An accessible introduction to philosophical logic, suitable for undergraduate courses and above. Rigorous yet accessible, Logical Methods introduces logical tools used in philosophy—including proofs, models, modal logics, meta-theory, two-dimensional logics, and quantification—for philosophy students at the undergraduate level and above. The approach developed by Greg Restall and Shawn Standefer is distinct from other texts because it presents proof construction on equal footing with model building and emphasizes connections to other areas of philosophy as the tools are developed. Throughout, the material draws on a broad range of examples to show readers how to develop and master tools of proofs and models for propositional, modal, and predicate logic; to construct and analyze arguments and to find their structure; to build counterexamples; to understand the broad sweep of formal logic’s development in the twentieth and twenty-first centuries; and to grasp key concepts used again and again in philosophy. This text is essential to philosophy curricula, regardless of specialization, and will also find wide use in mathematics and computer science programs. Features: An accessible introduction to proof theory for readers with no background in logic Covers proofs, models, modal logics, meta-theory, two-dimensional logics, quantification, and many other topics Provides tools and techniques of particular interest to philosophers and philosophical logicians Features short summaries of key concepts and skills at the end of each chapter Offers chapter-by-chapter exercises in two categories: basic, designed to reinforce important ideas; and challenge, designed to push students’ understanding and developing skills in new directions

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.

This report from the second Strategic Highway Research Program (SHRP 2), which is administered by the Transportation Research Board of the National Academies, catalogs highway design treatments that can be used to reduce nonrecurrent congestion and improve the reliability of urban and rural freeways.

After visiting hundreds of museums across Alberta, Lianne McTavish chronicles some of the most challenging and unexpected sites where the idea of the museum is being reshaped. The concept of the visit as a “voluntary detour” encapsulates the way visitors travel along backroads to find small-town and rural museums, as well as the agreement to turn away from standard museum scripts when they arrive. Addressing themes of place, land, colonization, rurality, heritage, childhood, and play, McTavish reveals the museum visitor as multifaceted, with locals and tourists often interpreting museums very differently. Case studies include the World Famous Gopher Hole Museum, Fort Chipewyan Bicentennial Museum, Blackfoot Crossing Historical Park, and the Museum of Fear and Wonder. A key chapter analyzing sites devoted to resource extraction explores how these places promote settler colonial understandings of land use. By contrast, Indigenous museums and cultural centres defy colonial messages in displays that adapt and refuse conventional museum formats. Honouring local, rural, and Indigenous knowledge, Voluntary Detours enriches critical accounts of the past, present, and future of museums.

This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.

Taking linguistics students beyond the classical forms often taught in introductory courses, Language and Logics offers a comprehensive introduction to the wide variety of useful non-classical logics that are commonly used in research. Including a brief review of classical logic and its major assumptions, this textbook provides a guided tour of modal, many valued and substructural logics. The textbook starts from simple and intuitive concepts, clearly explaining the logics of language for linguistics students who have little previous knowledge of logic or mathematics. Issues are presented and discussed clearly before going on to introduce symbolic notation.While not avoiding technical detail, the book focuses throughout on helping students develop an intuitive understanding of the field, with particular attention to conceptual questions and to the tailoring of logical systems to thinking about different applications in linguistics and beyond. This is an ideal introductory volume for advanced undergraduates and beginning postgraduate students in linguistics, and for those specializing in semantics.