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History and Philosophy of Constructive Type Theory

History and Philosophy of Constructive Type Theory Author Giovanni Sommaruga
ISBN-10 9789401593939
Release 2013-03-09
Pages 367
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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.

Axiomatic Method and Category Theory

Axiomatic Method and Category Theory Author Andrei Rodin
ISBN-10 9783319004044
Release 2013-10-14
Pages 285
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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

Types and Programming Languages Author Benjamin C. Pierce
ISBN-10 0262162091
Release 2002
Pages 623
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A comprehensive introduction to type systems and programming languages.

The Handbook of Contemporary Semantic Theory

The Handbook of Contemporary Semantic Theory Author Shalom Lappin
ISBN-10 9780470670736
Release 2015-09-28
Pages 776
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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

Business Language and Asymmetric Perceptions

Business Language and Asymmetric Perceptions Author Jack Douglas Stecher
ISBN-10 MINN:31951P00787063V
Release 2005
Pages 168
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Business Language and Asymmetric Perceptions has been writing in one form or another for most of life. You can find so many inspiration from Business Language and Asymmetric Perceptions also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Business Language and Asymmetric Perceptions book for free.

Reference Truth and Conceptual Schemes

Reference  Truth and Conceptual Schemes Author G. Forrai
ISBN-10 9789401728683
Release 2013-03-14
Pages 163
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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.

Truth Proof and Infinity

Truth  Proof and Infinity Author P. Fletcher
ISBN-10 9789401736169
Release 2013-06-29
Pages 470
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Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in terms of what constructions count as a proof of it. However, the meaning of the terms `construction' and `proof' has never been adequately explained (although Kriesel, Goodman and Martin-Löf have attempted axiomatisations). This monograph develops precise (though not wholly formal) definitions of construction and proof, and describes the algorithmic substructure underlying intuitionistic logic. Interpretations of Heyting arithmetic and constructive analysis are given. The philosophical basis of constructivism is explored thoroughly in Part I. The author seeks to answer objections from platonists and to reconcile his position with the central insights of Hilbert's formalism and logic. Audience: Philosophers of mathematics and logicians, both academic and graduate students, particularly those interested in Brouwer and Hilbert; theoretical computer scientists interested in the foundations of functional programming languages and program correctness calculi.

Mathematical Reviews

Mathematical Reviews Author
ISBN-10 UVA:X001409606
Release 1978
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Mathematical Reviews has been writing in one form or another for most of life. You can find so many inspiration from Mathematical Reviews also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematical Reviews book for free.

Logicism Intuitionism and Formalism

Logicism  Intuitionism  and Formalism Author Sten Lindström
ISBN-10 9781402089268
Release 2008-11-25
Pages 512
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This anthology reviews the programmes in the foundations of mathematics from the classical period and assesses their possible relevance for contemporary philosophy of mathematics. A special section is concerned with constructive mathematics.

The Concept of Time in Early Twentieth Century Philosophy

The Concept of Time in Early Twentieth Century Philosophy Author Flavia Santoianni
ISBN-10 9783319248950
Release 2015-11-26
Pages 259
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This book presents a collection of authoritative contributions on the concept of time in early twentieth-century philosophy. It is structured in the form of a thematic atlas: each section is accompanied by relevant elementary logic maps that reproduce in a “spatial” form the directionalities (arguments and/or discourses) reported on in the text. The book is divided into three main sections, the first of which covers phenomenology and the perception of time by analyzing the works of Bergson, Husserl, Sartre, Merleau-Ponty, Deleuze, Guattari and Derrida. The second section focuses on the language and conceptualization of time, examining the works of Cassirer, Wittgenstein, Heidegger, Lacan, Ricoeur and Foucault, while the last section addresses the science and logic of time as they appear in the works of Guillaume, Einstein, Reichenbach, Prigogine and Barbour. The purpose of the book is threefold: to provide readers with a comprehensive overview of the concept of time in early twentieth-century philosophy; to show how conceptual reasoning can be supported by accompanying linguistic and spatial representations; and to stimulate novel research in the humanistic field concerning the complex role of graphic representations in the comprehension of concepts.

Logic in Reality

Logic in Reality Author JOSEPH BRENNER
ISBN-10 9781402083754
Release 2008-05-20
Pages 362
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This book is both dif?cult and rewarding, affording a new perspective on logic and reality, basically seen in terms of change and stability, being and becoming. Most importantly it exemplifies a mode of doing philosophy of science that seems a welcome departure from the traditional focus on purely analytic arguments. The author approaches ontology, metaphysics, and logic as having offered a number of ways of constructing the description of reality, and aims at deepening their relationships in a new way. Going beyond the mere abstract and formal aspects of logical analysis, he offers a new architecture of logic that sees it as applied not only to the “reasoning processes” belonging to the first disciplinary group – ontology – but also directly concerned with en- ties, events, and phenomena studied by the second one – metaphysics. It is the task of the book to elaborate such a constructive logic, both by offering a lo- cal view of the structure of the reality in general and by proffering a wealth of models able to encompass its implications for science. In turning from the merely formal to the constructive account of logic Brenner overcomes the limitation of logic to linguistic concepts so that it can be not only a logic “of” reality but also “in” that reality which is constitutively characterized by a number of fundamental dualities (observer and observed, self and not-self, internal and external, etc.

Between Logic and Reality

Between Logic and Reality Author Majda Trobok
ISBN-10 9400723903
Release 2011-11-23
Pages 282
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Is reality logical and is logic real? What is the origin of logical intuitions? What is the role of logical structures in the operations of an intelligent mind and in communication? Is the function of logical structure regulative or constitutive or both in concept formation? This volume provides analyses of the logic-reality relationship from different approaches and perspectives. The point of convergence lies in the exploration of the connections between reality – social, natural or ideal – and logical structures employed in describing or discovering it. Moreover, the book connects logical theory with more concrete issues of rationality, normativity and understanding, thus pointing to a wide range of potential applications. The papers collected in this volume address cutting-edge topics in contemporary discussions amongst specialists. Some essays focus on the role of indispensability considerations in the justification of logical competence, and the wide range of challenges within the philosophy of mathematics. Others present advances in dynamic logical analysis such as extension of game semantics to non-logical part of vocabulary and development of models of contractive speech act.

The Argument of Mathematics

The Argument of Mathematics Author Andrew Aberdein
ISBN-10 9789400765344
Release 2013-07-01
Pages 393
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Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​

Foundations of logic and mathematics

Foundations of logic and mathematics Author Rudolf Carnap
ISBN-10 UOM:49015000673567
Release 1939
Pages 71
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Foundations of logic and mathematics has been writing in one form or another for most of life. You can find so many inspiration from Foundations of logic and mathematics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Foundations of logic and mathematics book for free.

The Logic of Scientific Discovery

The Logic of Scientific Discovery Author Karl Popper
ISBN-10 9781134470020
Release 2005-11-04
Pages 480
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Described by the philosopher A.J. Ayer as a work of 'great originality and power', this book revolutionized contemporary thinking on science and knowledge. Ideas such as the now legendary doctrine of 'falsificationism' electrified the scientific community, influencing even working scientists, as well as post-war philosophy. This astonishing work ranks alongside The Open Society and Its Enemies as one of Popper's most enduring books and contains insights and arguments that demand to be read to this day.

Language as Calculus vs Language as Universal Medium

Language as Calculus vs  Language as Universal Medium Author Maren Kusch
ISBN-10 0792303334
Release 1989-06-30
Pages 362
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I first became interested in Husserl and Heidegger as long ago as 1980, when as an undergraduate at the Freie Universitat Berlin I studied the books by Professor Ernst Tugendhat. Tugendhat's at tempt to bring together analytical and continental philosophy has never ceased to fascinate me, and even though in more recent years other influences have perhaps been stronger, I should like to look upon the present study as still being indebted to Tugendhat's initial incentive. It was my good fortune that for personal reasons I had to con tinue my academic training from 1981 onwards in Finland. Even though Finland is a stronghold of analytical philosophy, it also has a tradition of combining continental and Anglosaxon philosophical thought. Since I had already admired this line of work in Tugendhat, it is hardly surprising that once in Finland I soon became impressed by Professor Jaakko Hintikka's studies on Husserl and intentionality, and by Professor Georg Henrik von Wright's analytical hermeneu tics. While the latter influence has-at least in part-led to a book on the history of hermeneutics, the former influence has led to the present work. My indebtedness to Professor Hintikka is enormous. Not only is the research reported here based on his suggestions, but Hintikka has also commented extensively on different versions of the manuscript, helped me to make important contacts, found a publisher for me, and-last but not least-was a never failing source of encouragement.

Encyclopedia of Information Science and Technology Third Edition

Encyclopedia of Information Science and Technology  Third Edition Author Khosrow-Pour, Mehdi
ISBN-10 9781466658899
Release 2014-07-31
Pages 10384
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"This 10-volume compilation of authoritative, research-based articles contributed by thousands of researchers and experts from all over the world emphasized modern issues and the presentation of potential opportunities, prospective solutions, and future directions in the field of information science and technology"--Provided by publisher.