Does adherence to the principles of logic commit us to a particular way of viewing the world? Or are there ways of being - ways of behaving in the world, including ways of thinking, feeling, and speaking - that ground the normative constraints that logic imposes? Does the fact that assertions, the traditional elements of logic, are typically made about beings present a problem for metaphysical (or post-metaphysical) prospects of making assertions meaningfully about being? Does thinking about being (as opposed to beings) accordingly require revising or restricting logic's reach - and, if so, how is this possible? Or is there something precious about the very idea of thinking the limits of thinking? Contemporary scholars have become increasing sensitive to how Heidegger, much like Wittgenstein, instructively poses such questions. Heidegger on Logic is a collection of new essays by leading scholars who critically ponder the efficacy of his responses to them.

Things are particulars and their qualities are universals, but do universals have an existence distinct from the particular things describable by those terms? And what must be their nature if they do? This book provides a careful and assured survey of the central issues of debate surrounding universals, in particular those issues that have been a crucial part of the emergence of contemporary analytic ontology. The book begins with a taxonomy of extreme nominalist, moderate nominalist, and realist positions on properties, and outlines the way each handles the phenomena of predication, resemblance, and abstract reference. The debate about properties and philosophical naturalism is also examined. Different forms of extreme nominalism, moderate nominalism, and minimalist realism are critiqued. Later chapters defend a traditional realist view of universals and examine the objections to realism from various infinite regresses, the difficulties in stating identity conditions for properties, and problems with realist accounts of knowledge of abstract objects. In addition, the debate between Platonists and Aristotelians is examined alongside a discussion of the relationship between properties and an adequate theory of existence. The book's final chapter explores the problem of individuating particulars. The book makes accessible a difficult topic without blunting the sophistication of argument required by a more advanced readership.

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 Law of Non-Contradiction -- that no contradiction can be true -- has been a seemingly unassailable dogma since the work of Aristotle, in Book G of the Metaphysics. It is an assumption challenged from a variety of angles in this collection of original papers. Twenty-three of the world's leading experts investigate the "law," considering arguments for and against it and discussing methodological issues that arise whenever we question the legitimacy of logical principles. The result is a balanced inquiry into a venerable principle of logic, one that raises questions at the very center of logic itself.
The aim of this volume is to present a comprehensive debate about the Law of Non-Contradiction, from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the law, and to issues that raise challenges to the law, such as the Liar Paradox, and a "dialetheic" resolution of that paradox. The editors contribute an introduction which surveys the issues and serves to frame the debate, and a useful bibliography offering a guide to further reading.
This volume will be of interest to anyone working on philosophical logic, and to anyone who has ever wondered about the status of logical laws and about how one might proceed to mount arguments for or against them.

The first edition of the Cambridge Companion to Plato (1992), edited by Richard Kraut, shaped scholarly research and guided new students for thirty years. This new edition introduces students to fresh approaches to Platonic dialogues while advancing the next generation of research. Of its seventeen chapters, nine are entirely new, written by a new generation of scholars. Six others have been thoroughly revised and updated by their original authors. The volume covers the full range of Plato's interests, including ethics, political philosophy, epistemology, metaphysics, aesthetics, religion, mathematics, and psychology. Plato's dialogues are approached as unified works and considered within their intellectual context, and the revised introduction suggests a way of reading the dialogues that attends to the differences between them while also tracing their interrelations. The result is a rich and wide-ranging volume which will be valuable for all students and scholars of Plato.

Philosophy in the medieval Latin West before 1200 is often thought to have been dominated by Platonism. The articles in this volume question this view, by cataloguing, describing and investigating the tradition of Aristotelian logic during this period, examining its influence on authors usually placed within the Aristotelian tradition (Eriugena, Anselm, Gilbert of Poitiers), and also looking at some of the characteristics of early medieval Platonism. Abelard, the most brilliant logician of the age, is the main subject of three articles, and the book concludes with two more general discussions about how and why medieval philosophy should be studied.

Is mathematics 'entangled' with its various formalisations? Or are the central concepts of mathematics largely insensitive to formalisation, or 'formalism free'? What is the semantic point of view and how is it implemented in foundational practice? Does a given semantic framework always have an implicit syntax? Inspired by what she calls the 'natural language moves' of Goedel and Tarski, Juliette Kennedy considers what roles the concepts of 'entanglement' and 'formalism freeness' play in a range of logical settings, from computability and set theory to model theory and second order logic, to logicality, developing an entirely original philosophy of mathematics along the way. The treatment is historically, logically and set-theoretically rich, and topics such as naturalism and foundations receive their due, but now with a new twist.

In this exciting new collection, a distinguished international group of philosophers contribute new essays on central issues in philosophy of language and logic, in honor of Michael Dummett, one of the most influential philosophers of the late twentieth century. The essays are focused on areas particularly associated with Professor Dummett. Five are contributions to the philosophy of language, addressing in particular the nature of truth and meaning and the relation between language and thought. Two contributors discuss time, in particular the reality of the past. The last four essays focus on Frege and the philosophy of mathematics. The volume represents some of the best work in contemporary analytical philosophy.

One is often said to be reasoning well when they are reasoning logically. Many attempts to say what logical reasoning is have been proposed, but one commonly proposed system is first-order classical logic. This Element will examine the basics of first-order classical logic and discuss some surrounding philosophical issues. The first half of the Element develops a language for the system, as well as a proof theory and model theory. The authors provide theorems about the system they developed, such as unique readability and the Lindenbaum lemma. They also discuss the meta-theory for the system, and provide several results there, including proving soundness and completeness theorems. The second half of the Element compares first-order classical logic to other systems: classical higher order logic, intuitionistic logic, and several paraconsistent logics which reject the law of ex falso quodlibet.

"Topical Themes in Argumentation Theory" brings together twenty exploratory studies on important subjects of research in contemporary argumentation theory. The essays are based on papers that were presented at the 7th Conference of the International Society for the Study of Argumentation (ISSA) in Amsterdam in June 2010. They give an impression of the nature and the variety of the kind of research that has recently been carried out in the study of argumentation.

The volume starts with three essays that provide stimulating theoretical perspectives on argumentation. Subsequently, some views are explained on the intriguing topics of 'dissensus' and 'deep disagreement'. After a discussion of three different approaches to the treatment of types of argumentation some classical themes from antique argumentation theory are revisited. The new research area of visual argumentation is explored in the next part. The volume concludes with three reports of experimental studies concerning argumentative discourse.

The volume starts with three essays that provide stimulating theoretical perspectives on argumentation. Subsequently, some views are explained on the intriguing topics of 'dissensus' and 'deep disagreement'. After a discussion of three different approaches to the treatment of types of argumentation some classical themes from antique argumentation theory are revisited. The new research area of visual argumentation is explored in the next part. The volume concludes with three reports of experimental studies concerning argumentative discourse.

The volume starts with three essays that provide stimulating theoretical perspectives on argumentation. Subsequently, some views are explained on the intriguing topics of 'dissensus' and 'deep disagreement'. After a discussion of three different approaches to the treatment of types of argumentation some classical themes from antique argumentation theory are revisited. The new research area of visual argumentation is explored in the next part. The volume concludes with three reports of experimental studies concerning argumentative discourse."

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.

This Element takes a deep dive into Goedel's 1931 paper giving the first presentation of the Incompleteness Theorems, opening up completely passages in it that might possibly puzzle the student, such as the mysterious footnote 48a. It considers the main ingredients of Goedel's proof: arithmetization, strong representability, and the Fixed Point Theorem in a layered fashion, returning to their various aspects: semantic, syntactic, computational, philosophical and mathematical, as the topic arises. It samples some of the most important proofs of the Incompleteness Theorems, e.g. due to Kuratowski, Smullyan and Robinson, as well as newer proofs, also of other independent statements, due to H. Friedman, Weiermann and Paris-Harrington. It examines the question whether the incompleteness of e.g. Peano Arithmetic gives immediately the undecidability of the Entscheidungsproblem, as Kripke has recently argued. It considers set-theoretical incompleteness, and finally considers some of the philosophical consequences considered in the literature.

In just the last twenty years there has arisen a strong interest, especially among teachers of logic at the universities, in teaching techniques of applied logical reasoning and critical thinking. Many universities are now stressing these skills at an introductory level, and to meet the need, informal logic has begun to form and grow as a discipline in its own right. Like all subjects, it helps us to understand it if we can situate it in a context of historical development. This collection of essays provides the readings required to understand the development of a subject whose historical origins have been so far little studied. Many of the chapters are written by scholars in philosophy and speech communication who are themselves leading contributors to the subject, and their contemporary views throw light on how these earlier writers have influenced their thinking. This dimension gives an added interest to the essays, and indicates the way informal logic is currently evolving and seeking out its ancient historical origins.

Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, controversial axioms and undecided questions, and philosophical issues raised by technical developments.

This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theory, and its relationship to set theory. Section 3 introduces Local Set Theory (also known as higher-order intuitionistic logic), an important form of type theory based on intuitionistic logic. In Section 4 number of contemporary forms of type theory are described, all of which are based on the so-called 'doctrine of propositions as types'. We conclude with an Appendix in which the semantics for Local Set Theory - based on category theory - is outlined.

The International research Library of Philosophy collects in book form a wide range of important and influential essays in philosophy, drawn predominantly from English-language journals. Each volume in the library deals with a field of enquiry which has received significant attention in philosophy in the last 25 years and is edited by a philosopher noted in that field.

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.

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.

We all reason about what we ought to do, what should be, and what is permissible, but neither Standard Deontic Logic (SDL) nor its more recent variants adequately represent the principles of our deontic reasoning. In this groundbreaking new work, author James Forrester first explores the shortcomings of standard deontic systems, and concludes that we need a new type of deontic logic; in the second part of the book, he presents a new deontic logic and semantics that fit our deontic reasoning better than standard systems. Finally, in a third section, Forrester sketches some original implications of his new deontic logic for practical reasoning. This book will be of interest to all philosophers, especially those with an interest in questions of moral and practical reasoning.

This work represents an attempt to show that standard systems of deontic logic (taken as attempts to codify normal deontic reasoning) run into a number of difficulties. It also presents a new system of deontic logic and argues that it is free from the shortcomings of standard systems.

In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical - as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist (as opposed to actualist) approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends her approach against a number of possible objections, and she shows how a notion of logical possibility that is useful in formulating Potentialist set theory connects in important ways with philosophy of language, metametaphysics and philosophy of science. Her book will appeal to readers with interests in the philosophy of set theory, modal logic, and the role of mathematics in the sciences.

A new direction in philosophy
Between 1920 and 1940 logical empiricism reset the direction of philosophy of science and much of the rest of Anglo-American philosophy. It began as a relatively organized movement centered on the Vienna Circle, and like-minded philosophers elsewhere, especially in Berlin. As Europe drifted into the Nazi era, several important figures, especially Carnap and Neurath, also found common ground in their liberal politics and radical social agenda. Together, the logical empiricists set out to reform traditional philosophy with a new set of doctrines more firmly grounded in logic and science.
Criticism and decline
Because of Nazi persecution, most of the European adherents of logical empiricism moved to the United States in the late 1930s. During the 1940s, many of their most cherished tenets became targets of criticism from outsiders as well as from within their own ranks. Philosophers of science in the late 1950s and 1960s rejected logical empiricism and, starting in the 1970s, presented such alternative programs such as scientific realism with evolutionary epistemology.
A resurgence of interest
During the early 1980s, philosophers and historians of philosophy began to study logical empiricism as an important movement. Unlike their predecessors in the 1960s-for whom the debate over logical empiricism now seems to have been largely motivated by professional politics-these philosopher no longer have to take positions for or against logical empiricism. The result has been a more balanced view of that movement, its achievements, its failures, and its influence.
Hard-to-find core writings now available
This collection makes available aselection of the most influential and representative writings of the logical empiricists, important contemporary criticisms of their doctrines, their responses, as well as the recent reappraisals. Introductions to each volume examine the articles in historical context and provide importantbackground information that is vital to a full understanding of the issues discussed. They outline prevalent trends, identifying leading figures and summarize their positions and reasoning, as well as those of opposing thinkers.

A new direction in philosophy
Between 1920 and 1940 logical empiricism reset the direction of philosophy of science and much of the rest of Anglo-American philosophy. It began as a relatively organized movement centered on the Vienna Circle, and like-minded philosophers elsewhere, especially in Berlin. As Europe drifted into the Nazi era, several important figures, especially Carnap and Neurath, also found common ground in their liberal politics and radical social agenda. Together, the logical empiricists set out to reform traditional philosophy with a new set of doctrines more firmly grounded in logic and science.
Criticism and decline
Because of Nazi persecution, most of the European adherents of logical empiricism moved to the United States in the late 1930s. During the 1940s, many of their most cherished tenets became targets of criticism from outsiders as well as from within their own ranks. Philosophers of science in the late 1950s and 1960s rejected logical empiricism and, starting in the 1970s, presented such alternative programs such as scientific realism with evolutionary epistemology.
A resurgence of interest
During the early 1980s, philosophers and historians of philosophy began to study logical empiricism as an important movement. Unlike their predecessors in the 1960s-for whom the debate over logical empiricism now seems to have been largely motivated by professional politics-these philosopher no longer have to take positions for or against logical empiricism. The result has been a more balanced view of that movement, its achievements, its failures, and its influence.
Hard-to-find core writings now available
This collection makes available aselection of the most influential and representative writings of the logical empiricists, important contemporary criticisms of their doctrines, their responses, as well as the recent reappraisals. Introductions to each volume examine the articles in historical context and provide importantbackground information that is vital to a full understanding of the issues discussed. They outline prevalent trends, identifying leading figures and summarize their positions and reasoning, as well as those of opposing thinkers.

A new direction in philosophy
Between 1920 and 1940 logical empiricism reset the direction of philosophy of science and much of the rest of Anglo-American philosophy. It began as a relatively organized movement centered on the Vienna Circle, and like-minded philosophers elsewhere, especially in Berlin. As Europe drifted into the Nazi era, several important figures, especially Carnap and Neurath, also found common ground in their liberal politics and radical social agenda. Together, the logical empiricists set out to reform traditional philosophy with a new set of doctrines more firmly grounded in logic and science.
Criticism and decline
Because of Nazi persecution, most of the European adherents of logical empiricism moved to the United States in the late 1930s. During the 1940s, many of their most cherished tenets became targets of criticism from outsiders as well as from within their own ranks. Philosophers of science in the late 1950s and 1960s rejected logical empiricism and, starting in the 1970s, presented such alternative programs such as scientific realism with evolutionary epistemology.
A resurgence of interest
During the early 1980s, philosophers and historians of philosophy began to study logical empiricism as an important movement. Unlike their predecessors in the 1960s-for whom the debate over logical empiricism now seems to have been largely motivated by professional politics-these philosopher no longer have to take positions for or against logical empiricism. The result has been a more balanced view of that movement, its achievements, its failures, and its influence.
Hard-to-find core writings now available
This collection makes available aselection of the most influential and representative writings of the logical empiricists, important contemporary criticisms of their doctrines, their responses, as well as the recent reappraisals. Introductions to each volume examine the articles in historical context and provide importantbackground information that is vital to a full understanding of the issues discussed. They outline prevalent trends, identifying leading figures and summarize their positions and reasoning, as well as those of opposing thinkers.

First published in 1990 The Philosopher's Habitat introduces the subject by investigating a variety of the problems which are currently engaging philosophers, and which can be made intelligible to an absolute beginner. Rather than introducing philosophy by examining, in the traditional way, the writings of great philosophers, the author has inverted this procedure. The idea is that the reader will become absorbed in these dramas, will thereby come to appreciate the ways in which the stage was set by the great writers of the past, and will feel the urge to participate. Questions at the end of each chapter encourage the reader to push beyond the text. This book is a must read for students of philosophy.