"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as if it were the Third Eye, something only mathematical "mystics," like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser there will be a kind of Kantian argument underlying the entire book."

The essays in Powerful Arguments reconstruct the standards of validity underlying argumentative practices in a wide array of late imperial Chinese discourses, from the Song through the Qing dynasties. The fourteen case studies analyze concrete arguments defended or contested in areas ranging from historiography, philosophy, law, and religion to natural studies, literature, and the civil examination system. By examining uses of evidence, habits of inference, and the criteria by which some arguments were judged to be more persuasive than others, the contributions recreate distinct cultures of reasoning. Together, they lay the foundations for a history of argumentative practice in one of the richest scholarly traditions outside of Europe and add a chapter to the as yet elusive global history of rationality.

One of the great minds of the English Renaissance, Francis Bacon was a scholar, politician, and early advocate of scientific thinking who set no limits on the scope of his enquiries. In these compact and vibrant essays, Bacon addresses an astonishingly diverse range of subjects including religion, politics, personal relationships, morality and even architecture. Evident throughout the volume is his considerable rhetorical skill, incisive wit, and an unwavering belief in the power of reason.

Truth is one of the oldest and most central topics in philosophy. Formal theories explore the connections between truth and logic, and they address truth-theoretic paradoxes such as the Liar. Three leading philosopher-logicians now present a concise overview of the main issues and ideas in formal theories of truth. Beall, Glanzberg, and Ripley explain key logical techniques on which such formal theories rely, providing the formal and logical background needed to develop formal theories of truth. They examine the most important truth-theoretic paradoxes, including the Liar paradoxes. They explore approaches that keep principles of truth simple while relying on nonclassical logic; approaches that preserve classical logic but do so by complicating the principles of truth; and approaches based on substructural logics that change the shape of the target consequence relation itself. Finally, inconsistency and revision theories are reviewed, and contrasted with the approaches previously discussed. For any reader who has a basic grounding in logic, this book offers an ideal guide to formal theories of truth.

Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers. The first aim of this book, then, is to explore the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures. Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs.

Writing is essential to learning. One cannot be educated and yet unable to communicate one's ideas in written form. But, learning to write can occur only through a process of cultivation requiring intellectual discipline. As with any set of complex skills, there are fundamentals of writing that must be internalized and then applied using one's thinking. This guide focuses on the most important of those fundamentals.

For the most part, the papers collected in this volume stern from presentations given at a conference held in Tucson over the weekend of May 31 through June 2, 1985. We wish to record our gratitude to the participants in that conference, as well as to the National Science Foundation (Grant No. BNS-8418916) and the University of Arizona SBS Research Institute for their financial support. The advice we received from Susan Steele on organizational matters proved invaluable and had many felicitous consequences for the success of the con ference. We also would like to thank the staff of the Departments of Linguistics of the University of Arizona and the University of Massachusetts at Amherst for their help, as weIl as a number of individuals, including Lin Hall, Kathy Todd, and Jiazhen Hu, Sandra Fulmer, Maria Sandoval, Natsuko Tsujimura, Stuart Davis, Mark Lewis, Robin Schafer, Shi Zhang, Olivia Oehrle-Steele, and Paul Saka. Finally, we would like to express our gratitude to Martin Scrivener, our editor, for his patience and his encouragement. Vll INTRODUCTION The term 'categorial grammar' was introduced by Bar-Rillel (1964, page 99) as a handy way of grouping together some of his own earlier work (1953) and the work of the Polish logicians and philosophers Lesniewski (1929) and Ajdukiewicz (1935), in contrast to approaches to linguistic analysis based on phrase structure grammars."

The purpose of this book is to highlight Carl Stumpf's contributions to philosophy and to assess some of the aspects of his work. This book is divided into four sections, and also includes a general introduction on Stumpf's philosophy. The first section examines the historical sources of his philosophy, the second examines some of the central themes of his work and the third examines his relationship to other philosophers. The fourth section consists of notes taken by Husserl during Stumpf's lectures on metaphysics in Halle, Stumpf's introduction to the edition of his correspondence with Brentano, which he prepared in 1929, and some important letters pertaining to this correspondence. This book also provides a comprehensive bibliography of the works of Stumpf.

Klemens Szaniawski was born in Warsaw on March 3, 1925. He began to study philosophy in the clandestine Warsaw University during World War II. Tadeusz Kotarbinski, Jan Lukasiewicz, Maria and Stanislaw Ossowskis, Wladyslaw Tatarkiewicz, and Henryk Hii: were among his teachers. Sza- niawski was also a member of the Polish Home Army (AK), one of the young- est. He was arrested and spent the last period of the war as a prisoner in Auschwitz. After 1945, he continued his studies in the University of L6dz; his Master thesis was devoted to French moral thought of the 17th and 18th cen- turies. Then he worked in the Department of Ethics in L6dZ. In 1950, he received his Ph. D. on the basis of the dissertation on the concept of honour in knight groups in the Middle Ages; Maria Ossowska was the supervisor. In the early fifties he moved to Warsaw to the Department of Logic, directed by Kotarbinski. He took his habilitation exams in 1961. In 1969 he became a professor. Since 1970 he was the head of Department of the Logic at the Warsaw University. In the sixties Szaniawski was also the Dean of the Faculty of Philosophy and Sociology. In 1984 he was elected the Rector Magnificus of the Warsaw University but the Ministry overruled the autonomous democra- tic vote of the academic community. He served as the President of the Polish (since 1977) taking this post after Kotarbinski.

Games, Norms, and Reasons: Logic at the Crossroads provides an overview of modern logic focusing on its relationships with other disciplines, including new interfaces with rational choice theory, epistemology, game theory and informatics. This book continues a series called "Logic at the Crossroads" whose title reflects a view that the deep insights from the classical phase of mathematical logic can form a harmonious mixture with a new, more ambitious research agenda of understanding and enhancing human reasoning and intelligent interaction. The editors have gathered together articles from active authors in this new area that explore dynamic logical aspects of norms, reasons, preferences and beliefs in human agency, human interaction and groups. The book pays a special tribute to Professor Rohit Parikh, a pioneer in this movement.

The Routledge Handbook of Collective Intentionality provides a wide-ranging survey of topics in a rapidly expanding area of interdisciplinary research. It consists of 36 chapters, written exclusively for this volume, by an international team of experts. What is distinctive about the study of collective intentionality within the broader study of social interactions and structures is its focus on the conceptual and psychological features of joint or shared actions and attitudes, and their implications for the nature of social groups and their functioning. This Handbook fully captures this distinctive nature of the field and how it subsumes the study of collective action, responsibility, reasoning, thought, intention, emotion, phenomenology, decision-making, knowledge, trust, rationality, cooperation, competition, and related issues, as well as how these underpin social practices, organizations, conventions, institutions and social ontology. Like the field, the Handbook is interdisciplinary, drawing on research in philosophy, cognitive science, linguistics, legal theory, anthropology, sociology, computer science, psychology, economics, and political science. Finally, the Handbook promotes several specific goals: (1) it provides an important resource for students and researchers interested in collective intentionality; (2) it integrates work across disciplines and areas of research as it helps to define the shape and scope of an emerging area of research; (3) it advances the study of collective intentionality.

Frontiers in Belief Revision is a unique collection of leading edge research in Belief Revision. It contains the latest innovative ideas of highly respected and pioneering experts in the area, including Isaac Levi, Krister Segerberg, Sven Ove Hansson, Didier Dubois, and Henri Prade. The book addresses foundational issues of inductive reasoning and minimal change, generalizations of the standard belief revision theories, strategies for iterated revisions, probabilistic beliefs, multiagent environments and a variety of data structures and mechanisms for implementations. This book is suitable for students and researchers interested in knowledge representation and in the state of the art of the theory and practice of belief revision.

This is a collection of, mostly unpublished, papers on topics surrounding decision theory. It addresses the most important areas in the philosophical study of rationality and knowledge, for example: causal vs. evidential decision theory, game theory, backwards induction, bounded rationality, counterfactual reasoning in games and in general, and analyses of the famous common knowledge assumptions in game theory.

1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory, the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I-VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin's discovery.

Paris of the year 1900 left two landmarks: the Tour Eiffel, and David Hilbert's celebrated list of twenty-four mathematical problems presented at a conference opening the new century. Kurt Goedel, a logical icon of that time, showed Hilbert's ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Goedel's incompleteness theorem. Goedel then went on to attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers. By 1963, it became clear that Hilbert's first question could not be answered by any known means, half of the credit of this seeming faux pas going to Goedel. The second is a problem still wide open. Goedel worked on it for years, with no definitive results; The best he could offer was a start with the arithmetic of the entire numbers. This book, Goedel's lectures at the famous Princeton Institute for Advanced Study in 1941, shows how far he had come with Hilbert's second problem, namely to a theory of computable functionals of finite type and a proof of the consistency of ordinary arithmetic. It offers indispensable reading for logicians, mathematicians, and computer scientists interested in foundational questions. It will form a basis for further investigations into Goedel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers. The book also gives insights into the conceptual and formal work that is needed for the solution of profound scientific questions, by one of the central figures of 20th century science and philosophy.

Contemporary analytic philosophy can generally be characterized by the following tendencies: commitment to first-order predicate logic as the only viable formal logic; rejection of correspondence theories of truth; a view of existence as something expressed by the existential quantifier; a metaphysics that doesn t give the world as a whole its due. This book seeks to offer an alternative analytic theory, one that provides a unified account of what there is, how we speak about it, the underlying logic of our language, how the truth of what we say is determined, and the central role of the real world in all of this. The result is a robust account of reality. The inspiration for many of the ideas that constitute this overall theory comes from such sources as Aristotle, Leibniz, Ryle, and Sommers."

Since the ground-breaking work of Saul Kripke, David Lewis, and others in the 1960s and 70s, one dominant interest of analytic philosophers has been in modal truths, which concerns the questions of what is possible and what is necessary. However, there is considerable controversy over the source and nature of necessity. In Modality and Explanatory Reasoning, Boris Kment takes a novel approach to the study of modality that places special emphasis on understanding the origin of modal notions in everyday thought. Kment argues that the concepts of necessity and possibility originate in a common type of thought experiment-counterfactual reasoning-that allows us to investigate explanatory connections. This procedure is closely related to the controlled experiments of empirical science. Necessity is defined in terms of causation and other forms of explanation such as grounding, the relation that connects metaphysically fundamental facts to non-fundamental ones. Therefore, contrary to a widespread view, explanation is more fundamental than modality. The study of modal facts is important for philosophy, not because these facts are of much metaphysical interest in their own right, but because they provide evidence about explanatory relationships. In the course of developing this position, the book offers new accounts of possible worlds, counterfactual conditionals, essential truths and their role in grounding, and a novel theory of how counterfactuals relate to causation and explanation.

The issue of a logic foundation for African thought connects well with the question of method. Do we need new methods for African philosophy and studies? Or, are the methods of Western thought adequate for African intellectual space? These questions are not some of the easiest to answer because they lead straight to the question of whether or not a logic tradition from African intellectual space is possible. Thus in charting the course of future direction in African philosophy and studies, one must be confronted with this question of logic. The author boldly takes up this challenge and becomes the first to do so in a book by introducing new concepts and formulating a new African culture-inspired system of logic called Ezumezu which he believes would ground new methods in African philosophy and studies. He develops this system to rescue African philosophy and, by extension, sundry fields in African Indigenous Knowledge Systems from the spell of Plato and the hegemony of Aristotle. African philosophers can now ground their discourses in Ezumezu logic which will distinguish their philosophy as a tradition in its own right. On the whole, the book engages with some of the lingering controversies in the idea of (an) African logic before unveiling Ezumezu as a philosophy of logic, methodology and formal system. The book also provides fresh arguments and insights on the themes of decolonisation and Africanisation for the intellectual transformation of scholarship in Africa. It will appeal to philosophers and logicians-undergraduates and post graduate researchers-as well as those in various areas of African studies.

For thousands of years, mathematicians have used the timeless art of logic to see the world more clearly. In The Art of Logic, Royal Society Science Book Prize nominee Eugenia Cheng shows how anyone can think like a mathematician - and see, argue and think better.

Learn how to simplify complex decisions without over-simplifying them. Discover the power of analogies and the dangers of false equivalences. Find out how people construct misleading arguments, and how we can argue back.

Eugenia Cheng teaches us how to find clarity without losing nuance, taking a careful scalpel to the complexities of politics, privilege, sexism and dozens of other real-world situations. Her Art of Logic is a practical and inspiring guide to decoding the modern world.