In 1911, Bertrand Russell began a historically formative interchange about the nature of logic and cognition with his student, Ludwig Wittgenstein. In 1913, Russell set to work on a manuscript, the "Theory of Knowledge", designed to move from the analysis of perception to judgement and on to knowledge of the world. After Wittgenstein interrupted Russell's daily writing with a series of objections to his doctrine of judgement and conception of logic, Russell abandoned his project in despair, leaving it unfinished. His subsequent work can be understood largely as an attempt to assimilate and respond to Wittgenstein's challenge in 1913. "Russell and Wittgenstein on the Nature of Judgement" is the first book-length treatment of Russell's decisive 1913 exchanges with Wittgenstein. Rosalind Carey incorporates little-known notes and diagrams into a new analysis of the problems Russell was facing. She also evaluates the numerous interpretations of Russell's positions and Wittgenstein's objections to them. The result is a new perspective on both these great thinkers, at a crucial point in the development of twentieth-century philosophy.

This book focuses on logic and logical language. It examines different types of words, terms and propositions in detail. While discussing the nature of propositions, it illustrates the procedures used to determine the truth and falsity of a proposition, and the validity and invalidity of an argument. In addition, the book provides a clear exposition of the pure and mixed form of syllogism with suitable examples. The book encompasses sentential logic, predicate logic, symbolic logic, induction and set theory topics. The book is designed to serve all those involved in teaching and learning courses on logic. It offers a valuable resource for students and researchers in philosophy, mathematics and computer science disciplines. Given its scope, it is an essential read for everyone interested in logic, language, formulation of the hypotheses for the scientific enquiries and research studies, and judging valid and invalid arguments in the natural language discourse.

ways of doing it, but it is wrong to project it far into the past: it did not exist at the turn of the century and only became clearly apparent after the Second World War. I recently taught at an American university on the his tory of philosophy from Balzano to Husserl. The course title had to come from a fixed pool and gave trouble. Was it philosophical logic, the nine teenth century, or phenomenology? A logic title would connote over this period Frege, Russell, Carnap, perhaps a mention of Boole: not continental enough. The nineteenth century? The century of Kant's successors: Fichte, Hegel, Schopenhauer, Feuer bach, Marx, Nietzsche? What have they to do with Balzano, Lotze, Brentano, Meinong, Husserl and Twardowski? Even tually 'Phenomenology' was chosen, misdescribing more than half of the course. That illustrates the problems one faces in trying to work against the picture of the period which is ingrained in minds and syllabuses. This book arises from my efforts to combat that picture. I backed into writing about the history of recent philosophy rather than setting out to do so. The beginning was chance. In Manchester in the early seventies, at a time when most English philosophy departments breathed re cycled Oxford air, the intellectual atmosphere derived from Cambridge and Warsaw, spiced with a breath of Freiburg and Paris."

Logical consequence is the relation that obtains between premises and conclusion(s) in a valid argument. Orthodoxy has it that valid arguments are necessarily truth-preserving, but this platitude only raises a number of further questions, such as: how does the truth of premises guarantee the truth of a conclusion, and what constraints does validity impose on rational belief? This volume presents thirteen essays by some of the most important scholars in the field of philosophical logic. The essays offer ground-breaking new insights into the nature of logical consequence; the relation between logic and inference; how the semantics and pragmatics of natural language bear on logic; the relativity of logic; and the structural properties of the consequence relation.

This book attempts to explicate and expand upon Frank Ramsey's notion of the realistic spirit. In so doing, it provides a systematic reading of his work, and demonstrates the extent of Ramsey's genius as evinced by both his responses to the Tractatus Logico-Philosophicus, and the impact he had on Wittgenstein's later philosophical insights.

Necessary Beings is concerned with two central areas of metaphysics: modality-the theory of necessity, possibility, and other related notions; and ontology-the general study of what kinds of entities there are. Bob Hale's overarching purpose is to develop and defend two quite general theses about what is required for the existence of entities of various kinds: that questions about what kinds of things there are cannot be properly understood or adequately answered without recourse to considerations about possibility and necessity, and that, conversely, questions about the nature and basis of necessity and possibility cannot be satisfactorily tackled without drawing on what might be called the methodology of ontology. Taken together, these two theses claim that ontology and modality are mutually dependent upon one another, neither more fundamental than the other. Hale defends a broadly Fregean approach to metaphysics, according to which ontological distinctions among different kinds of things (objects, properties, and relations) are to be drawn on the basis of prior distinctions between different logical types of expression. The claim that facts about what kinds of things exist depend upon facts about what is possible makes little sense unless one accepts that at least some modal facts are fundamental, and not reducible to facts of some other, non-modal, sort. He argues that facts about what is absolutely necessary or possible have this character, and that they have their source or basis, not in meanings or concepts nor in facts about alternative 'worlds', but in the natures or essences of things.

This book examines the nature, sources, and implications of fallacies in philosophical reasoning. In doing so, it illustrates and evaluates various historical instances of this phenomenon. There is widespread interest in the practice and products of philosophizing, yet the important issue of fallacious reasoning in these matters has been effectively untouched. Nicholas Rescher fills this gap by presenting a systematic account of the principal ways in which philosophizing can go astray.

The present volume of the "Handbook of the History of Logic" is designed to establish 19th century Britain as a substantial force in logic, developing new ideas, some of which would be overtaken by, and other that would anticipate, the century's later capitulation to the mathematization of logic.
"British Logic in the Nineteenth Century" is indispensable reading and a definitive research resource for anyone with an interest in the history of logic.
- Detailed and comprehensive chapters covering the entire range of modal logic
- Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic

Our conception of logical space is the set of distinctions we use to navigate the world. In The Construction of Logical Space Agustin Rayo defends the idea that one's conception of logical space is shaped by one's acceptance or rejection of 'just is'-statements: statements like 'to be composed of water just is to be composed of H2O', or 'for the number of the dinosaurs to be zero just is for there to be no dinosaurs'. The resulting picture is used to articulate a conception of metaphysical possibility that does not depend on a reduction of the modal to the non-modal, and to develop a trivialist philosophy of mathematics, according to which the truths of pure mathematics have trivial truth-conditions.

Wittgenstein's Tractatus Logico-Philosophicus, first published in 1921, has had a profound influence on modern philosophic thought. Prototractatus is a facsimile reproduction of an early version of Tractatus, only discovered in 1965. The original text has a parallel English translation and the text is edited to indicate all relevant deviations from the final version.

This book features more than 20 papers that celebrate the work of Hajnal Andreka and Istvan Nemeti. It illustrates an interaction between developing and applying mathematical logic. The papers offer new results as well as surveys in areas influenced by these two outstanding researchers. They also provide details on the after-life of some of their initiatives. Computer science connects the papers in the first part of the book. The second part concentrates on algebraic logic. It features a range of papers that hint at the intricate many-way connections between logic, algebra, and geometry. The third part explores novel applications of logic in relativity theory, philosophy of logic, philosophy of physics and spacetime, and methodology of science. They include such exciting subjects as time travelling in emergent spacetime. The short autobiographies of Hajnal Andreka and Istvan Nemeti at the end of the book describe an adventurous journey from electric engineering and Maxwell's equations to a complex system of computer programs for designing Hungary's electric power system, to exploring and contributing deep results to Tarskian algebraic logic as the deepest core theory of such questions, then on to applications of the results in such exciting new areas as relativity theory in order to rejuvenate logic itself.

Individual objects have potentials: paper has the potential to burn, an acorn has the potential to turn into a tree, some people have the potential to run a mile in less than four minutes. Barbara Vetter provides a systematic investigation into the metaphysics of such potentials, and an account of metaphysical modality based on them. In contemporary philosophy, potentials have been recognized mostly in the form of so-called dispositions: solubility, fragility, and so on. Vetter takes dispositions as her starting point, but argues for and develops a more comprehensive conception of potentiality. She shows how, with this more comprehensive conception, an account of metaphysical modality can be given that meets three crucial requirements: (1) Extensional correctness: providing the right truth-values for statements of possibility and necessity; (2) formal adequacy: providing the right logic for metaphysical modality; and (3) semantic utility: providing a semantics that links ordinary modal language to the metaphysics of modality. The resulting view of modality is a version of dispositionalism about modality: it takes modality to be a matter of the dispositions of individual objects (and, crucially, not of possible worlds). This approach has a long philosophical tradition going back to Aristotle, but has been largely neglected in contemporary philosophy. In recent years, it has become a live option again due to the rise of anti-Humean, powers-based metaphysics. The aim of Potentiality is to develop the dispositionalist view in a way that takes account of contemporary developments in metaphysics, logic, and semantics.

Gottlob Frege's Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, was intended to be his magnum opus, the book in which he would finally establish his logicist philosophy of arithmetic. But because of the disaster of Russell's Paradox, which undermined Frege's proofs, the more mathematical parts of the book have rarely been read. Richard G. Heck, Jr., aims to change that, and establish it as a neglected masterpiece that must be placed at the center of Frege's philosophy. Part I of Reading Frege's Grundgesetze develops an interpretation of the philosophy of logic that informs Grundgesetze, paying especially close attention to the difficult sections of Frege's book in which he discusses his notorious 'Basic Law V' and attempts to secure its status as a law of logic. Part II examines the mathematical basis of Frege's logicism, explaining and exploring Frege's formal arguments. Heck argues that Frege himself knew that his proofs could be reconstructed so as to avoid Russell's Paradox, and presents Frege's arguments in a way that makes them available to a wide audience. He shows, by example, that careful attention to the structure of Frege's arguments, to what he proved, to how he proved it, and even to what he tried to prove but could not, has much to teach us about Frege's philosophy.

Deflationist accounts of truth are widely held in contemporary philosophy: they seek to show that truth is a dispensable concept with no metaphysical depth. However, logical paradoxes present problems for deflationists that their work has struggled to overcome. In this volume of fourteen original essays, a distinguished team of contributors explore the extent to which, if at all, deflationism can accommodate paradox. The volume will be of interest to philosophers of logic, philosophers of language, and anyone working on truth.
Contributors include Bradley Armour-Garb, Jody Azzouni, JC Beall, Hartry Field, Christopher Gauker, Michael Glanzberg, Dorothy Grover, Anil Gupta, Volker Halbach, Leon Horsten, Paul Horwich, Graham Priest, Greg Restall, and Alan Weir

It is the aim of the present study to introduce the reader to the ways of thinking of those contemporary philosophers who apply the tools of symbolic logic to classical philosophical problems. Unlike the "conti nental" reader for whom this work was originally written, the English speaking reader will be more familiar with most of the philosophers dis cussed in this book, and he will in general not be tempted to dismiss them indiscriminately as "positivists" and "nominalists." But the English version of this study may help to redress the balance in another respect. In view of the present emphasis on ordinary language and the wide spread tendency to leave the mathematical logicians alone with their technicalities, it seems not without merit to revive the interest in formal ontology and the construction of formal systems. A closer look at the historical account which will be given here, may convince the reader that there are several points in the historical develop ment whose consequences have not yet been fully assessed: I mention, e. g., the shift from the traditional three-level semantics of sense and deno tation to the contemporary two-level semantics of representation; the relation of extensional structure and intensional content in the extensional systems of Wittgenstein and Carnap; the confusing changes in labelling the different kinds of analytic and apriori true sentences; etc. Among the philosophically interesting tools of symbolic logic Lesniewski's calculus of names deserves special attention."

A classic of how to think clearly and critically and ahead of its time in anticipating the threats to democracy by poor argument and shoddy reasoning Engaging, clear and witty, it is a brilliant example of how philosophy can connect with the concerns with everyone and requires no knowledge of the subject Susan Stebbing was the first woman in the UK to be appointed a professor of philosophy, in 1933 A new foreword by Nigel Warburton and introduction by Peter West help to set Stebbing book in helpful context

While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the rise of experimental mathematics on the one hand and computerized formal proofs on the other hand. The main theses of Rigor and Structure are that the features of mathematical practice that a large group of philosophers of mathematics, the structuralists, have attributed to the peculiar nature of mathematical objects are better explained in a different way, as artefacts of the manner in which the ancient ideal of rigor is realized in modern mathematics. Notably, the mathematician must be very careful in deriving new results from the previous literature, but may remain largely indifferent to just how the results in the previous literature were obtained from first principles. Indeed, the working mathematician may remain largely indifferent to just what the first principles are supposed to be, and whether they are set-theoretic or category-theoretic or something else. Along the way to these conclusions, a great many historical developments in mathematics, philosophy, and logic are surveyed. Yet very little in the way of background knowledge on the part of the reader is presupposed.

Composition is the relation between a whole and its parts-the parts are said to compose the whole; the whole is composed of the parts. But is a whole anything distinct from its parts taken collectively? It is often said that 'a whole is nothing over and above its parts'; but what might we mean by that? Could it be that a whole just is its parts? This collection of essays is the first of its kind to focus on the relationship between composition and identity. Twelve original articles-written by internationally renowned scholars and rising stars in the field-argue for and against the controversial doctrine that composition is identity. An editor's introduction sets out the formal and philosophical groundwork to bring readers to the forefront of the debate.

Axiomatic Formal Ontology is a fairly comprehensive systematic treatise on general metaphysics. The axiomatic method is applied throughout the book. Its main theme is the construction of a general non-set-theoretical theory of intensional entities. Other important matters discussed are the metaphysics of modality, the nature of actual existence, mereology and the taxonomy of entities.

Roy T Cook examines the Yablo paradox-a paradoxical, infinite sequence of sentences, each of which entails the falsity of all others later than it in the sequence-with special attention paid to the idea that this paradox provides us with a semantic paradox that involves no circularity. The three main chapters of the book focus, respectively, on three questions that can be (and have been) asked about the Yablo construction. First we have the Characterization Problem, which asks what patterns of sentential reference (circular or not) generate semantic paradoxes. Addressing this problem requires an interesting and fruitful detour through the theory of directed graphs, allowing us to draw interesting connections between philosophical problems and purely mathematical ones. Next is the Circularity Question, which addresses whether or not the Yablo paradox is genuinely non-circular. Answering this question is complicated: although the original formulation of the Yablo paradox is circular, it turns out that it is not circular in any sense that can bear the blame for the paradox. Further, formulations of the paradox using infinitary conjunction provide genuinely non-circular constructions. Finally, Cook turns his attention to the Generalizability Question: can the Yabloesque pattern be used to generate genuinely non-circular variants of other paradoxes, such as epistemic and set-theoretic paradoxes? Cook argues that although there are general constructions-unwindings-that transform circular constructions into Yablo-like sequences, it turns out that these sorts of constructions are not 'well-behaved' when transferred from semantic puzzles to puzzles of other sorts. He concludes with a short discussion of the connections between the Yablo paradox and the Curry paradox.

Descartes and the First Cartesians adopts the perspective that we should not approach Rene Descartes as a solitary thinker, but as a philosopher who constructs a dialogue with his contemporaries, so as to engage them and elements of his society into his philosophical enterprise. Roger Ariew argues that an important aspect of this engagement concerns the endeavor to establish Cartesian philosophy in the Schools, that is, to replace Aristotle as the authority there. Descartes wrote the Principles of Philosophy as something of a rival to Scholastic textbooks, initially conceiving the project as a comparison of his philosophy and that of the Scholastics. Still, what Descartes produced was inadequate for the task. The topics of Scholastic textbooks ranged more broadly than those of Descartes; they usually had quadripartite arrangements mirroring the structure of the collegiate curriculum, divided as they typically were into logic, ethics, physics, and metaphysics. But Descartes produced at best only what could be called a general metaphysics and a partial physics. These deficiencies in the Cartesian program and in its aspiration to replace Scholastic philosophy in the schools caused the Cartesians to rush in to fill the voids. The attempt to publish a Cartesian textbook that would mirror what was taught in the schools began in the 1650s with Jacques Du Roure and culminated in the 1690s with Pierre-Sylvain Regis and Antoine Le Grand. Ariew's original account thus considers the reception of Descartes' work, and establishes the significance of his philosophical enterprise in relation to the textbooks of the first Cartesians and in contrast with late Scholastic textbooks.

For nearly four centuries, when logic was the heart of what we now call the 'undergraduate curriculum', Peter of Spain's Summaries of Logic (c. 1230) was the basis for teaching that subject. Because Peter's students were teenagers, he wrote simply and organized his book carefully. Since no book about logic was read by more people until the twentieth century, the Summaries has extensively and profoundly influenced the distinctly Western way of speaking formally and writing formal prose by constructing well-formed sentences, making valid arguments, and refuting and defending arguments in debate. Some books, like the Authorized Version of the English Bible and the collected plays of Shakespeare, have been more influential in the Anglophone world than Peter's Summaries-but not many. This new English translation, based on an update of the Latin text of Lambertus De Rijk, comes with an extensive introduction that deals with authorship, dating, and the place of the Summaries in the development of logic, before providing a chapter-by-chapter analysis of Peter's book, followed by an analysis of his system from the point of view of modern logic. The Latin text is presented on facing pages with the English translation, accompanied by notes, and the book includes a full bibliography.