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Author : Paul Lorenzen
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (935 download)
Download or read book Einführung in die operative Logik und Mathematik written by Paul Lorenzen and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul Lorenzen
Publisher :
ISBN 13 :
Total Pages : 298 pages
Book Rating : 4.:/5 (954 download)
Download or read book Einfuhrung in Die Operative Logik und Mathematik written by Paul Lorenzen and published by . This book was released on 1955 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Library of Congress. Copyright Office
Publisher : Copyright Office, Library of Congress
ISBN 13 :
Total Pages : 810 pages
Book Rating : 4.F/5 ( download)
Download or read book Catalog of Copyright Entries. Third Series written by Library of Congress. Copyright Office and published by Copyright Office, Library of Congress. This book was released on 1956 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes Part 1, Number 2: Books and Pamphlets, Including Serials and Contributions to Periodicals (July - December)
Author : Gerhard Heinzmann
Publisher : Springer Nature
ISBN 13 : 3030658244
Total Pages : 268 pages
Book Rating : 4.0/5 (36 download)
Download or read book Paul Lorenzen -- Mathematician and Logician written by Gerhard Heinzmann and published by Springer Nature. This book was released on 2021-08-17 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen’s systematical ideas in today’s debates on proof-theoretic semantics, databank management, and stochastics. Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen’s work on lattice-groups and divisibility theory, and modern set theory and Lorenzen’s critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen’s consistency proof and Hilbert’s larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz.
Author : Maria G. Bartolini Bussi
Publisher : Springer
ISBN 13 : 3319635557
Total Pages : 548 pages
Book Rating : 4.3/5 (196 download)
Download or read book Building the Foundation: Whole Numbers in the Primary Grades written by Maria G. Bartolini Bussi and published by Springer. This book was released on 2018-03-29 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This twenty-third ICMI Study addresses for the first time mathematics teaching and learning in the primary school (and pre-school) setting, while also taking international perspectives, socio-cultural diversity and institutional constraints into account. One of the main challenges of designing the first ICMI primary school study of this kind is the complex nature of mathematics at the early level. Accordingly, a focus area that is central to the discussion was chosen, together with a number of related questions. The broad area of Whole Number Arithmetic (WNA), including operations and relations and arithmetic word problems, forms the core content of all primary mathematics curricula. The study of this core content area is often regarded as foundational for later mathematics learning. However, the principles and main goals of instruction on the foundational concepts and skills in WNA are far from universally agreed upon, and practice varies substantially from country to country. As such, this study presents a meta-level analysis and synthesis of what is currently known about WNA, providing a useful base from which to gauge gaps and shortcomings, as well as an opportunity to learn from the practices of different countries and contexts.
Author : Jacques Havet
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111616584
Total Pages : 684 pages
Book Rating : 4.1/5 (116 download)
Download or read book Legal science, philosophy written by Jacques Havet and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-04 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Legal science, philosophy".
Author : Hans-Hermann Hoppe
Publisher : Ludwig von Mises Institute
ISBN 13 : 1610164687
Total Pages : 446 pages
Book Rating : 4.6/5 (11 download)
Download or read book Economics and Ethics of Private Property written by Hans-Hermann Hoppe and published by Ludwig von Mises Institute. This book was released on 2006 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Antonio Piccolomini d’Aragona
Publisher : Springer Nature
ISBN 13 : 3031202945
Total Pages : 284 pages
Book Rating : 4.0/5 (312 download)
Download or read book Prawitz's Epistemic Grounding written by Antonio Piccolomini d’Aragona and published by Springer Nature. This book was released on 2023-01-01 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an in-depth and critical reconstruction of Prawitz’s epistemic grounding, and discusses it within the broader field of proof-theoretic semantics. The theory of grounds is also provided with a formal framework, through which several relevant results are proved. Investigating Prawitz’s theory of grounds, this work answers one of the most fundamental questions in logic: why and how do some inferences have the epistemic power to compel us to accept their conclusion, if we have accepted their premises? Prawitz proposes an innovative description of inferential acts, as applications of constructive operations on grounds for the premises, yielding a ground for the conclusion. The book is divided into three parts. In the first, the author discusses the reasons that have led Prawitz to abandon his previous semantics of valid arguments and proofs. The second part presents Prawitz’s grounding as found in his ground-theoretic papers. Finally, in the third part, a formal apparatus is developed, consisting of a class of languages whose terms are equipped with denotation functions associating them to operations and grounds, as well as of a class of systems where important properties of the terms can be proved.
Author : Dag Prawitz
Publisher : Courier Dover Publications
ISBN 13 : 0486446557
Total Pages : 132 pages
Book Rating : 4.4/5 (864 download)
Download or read book Natural Deduction written by Dag Prawitz and published by Courier Dover Publications. This book was released on 2006-02-24 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: An innovative approach to the semantics of logic, proof-theoretic semantics seeks the meaning of propositions and logical connectives within a system of inference. Gerhard Gentzen invented proof-theoretic semantics in the early 1930s, and Dag Prawitz, the author of this study, extended its analytic proofs to systems of natural deduction. Prawitz's theories form the basis of intuitionistic type theory, and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics. The concept of natural deduction follows a truly natural progression, establishing the relationship between a noteworthy systematization and the interpretation of logical signs. As this survey explains, the deduction's principles allow it to proceed in a direct fashion — a manner that permits every natural deduction's transformation into the equivalent of normal form theorem. A basic result in proof theory, the normal form theorem was established by Gentzen for the calculi of sequents. The proof of this result for systems of natural deduction is in many ways simpler and more illuminating than alternative methods. This study offers clear illustrations of the proof and numerous examples of its advantages.
Author : Carl Faith
Publisher : Springer Science & Business Media
ISBN 13 : 3642806341
Total Pages : 589 pages
Book Rating : 4.6/5 (428 download)
Download or read book Algebra written by Carl Faith and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: VI of Oregon lectures in 1962, Bass gave simplified proofs of a number of "Morita Theorems", incorporating ideas of Chase and Schanuel. One of the Morita theorems characterizes when there is an equivalence of categories mod-A R::! mod-B for two rings A and B. Morita's solution organizes ideas so efficiently that the classical Wedderburn-Artin theorem is a simple consequence, and moreover, a similarity class [AJ in the Brauer group Br(k) of Azumaya algebras over a commutative ring k consists of all algebras B such that the corresponding categories mod-A and mod-B consisting of k-linear morphisms are equivalent by a k-linear functor. (For fields, Br(k) consists of similarity classes of simple central algebras, and for arbitrary commutative k, this is subsumed under the Azumaya [51]1 and Auslander-Goldman [60J Brauer group. ) Numerous other instances of a wedding of ring theory and category (albeit a shot gun wedding!) are contained in the text. Furthermore, in. my attempt to further simplify proofs, notably to eliminate the need for tensor products in Bass's exposition, I uncovered a vein of ideas and new theorems lying wholely within ring theory. This constitutes much of Chapter 4 -the Morita theorem is Theorem 4. 29-and the basis for it is a corre spondence theorem for projective modules (Theorem 4. 7) suggested by the Morita context. As a by-product, this provides foundation for a rather complete theory of simple Noetherian rings-but more about this in the introduction.
Author : Jacques Louis Lions
Publisher : Springer Science & Business Media
ISBN 13 : 3642653936
Total Pages : 323 pages
Book Rating : 4.6/5 (426 download)
Download or read book Non-Homogeneous Boundary Value Problems and Applications written by Jacques Louis Lions and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Our essential objective is the study of the linear, non-homogeneous problems: (1) Pu = I in CD, an open set in RN, (2) fQjtl = gj on am (boundary of m), lor on a subset of the boundm"J am 1
Author : Klaus Mainzer
Publisher : World Scientific
ISBN 13 : 9813225505
Total Pages : 471 pages
Book Rating : 4.8/5 (132 download)
Download or read book Digital And The Real World, The: Computational Foundations Of Mathematics, Science, Technology, And Philosophy written by Klaus Mainzer and published by World Scientific. This book was released on 2017-11-17 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 21st century, digitalization is a global challenge of mankind. Even for the public, it is obvious that our world is increasingly dominated by powerful algorithms and big data. But, how computable is our world? Some people believe that successful problem solving in science, technology, and economies only depends on fast algorithms and data mining. Chances and risks are often not understood, because the foundations of algorithms and information systems are not studied rigorously. Actually, they are deeply rooted in logics, mathematics, computer science and philosophy.Therefore, this book studies the foundations of mathematics, computer science, and philosophy, in order to guarantee security and reliability of the knowledge by constructive proofs, proof mining and program extraction. We start with the basics of computability theory, proof theory, and information theory. In a second step, we introduce new concepts of information and computing systems, in order to overcome the gap between the digital world of logical programming and the analog world of real computing in mathematics and science. The book also considers consequences for digital and analog physics, computational neuroscience, financial mathematics, and the Internet of Things (IoT).
Author : Lev D. Beklemishev
Publisher : Elsevier
ISBN 13 : 0080957412
Total Pages : 235 pages
Book Rating : 4.0/5 (89 download)
Download or read book Axiomatic Set Theory written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Axiomatic Set Theory
Author : Haskell Brooks Curry
Publisher : Courier Corporation
ISBN 13 : 9780486634623
Total Pages : 420 pages
Book Rating : 4.6/5 (346 download)
Download or read book Foundations of Mathematical Logic written by Haskell Brooks Curry and published by Courier Corporation. This book was released on 1977-01-01 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.
Author : W. Stegmüller
Publisher : Springer Science & Business Media
ISBN 13 : 940101129X
Total Pages : 328 pages
Book Rating : 4.4/5 (1 download)
Download or read book Collected Papers on Epistemology, Philosophy of Science and History of Philosophy written by W. Stegmüller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two volumes contain all of my articles published between 1956 and 1975 which might be of interest to readers in the English-speaking world. The first three essays in Vol. 1 deal with historical themes. In each case I as far as possible, meets con have attempted a rational reconstruction which, temporary standards of exactness. In The Problem of Universals Then and Now some ideas of W.V. Quine and N. Goodman are used to create a modern sketch of the history of the debate on universals beginning with Plato and ending with Hao Wang's System L. The second article concerns Kant's Philosophy of Science. By analyzing his position vis-a-vis I. Newton, Christian Wolff, and D. Hume, it is shown that for Kant the very notion of empirical knowledge was beset with a funda mental logical difficulty. In his metaphysics of experience Kant offered a solution differing from all prior as well as subsequent attempts aimed at the problem of establishing a scientific theory. The last of the three historical papers utilizes some concepts of modern logic to give a precise account of Wittgenstein's so-called Picture Theory of Meaning. E. Stenius' interpretation of this theory is taken as an intuitive starting point while an intensional variant of Tarski's concept of a relational system furnishes a technical instrument. The concepts of inodel world and of logical space, together with those of homomorphism and isomorphism be tween model worlds and between logical spaces, form the conceptual basis of the reconstruction.
Author : A.A. Fraenkel
Publisher : Elsevier
ISBN 13 : 0080887058
Total Pages : 415 pages
Book Rating : 4.0/5 (88 download)
Download or read book Foundations of Set Theory written by A.A. Fraenkel and published by Elsevier. This book was released on 1973-12-01 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.
Author : Hans-Hermann Hoppe
Publisher : Ludwig von Mises Institute
ISBN 13 : 1610164784
Total Pages : 93 pages
Book Rating : 4.6/5 (11 download)
Download or read book Economic Science and the Austrian Method written by Hans-Hermann Hoppe and published by Ludwig von Mises Institute. This book was released on 1995 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
