The mathematical proof is the most important form of justification in mathematics. It is not, however, the only kind of justification for mathematical propositions. The existence of other forms, some of very significant strength, places a question mark over the prominence given to proof within mathematics. This collection of essays, by leading figures working within the philosophy of mathematics, is a response to the challenge of understanding the nature and role of the proof.

From academic writing to personal and public discourse, the need for good arguments and better ways of arguing is greater than ever before. This timely fifth edition of A Rulebook for Arguments sharpens an already-classic text, adding updated examples and a new chapter on public debates that provides rules for the etiquette and ethics of sound public dialogue as well as clear and sound thinking in general.

The introduction of Greek philosophy into the Muslim world left an indelible mark on Islamic intellectual history. Philosophical discourse became a constant element in even traditionalist Islamic sciences. However, Aristotelian metaphysics gave rise to doctrines about God and the universe that were found highly objectionable by a number of Muslim theologians, among whom the fourteenth-century scholar Ibn Taymiyya stood foremost.

Ibn Taymiyya, one of the greatest and most prolific thinkers in medieval Islam, held Greek logic responsible for the `heretical' metaphysical conclusions reached by Islamic philosophers, theologians, mystics, and others. He therefore set out to refute philosophical logic, a task which culminated in one of the most devastating attacks ever levelled against the logical system upheld by the early Greeks, the later commentators, and their Muslim followers. His argument is grounded in an empirical approach that in many respects prefigures the philosophies of the British empiricists.

Professor Hallaq's translation, with a substantial introduction and extensive notes, makes this important work available to a wider audience for the first time.

First published in 1943, and revised for this 1952 edition, this book was intended for use by students of philosophy and as such traditional and modern developments in logic have been combined in a unified treatment. The author envisaged this volume as filling a gap for a simple, introductory text on formal logic, written from a modern point of view, unencumbered by traditional doctrine. This title provides a thorough introduction and grounding in the philosophy of logic, and was later revised after the author's death to correct a number of logical errors - making this edition the most complete version of the work.

This work investigates problems about mind, meaning and mathematics rooted in preconceptions of language. It deals in particular with problems which are connected with our tendency to be misled by certain prevailing views and preconceptions about language. Philosophical claims made by theorists of meaning are scrutinized and shown to be connected with common views about the nature of certain mathematical notions and methods. Drawing in particular on Wittgenstein's ideas, the author demonstrates a strategy for tracing out and resolving conceptual and philosophical problems. By a critical examination of examples from different areas of philosophy, he shows that many problems arise through the transgression of the limits of the use of technical concepts and formal methods. Many 'prima facie' different kinds of problems are shown to have common roots, and should thus be dealt with and resolved together. Such an approach is usually prevented by the influence of traditional philosophical terminology and classification. The results of this investigation make it clear that the received ways of subdividing the subject matter of philosophy often conceal the roots of the problem.

First published in 1985. Routledge is an imprint of Taylor & Francis, an informa company.

The volume consists of thirteen papers devoted to various problems of the philosophy of logic and mathematics. They can be divided into two groups. The first group contains papers devoted to some general problems of the philosophy of mathematics whereas the second group - papers devoted to the history of logic in Poland and to the work of Polish logicians and math-ematicians in the philosophy of mathematics and logic. Among considered problems are: meaning of reverse mathematics, proof in mathematics, the status of Church's Thesis, phenomenology in the philosophy of mathematics, mathematics vs. theology, the problem of truth, philosophy of logic and mathematics in the interwar Poland.

Fourteen new essays by a distinguished team of authors offer a broad and stimulating re-examination of transcendental arguments. This is the philosophical method of arguing that what is doubted or denied by the opponent must be the case, as a condition for the possibility of experience, language, or thought. The line-up of contributors features leading figures in the field from both sides of the Atlantic; they discuss the nature of transcendental arguments, and consider their role and value. In particular, they consider how successful such arguments are as a response to sceptical problems. The editor's introduction provides historical context and philosophical orientation for the discussions. This is the first major appraisal of transcendental arguments since the 1970s; they have continued to play a significant role in philosophy, and recent developments in epistemology and metaphysics have raised new questions and challenges for them. Transcendental Arguments will be essential reading for anyone interested in this area of philosophy, and the starting-point for future work.

This book is intended as a first introduction to the subject. It deals with questions of truth and meaning, questions which provide a basis for much of what is discussed in philosophy in general. This book should be of interest to students of philosophy.

Marx's Grundrisse is acknowledged as the vital link between Marx's early and late work. It is also a crucial text in elucidating Marx's debt to the idealist philosopher G.W.F. Hegel. This book, first published in 1988, is the first full-length study of that relationship, in a thorough textual analysis which makes the connections explicit and also the Grundrisse's relations to the works of Adam Smith and Aristotle. This book argues that Marx's critique of political economy, and his critique of Hegel, are double interrelated. Not only did Marx adapt Hegelian logic in order to analyse the economic categories crucial to modern society but it is argued that those logical categories were themselves seen as reflections of the productive processes of contemporary commercial society. Uchida reveals a conceptual structure common to the apparently rarefied world of Hegelian conceptual logic and to the supposedly common-sensical world of economic science. Demonstrating this is a considerable achievement, and it allows us to consider precisely what is valuable today in Marx's critical commentary on this conceptual structure and on the type of society in which it is manifested. Uchida's subject, like Marx's, is 'the force of capital on modern life'.

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and in theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (2nd Edition), Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects , J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning , and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2 .

This second volume in the series Logic, Epistemology, and the Unity of Science brings a pragmatic perspective to the discussion of the unity of science.

Contemporary philosophy and cognitive science increasingly acknowledge the systematic interrelation of language, thought and action. The principal function of language is to enable speakers to communicate their intentions to others, to respond flexibly in a social context and to act cooperatively in the world. This book will contribute to our understanding of this dynamic process by clearly presenting and discussing the most important hypotheses, issues and theories in philosophical and logical study of language, thought and action. Among the fundamental issues discussed are the rationality and freedom of agents, theoretical and practical reasoning, individual and collective attitudes and actions, the nature of cooperation and communication, the construction and conditions of adequacy of scientific theories, propositional contents and their truth conditions, illocutionary force, time, aspect and presupposition in meaning, speech acts within dialogue, the dialogical approach to logic and the structure of dialogues and other language games, as well as formal methods needed in logic or artificial intelligence to account for choice, paradoxes, uncertainty and imprecision.

This volume contains major contributions by leading logicians, analytic philosophers, linguists and computer scientists. It will be of interest to graduate students and researchers from philosophy, logic, linguistics, cognitive science and artificial intelligence. There is no comparable survey in the existing literature.

Naturalism, Reference, and Ontology is a collection of twelve original essays honoring Roger F. Gibson, who has been a leading proponent and defender of W. V. Quine's philosophy for nearly thirty years. The essays address a wide range of topics, including normativity and naturalized epistemology, holism, consciousness, the philosophy of logic, perception, value theory, and the arts. The contributors are an international group of prominent philosophers as well as rising scholars including: Robert Barrett, Lars Bergstrom, Richard Creath, David Henderson, Terence Horgan, Ernest Lepore, Pete Mandik, Alex Orenstein, Kenneth Shockley, J. Robert Thompson, Josefa Toribio, Joseph Ullian, Josh Weisberg, and Chase B. Wrenn.

When this book was originally published in 1957 there had been lively debates on the air and in the press about the bearing of modern philosophy upon Christianity, but there had been relatively little sustained discussion of the subject. This book of essays was the product of a small group of Oxford philosophers and theologians, who had met and talked informally for some years before writing it. It is an attempt to discuss with care and candour some of the problems raised for Christian belief by contemporary analytical philosophy. In asking the questions raised, this book makes articulate the perplexities of many intelligent people, both believers and unbelievers. The contributors concentrate on the way such concepts as God, Revelation, the Soul, Grace are actually used rather than asserting or denying some very general theory of meaning.

Homo Mysticus presents three renowned lectures delivered by Wolfgang Struve from 1974 to 1984, translated into English in this volume. The first two were published in German in 1983 and serve to develop the fundamental difference between world and reality, philosophy and mysticism, and relative and absolute transcendence. The third lecture was given in 1984 and seeks to present the non-conformity of reality with all natural and reflective experience of the I and what imaginings and volition proceed from it. It shows how the terror and the horror at this non-conformity pervades the thinking and feeling of mankind and, properly endured, translates man into the real. In the confusion and quagmire of contemporary "mysticism," "religious thought," "alternative thought," "esotericism," and so on, it is refreshing to find a truly philosophical discussion of mysticism that is rigorous and analytical. Philosophical and mystical experiences are finally given expression in this remarkable collection.

First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general method of approach called substantial factualism which the author asserts allows for the development of a more comprehensive philosophical position by not trivialising or distorting substantial facts of human knowledge.

This volume is a direct result of the International Symposium on Japanese Sentence Processing held at Duke University. The symposium provided the first opportunity for researchers in three disciplinary areas from both Japan and the United States to participate in a conference where they could discuss issues concerning Japanese syntactic processing. The goals of the symposium were three-fold: * to illuminate the mechanisms of Japanese sentence processing from the viewpoints of linguistics, psycholinguistics and computer science; * to synthesize findings about the mechanisms of Japanese sentence processing by researchers in these three fields in Japan and the United States; * to lay foundations for future interdisciplinary research in Japanese sentence processing, as well as international collaborations between researchers in Japan and the United States. The chapters in this volume have been written from the points of view of three different disciplines, with various immediate objectives -- from building usable speech understanding systems to investigating the nature of competence grammars for natural languages. All of the papers share the long term goal of understanding the nature of human language processing mechanisms. The book is concerned with two central issues -- the universality of language processing mechanisms, and the nature of the relation between the components of linguistic knowledge and language processing. This volume demonstrates that interdisciplinary research can be fruitful, and provides groundwork for further research in Japanese sentence processing.

What do we understand 'noise' to be? The term 'noise' no longer suggests only aesthetic judgement, as in acoustic or visual noise, and is now relevant to domains as varied as communication theory, physics and biology. This trans-disciplinary usage leads to confusion and complication, and reveals that the question of noise is a properly philosophical problem. Presenting an analysis of the rising interest in the notion of noise, this book investigates if there can be a coherent understanding of what it is, that can be effectively shared among the natural and human sciences, technology and the arts. Drawing the philosophical consequences of noise for the theory of knowledge, Malaspina undertakes a philosophical revaluation of Shannon and Weaver's theory of 'information entropy'; this forms the basis upon which to challenge the common idea that noise can be reduced to notions of error, disorder or disorganization. The wider consequences of this analysis relate the technological and scientific aspect of noise, with its cultural and psycho-social aspects. At the heart of Malaspina's argument is the contestation of the ground upon which we judge and distinguish noise from information and finally the exploration of its emancipatory potential.

A complete introduction to logic for first-year university students with no background in logic, philosophy or mathematics. In easily understood steps it shows the mechanics of the formal analysis of arguments.

The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds of linguistic context in a fully compositional and anti-contextual way.

Philosophy means 'love of wisdom,' but author Edmond Holmes fears the encroaching dominance of intellect over feeling. In this title, Holmes argues that metaphysics' reliance on intellect and pure reason undermines the study of philosophy. Rather, Holmes suggests a return to intuitional philosophy, combining thought and feeling. First published in 1930, this title will be ideal for students interested in Philosophy and Western Civilisation.

The three ancient philosophical introductions translated in this volume flesh out our picture of what it would have been like to sit in a first-year Philosophy course in ancient Alexandria. Ammonius (AD 445-517/26) set up a new teaching programme in Alexandria with up to six introductions to the philosophy curriculum, which made it far more accessible, and encouraged its spread from Greek to other cultures. This volume's three introductory texts include one by his student Olympiodorus and one each by Olympiodorus' students Elias and David. Elias' Introductions to Philosophy starts with six definitions of Philosophy, to which David adds replies to the sceptical question whether there is such a thing as Philosophy. Olympiodorus' text translated here is an Introduction to Logic, which is just one of the three introductions he wrote himself.

Marx's Grundrisse is acknowledged as the vital link between Marx's early and late work. It is also a crucial text in elucidating Marx's debt to the idealist philosopher G.W.F. Hegel. This book, first published in 1988, is the first full-length study of that relationship, in a thorough textual analysis which makes the connections explicit and also the Grundrisse's relations to the works of Adam Smith and Aristotle. This book argues that Marx's critique of political economy, and his critique of Hegel, are double interrelated. Not only did Marx adapt Hegelian logic in order to analyse the economic categories crucial to modern society but it is argued that those logical categories were themselves seen as reflections of the productive processes of contemporary commercial society. Uchida reveals a conceptual structure common to the apparently rarefied world of Hegelian conceptual logic and to the supposedly common-sensical world of economic science. Demonstrating this is a considerable achievement, and it allows us to consider precisely what is valuable today in Marx's critical commentary on this conceptual structure and on the type of society in which it is manifested. Uchida's subject, like Marx's, is 'the force of capital on modern life'.