Results by Title
30 books about Logic, Symbolic and mathematical

The Best of All Possible Worlds: Mathematics and Destiny
Ivar Ekeland
University of Chicago Press, 2006
Library of Congress Q172.E36 2006  Dewey Decimal 509
Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer.
This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization, or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today.
Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition—one that will be essential reading for popularscience buffs and historians of science alike.
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Elementary Logic: Revised Edition
W. V. Quine
Harvard University Press, 1980
Library of Congress BC135.Q46 2001  Dewey Decimal 160
Now much revised since its first appearance in 1941, this book, despite its brevity, is notable for its scope and rigor. It provides a single strand of simple techniques for the central business of modern logic. Basic formal concepts are explained, the paraphrasing of words into symbols is treated at some length, and a testing procedure is given for truthfunction logic along with a complete proof procedure for the logic of quantifiers. Fully one third of this revised edition is new, and presents a nearly complete turnover in crucial techniques of testing and proving, some change of notation, and some updating of terminology. The study is intended primarily as a convenient encapsulation of minimum essentials, but concludes by giving brief glimpses of further matters.
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Formal Logic: A Philosophical Approach
Paul HoyningenHuene
University of Pittsburgh Press, 2004
Library of Congress BC135.H6913 2004  Dewey Decimal 160
Many texts on logic are written with a mathematical emphasis, and focus primarily on the development of a formal apparatus and associated techniques. In other, more philosophical texts, the topic is often presented as an indulgent collection of musings on issues for which technical solutions have long since been devised.
What has been missing until now is an attempt to unite the motives underlying both approaches. Paul HoyningenHuene’s Formal Logic seeks to find a balance between the necessity of formal considerations and the importance of full reflection and explanation about the seemingly arbitrary steps that occasionally confound even the most serious student of logic. Alex Levine’s artful translation conveys both the content and style of the German edition. Filled with examples, exercises, and a straightforward look at some of the most common problems in teaching the subject, this work is eminently suitable for the classroom.
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Foundations and Methods from Mathematics to Neuroscience: Essays Inspired by Patrick Suppes
Edited by Colleen E Crangle, Adolfo García de la Sienra, and Helen E. Longino
CSLI, 2014
Library of Congress Q175.C8825 2015  Dewey Decimal 501
During his long and continuing scholarly career, Patrick Suppes has contributed significantly both to the sciences and to scientific philosophies. In this volume, an international group of Suppes’s colleagues, collaborators, and students seeks to build upon Suppes’s insights. Each of their essays is accompanied by a response from Suppes himself, which together create a uniquely engaging dialogue. Suppes and his peers explore a diverse array of topics including the relationship between science and philosophy; the philosophy of physics; problems in the foundations of mathematics; theory of measurement, decision theory, and probability; the foundations of economics and political theory; psychology, language, and the philosophy of language; Suppes’s most recent research in neurobiology; and the alignment (or misalignment) of method and policy.
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Frege: Philosophy of Mathematics
Michael Dummett
Harvard University Press, 1991
Library of Congress QA8.4.D86 1991  Dewey Decimal 510.1
No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments.
Gottlob Frege (18481925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentiethcentury AngloAmerican philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.
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Frege's Logic
Danielle Macbeth
Harvard University Press, 2005
Library of Congress B3245.F24M36 2005  Dewey Decimal 160.92
For many philosophers, modern philosophy begins in 1879 with the publication of Gottlob Frege's Begriffsschrift, in which Frege presents the first truly modern logic in his symbolic language, Begriffsschrift, or conceptscript. Danielle Macbeth's book, the first fulllength study of this language, offers a highly original new reading of Frege's logic based directly on Frege's own twodimensional notation and his various writings about logic.
Setting out to explain the nature of Frege's logical notation, Macbeth brings clarity not only to Frege's symbolism and its motivation, but also to many other topics central to his philosophy. She develops a uniquely compelling account of Frege's Sinn/Bedeutung distinction, a distinction central to an adequate logical language; and she articulates a novel understanding of concepts, both of what they are and of how their contents are expressed in properly logical language. In her reading, Frege's Begriffsschrift emerges as a powerful and deeply illuminating alternative to the quantificational logic it would later inspire.
The most enlightening examination to date of the developments of Frege's thinking about his logic, this book introduces a new kind of logical language, one that promises surprising insight into a range of issues in metaphysics and epistemology, as well as in the philosophy of logic.
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Frege’s Philosophy of Mathematics
William Demopoulos
Harvard University Press, 1995
Library of Congress QA8.6.F74 1995  Dewey Decimal 510.1
Widespread interest in Frege's general philosophical writings is, relatively speaking, a fairly recent phenomenon. But it is only very recently that his philosophy of mathematics has begun to attract the attention it now enjoys. This interest has been elicited by the discovery of the remarkable mathematical properties of Frege's contextual definition of number and of the unique character of his proposals for a theory of the real numbers.
This collection of essays addresses three main developments in recent work on Frege's philosophy of mathematics: the emerging interest in the intellectual background to his logicism; the rediscovery of Frege's theorem; and the reevaluation of the mathematical content of The Basic Laws of Arithmetic. Each essay attempts a sympathetic, if not uncritical, reconstruction, evaluation, or extension of a facet of Frege's theory of arithmetic. Together they form an accessible and authoritative introduction to aspects of Frege's thought that have, until now, been largely missed by the philosophical community.
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Introduction Wittgensteins Tractatus
G.E.M. Anscombe
St. Augustine's Press, 2000
Library of Congress B3376.W563T73199 2000  Dewey Decimal 192


Language and Grammar: Studies in Mathematical Linguistics and Natural Language
Edited by Claudia Casadio, Philip Scott, and Robert Seely
CSLI, 2005
Library of Congress P39.L36 2005  Dewey Decimal 415.018
The application of logic to grammar is a fundamental issue in philosophy and has been investigated by such renowned philosophers as Leibniz, Bolzano, Frege, and Husserl. Language and Grammar examines categorial grammars and typelogical grammars, two linguistic theories that play a significant role in this area of study yet have been overshadowed until recently. The prominent scholars contributing to this volume also explore the impact of the Lambek program on linguistics and logical grammar, producing, ultimately, an exciting and important resource that demonstrates how typelogical grammars are promising future models of reasoning and computation.
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Lectures on Linear Logic
A. S. Troelstra
CSLI, 1992
Library of Congress QA9.T76 1991  Dewey Decimal 511.3
Linear logic is an example of a "resourcesensitive" logic, keeping track of the number of times data of given types are used. Formulas in linear logic represent either the data themselves or data types, whereas in ordinary logic a formula is a proposition. If ordinary logic is a logic of truth, linear logic is a logic of actions.
Linear logic and its implications are explored in depth in this volume. Particular attention has been given to the various formalisms for linear logic, embeddings of classical and intuitionistic logic into linear logic, the connection with certain types of categories, the "formulasastypes" paradigm for linear logic and associated computational interpretations, and Girard's proof nets for classical linear logic as an analogue of natural deduction. It is also shown that linear logic is undecidable. A final section, contributed by D. Roorda, presents a proof of strong normalization for cut elimination in linear logic.
Linear logic is of interest to logicians and computer scientists, and shows links with many other topics, such as coherence theorems in category theory, the theory of Petri nets, and abstract computing machines without garbage collection
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Logic and Automata: History and Perspectives
Edited by Jörg Flum, Erich Grädel, and Thomas Wilke
Amsterdam University Press, 2008
Library of Congress QA267.L624 2008  Dewey Decimal 340349
Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d’horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field.
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Logic and the Foundations of Game and Decision Theory (LOFT 7)
Edited by Giacomo Bonanno, Wiebe van der Hoek, and Michael Wooldridge
Amsterdam University Press, 2008
Library of Congress QA9.A1L6275 2008
This volume is a collects papers originally presented at the 7th Conference on Logic and the Foundations of Game and Decision Theory (LOFT), held at the University of Liverpool in July 2006. LOFT is a key venue for presenting research at the intersection of logic, economics, and computer science, and this collection gives a lively and wideranging view of an exciting and rapidly growing area.
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Logic and Visual Information
Eric M. Hammer
CSLI, 1995
Library of Congress Q387.2.H36 1995  Dewey Decimal 511.30223


Logic Colloquium '92
Edited by Lázló Csirmaz, Dov M. Gabbay, and Maarten de Rijke
CSLI, 1995
Library of Congress BC135.L576 1995  Dewey Decimal 511.3
Logic Colloquium '92, the European Summer Meeting of the Association for Symbolic Logic, was held in Veszpre;m, Hungary, in August 1992. Two of the main themes of the event were algebraic logic, and axiomatisability and decidability of logical systems. The present volume contains a selection of papers that grew out of invited and contributed talks on these themes. Most of the papers have a strong interdisciplinary flavour as they investigate logical properties of formal systems by studying algebraic properties of corresponding classes of algebras, or vice versa. The remaining papers focus on connected areas from model theory and the combination of logics. This is a useful and timely volume on algebraic logic and related areas, with contributions by leading people in the field.
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Logic, Langage and Computation, Volume 2
Edited by Lawrence S. Moss, Jonathan Ginzburg, and Maarten de Rijke
CSLI, 1999
Library of Congress P39.L593 1996  Dewey Decimal 410.285
The fields of logic, linguistics and computer science are intimately related, and modern research has uncovered a wide range of connections. This collection focuses on work that is based on the unifying concept of information. This collection of nineteen papers covers subjects such as channel theory, presupposition and constraints, the modeling of discourse, and belief. They were all presented at the 1996 Conference on InformationTheoretic Approaches to Logic, Language, Information, and Computation.
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Logic, Language and Computation
Edited by Jerry Seligman and Dag Westerståhl
CSLI, 1996
Library of Congress P39.L593 1996  Dewey Decimal 410.285
Subject: Linguistics; Logic; Computational Linguistics
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Mathematical Reasoning with Diagrams
Mateja Jamnik
CSLI, 2001
Library of Congress QA90.J33 2001  Dewey Decimal 511.3
Mathematicians at every level use diagrams to prove theorems. Mathematical Reasoning with Diagrams investigates the possibilities of mechanizing this sort of diagrammatic reasoning in a formal computer proof system, even offering a semiautomatic formal proof system—called Diamond—which allows users to prove arithmetical theorems using diagrams.
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Mathematical Structures in Languages
Edward Keenan and Larry Moss
CSLI, 2015
Library of Congress P138.K44 2016  Dewey Decimal 410.151
Mathematical Structures in Languages introduces a number of mathematical concepts that are of interest to the working linguist. The areas covered include basic set theory and logic, formal languages and automata, trees, partial orders, lattices, Boolean structure, generalized quantifier theory, and linguistic invariants, the last drawing on Edward L. Keenan and Edward Stabler’s Bare Grammar: A Study of Language Invariants, also published by CSLI Publications. Ideal for advanced undergraduate and graduate students of linguistics, this book contains numerous exercises and will be a valuable resource for courses on mathematical topics in linguistics. The product of many years of teaching, Mathematic Structures in Languages is very much a book to be read and learned from.
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Notebooks, 19141916
Ludwig Wittgenstein
University of Chicago Press, 1979
Library of Congress B3376.W563N6 1979  Dewey Decimal 193
This considerably revised second edition of Wittgenstein's 191416 notebooks contains a new appendix with photographs of Wittgenstein's original work, a new preface by Elizabeth Anscombe, and a useful index by E.D. Klemke. Corrections have been made throughout the text, and notes have been added, making this the definitive edition of the notebooks. The writings intersperse Wittgenstein's technical logical notations with his thoughts on the meaning of life, happiness, and death.
"When the first edition of this collection of remarks appeared in 1961 we were provided with a glimpse of the workings of Wittgenstein's mind during the period when the seminal ideas of the Tractatus LogicoPhilosophicus were being worked out. This second edition provided the occasion to be struck anew by the breadth, rigor, and above all the restlessness of that mind."—T. Michael McNulty, S. J., The Modern Schoolman
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A Paradigm for Program Semantics: Power Structures and Duality
Chris Brink and Ingrid Rewitsky
CSLI, 2001
Library of Congress BC135.B747 2001  Dewey Decimal 160
This book provides a synthesis of four versions of program semantic—srelational semantics, predicate transformer semantics, information systems, and domain theory—showing, through an exhaustive case study analysis, that it is possible to do backandforth translation from any of these versions of program semantics into any of the others, and demonstrating that while there are many variations of each, in principle they may be thought of as intertranslatable.
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Peeling Potatoes or Grinding Lenses: Spinoza and Young Wittgenstein Converse on Immanence and Its Logic
Aristides Baltas
University of Pittsburgh Press, 2012
Library of Congress B3974.B35 2012  Dewey Decimal 192
“I can work best now while peeling potatoes. . . . It is for me what lensgrinding was for Spinoza.”—L. Wittgenstein
More than 250 years separate the publication of Baruch Spinoza’s Ethics and Ludwig Wittgenstein’s Tractatus LogicoPhilosophicus. Both are considered monumental philosophical treatises, produced during markedly different times in human history, and notoriously challenging to interpret. In Peeling Potatoes or Grinding Lenses, Aristides Baltas contends that these works bear a striking similarity based on the idea of “radical immanence.” Each purports to understand the world, thought, and language from the inside and in a way leading to the dissolution of all philosophy. In that guise, both offer a powerful argument against fundamentalism of all sorts and kinds.
To Spinoza, God is just Nature. God is not above or separate from the world, humanity, or mere objects for, as Nature, He inheres in everything. To Wittgenstein, logic is not above or separate from language, thought, and the world. The hardness of the logical “must” inheres in states of affairs, facts, thoughts, and linguistic acts. Outside there are no truths or sense—only nonsense.
Through close readings of the texts based on lessons drawn from radical paradigm change in science, Baltas finds in both works a singleminded purpose, implacable reasoning, and an austerity of style that are rare in the history of philosophy. He analyzes the structure and content of each treatise, the authors’ intentions, the limitations and possibilities afforded by scientific discovery in their respective eras, their radical opposition to prevailing philosophical views, and draws out the particulars, as well as the implications, of the arresting match between the two.
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Philosophical Remarks
Ludwig Wittgenstein
University of Chicago Press, 1980
Library of Congress B3376.W563P513 1980  Dewey Decimal 192
When in May 1930, the Council of Trinity College, Cambridge, had to decide whether to renew Wittgenstein's research grant, it turned to Bertrand Russell for an assessment of the work Wittgenstein had been doing over the past year. His verdict: "The theories contained in this new work . . . are novel, very original and indubitably important. Whether they are true, I do not know. As a logician who likes simplicity, I should like to think that they are not, but from what I have read of them I am quite sure that he ought to have an opportunity to work them out, since, when completed, they may easily prove to constitute a whole new philosophy."
"[Philosophical Remarks] contains the seeds of Wittgenstein's later philosophy of mind and of mathematics. Principally, he here discusses the role of indispensable in language, criticizing Russell's The Analysis of Mind. He modifies the Tractatus's picture theory of meaning by stressing that the connection between the proposition and reality is not found in the picture itself. He analyzes generality in and out of mathematics, and the notions of proof and experiment. He formulates a pain/privatelanguage argument and discusses both behaviorism and the verifiability principle. The work is difficult but important, and it belongs in every philosophy collection."—Robert Hoffman, Philosophy
"Any serious student of Wittgenstein's work will want to study his Philosophical Remarks as a transitional book between his two great masterpieces. The Remarks is thus indispensible for anyone who seeks a complete understanding of Wittgenstein's philosophy."—Leonard Linsky, American Philosophical Association
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Philosophy of Mathematics in the Twentieth Century: Selected Essays
Charles Parsons
Harvard University Press, 2014
Library of Congress QA9.2.P372 2014  Dewey Decimal 510.1
In this illuminating collection, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the course of the past century.
Parsons begins with a discussion of the Kantian legacy in the work of L. E. J. Brouwer, David Hilbert, and Paul Bernays, shedding light on how Bernays revised his philosophy after his collaboration with Hilbert. He considers Hermann Weyl's idea of a "vicious circle" in the foundations of mathematics, a radical claim that elicited many challenges. Turning to Kurt Gödel, whose incompleteness theorem transformed debate on the foundations of mathematics and brought mathematical logic to maturity, Parsons discusses his essay on Bertrand Russell's mathematical logicGödel's first mature philosophical statement and an avowal of his Platonistic view.
Philosophy of Mathematics in the Twentieth Century insightfully treats the contributions of figures the author knew personally: W. V. Quine, Hilary Putnam, Hao Wang, and William Tait. Quine's early work on ontology is explored, as is his nominalistic view of predication and his use of the genetic method of explanation in the late work The Roots of Reference. Parsons attempts to tease out Putnam's views on existence and ontology, especially in relation to logic and mathematics. Wang's contributions to subjects ranging from the concept of set, minds, and machines to the interpretation of Gödel are examined, as are Tait's axiomatic conception of mathematics, his minimalist realism, and his thoughts on historical figures.
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Selected Logic Papers: Enlarged Edition
W. V. Quine
Harvard University Press, 1995
Library of Congress B945.Q53S45 1995  Dewey Decimal 511.3
For more than two generations, W. V. Quine has contributed fundamentally to the substance, the pedagogy, and the philosophy of mathematical logic. Selected Logic Papers, long out of print and now reissued with eight additional essays, includes much of the author’s important work on mathematical logic and the philosophy of mathematics from the past sixty years.
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Studies in Weak Arithmetics, Volume 1
Edited by Patrick Cégielski
CSLI, 2009
Library of Congress QA241.S824 2010  Dewey Decimal 512.7
The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. In this volume, after a general presentation of weak arithmetics, the following topics are studied: the properties of integers of a real closed field equipped with exponentiation; conservation results for the induction schema restricted to firstorder formulas with a finite number of alternations of quantifiers; a survey on a class of tools called pebble games; the fact that the reals e and pi have approximations expressed by firstorder formulas using bounded quantifiers; properties of infinite pictures depending on the universe of sets used; a language that simulates in a sufficiently nice manner all algorithms of a certain restricted class; the logical complexity of the axiom of infinity in some variants of set theory without the axiom of foundation; and the complexity to determine whether a trace is included in another one.
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Studies in Weak Arithmetics, Volume 2
Edited by Patrick Cégielski, Charalampos Cornaros, and Costas Dimitracopoulos
CSLI, 2013
Library of Congress QA241.N465 2013  Dewey Decimal 512.7
The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. New Studies in Weak Arithmetics is dedicated to late Australian mathematician Alan Robert Woods (19532011), whose seminal thesis is published here for the first time. This volume also contains the unpublished but significant thesis of Hamid Lesan (19512006) as well as other original papers on topics addressed in Woods’s thesis and life’s work that were first presented at the 31st Journées sur les Arithmétiques Faibles meeting held in Samos, Greece, in 2012.
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Studies in Weak Arithmetics, Volume 3
Edited by Patrick Cegielski, Ali Enayat, and Roman Kossak
CSLI, 2013
Library of Congress QA241.N465 2013  Dewey Decimal 512.7
The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. This third volume in the weak arithmetics collection contains nine substantive papers based on lectures delivered during the two last meetings of the conference series Journées sur les Arithmétiques, held in 2014 at the University of Gothenburg, Sweden, and in 2015 at the City University of New York Graduate Center.
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Transcendence and Wittgenstein's Tractatus
Michael P. Hodges
Temple University Press, 1990
Library of Congress B3376.W563T73345 1990  Dewey Decimal 192
Although Wittgenstein claimed that his first book, the Tractatus LogicoPhilosophicus, was essentially an ethical work, it has been viewed insistently as a purely logical one. His later work, Philosophical Investigations, is generally seen as presenting totally different ideas from his earlier writings. In this book, Michael Hodges shows how Wittgenstein’s later work emerged from his earlier Tractatus, and he unifies the early philosophy, both its wellknown logical aspects and the lesser known ethical dimensions, in terms of the notion of transcendence.
Hodges studies the Tractatus in light of Wittgenstein’s own claim that the Philosophical Investigations can only be understood when read against the background of the Tractatus. At the heart of an understanding of the earlier work is the idea of transcendence which structures both Wittgenstein’s logical and ethical insights. Seen in terms of this notion, the rigorous unity of Wittgenstein’s early thinking becomes apparent and the gestalt shift to the later philosophy comes clearly into focus.
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Universal Logic
Ross Brady
CSLI, 2001
Library of Congress BC135.B745 2006  Dewey Decimal 160
Throughout the twentieth century, the classical logic of Frege and Russell dominated the field of formal logic. But, as Ross Brady argues, a new type of weak relevant logic may prove to be better equipped to present new solutions to persistent paradoxes. Universal Logic begins with an overview of classical and relevant logic and discusses the limitations of both in analyzing certain paradoxes. It is the first text to demonstrate how the main settheoretic and semantic paradoxes can be solved in a systematic way and as such will be of great interest to both scholars and students of logic.
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Wittgenstein's Tractatus: An Introduction
H. O. Mounce
University of Chicago Press, 1981
Library of Congress B3376.W563T7346  Dewey Decimal 192


