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Author : Heinrich Scholz
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (16 download)
Download or read book Grundzüge der mathematischen Logik written by Heinrich Scholz and published by . This book was released on 1947 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P. Lorenzen
Publisher : Springer Science & Business Media
ISBN 13 : 9401715823
Total Pages : 131 pages
Book Rating : 4.4/5 (17 download)
Download or read book Formal Logic written by P. Lorenzen and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Logic", one of the central words in Western intellectual history, compre hends in its meaning such diverse things as the Aristotelian syllogistic, the scholastic art of disputation, the transcendental logic of the Kantian critique, the dialectical logic of Hegel, and the mathematical logic of the Principia Mathematica of Whitehead and Russell. The term "Formal Logic", following Kant is generally used to distinguish formal logical reasonings, precisely as formal, from the remaining universal truths based on reason. (Cf. SCHOLZ, 1931). A text-book example of a formal-logical inference which from "Some men are philosophers" and "All philosophers are wise" concludes that "Some men are wise" is called formal, because the validity of this inference depends only on the form ofthe given sentences -in particular it does not depend on the truth or falsity of these sentences. (On the dependence of logic on natural language, English, for example, compare Section 1 and 8). The form of a sentence like "Some men are philosophers", is that which remains preserved when the given predicates, here "men" and "philosophers" are replaced by arbitrary ones. The form itself can thus be represented by replacing the given predicates by variables. Variables are signs devoid of meaning, which may serve merely to indicate the place where meaningful constants (here the predicates) are to be inserted. As variables we shall use - as did Aristotle - letters, say P, Q and R, as variables for predicates.
Author : Steve Awodey
Publisher : Oxford University Press
ISBN 13 : 0198907443
Total Pages : 528 pages
Book Rating : 4.1/5 (989 download)
Download or read book Rudolf Carnap: Studies in Semantics written by Steve Awodey and published by Oxford University Press. This book was released on 2024-05-07 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains Carnap's Studies in Semantics, a series of three interlocking books: Introduction to Semantics (1942), Formalization of Logic (1942), and Meaning and Necessity (1947). They were extremely influential in their time, especially the third, and shaped the direction of analytic philosophy during the 1950s and 1960s. They constitute the background to a number of celebrated controversies of that period, especially those between Carnap and Quine. Most of the philosophical debates today in philosophical logic and the philosophy of language ultimately had their origins here. This new edition situates these works in their context, both within Carnap's philosophical development and within the philosophical debates they responded to and influenced. The editors' introduction explains how Carnap arrived at the project of semantics in the 1930s and how it developed into these three successive publications, how the three books fit together, and how the project developed and changed in the course of the 1940s. It also describes the reception of the books as they appeared, as well as Carnap's response. The editorial and textual notes give variant readings, Carnap's own marginal notes on these texts in his personal copies, and elucidatory commentary where Carnap's terminology or notation are no longer familiar. This will be an indispensable volume for anyone interested in the origins and preoccupations of present-day analytic philosophy, especially philosophical logic and philosophy of language.
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 : J.M. Bochenski
Publisher : Springer Science & Business Media
ISBN 13 : 9401705925
Total Pages : 109 pages
Book Rating : 4.4/5 (17 download)
Download or read book A Precis of Mathematical Logic written by J.M. Bochenski and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work of which this is an English translation appeared originally in French as Precis de logique mathematique. In 1954 Dr. Albert Menne brought out a revised and somewhat enlarged edition in German (Grund riss der Logistik, F. Schoningh, Paderborn). In making my translation I have used both editions. For the most part I have followed the original French edition, since I thought there was some advantage in keeping the work as short as possible. However, I have included the more extensive historical notes of Dr. Menne, his bibliography, and the two sections on modal logic and the syntactical categories (§ 25 and 27), which were not in the original. I have endeavored to correct the typo graphical errors that appeared in the original editions and have made a few additions to the bibliography. In making the translation I have profited more than words can tell from the ever-generous help of Fr. Bochenski while he was teaching at the University of Notre Dame during 1955-56. OTTO BIRD Notre Dame, 1959 I GENERAL PRINCIPLES § O. INTRODUCTION 0. 1. Notion and history. Mathematical logic, also called 'logistic', ·symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the last century with the aid of an artificial notation and a rigorously deductive method.
Author : Rudolf Carnap
Publisher : Courier Corporation
ISBN 13 : 048614349X
Total Pages : 272 pages
Book Rating : 4.4/5 (861 download)
Download or read book Introduction to Symbolic Logic and Its Applications written by Rudolf Carnap and published by Courier Corporation. This book was released on 2012-07-12 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear, comprehensive, and rigorous treatment develops the subject from elementary concepts to the construction and analysis of relatively complex logical languages. Hundreds of problems, examples, and exercises. 1958 edition.
Author :
Publisher :
ISBN 13 :
Total Pages : 504 pages
Book Rating : 4.:/5 (138 download)
Download or read book Grundzüge Der Mathematischen Logik written by and published by . This book was released on 1961 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lorenz J. Halbeisen
Publisher : Springer
ISBN 13 : 3319602314
Total Pages : 594 pages
Book Rating : 4.3/5 (196 download)
Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen and published by Springer. This book was released on 2017-12-20 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.
Author : Anna-Teresa Tymieniecka
Publisher : Elsevier
ISBN 13 : 1483274888
Total Pages : 346 pages
Book Rating : 4.4/5 (832 download)
Download or read book Contributions to Logic and Methodology written by Anna-Teresa Tymieniecka and published by Elsevier. This book was released on 2014-05-12 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributions to Logic and Methodology in Honor of J. M. Boche?ski focuses on the influence, contributions, and legacy of J. M. Boche?ski in the fields of logic and methodology. The selection first offers information on some remarks on inferential deduction, modal logic with eight modalities, and method and logic in presocratic explanation. Discussions focus on inference, evidence, hypothesis, generalization, semantical discussion, proof of necessity, multiple dialogues, and construction trees. The text then elaborates on reification, quotation, and nominalization, logic of preference and choice, and sense, denotation, and the context of sentences. Topics include axioms of preference and of choice, economic context, methodological remarks, reification, nominalization, and quotation. The manuscript examines conjectural inference and phenomenological analysis, including anticipatory evidence and choice of method, conjecture of the universal order, conjectural requirement of the architectonic project, and outline of the program of conjectural inquiry. The selection is a dependable source of information for philosophers and researchers interested in the influence and contributions of J. M. Boche?ski to logic and methodology.
Author : Fernando Ferreira
Publisher : Springer Nature
ISBN 13 : 3030776573
Total Pages : 209 pages
Book Rating : 4.0/5 (37 download)
Download or read book Axiomatic Thinking I written by Fernando Ferreira and published by Springer Nature. This book was released on 2022-10-13 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations. Chapter 8 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Author : W. Stegmüller
Publisher : Springer Science & Business Media
ISBN 13 : 9401033757
Total Pages : 585 pages
Book Rating : 4.4/5 (1 download)
Download or read book Main Currents in Contemporary German, British, and American Philosophy written by W. Stegmüller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : E.W. Beth
Publisher : Springer Science & Business Media
ISBN 13 : 9401722072
Total Pages : 220 pages
Book Rating : 4.4/5 (17 download)
Download or read book Mathematical Thought written by E.W. Beth and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: In contributing a foreword to this book I am complying with a wish my husband expressed a few days before his death. He had completed the manuscript of this work, which may be considered a companion volume to his book Formal Methods. The task of seeing it through the press was undertaken by Mr. J. J. A. Mooij, acting director of the Institute for Research in Foundations and the Philosophy of Science (Instituut voor Grondslagenonderzoek en Filoso:fie der Exacte Wetenschappen) of the University of Amsterdam, with the help of Mrs. E. M. Barth, lecturer at the Institute. I wish to thank Mr. Mooij and Mrs. Barth most cordially for the care with which they have acquitted themselves of this delicate task and for the speed with which they have brought it to completion. I also wish to express my gratitude to Miss L. E. Minning, M. A. , for the helpful advice she has so kindly given to Mr. Mooij and Mrs. Barth during the proof reading. C. P. C. BETH-PASTOOR VII PREFACE A few years ago Mr. Horace S.
Author : E.W. Beth
Publisher : Springer Science & Business Media
ISBN 13 : 9401033323
Total Pages : 186 pages
Book Rating : 4.4/5 (1 download)
Download or read book Aspects of Modern Logic written by E.W. Beth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is common to consider an area of science as a system of real or sup posed truths which not only continuously extends itself, but also needs periodical revision and therefore tests the inventive capacity of each generation of scholars anew. It sounds highly implausible that a science at one time would be completed, that at that point within its scope there would be no problems left to solve. Indeed, the solution of a scientific problem inevitably raises new questions, so that our eagerness for knowledge will never find lasting satisfaction. Nevertheless there is one science which seems to form an exception to this rule, formal logic, the theory of rigorous argumentation. It seems to have reached the ideal endpoint of every scientific aspiration already very shortly after its inception; using the work of some predecessors, Aristotle, or so it is at least assumed by many, has brought this branch of science once and for all to a conclusion. Of course this doesn't sound that implausible. We apparently know what rigorous argumentation is; otherwise various sciences, in particular pure mathematics, would be completely impossible. And if we know what rigorous argumentation is, then it cannot be difficult to trace once and for all the rules which govern it. The unique subject of formal logic would therefore entail that this science, in variance with the rule which holds for all other sciences, has been able to reach completion at a certain point in history.
Author : Leila Haaparanta
Publisher : Oxford University Press
ISBN 13 : 9780199722723
Total Pages : 1008 pages
Book Rating : 4.7/5 (227 download)
Download or read book The Development of Modern Logic written by Leila Haaparanta and published by Oxford University Press. This book was released on 2009-06-18 with total page 1008 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume presents a comprehensive history of modern logic from the Middle Ages through the end of the twentieth century. In addition to a history of symbolic logic, the contributors also examine developments in the philosophy of logic and philosophical logic in modern times. The book begins with chapters on late medieval developments and logic and philosophy of logic from Humanism to Kant. The following chapters focus on the emergence of symbolic logic with special emphasis on the relations between logic and mathematics, on the one hand, and on logic and philosophy, on the other. This discussion is completed by a chapter on the themes of judgment and inference from 1837-1936. The volume contains a section on the development of mathematical logic from 1900-1935, followed by a section on main trends in mathematical logic after the 1930s. The volume goes on to discuss modal logic from Kant till the late twentieth century, and logic and semantics in the twentieth century; the philosophy of alternative logics; the philosophical aspects of inductive logic; the relations between logic and linguistics in the twentieth century; the relationship between logic and artificial intelligence; and ends with a presentation of the main schools of Indian logic. The Development of Modern Logic includes many prominent philosophers from around the world who work in the philosophy and history of mathematics and logic, who not only survey developments in a given period or area but also seek to make new contributions to contemporary research in the field. It is the first volume to discuss the field with this breadth of coverage and depth, and will appeal to scholars and students of logic and its philosophy.
Author : Paul Leo Butzer
Publisher : Springer Science & Business Media
ISBN 13 : 3642460666
Total Pages : 331 pages
Book Rating : 4.6/5 (424 download)
Download or read book Semi-Groups of Operators and Approximation written by Paul Leo Butzer and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years important progress has been made in the study of semi-groups of operators from the viewpoint of approximation theory. These advances have primarily been achieved by introducing the theory of intermediate spaces. The applications of the theory not only permit integration of a series of diverse questions from many domains of mathematical analysis but also lead to significant new results on classical approximation theory, on the initial and boundary behavior of solutions of partial differential equations, and on the theory of singular integrals. The aim of this book is to present a systematic treatment of semi groups of bounded linear operators on Banach spaces and their connec tions with approximation theoretical questions in a more classical setting as well as within the setting of the theory of intermediate spaces. However, no attempt is made to present an exhaustive account of the theory of semi-groups of operators per se, which is the central theme of the monumental treatise by HILLE and PHILLIPS (1957). Neither has it been attempted to give an account of the theory of approximation as such. A number of excellent books on various aspects of the latter theory has appeared in recent years, so for example CHENEY (1966), DAVIS (1963), LORENTZ (1966), MEINARDUS (1964), RICE (1964), SARD (1963). By contrast, the present book is primarily concerned with those aspects of semi-group theory that are connected in some way or other with approximation.
Author : Bartel Leendert van der Waerden
Publisher : Springer Science & Business Media
ISBN 13 : 3662221373
Total Pages : 384 pages
Book Rating : 4.6/5 (622 download)
Download or read book Mathematical Statistics written by Bartel Leendert van der Waerden and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since my days as a student, economists, doctors, physiologists, biologists, and engineers have come to me with queries of a statistical nature. This book is the product of my long interest in practical solutions to such problems. Study of the literature and my own ideas have repeat edly led me to improved methods, which will be established here and applied to instructive examples taken from the natural and social sciences. Thus, I hope to help the reader avoid the many fruitless direc tions in which I worked at first. The examples are not artificially con structed from theoretical considerations but are instead taken from real situations; consequently, many of the examples require detailed explana tion. The presentation of the basic mathematical concepts is, I hope, as brief as possible without becoming incomprehensible. Some rather long theoretical arguments have been necessary, but, whenever possible, references for the more difficult proofs have been made to good text books already in existence. There would be no point in developing again the mathematical theories which have been presented clearly and in detail by Kolmogorov, Caratheodory, and Cramer.
Author : Leo Sario
Publisher : Springer Science & Business Media
ISBN 13 : 3642482694
Total Pages : 469 pages
Book Rating : 4.6/5 (424 download)
Download or read book Classification Theory of Riemann Surfaces written by Leo Sario and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the present monograph is to systematically develop a classification theory of Riemann surfaces. Some first steps will also be taken toward a classification of Riemannian spaces. Four phases can be distinguished in the chronological background: the type problem; general classification; compactifications; and extension to higher dimensions. The type problem evolved in the following somewhat overlapping steps: the Riemann mapping theorem, the classical type problem, and the existence of Green's functions. The Riemann mapping theorem laid the foundation to classification theory: there are only two conformal equivalence classes of (noncompact) simply connected regions. Over half a century of efforts by leading mathematicians went into giving a rigorous proof of the theorem: RIEMANN, WEIERSTRASS, SCHWARZ, NEUMANN, POINCARE, HILBERT, WEYL, COURANT, OSGOOD, KOEBE, CARATHEODORY, MONTEL. The classical type problem was to determine whether a given simply connected covering surface of the plane is conformally equivalent to the plane or the disko The problem was in the center of interest in the thirties and early forties, with AHLFORS, KAKUTANI, KOBAYASHI, P. MYRBERG, NEVANLINNA, SPEISER, TEICHMÜLLER and others obtaining incisive specific results. The main problem of finding necessary and sufficient conditions remains, however, unsolved.
