynes' Hauptwerk bereitete bisher gewisse Probleme. Das lag zum einen an der Organisation des Stoffes [...]. Der zweite Grund war die deutsche Übersetzung. Dass es besser geht, beweisen [...] Jürgen Kromphardt, Gründer der deutschen Keynes-Gesellschaft und ein früherer Wirtschaftsweiser, und Stephanie Schneider. Sie haben unzeitgemäße Ausdrücke ersetzt, die den Zugang zum Werk erschwert hatten, und sie besserten allerhand Übersetzungsfehler aus. [...] Also liest sich die neue Ausgabe leichter. Zudem bietet sie ein deutsch-englisches Lexikon volkswirtschaftlicher Begriffe und ein Symbolverzeichnis. Sie ist ein echter Gewinn." Reinhard Blomert, in: DIE ZEIT, März 2007Die neue 11. Auflage soll die Lesbarkeit von Keynes' Hauptwerk weiter erhöhen und sein Verständnis erleichtern. Deshalb wurde die Übersetzung erneut überarbeitet; außerdem wird von uns der Aufbau des Buches erläutert, damit der Stellenwert der einzelnen Kapitel und die Zusammenhänge zwischen ihnen leichter erkennbar werden.Jürgen Kromphardt und Stephanie Schneider

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