Greg Restall

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 logicCovers proofs, models, modal logics, meta-theory, two-dimensional logics, quantification, and many other topicsProvides tools and techniques of particular interest to philosophers and philosophical logiciansFeatures short summaries of key concepts and skills at the end of each chapterOffers 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

This Element is an introduction to recent work proofs and models in philosophical logic, with a focus on the semantic paradoxes the sorites paradox. It introduces and motivates different proof systems and different kinds of models for a range of logics, including classical logic, intuitionistic logic, a range of three-valued and four-valued logics, and substructural logics. It also compares and contrasts the different approaches to substructural treatments of the paradox, showing how the structural rules of contraction, cut and identity feature in paradoxical derivations. It then introduces model theoretic treatments of the paradoxes, including a simple fixed-point model construction which generates three-valued models for theories of truth, which can provide models for a range of different non-classical logics. The Element closes with a discussion of the relationship between proofs and models, arguing that both have their place in the philosophers' and logicians' toolkits.

The methods of logic are essential to an understanding of philosophy and are crucial in the study of mathematics, computing, linguistics and many other subjects. Introducing the major concepts and techniques involved in the study of logic, this authoritative book explores both formal and philosophical logic, and the ways in which we can achieve good reasoning. Individual chapters include:* Propositions and Arguments* Truth Tables* Trees* Conditionality* Natural Deduction* Predicates, Names and Quantifiers* Definite Descriptions.This exceptionally clear introduction to the subject is ideally suited to students taking introductory courses in logic.

The methods of logic are essential to an understanding of philosophy and are crucial in the study of mathematics, computing, linguistics and many other subjects. Introducing the major concepts and techniques involved in the study of logic, this authoritative book explores both formal and philosophical logic, and the ways in which we can achieve good reasoning. Individual chapters include:* Propositions and Arguments* Truth Tables* Trees* Conditionality* Natural Deduction* Predicates, Names and Quantifiers* Definite Descriptions.This exceptionally clear introduction to the subject is ideally suited to students taking introductory courses in logic.

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them. In particular, they argue that broadly classical, intuitionistic, and relevant accounts of deductive logic are genuine logical consequence relations; we should not search for one true logic, since there are many. Their conclusions have profound implications for many linguists as well as for philosophers.

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many.

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered:* Proof Theory* Propositional Structures* Frames* Decidability* CodaBoth students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered:* Proof Theory* Propositional Structures* Frames* Decidability* CodaBoth students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.