Arising from a special session held at the 2010 North American Annual Meeting of the Association for Symbolic Logic, this volume is an international cross-disciplinary collaboration with contributions from leading experts exploring connections across their respective fields. Themes range from philosophical examination of the foundations of physics and quantum logic, to exploitations of the methods and structures of operator theory, category theory, and knot theory in an effort to gain insight into the fundamental questions in quantum theory and logic. The book will appeal to researchers and students working in related fields, including logicians, mathematicians, computer scientists, and physicists. A brief introduction provides essential background on quantum mechanics and category theory, which, together with a thematic selection of articles, may also serve as the basic material for a graduate course or seminar.

Language and Philosophical Problems investigates problems about mind, meaning and mathematics rooted in preconceptions of language. It deals in particular with problems which are connected with our tendency to be misled by certain prevailing views and preconceptions about language. Philosophical claims made by theorists of meaning are scrutinized and shown to be connected with common views about the nature of certain mathematical notions and methods. Drawing in particular on Wittgenstein's ideas, Sren Stenlund demonstrates a strategy for tracing out and resolving conceptual and philosophical problems. By a critical examination of examples from different areas of philosophy, he shows that many problems arise through the transgression of the limits of the use of technical concepts and formal methods. Many prima facie different kinds of problems are shown to have common roots, and should thus be dealt and resolved together. Such an approach is usually prevented by the influence of traditional philosophical terminology and classification. The results of this investigation make it clear that the received ways of subdividing the subject matter of philosophy often conceal the roots of the problem.

Paradoxes of the Infinite presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19th century: Dr Bernard Bolzano's Paradoxien. This volume contains an adept translation of the work itself by Donald A. Steele S.J., and in addition an historical introduction, which includes a brief biography as well as an evaluation of Bolzano the mathematician, logician and physicist.

This is an important collection of new essays on various topics relating to realism and its rivals in metaphysics, logic, metaethics, and epistemology. The contributors include some of the leading authors in these fields and in several cases their essays constitute definitive statements of their views. Although not primarily historical this volume includes discussion of philosophers from the Middle Ages to the present day, from Aquinas to Wittgenstein. No one seriously interested in questions about realism can afford to be without this collection.

In this challenging and provocative analysis, Dale Jacquette argues that contemporary philosophy labours under a number of historically inherited delusions about the nature of logic and the philosophical significance of certain formal properties of specific types of logical constructions. Exposing some of the key misconceptions about formal symbolic logic and its relation to thought, language and the world, Jacquette clears the ground of some very well-entrenched philosophical doctrines about the nature of logic, including some of the most fundamental seldom-questioned parts of elementary propositional and predicate-quantificational logic. Having presented difficulties for conventional ways of thinking about truth functionality, the metaphysics of reference and predication, the role of a concept of truth in a theory of meaning, among others, Jacquette proceeds to reshape the network of ideas about traditional logic that philosophy has acquired along with modern logic itself. In so doing Jacquette is able to offer a new perspective on a number of existing problems in logic and philosophy of logic.

Making Your Mind Matter is a practical guide to effective thinking in college and in everyday life. Critical thinking guru Vincent Ryan Ruggiero explains how and why the mind has been neglected in American education, then teaches readers how to take charge of their own mental development. Ruggiero presents a simple but powerful model the WISE model (Wonder, Investigate, Speculate, Evaluate). This model illustrates how to overcome obstacles to thinking, resist manipulation, test ideas, analyze arguments, form judgments, analyze ethical issues, and discuss ideas courteously and effectively. This book is a brief, comprehensive, authoritative, and accessible introduction to critical thinking, perfect for all students and others interested in increasing the power of their minds.

All of us are faced countless times with the challenge of persuading others, whether we're trying to win a trivial argument with a friend or convince our coworkers about an important decision. Instead of relying on untrained instinct--and often floundering or failing as a result--we'd win more arguments if we learned the timeless art of verbal persuasion, rhetoric. How to Win an Argument gathers the rhetorical wisdom of Cicero, ancient Rome's greatest orator, from across his works and combines it with passages from his legal and political speeches to show his powerful techniques in action. The result is an enlightening and entertaining practical introduction to the secrets of persuasive speaking and writing--including strategies that are just as effective in today's offices, schools, courts, and political debates as they were in the Roman forum. How to Win an Argument addresses proof based on rational argumentation, character, and emotion; the parts of a speech; the plain, middle, and grand styles; how to persuade no matter what audience or circumstances you face; and more. Cicero's words are presented in lively translations, with illuminating introductions; the book also features a brief biography of Cicero, a glossary, suggestions for further reading, and an appendix of the original Latin texts. Astonishingly relevant, this unique anthology of Cicero's rhetorical and oratorical wisdom will be enjoyed by anyone who ever needs to win arguments and influence people--in other words, all of us.

Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Classic formalists claimed implausibly that mathematical utterances are truth-valueless moves in a game. Alan Weir aims to develop a more satisfactory successor to game formalism utilising a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance. This framework allows for sentences whose truth-conditions are not representational, which are made true or false by conditions residing in the circumstances of utterances but not transparently in the sense.
Applications to projectivism and fiction pave the way for the claim that mathematical utterances are made true or false by the existence of concrete proofs or refutations, though these truth-making conditions form no part of their sense or informational content.
The position is compared with rivals, an account of the applicability of mathematics developed, and a new account of the nature of idealisation proffered in which it is argued that the finitistic limitations Godel placed on proofs are without rational justification. Finally a non-classical logical system is provided in which excluded middle fails, yet enough logical power remains to recapture the results of standard mathematics.

In 1942 G.E. Moore first wrote about the curious sort of 'nonsense' exhibited by the statement 'it is raining but I do not believe it'. What Moore discovered was a species of blindspots: consistent propositions that cannot be rationally accepted by certain individuals even though they might be true. In this book, Professor Sorenson aims to provide a unified solution to a large family of philosophical puzzles and paradoxes through a study of blindspots . He devotes special attention to revealing their role in 'slippery slope' reasoning.

Originally published in 1966 On the Syllogism and Other Logical Writings assembles for the first time the five celebrated memoirs of Augustus De Morgan on the syllogism. These are collected together with the more condensed accounts of his researches given in his Syllabus of a Proposed System of Logic an article on Logic contributed to the English Cyclopaedia. De Morgan was among the most distinguished of nineteenth century British mathematicians but is chiefly remembered today as one of the founders of modern mathematical logic. His writings on this subject have been little read, however since apart from his Formal Logic, they lie buried for the most part in inaccessible periodicals. De Morgan's own later amendments are inserted in the text and the editorial introduction gives a summary of the whole and traces in some detail the course of the once-famous feud with Sir William Hamilton of Edinburgh.

This reissue, first published in 1971, provides a brief historical account of the Theory of Logical Types; and describes the problems that gave rise to it, its various different formulations (Simple and Ramified), the difficulties connected with each, and the criticisms that have been directed against it. Professor Copi seeks to make the subject accessible to the non-specialist and yet provide a sufficiently rigorous exposition for the serious student to see exactly what the theory is and how it works.

"Everything one might want for a course on [Frege and Russell] is included, along with a seventy-five-page introduction that carefully lays out the contributions of each essay." -- Bernard Linsky, University of Alberta

"The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics. The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.

This unique introduction fully engages and clearly explains pragmatism, an approach to knowledge and philosophy that rejects outmoded conceptions of objectivity while avoiding relativism and subjectivism. It follows pragmatism's focus on the process of inquiry rather than on abstract justifications meant to appease the skeptic. According to pragmatists, getting to know the world is a creative human enterprise, wherein we fashion our concepts in terms of how they affect us practically, including in future inquiry. This book fully illuminates that enterprise and the resulting radical rethinking of basic philosophical conceptions like truth, reality, and reason. Author Cornelis de Waal helps the reader recognize, understand, and assess classical and current pragmatist contributions-from Charles S. Peirce to Cornel West-evaluate existing views from a pragmatist angle, formulate pragmatist critiques, and develop a pragmatist viewpoint on a specific issue. The book discusses: Classical pragmatists, including Peirce, James, Dewey, and Addams; Contemporary figures, including Rorty, Putnam, Haack, and West; Connections with other twentieth-century approaches, including phenomenology, critical theory, and logical positivism; Peirce's pragmatic maxim and its relation to James's Will to Believe; Applications to philosophy of law, feminism, and issues of race and racism.

First published in 1952, professor's Strawson's highly influential Introduction to Logical Theory provides a detailed examination of the relationship between the behaviour of words in common language and the behaviour of symbols in a logical system. He seeks to explain both the exact nature of the discipline known as Formal Logic, and also to reveal something of the intricate logical structure of ordinary unformalised discourse.

In 1945 Alonzo Church issued a pair of referee reports in which he anonymously conveyed to Frederic Fitch a surprising proof showing that wherever there is (empirical) ignorance there is also logically unknowable truth. Fitch published this and a generalization of the result in 1963. Ever since, philosophers have been attempting to understand the significance and address the counter-intuitiveness of this, the so-called paradox of knowability.
This collection assembles Church's referee reports, Fitch's 1963 paper, and nineteen new papers on the knowability paradox. The contributors include logicians and philosophers from three continents, many of whom have already made important contributions to the discussion of the problem. The volume contains a general introduction to the paradox and the background literature, and is divided into seven sections that roughly mark the central points of debate. The sections include the history of the paradox, Michael Dummett's constructivism, issues of paraconsistency, developments of modal and temporal logics, Cartesian restricted theories of truth, modal and mathematical fictionalism, and reconsiderations about how, and whether, we ought to construe an anti-realist theory of truth.

This multidisciplinary event was attended by 1,850 people from 61 countries brought together professionals from a broad spectrum of disciplines, ranging from engineering and the sciences to the arts, politics, economics and social sciences. Contributors included Manfred Max-Eduardo Galeano, Robert Chambers and Orlando Fals Borda.

This book aims to develop certain aspects of Gottlob Frege's theory of meaning, especially those relevant to intentional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege.

The Collected Works of John Stuart Mill took thirty years to complete and is acknowledged as the definitive edition of J.S. Mill and as one of the finest works editions ever completed. Mill's contributions to philosophy, economics, and history, and in the roles of scholar, politician and journalist can hardly be overstated and this edition remains the only reliable version of the full range of Mill's writings. Each volume contains extensive notes, a new introduction and an index. Many of the volumes have been unavailable for some time, but the Works are now again available, both as a complete set and as individual volumes.

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual.

First Published in 1964, Studies in Metaphilosophy presents and develop the hypothesis about the nature of metaphysical theories. Each study is a fresh attempt to improve our understanding of what a philosophical theory is and what its supporting arguments come to. Author argues that philosophical theories are nothing more substantial than linguistic chimeras and has the important function of pointing up the need for the examination of the whole subject. The volume discusses important themes like concept analysis, systematic doubt, the method of deduction from fact, logical necessitation, the nature of philosophical analysis, the nature of value, the metaphysical concept of space, Moore and philosophical analysis, the hidden structure of philosophical theories, and the relevance of psychoanalysis to philosophy. This volume will be an essential source for scholars and researchers of philosophy, logic, and metaphysics.

In this book, Livingston develops the political implications of formal results obtained over the course of the twentieth century in set theory, metalogic, and computational theory. He argues that the results achieved by thinkers such as Cantor, Russell, Godel, Turing, and Cohen, even when they suggest inherent paradoxes and limitations to the structuring capacities of language or symbolic thought, have far-reaching implications for understanding the nature of political communities and their development and transformation. Alain Badiou's analysis of logical-mathematical structures forms the backbone of his comprehensive and provocative theory of ontology, politics, and the possibilities of radical change. Through interpretive readings of Badiou's work as well as the texts of Giorgio Agamben, Jacques Lacan, Jacques Derrida, Gilles Deleuze, and Ludwig Wittgenstein, Livingston develops a formally based taxonomy of critical positions on the nature and structure of political communities. These readings, along with readings of Parmenides and Plato, show how the formal results can transfigure two interrelated and ancient problems of the One and the Many: the problem of the relationship of a Form or Idea to the many of its participants, and the problem of the relationship of a social whole to its many constituents.

Over fifteen years have passed since Cora Diamond and James Conant turned Wittgenstein scholarship upside down with the program of "resolute" reading, and ten years since this reading was crystallized in the major collection The New Wittgenstein. This approach remains at the center of the debate about Wittgenstein and his philosophy, and this book draws together the latest thinking of the world's leading Tractatarian scholars and promising newcomers. Showcasing one piece alternately from each "camp", Beyond the Tractatus Wars pairs newly commissioned pieces addressing differing views on how to understand early Wittgenstein, providing for the first time an arena in which the debate between "strong" resolutists, "mild" resolutists and "elucidatory" readers of the book can really take place. The collection includes famous "samizdat" essays by Warren Goldfarb and Roger White that are finally seeing the light of day.