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203 results in Logic

Page 1 of 11

An Introduction to Classical and Modal Logics
  • The Outlines of Knowledge
  • Adam Bjorndahl
  • Published online:
    08 February 2025
    Print publication:
    21 November 2024
  • Classical logic – which studies the structural features of purported claims of fact – and modal logic – which studies relations of necessity and possibility – are different but complementary areas of logical thought. In this lively and accessible textbook, Adam Bjorndahl provides a comprehensive and unified introduction to the two subjects, treating them with the same level of rigour and detail and showing how they fit together. The core material appears in the main text, with hundreds of supplemental examples, comments, clarifications, and connections presented throughout in easy-to-read sidenotes, giving the book a distinct conversational feel. A detailed, multi-part appendix covers important background mathematical material that some students may lack, such as induction or the concept of countable infinity. A fully self-contained learning resource, this book will be ideal for a semester-long upper-level university course on either or both of the topics.

The Logic of Precedent
  • Constraint, Freedom, and Common Law Reasoning
  • John Horty
  • Published online:
    16 January 2025
    Print publication:
    27 February 2025
  • Unlike statutory law, which relies on the explicit formulation of rules, common law is thought to emerge from a complex doctrine of precedential constraint, according to which decisions in earlier cases constrain later courts while still allowing these courts the freedom to address new situations in creative ways. Although this doctrine is applied by legal practitioners on a daily basis, it has proved to be considerably more difficult to develop an adequate theoretical account of the doctrine itself. Drawing on recent work in legal theory, as well as AI and law, this book develops a new account of precedential constraint and the balance achieved in the common law between constraint and freedom. This account, which involves construction of a group priority ordering among reasons, is then applied to other topics including the semantics of open-textured predicates and the practice of making exceptions to general rules.

The Road to Paradox
  • A Guide to Syntax, Truth and Modality
  • Volker Halbach, Graham E. Leigh
  • Published online:
    17 October 2024
    Print publication:
    31 October 2024
  • Truth, provability, necessity, and other concepts are fundamental to many branches of philosophy, mathematics, computer science, and linguistics. Their study has led to some of the most celebrated achievements in logic, such as Gödel's incompleteness theorems, Tarski's theorem on the undefinability of truth, and numerous accounts of the paradoxes associated with these concepts. This book provides a clear and direct introduction to the theory of paradoxes and the Gödel incompleteness theorems. It offers new analyses of the ideas of self-reference, circularity, and the semantic paradoxes, and helps readers to see both how paradoxes arise and what their common features are. It will be valuable for students and researchers with a minimal background in logic and will equip them to understand and discuss a wide variety of topics in philosophical logic.

Theory of Categories
  • Key Instruments of Human Understanding
  • Nicholas Rescher, Patrick Grim
  • Published by:
    Anthem Press
    Published online:
    29 February 2024
    Print publication:
    05 September 2023
  • Categorization is an essential and unavoidable instrumentality for conceptually navigating a world-indeed for being able to conceptualize a world to be navigated. Classification is a pivotal instrument for scientific systemization, featured as a basis for the philosophical understanding of reality since Aristotle, but classificatory concepts of sorts, types and natural kinds inevitably pervade our understanding of ourselves and our position in the social as well as the natural world at all levels. The authors argue that the character, purpose-, context-, and culture-relativity of categories and categorization have been widely misunderstood - that standard philosophical views are substantially correct in some respects but markedly mistaken in others. The book offers a comprehensive survey of basic principles of classification and categorization, a survey of relevant empirical work, and a multitude of illustrative examples accompanied by instructive analysis of ways and means. The work traces wide-ranging implications of the current approach for philosophical problematic and paradox in philosophy of mind, epistemology and metaphysics, philosophy of science, social philosophy and ethics.

The Logic of Entailment and its History
  • Edwin Mares
  • Published online:
    08 February 2024
    Print publication:
    15 February 2024
  • What follows from what, and how do we make statements (whether true or false) about which inferences are correct? In this book, Edwin Mares provides a new philosophical, semantical and historical analysis of and justification for the relevant logic of entailment. In the first half of the book he examines some key ideas in the historical development of the logic of entailment, looking in particular at the notion 'is derivable from' and at how symbolic logic has attempted to capture this notion. In the second half of the book he develops his own theory connecting ideas from the traditions in mathematical logic with some ideas in the philosophy of science. The book's fresh and original perspective on the logic of entailment will be valuable for all who want to know more about the historical and philosophical origins of modern symbolic logic.

An Inquiry into Analytic-Continental Metaphysics
  • Truth, Relevance and Metaphysics
  • Jeffrey A. Bell
  • Published by:
    Edinburgh University Press
    Published online:
    25 October 2023
    Print publication:
    30 September 2022
  • By developing a metaphysics of problems, Jeffrey Bell shows how the history of both the analytic and continental traditions of philosophy can be seen to be an ongoing response to the problem of regresses. By highlighting this shared history, Bell brings these two traditions back together to address problems that have been essential to their projects all along and central to much of the history of philosophy.

Towards a Critical Existentialism
  • Truth, Relevance and Politics
  • Jeffrey Bell
  • Published by:
    Edinburgh University Press
    Published online:
    18 October 2023
    Print publication:
    30 September 2022
  • Jeffrey Bell argues that a motivating problematic for existentialist writers is the attempt to think through the implications of the problematic nature of life. He applies a Deleuzian theory of problems to an analysis of some key concepts in contemporary social and political theory. Building on the metaphysics of problems set out in his book, An Inquiry into Analytic-Continental Metaphysics, he provides a new way of integrating the concerns of existentialist writers into contemporary political and social debates.

A Theory of Truth
  • Yannis Stephanou
  • Published online:
    07 October 2023
    Print publication:
    12 October 2023
  • How should we treat the liar and kindred paradoxes? A Theory of Truth argues that we should diverge from classical logic, and presents a new formal theory of truth. The theory does not incorporate contradictions and is not substructural, but deviates from classical logic significantly, and endorses principles like 'No sentence is both true and false' and 'No sentence is neither true nor false'. The book starts with an introduction to the paradoxes, suitable for newcomers to the subject, before presenting its approach. Four versions of the theory are covered, extending the theory to a determinacy operator and to a full first-order language with quantifiers. Each includes all Tarskian biconditionals that can be formulated in its language. The author uses original methods to prove the consistency of each version and compares the theory to alternative non-classical theories, including Field's paracomplete approach, Ripley's nontransitive system and Zardini's contraction-free calculus.

Logical Pluralism and Logical Consequence
  • Erik Stei
  • Published online:
    23 March 2023
    Print publication:
    30 March 2023
  • Logical pluralism is the view that there is more than one correct logic. This is not necessarily a controversial claim but in its most exciting formulations, pluralism extends to logics that have typically been considered rival accounts of logical consequence – to logics, that is, which adopt seemingly contradictory views about basic logical laws or arguments. The logical pluralist challenges the philosophical orthodoxy that an argument is either deductively valid or invalid by claiming that there is more than one way for an argument to be valid. In this book, Erik Stei defends logical monism, provides a detailed analysis of different possible formulations of logical pluralism, and offers an original account of the plurality of correct logics that incorporates the benefits of both pluralist and monist approaches to logical consequence. His book will be valuable for a range of readers in the philosophy of logic.

Argumentation in Complex Communication
  • Managing Disagreement in a Polylogue
  • Marcin Lewiński, Mark Aakhus
  • Published online:
    22 February 2023
    Print publication:
    22 December 2022
  • A pervasive aspect of human communication and sociality is argumentation: the practice of making and criticizing reasons in the context of doubt and disagreement. Argumentation underpins and shapes the decision-making, problem-solving, and conflict management which are fundamental to human relationships. However, argumentation is predominantly conceptualized as two parties arguing pro and con positions with each other in one place. This dyadic bias undermines the capacity to engage argumentation in complex communication in contemporary, digital society. This book offers an ambitious alternative course of inquiry for the analysis, evaluation, and design of argumentation as polylogue: various players arguing over many positions across multiple places. Taking up key aspects of the twentieth-century revival of argumentation as a communicative, situated practice, the polylogue framework engages a wider range of discourses, messages, interactions, technologies, and institutions necessary for adequately engaging the contemporary entanglement of argumentation and complex communication in human activities.

Modern Mathematical Logic
  • Joseph Mileti
  • Published online:
    08 December 2022
    Print publication:
    22 September 2022
  • This textbook gives a complete and modern introduction to mathematical logic. The author uses contemporary notation, conventions, and perspectives throughout, and emphasizes interactions with the rest of mathematics. In addition to covering the basic concepts of mathematical logic and the fundamental material on completeness, compactness, and incompleteness, it devotes significant space to thorough introductions to the pillars of the modern subject: model theory, set theory, and computability. Requiring only a modest background of undergraduate mathematics, the text can be readily adapted for a variety of one- or two-semester courses at the upper-undergraduate or beginning-graduate level. Numerous examples reinforce the key ideas and illustrate their applications, and a wealth of classroom-tested exercises serve to consolidate readers' understanding. Comprehensive and engaging, this book offers a fresh approach to this enduringly fascinating and important subject.

Paradoxes and Inconsistent Mathematics
  • Zach Weber
  • Published online:
    08 October 2021
    Print publication:
    21 October 2021
  • Logical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses “dialetheic paraconsistency” – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.

The Semantic Conception of Logic
  • Essays on Consequence, Invariance, and Meaning
  • Edited by Gil Sagi, Jack Woods
  • Published online:
    27 August 2021
    Print publication:
    09 September 2021
  • This collection of new essays presents cutting-edge research on the semantic conception of logic, the invariance criteria of logicality, grammaticality, and logical truth. Contributors explore the history of the semantic tradition, starting with Tarski, and its historical applications, while central criticisms of the tradition, and especially the use of invariance criteria to explain logicality, are revisited by the original participants in that debate. Other essays discuss more recent criticism of the approach, and researchers from mathematics and linguistics weigh in on the role of the semantic tradition in their disciplines. This book will be invaluable to philosophers and logicians alike.

Lotteries, Knowledge, and Rational Belief
  • Essays on the Lottery Paradox
  • Edited by Igor Douven
  • Published online:
    29 January 2021
    Print publication:
    04 February 2021
  • We talk and think about our beliefs both in a categorical (yes/no) and in a graded way. How do the two kinds of belief hang together? The most straightforward answer is that we believe something categorically if we believe it to a high enough degree. But this seemingly obvious, near-platitudinous claim is known to give rise to a paradox commonly known as the 'lottery paradox' – at least when it is coupled with some further seeming near-platitudes about belief. How to resolve that paradox has been a matter of intense philosophical debate for over fifty years. This volume offers a collection of newly commissioned essays on the subject, all of which provide compelling reasons for rethinking many of the fundamentals of the debate.

Properties and Propositions
  • The Metaphysics of Higher-Order Logic
  • Robert Trueman
  • Published online:
    17 December 2020
    Print publication:
    07 January 2021
  • This book articulates and defends Fregean realism, a theory of properties based on Frege's insight that properties are not objects, but rather the satisfaction conditions of predicates. Robert Trueman argues that this approach is the key not only to dissolving a host of longstanding metaphysical puzzles, such as Bradley's Regress and the Problem of Universals, but also to understanding the relationship between states of affairs, propositions, and the truth conditions of sentences. Fregean realism, Trueman suggests, ultimately leads to a version of the identity theory of truth, the theory that true propositions are identical to obtaining states of affairs. In other words, the identity theory collapses the gap between mind and world. This book will be of interest to anyone working in logic, metaphysics, the philosophy of language or the philosophy of mind.

The Dialogical Roots of Deduction
  • Historical, Cognitive, and Philosophical Perspectives on Reasoning
  • Catarina Dutilh Novaes
  • Published online:
    10 December 2020
    Print publication:
    17 December 2020
  • This comprehensive account of the concept and practices of deduction is the first to bring together perspectives from philosophy, history, psychology and cognitive science, and mathematical practice. Catarina Dutilh Novaes draws on all of these perspectives to argue for an overarching conceptualization of deduction as a dialogical practice: deduction has dialogical roots, and these dialogical roots are still largely present both in theories and in practices of deduction. Dutilh Novaes' account also highlights the deeply human and in fact social nature of deduction, as embedded in actual human practices; as such, it presents a highly innovative account of deduction. The book will be of interest to a wide range of readers, from advanced students to senior scholars, and from philosophers to mathematicians and cognitive scientists.

Mediality in the Middle Ages
  • Abundance and Lack
  • Christian Kiening
  • Translated by Nicola Barfoot
  • Published by:
    Amsterdam University Press
    Published online:
    20 November 2020
    Print publication:
    31 December 2019
  • In medieval culture, media forms were places of mediated immediacy. They transported a presence of the divine, but also knowledge of its unattainability. This volume investigates the multi-layered and fascinating approaches of medieval authors to the word and writing, the body and materiality, and their experimentation with the possibilities of media before the concept was invented. The book presents, for the first time, a coherent, tightly argued history of medieval mediality, which also casts a new light on modern thinking about the medial.

The Significance of the New Logic
  • Willard Van Orman Quine
  • Edited and translated by Walter Carnielli, Frederique Janssen-Lauret, William Pickering
  • Published online:
    20 October 2020
    Print publication:
    10 May 2018
  • W. V. Quine was one of the most influential figures of twentieth-century American analytic philosophy. Although he wrote predominantly in English, in Brazil in 1942 he gave a series of lectures on logic and its philosophy in Portuguese, subsequently published as the book O Sentido da Nova Lógica. The book has never before been fully translated into English, and this volume is the first to make its content accessible to Anglophone philosophers. Quine would go on to develop revolutionary ideas about semantic holism and ontology, and this book provides a snapshot of his views on logic and language at a pivotal stage of his intellectual development. The volume also includes an essay on logic which Quine also published in Portuguese, together with an extensive historical-philosophical essay by Frederique Janssen-Lauret. The valuable and previously neglected works first translated in this volume will be essential for scholars of twentieth-century philosophy.

An Introduction to Formal Logic
  • 2nd edition
  • Peter Smith
  • Published online:
    10 July 2020
    Print publication:
    25 June 2020
  • Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this very accessible book, extensively revised and rewritten for the second edition, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and develops natural deduction systems for evaluating arguments translated into these languages. His discussion is richly illustrated with worked examples and exercises, and alongside the formal work there is illuminating philosophical commentary. This book will make an ideal text for a first logic course and will provide a firm basis for further work in formal and philosophical logic.

Victorian Poetry and the Poetics of the Literary Periodical
  • Caley Ehnes
  • Published by:
    Edinburgh University Press
    Published online:
    14 December 2019
    Print publication:
    31 October 2018
  • Redrawing the conventional map of Victorian Poetics. Victorian Poetry and the Poetics of the Literary Periodical offers an alternative history of Victorian poetry that asserts the fundamental importance of popular periodical poetry to our understanding of Victorian poetics. Reading the poetry of un-anthologised, unnamed and underappreciated poets alongside that of Tennyson, Barrett Browning and Rossetti, Ehnes argues that the popular poet is not a marginal poet: he, and especially she, occupies the centre of literary culture, producing the poetry consumed by the majority of Victorian readers.

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