Jean van Heijenoort's Books

From Frege to Gödel

A Source Book in Mathematical Logic, 1879–1931

By: Jean van Heijenoort

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From Frege to Gödel

A Source Book in Mathematical Logic, 1879–1931

By: Jean van Heijenoort

The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for the first time. Modern logic, heralded by Leibniz, may be said to have been initiated by Boole, De Morgan, and Jevons, but it was the publication in 1879 of Gottlob Frege’s Begriffsschrift that opened a great epoch in the history of logic by presenting, in full-fledged form, the propositional calculus and quantification theory. Frege’s book, translated in its entirety, begins the present volume. The emergence of two new fields, set theory and foundations of mathematics, on the borders of logic, mathematics, and philosophy, is depicted by the texts that follow. Peano and Dedekind illustrate the trend that led to Principia Mathematica. Burali-Forti, Cantor, Russell, Richard, and König mark the appearance of the modern paradoxes. Hilbert, Russell, and Zermelo show various ways of overcoming these paradoxes and initiate, respectively, proof theory, the theory of types, and axiomatic set theory. Skolem generalizes Löwenheim’s theorem, and he and Fraenkel amend Zermelo’s axiomatization of set theory, while von Neumann offers a somewhat different system. The controversy between Hubert and Brouwer during the twenties is presented in papers of theirs and in others by Weyl, Bernays, Ackermann, and Kolmogorov. The volume concludes with papers by Herbrand and by Gödel, including the latter’s famous incompleteness paper. Of the forty-five contributions here collected all but five are presented in extenso. Those not originally written in English have been translated with exemplary care and exactness; the translators are themselves mathematical logicians as well as skilled interpreters of sometimes obscure texts. Each paper is introduced by a note that sets it in perspective, explains its importance, and points out difficulties in interpretation. Editorial comments and footnotes are interpolated where needed, and an extensive bibliography is included.

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684

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Harvard University Press

Published Date

ISBN 10

0674257243

ISBN 13

9780674257245

Consequences of the Axiom of Choice

By: Paul Howard,Jean E. Rubin

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Consequences of the Axiom of Choice

By: Paul Howard,Jean E. Rubin

This book, Consequences of the Axiom of Choice, is a comprehensive listing of statements that have been proved in the last 100 years using the axiom of choice. Each consequence, also referred to as a form of the axiom of choice, is assigned a number. Part I is a listing of the forms by number. In this part each form is given together with a listing of all statements known to be equivalent to it (equivalent in set theory without the axiom of choice). In Part II the forms are arranged by topic. In Part III we describe the models of set theory which are used to show non-implications between forms. Part IV, the notes section, contains definitions, summaries of important sub-areas and proofs that are not readily available elsewhere. Part V gives references for the relationships between forms and Part VI is the bibliography. Part VII is contained on the floppy disk which is enclosed in the book. It contains a table with form numbers as row and column headings. The entry in the table in row $n$, column $k$ gives the status of the implication ``form $n$ implies form $k$''. Software for easily extracting information from the table is also provided. Features: complete summary of all the work done in the last 100 years on statements that are weaker than the axiom of choice software provided gives complete, convenient access to information about relationships between the various consequences of the axiom of choice and about the models of set theory descriptions of more than 100 models used in the study of the axiom of choice an extensive bibliography About the software: Tables 1 and 2 are accessible on the PC-compatible software included with the book. In addition, the program maketex.c in the software package will create TeX files containing copies of Table 1 and Table 2 which may then be printed. (Tables 1 and 2 are also available at the authors' Web sites: http://www.math.purdue.edu/$\sim$jer/ or http://www.emunix.emich.edu/$\sim$phoward/.) Detailed instructions for setting up and using the software are included in the book's Introduction, and technical support is available directly from the authors.

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Page Count

442

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821809776

ISBN 13

9780821809778

Logic for Computer Science

Foundations of Automatic Theorem Proving, Second Edition

By: Jean H. Gallier

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Logic for Computer Science

Foundations of Automatic Theorem Proving, Second Edition

By: Jean H. Gallier

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.

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532

Publisher

Courier Dover Publications

Published Date

ISBN 10

0486805085

ISBN 13

9780486805085

Membrane Proteins in Aqueous Solutions

From Detergents to Amphipols

By: Jean-Luc Popot

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Membrane Proteins in Aqueous Solutions

From Detergents to Amphipols

By: Jean-Luc Popot

This book is the first to be entirely devoted to the challenging art of handling membrane proteins out of their natural environment, a key process in biological and pharmaceutical research, but one plagued with difficulties and pitfalls. Written by one of the foremost experts in the field, Membrane Proteins in Aqueous Solutions is accessible to any member of a membrane biology laboratory. After presenting the structure, functions, dynamics, synthesis, natural environment and lipid interactions of membrane proteins, the author discusses the principles of extracting them with detergents, the mechanisms of detergent-induced destabilization, countermeasures, and recent progress in developing detergents with weaker denaturing properties. Non-conventional alternatives to detergents, including bicelles, nanodiscs, amphipathic peptides, fluorinated surfactants and amphipols, are described, and their relative advantages and drawbacks are compared. The synthesis and solution properties of the various types of amphipols are presented, as well as the formation and properties of membrane protein/amphipol complexes and the transfer of amphipol-trapped proteins to detergents, nanodiscs, lipidic mesophases, or living cells. The final chapters of the book deal with applications: membrane protein in vitro folding and cell-free expression, solution studies, NMR, crystallography, electron microscopy, mass spectrometry, amphipol-mediated immobilization of membrane proteins, and biomedical applications. Important features of the book include introductory sections describing foundations as well as the state-of-the-art for each of the biophysical techniques discussed, and topical tables which organize a widely dispersed literature. Boxes and annexes throughout the book explain technical aspects, and twelve detailed experimental protocols, ranging from in vitro folding of membrane proteins to single-particle electron cryomicroscopy, have been contributed by and commented on by experienced users. Membrane Proteins in Aqueous Solutions offers a concise, accessible introduction to membrane protein biochemistry and biophysics, as well as comprehensive coverage of the properties and uses of conventional and non-conventional surfactants. It will be useful both in basic and applied research laboratories and as a teaching aid for students, instructors, researchers, and professionals within the field.

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Page Count

724

Publisher

Springer

Published Date

ISBN 10

3319731483

ISBN 13

9783319731483

Computational Semiotics

By: Jean-Guy Meunier

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Computational Semiotics

By: Jean-Guy Meunier

Can semiotics and computers be compatible? Can computation advance semiotics by enhancing the scientific basis of the theory of signs? Coupling semiotics, a philosophical and phenomenological tradition concerned with theories of signs, with computation, a formal discipline, may seem controversial and paradoxical. Computational Semiotics tackles these controversies head-on and attempts to bridge this gap. Showing how semiotics can build the same type of conceptual, formal, and computational models as other scientific projects, this book opens up a rich domain of inquiry toward the formal understanding of semiotic artifacts and processes. Examining how pairing semiotics with computation can bring more methodological rigor and logical consistency to the epistemic quest for the forms and functions of meaning, without compromising the important interpretive dynamics of semiotics, this book offers a new cutting-edge, model-driven theory to the field.

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289

Publisher

Bloomsbury Publishing

Published Date

ISBN 10

1350166634

ISBN 13

9781350166639

Heidegger from Metaphysics to Thought

By: Dominique Janicaud,Jean-Fran?cois Matt?ei

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Heidegger from Metaphysics to Thought

By: Dominique Janicaud,Jean-Fran?cois Matt?ei

Philosophy has come to an end" claimed Heidegger in the final posthumous interview he granted to Der Spiegel. The goal of Janicaud's chapters ("Overcoming Metaphysics?," "Heideggeriana," "Metamorphosis of the Undecidable," and the dialogue "Heidegger in New York") first of all is to clarify the project of "overcoming" metaphysics, a project that Heidegger himself recognized as open to innumerable misunderstandings. Is it really possible to surmount metaphysics, not by transgressing it, but by means of a patient elucidation of its key concepts? In the effort to underscore the originality of his own enterprise, doesn't Heidegger tend to project too harsh a dichotomy between the forgetfulness of Being and its authentic recollection? By raising these questions, Janicaud suggests that Heidegger himself does not elude the objections that he directs toward the great metaphysical thinkers. The final recourse to dialogue in the midst of twentieth-century New York - a landscape intentionally "different" from one expectedly Heideggerian - intends to hint at another possibility than the indefinite deconstruction of metaphysical texts. It suggests new ways for thoughtful meditation and a new cast for action. At the center of the book, Mattei evokes the "Heideggerian Chiasmus or the Setting-apart of Philosophy." Through an inquiry into the major Heideggerian texts produced between 1935 and 1969 and inspired by Holderlin's poetry, Mattei gradually detects the cosmic figure of the Geviert, the initial Fourfold where "earth and sky, the divine ones and the mortals" gather. Such a community, whose meaning Heidegger is the only one to decipher in our times, silently conforms to what is truly the archaic path to philosophy. The cosmic game of the Geviert also evokes, for Heidegger, the path of the Tao in the Chinese tradition. In this epoch characterized by the destruction of ontology, the two paths in which East and West meet may grant us moderns the hope one day of "dwelling" in the world.

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296

Publisher

SUNY Press

Published Date

ISBN 10

0791421031

ISBN 13

9780791421031

How to Think About Catastrophe

Toward a Theory of Enlightened Doomsaying

By: Jean-Pierre Dupuy

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How to Think About Catastrophe

Toward a Theory of Enlightened Doomsaying

By: Jean-Pierre Dupuy

During the last century humanity acquired the ability to destroy itself. The direct approach to destruction can be seen in such facts as the ever-present threat of nuclear war, but we have also developed the capacity to do indirect harm by altering conditions necessary for survival, including the looming cloud of climate change. How can we look forward and work past the dire position we now find ourselves in to achieve a sustainable future? This volume presents a new way of thinking about the future as it examines catastrophe and the human response. It examines different kinds of catastrophes that range from natural (e.g., earthquakes) to industrial (e.g., Chernobyl) and concludes that the traditional distinctions between them are only becoming blurrier by the day. This book aims to build a general theory of catastrophes—a new form of apocalyptic thinking that is grounded in science and philosophy. An ethics for the sake of the future is what is required, which in turn necessitates a new metaphysics of temporality. If a way out of the imminent danger in which we find ourselves is to be found, we must first look to radically alter our ethics.

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223

Publisher

MSU Press

Published Date

ISBN 10

1628954744

ISBN 13

9781628954746

Understanding Formal Methods

By: Jean-Francois Monin

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Understanding Formal Methods

By: Jean-Francois Monin

This is an excellent introduction to formal methods which will bring anyone who needs to know about this important topic up to speed. It is comprehensive, giving the reader all the information needed to explore the field of formal methods in more detail. It offers: a guide to the mathematics required; comprehensive but easy-to-understand introductions to various methods; a run-down of how formal methods can help to develop high-quality systems that come in on time, within budget, and according to requirements.

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288

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1447100433

ISBN 13

9781447100430

Conclog: A Methodological Approach to Concurrent Logic Programming

By: Jean-Marie Jacquet

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Conclog: A Methodological Approach to Concurrent Logic Programming

By: Jean-Marie Jacquet

This book presents a new concurrent logic programming language called Conclog and a methodology for programming in it. Conclog was designed bytaking the ideal features of logic programming as reference, rather than by concentrating directly on operational tricks to ensure efficiency. This leads to quite easy declarative programming. Concern for soundness and completeness ensures that multi-directional and multi-solution correct procedures can be coded quite straightforwardly. Assuming suitable hypotheses on their uses, they can be transformed into very efficient versions thanks to the introduction of appropriate control information. Correctness-preserving properties are given for that purpose. The designof Conclog involves three steps. First, a sound and complete parallel execution model of Horn clause programs is proposed which reduces subgoals of conjunctions independently and uses a calculus for reconciling inconsistent bindings. Second, this is extended to handle negation as completely as possible. Third, a minimal and reasonably complete set of extra-logical features are defined for optimization and practical purposes. The second part of the book presents a methodology for constructing Conclog in a rigorous way. This covers the entire programming process, from informal specifications via logic descriptions to efficient programs. The methodology can be adapted to other languages.

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806

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540549382

ISBN 13

9783540549383

Proof Theory and Automated Deduction

By: Jean Goubault-Larrecq,I. Mackie

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Proof Theory and Automated Deduction

By: Jean Goubault-Larrecq,I. Mackie

Interest in computer applications has led to a new attitude to applied logic in which researchers tailor a logic in the same way they define a computer language. In response to this attitude, this text for undergraduate and graduate students discusses major algorithmic methodologies, and tableaux and resolution methods. The authors focus on first-order logic, the use of proof theory, and the computer application of automated searches for proofs of mathematical propositions. Annotation copyrighted by Book News, Inc., Portland, OR

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448

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Springer Science & Business Media

Published Date

ISBN 10

1402003684

ISBN 13

9781402003684

The Blind Spot

Lectures on Logic

By: Jean-Yves Girard

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The Blind Spot

Lectures on Logic

By: Jean-Yves Girard

These lectures on logic, more specifically proof theory, are basically intended for postgraduate students and researchers in logic. The question at stake is the nature of mathematical knowledge and the difference between a question and an answer, i.e., the implicit and the explicit. The problem is delicate mathematically and philosophically as well: the relation between a question and its answer is a sort of equality where one side is ``more equal than the other'': one thus discovers essentialist blind spots. Starting with Godel's paradox (1931)--so to speak, the incompleteness of answers with respect to questions--the book proceeds with paradigms inherited from Gentzen's cut-elimination (1935). Various settings are studied: sequent calculus, natural deduction, lambda calculi, category-theoretic composition, up to geometry of interaction (GoI), all devoted to explicitation, which eventually amounts to inverting an operator in a von Neumann algebra. Mathematical language is usually described as referring to a preexisting reality. Logical operations can be given an alternative procedural meaning: typically, the operators involved in GoI are invertible, not because they are constructed according to the book, but because logical rules are those ensuring invertibility. Similarly, the durability of truth should not be taken for granted: one should distinguish between imperfect (perennial) and perfect modes. The procedural explanation of the infinite thus identifies it with the unfinished, i.e., the perennial. But is perenniality perennial? This questioning yields a possible logical explanation for algorithmic complexity. This highly original course on logic by one of the world's leading proof theorists challenges mathematicians, computer scientists, physicists, and philosophers to rethink their views and concepts on the nature of mathematical knowledge in an exceptionally profound way.

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554

Publisher

European Mathematical Society

Published Date

ISBN 10

3037190884

ISBN 13

9783037190883

Book's by Jean van Heijenoort

From Frege to Gödel

From Frege to Gödel

Consequences of the Axiom of Choice

Consequences of the Axiom of Choice

Logic for Computer Science

Logic for Computer Science

Membrane Proteins in Aqueous Solutions

Membrane Proteins in Aqueous Solutions

Computational Semiotics

Computational Semiotics

Heidegger from Metaphysics to Thought

Heidegger from Metaphysics to Thought

How to Think About Catastrophe

How to Think About Catastrophe

Understanding Formal Methods

Understanding Formal Methods

Conclog: A Methodological Approach to Concurrent Logic Programming

Conclog: A Methodological Approach to Concurrent Logic Programming

Proof Theory and Automated Deduction

Proof Theory and Automated Deduction

The Blind Spot

The Blind Spot

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