# mathematical logic in the 20th century

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## Mathematical Logic In The 20th Century

**Author :**Gerald E Sacks

**ISBN :**9789814490191

**Genre :**Mathematics

**File Size :**64. 19 MB

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This invaluable book is a collection of 31 important — both in ideas and results — papers published by mathematical logicians in the 20th Century. The papers have been selected by Professor Gerald E Sacks. Some of the authors are Gödel, Kleene, Tarski, A Robinson, Kreisel, Cohen, Morley, Shelah, Hrushovski and Woodin. Contents:The Independence of the Continuum Hypothesis (P J Cohen)Higher Set Theory and Mathematical Practice (H M Friedman)Measurable Cardinals and Analytic Games (D A Martin)Categoricity in Power (M Morley)Hyperanalytic Predicates (Y N Moschovakis)Stable Theories (S Shelah)On the Singular Cardinals Problem (J Silver)On Degrees of Recursive Unsolvability (C Spector)Denumerable Models of Complete Theories (R L Vaught)Supercompact Cardinals, Sets of Reals, and Weakly Homogeneous Trees (W H Woodin)and other papers Readership: Researchers and graduate students in logic. Keywords:JFM 65.0185.02;Mathematical LogicReviews:“… overall we must be grateful for getting all this wonderful stuff available in one convenient place.” Zentralblatt MATH “This volume makes an indispensable addition to the numerous lecture notes and monographs on mathematical logic lying on our bookshelves.”Acta Scientiarum Mathematicarum

## Philosophy Of Science Logic And Mathematics In The Twentieth Century

**Author :**Stuart Shanker

**ISBN :**041530881X

**Genre :**Philosophy

**File Size :**37. 48 MB

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Contents - Introduction. 1. Philosophy of logic 2. Philosophy of mathematics in the 20th century. 3. Frege 4. Wittgenstein's Tractatus 5. Logical postivism 6. The philosophy of physics 7. The philosophy of science 8. Chance, cause and conduct; probability

## The Development Of Modern Logic

**Author :**Leila Haaparanta

**ISBN :**0199722722

**Genre :**Philosophy

**File Size :**22. 17 MB

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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.

## Logic From Russell To Church

**Author :**Dov M. Gabbay

**ISBN :**9780080885476

**Genre :**Mathematics

**File Size :**84. 77 MB

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This volume is number five in the 11-volume Handbook of the History of Logic. It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. • The entire range of modal logic is covered • Serves as a singular contribution to the intellectual history of the 20th century • Contains the latest scholarly discoveries and interpretative insights

## Mathematics Of The 19th Century

**Author :**KOLMOGOROV

**ISBN :**9783034851121

**Genre :**Mathematics

**File Size :**33. 41 MB

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This multi-authored effort, Mathematics of the nineteenth century (to be fol lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics fram antiquity to the early nineteenth century, published in three 1 volumes from 1970 to 1972. For reasons explained below, our discussion of twentieth-century mathematics ends with the 1930s. Our general objectives are identical with those stated in the preface to the three-volume edition, i. e. , we consider the development of mathematics not simply as the process of perfecting concepts and techniques for studying real-world spatial forms and quantitative relationships but as a social process as weIl. Mathematical structures, once established, are capable of a certain degree of autonomous development. In the final analysis, however, such immanent mathematical evolution is conditioned by practical activity and is either self-directed or, as is most often the case, is determined by the needs of society. Proceeding from this premise, we intend, first, to unravel the forces that shape mathe matical progress. We examine the interaction of mathematics with the social structure, technology, the natural sciences, and philosophy. Throughan anal ysis of mathematical history proper, we hope to delineate the relationships among the various mathematical disciplines and to evaluate mathematical achievements in the light of the current state and future prospects of the science. The difficulties confronting us considerably exceeded those encountered in preparing the three-volume edition.

## Philosophy Of Mathematics In The Twentieth Century

**Author :**Charles Parsons

**ISBN :**9780674419490

**Genre :**Philosophy

**File Size :**33. 92 MB

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In these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.

## Logic And The Modalities In The Twentieth Century

**Author :**Dov M. Gabbay

**ISBN :**0080463037

**Genre :**Mathematics

**File Size :**73. 5 MB

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Logic and the Modalities in the Twentieth Century is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and artificial intelligence, linguistics, cognitive science, argumentation theory, philosophy, and the history of ideas. This volume is number seven in the eleven volume Handbook of the History of Logic. It concentrates on the development of modal logic in the 20th century, one of the most important undertakings in logic’s long history. Written by the leading researchers and scholars in the field, the volume explores the logics of necessity and possibility, knowledge and belief, obligation and permission, time, tense and change, relevance, and more. Both this volume and the Handbook as a whole are definitive reference tools for students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, artificial intelligence, for whom the historical background of his or her work is a salient consideration. · Detailed and comprehensive chapters covering the entire range of modal logic. · Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic.

## Philosophy Of Science Logic And Mathematics In The Twentieth Century

**Author :**Stuart Shanker

**ISBN :**1135000131

**Genre :**Electronic books

**File Size :**85. 31 MB

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## Mathematical Logic

**Author :**Stephen Cole Kleene

**ISBN :**9780486317076

**Genre :**Mathematics

**File Size :**28. 92 MB

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Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.

## The Principles Of Mathematics

**Author :**Bertrand Russell

**ISBN :**UOMDLP:aat1273:0001.001

**Genre :**

**File Size :**64. 40 MB

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