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Logic: The Basics
Logic: The Basics is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic, such as: · mathematical preliminaries · propositional logic · quantified logic (first monadic, then polyadic) · English and standard ‘symbolic translations’ · tableau procedures. Alongside comprehensive coverage of the standard topics, this thoroughly revised second edition also introduces several philosophically important nonclassical logics, free logics, and modal logics, and gives the reader an idea of how they can take their knowledge further. With its wealth of exercises (solutions available in the encyclopedic online supplement), Logic: The Basics is a useful textbook for courses ranging from the introductory level to the early graduate level, and also as a reference for students and researchers in philosophical logic.
Relevance Logic
Relevance logics are a misunderstood lot. Despite being the subject of intense study for nearly a century, they remain maligned as too complicated, too abstruse, or too silly to be worth learning much about. This Element aims to dispel these misunderstandings. By focusing on the weak relevant logic B, the discussion provides an entry point into a rich and diverse family of logics. Also, it contains the first-ever textbook treatment of quantification in relevance logics, as well as an overview of the cutting edge on variable sharing results and a guide to further topics in the field.
The Philosopher's Toolkit
A new edition of the bestselling guide to the study of philosophy: the ideal intellectual ‘toolkit’ for sharpening analytical skills and building philosophical acuity Whether used as a guide to basic principles or a resource for key concepts and methods, The Philosopher's Toolkit equips readers with all the intellectual ‘tools’ necessary for engaging closely with philosophical argument and developing fluency in the methods and language of philosophical inquiry. Featuring accessible explanations, practical examples, and expert guidance, this text empowers readers to understand traditional philosophical thinking and to engage with new ideas. Focuses on the practical methods and concept...
Algebraic Perspectives on Substructural Logics
This volume presents the state of the art in the algebraic investigation into substructural logics. It features papers from the workshop AsubL (Algebra & Substructural Logics - Take 6). Held at the University of Cagliari, Italy, this event is part of the framework of the Horizon 2020 Project SYSMICS: SYntax meets Semantics: Methods, Interactions, and Connections in Substructural logics. Substructural logics are usually formulated as Gentzen systems that lack one or more structural rules. They have been intensively studied over the past two decades by logicians of various persuasions. These researchers include mathematicians, philosophers, linguists, and computer scientists. Substructural log...
Analytic Christology and the Theological Interpretation of the New Testament
This study draws upon the resources of both contemporary analytic theology and the theological interpretation of the New Testament in order to investigate a set of important issues in Christology. It is the first work in analytic Christology to draw upon both recent scholarship in biblical studies and recent contributions to analytic philosophy and theology. Thomas H. McCall explores the themes of union with Christ and the faith of Christ as these are developed by the "apocalyptic" and "New Perspective" interpreters of Pauline theology. The volume offers a careful analysis of recent dogmatic proposals about the identity of Christ and the doctrine of election, and provides an examination of debates over the subordination of the Son in Hebrews. It also probes the relationship of the incarnate Son to his Father in Johannine theology. McCall presents an exegetically-grounded theological engagement with recent work on the place of logic in the doctrine of the incarnation.
Propositional Quantifiers
Propositional quantifiers are quantifiers binding proposition letters, understood as variables. This Element introduces propositional quantifiers and explains why they are especially interesting in the context of propositional modal logics. It surveys the main results on propositionally quantified modal logics which have been obtained in the literature, presents a number of open questions, and provides examples of applications of such logics to philosophical problems.
Logic and Information
This Element looks at two projects that relate logic and information: the project of using logic to integrate, manipulate and interpret information and the proect of using the notion of information to provide interpretations of logical systems. The Element defines 'information' in a manner that includes misinformation and disinformation and uses this general concept of information to provide an interpretation of various paraconsistent and relevant logics. It also integrates these logics into contemporary theories of informational updating, probability theory and (rather informally) some ideas from the theory of the complexity of proofs. The Element assumes some prior knowledge of modal logic and its possible world semantics, but all the other necessary background is provided.
Paradox and Contradiction in Theology
This book explores and expounds upon questions of paradox and contradiction in theology with an emphasis on recent contributions from analytic philosophical theology. It addresses questions such as: What is the place of paradox in theology? Where might different systems of logic (e.g. paraconsistent ones) find a place in theological discourse (e.g. Christology)? What are proper responses to the presence of contradiction(s) in one’s theological theories? Are appeals to analogical language enough to make sense of paradox? Bringing together an impressive line-up of theologians and philosophers, the volume offers a range of fresh perspectives on a central topic. It is valuable reading for scholars of theology and philosophy of religion.
Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs
This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart’s work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart. Alasdair Urquhart has made extremely important contributions to a variety of fields in logic. He produced some of the earliest work on the semantics of relevant logic. He provided the undecidability of the logics R (of relevant implication) and E (of relevant en...
