This book offers an original philosophical perspective on exemplarity. Inspired by Wittgenstein's later work and Derrida's theory of deconstruction, it argues that examples are not static entities but rather oscillate between singular and universal moments. There is a broad consensus that exemplary cases mediate between singular instances and universal concepts or norms. In the first part of the book, Macha contends that there is a kind of differance between singular examples and general exemplars or paradigms. Every example is, in part, also an exemplar, and vice versa. Furthermore, he develops a paracomplete approach to the logic of exemplarity, which allows us to say of an exemplar of X neither that it is an X nor that it is not an X. This paradox is structurally isomorphic to Russell's paradox and can be addressed in similar ways. In the second part of the book, Macha presents four historical studies that exemplify the ideas developed in the first part. This part begins with Plato's Forms, understood as standards/paradigms, before considering Kant's theory of reflective judgment as a general epistemological account of exemplarity. This is then followed by analyses of Hegel's conceptual moment of particularity and Kuhn's concept of paradigm. The book concludes by discussing the speculative hypothesis that all our knowledge is based on paradigms, which, following the logic of exemplarity, are neither true nor false. The Philosophy of Exemplarity will be of interest to scholars and advanced students working in philosophy of language, logic, history of philosophy, and literary theory.

A `slippery slope argument' is a kind of argument which warns you that, if you take a first step, you will find yourself caught up in a sequence of consequences from which you will be unable to extricate yourself, and that eventually you will end up speeding ever faster towards some disastrous outcome. Many textbooks on informal logic and critical thinking treat the slippery slope argument as a fallacy. Douglas Walton argues that slippery slope arguments can be used correctly in some cases as a reasonable type of argument to shift a burden of proof in a critical discussion, while in other cases they are used incorrectly. In the four central chapters he identifies and analyses four types of slippery slope argument. In each chapter he presents guidelines that show how each type of slippery slope argument can be used correctly or incorrectly, using over fifty case studies of argumentation on controversial issues. These include abortion, medical research on human embryos, euthanasia, the decriminalization of marijuana, pornography and censorship, and whether or not the burning of the American flag should be banned.

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed development of higher-order logic, including a comprehensive discussion of its semantics. Professor Shapiro demonstrates the prevalence of second-order notions in mathematics is practised, and also the extent to which mathematical concepts can be formulated in second-order languages . He shows how first-order languages are insufficient to codify many concepts in contemporary mathematics, and thus that higher-order logic is needed to fully reflect current mathematics. Throughout, the emphasis is on discussing the philosophical and historical issues associated with this subject, and the implications that they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic as might be gained from a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in this subject.

This book develops a new Wittgenstein interpretation called Wittgenstein's Metametaphysics. The basic idea is that one major strand in Wittgenstein's early and later philosophy can be described as undermining the dichotomy between realism and idealism. The aim of this book is to contribute to a better understanding of the relation between language and reality and to open up avenues of dialogue to overcome deep divides in the research literature. In the course of developing a comprehensive and in-depth interpretation, the author provides fresh and original analyses of the latest issues in Wittgenstein scholarship and gives new answers to both major exegetical and philosophical problems. This makes the book an illuminating study for scholars and advanced students alike.

The Routledge Companion to Pragmatism offers 44 cutting-edge chapters-written specifically for this volume by an international team of distinguished researchers-that assess the past, present, and future of pragmatism. Going beyond the exposition of canonical texts and figures, the collection presents pragmatism as a living philosophical idiom that continues to devise promising theses in contemporary debates. The chapters are organized into four major parts: Pragmatism's history and figures Pragmatism and plural traditions Pragmatism's reach Pragmatism's relevance Each chapter provides up-to-date research tools for philosophers, students, and others who wish to locate pragmatist options in their contemporary research fields. As a whole, the volume demonstrates that the vitality of pragmatism lies in its ability to build upon, and transcend, the ideas and arguments of its founders. When seen in its full diversity, pragmatism emerges as one of the most successful and influential philosophical movements in Western philosophy.

This book examines the philosophical conception of abductive reasoning as developed by Charles S. Peirce, the founder of American pragmatism. It explores the historical and systematic connections of Peirce's original ideas and debates about their interpretations. Abduction is understood in a broad sense which covers the discovery and pursuit of hypotheses and inference to the best explanation. The analysis presents fresh insights into this notion of reasoning, which derives from effects to causes or from surprising observations to explanatory theories. The author outlines some logical and AI approaches to abduction as well as studies various kinds of inverse problems in astronomy, physics, medicine, biology, and human sciences to provide examples of retroductions and abductions. The discussion covers also everyday examples with the implication of this notion in detective stories, one of Peirce's own favorite themes. The author uses Bayesian probabilities to argue that explanatory abduction is a method of confirmation. He uses his own account of truth approximation to reformulate abduction as inference which leads to the truthlikeness of its conclusion. This allows a powerful abductive defense of scientific realism. This up-to-date survey and defense of the Peircean view of abduction may very well help researchers, students, and philosophers better understand the logic of truth-seeking.

This book gathers the proceedings of the conference "Cultures of Mathematics and Logic," held in Guangzhou, China. The event was the third in a series of interdisciplinary, international conferences emphasizing the cultural components of philosophy of mathematics and logic. It brought together researchers from many disciplines whose work sheds new light on the diversity of mathematical and logical cultures and practices. In this context, the cultural diversity can be diachronical (different cultures in different historical periods), geographical (different cultures in different regions), or sociological in nature.

We share the capacity for knowledge with animals, but it is the nature and the scope of what we may rationally believe that makes us human. Yet what kind of beliefs do qualify as 'rational'? This challenging and refreshingly innovative book addresses certain fundamental questions concerning rational legitimacy of some widely held beliefs and provides argument-based answers to such questions, while at the same time encouraging the reader to actively engage with the views put forward and form his/her own judgement. The book is typically discursive rather than simply informative, and introduces philosophy by doing it.

The operation of developing a concept is a common procedure in mathematics and in natural science, but has traditionally seemed much less possible to philosophers and, especially, logicians. Meir Buzaglo's innovative study proposes a way of expanding logic to include the stretching of concepts, while modifying the principles which block this possibility. He offers stimulating discussions of the idea of conceptual expansion as a normative process, and of the relation of conceptual expansion to truth, meaning, reference, ontology and paradox, and analyzes the views of Kant, Wittgenstein, Godel, and others, paying especially close attention to Frege. His book will be of interest to a wide range of readers, from philosophers (of logic, mathematics, language, and science) to logicians, mathematicians, linguists, and cognitive scientists.

This accessible book provides a practical discussion of the main elements of argumentation as illustrated by 30 public arguments from a recent year on a wide variety of social, cultural, and scientific topics. Arguing is an important form of communication in any society and a principal way in which ideas are exposed, discussed, and modified. The real-life examples examined in this book reflect the different considerations that go into composing arguments and the range of strategies that can be chosen as vehicles for our positions. They demonstrate the roles that emotion can play along with other modes of conveying evidence, from the use of images to the use of gestures. They show the power of threats, comparisons, and consequences. What emerges is an instructive discussion that illustrates the way we argue and that shows argument, invention, and evaluation in action. This book is a stimulating read for anyone interested in argument and public discourse and can be used as a supplemental text for courses in argumentation, persuasive communication, critical thinking, composition, and informal logic.

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual.

This collection of essays is on the relation between probabilities, especially conditional probabilities, and conditionals. It provides negative results which sharply limit the ways conditionals can be related to conditional probabilities. There are also positive ideas and results which will open up areas of research. The collection is intended to honour Ernest W. Adams, whose seminal work is largely responsible for creating this area of inquiry. As well as describing, evaluating, and applying Adams's work the contributions extend his ideas in directions he may or may not have anticipated, but that he certainly inspired. In addition to a wide range of philosophers of science, the volume should interest computer scientists and linguists.

Propositions are routinely invoked by philosophers, linguists, logicians, and other theorists engaged in the study of meaning, communication, and the mind. To investigate the nature of propositions is to investigate the very nature of our connection to each other, and to the world around us. As one of the only volumes of its kind, The Routledge Handbook of Propositions provides a comprehensive overview of the philosophy of propositions, from both historical and contemporary perspectives. Comprising 33 original chapters by an international team of scholars, the volume addresses both traditional and emerging questions concerning the nature of propositions, and our capacity to engage with them in thought and in communication. The chapters are clearly organized into the following three sections: I. Foundational Issues in the Theory of Propositions II. Historical Theories of Propositions III. Contemporary Theories of Propositions Essential reading for philosophers of language and mind, and for those working in neighboring areas, The Routledge Handbook of Propositions is suitable for upper-level undergraduate study, as well as graduate and professional research.

Godel's modal ontological argument is the centerpiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and the Prawitz/Takahashi completeness proof is given. Then modal machinery is added to produce a modified version of Montague/Gallin intensional logic. Finally, various ontological proofs for the existence of God are discussed informally, and the Godel argument is fully formalized. Parts of the book are mathematical, parts philosophical. "

Part I of this book presents a theory of modal metaphysics in the possible-worlds tradition. `Worlds' themselves are understood as structured sets of properties; this `Ersatzist' view is defended against its most vigorous competitors, Meinongianism and David Lewis' theory of existent concrete worlds. Related issues of essentialism and linguistic reference are explored. Part II takes up the question of lexical meaning in the context of possible-world semantics. There are skeptical analyses of analyticity and the notion of a logical constant; and an `infinite polysemy' thesis is defended. The book will be of particular interest to metaphysicians, possible-world semanticists, philosophers of language, and linguists concerned with lexical semantics.

Russell's first book on philosophy and a fascinating insight into his early thinking A classic in the history and philosophy of mathematics and logic by one of the greatest philosophers of the 20th century This Routledge Classics edition includes a new foreword by Michael Potter, a renowned expert on analytic philosophy

Brilliant introduction to the philosophy of mathematics, from the question 'what is a number?' up to the concept of infinity, descriptions, classes and axioms Russell deploys all his skills and brilliant prose to write an introductory book - a real gem by one of the 20th century's most celebrated philosophers New foreword by Michael Potter to the Routledge Classics edition places the book in helpful context and explains why it's a classic

Superb insight into the development of Russell's thinking by the master himself Clearly and engaging written, charting his intellectual development from young idealist to celebrated sceptic This Routledge Classics edition includes a new foreword by Nicholas Griffin Ideal companion to Russell's own Autobiography, which is concerned with his incredibly colourful life rather than philosophy

"The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics. The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.

This volume consists of papers delivered at the conference 'The Lvov-Warsaw School and Contemporary Philosophy', organised in celebration of the hun- dredth anniversary ofKazimierz Twardowski's first lecture as Professor of Phi- losophy at Lvov University. This lecture can be regarded as the starting point of the development of analytic philosophy in Poland, which culminated in the Warsaw School of Logic. The conference was held in Lvov (15-17 November) and Warsaw (19-21 November 1995). It was organised jointly by the Ukrainian Academy of Sci- ences and the Polish Academy of Sciences. The general organisation was un- dertaken by Professor Andrzej Grzegorczyk (polish Academy of Sciences) and Professor Marat Vernikov (Ukrainian Academy of Sciences). Professors Jaroslaw Isaievich (Ukrainian Academy of Sciences) and Jan Wolenski (Jagiel- Ionian University) were responsible for the scientific programme. Over 100 philosophers participated in the conference. Papers published in this volume are organised according to the sections of the conference and rep- of the papers delivered. resent a selection The editors would like to express their gratitude to Professor Andrzej Grze- gorczyk, spiritus movens of the conference, who, by including the present vol- ume in a programme of publications connected with the hundredth anniversary of the Lvov-Warsaw School, provided financial support for its preparation. Fi- nally, we express our gratitude to Dr Timothy Childers of the Academy of Sciences of the Czech Republic for correcting the English of the papers.

This is a collection of Isaac Levi's philosophical papers. Over the period represented by the work here, Professor Levi has developed an interrelated set of views, in the tradition of Peirce and Dewey, on epistemology and the philosophy of science and social science. This focus has been on the problem of induction and the growth of knowledge, the foundations of probability and the theory of rational decision-making. His most important essays in these areas are assembled here, with an introduction setting out their main themes and connections. As a whole the volume presents a coherent, elaborated position which will be of great interest to a range of philosophers, decision theorists, welfare and social choice theorists and cognitive scientists.

This book puts forward an interpretation of rationality which is much broader than the one underlying the current polarity between analytic and continental philosophy. It will help to reaffirm a range of ideas which have long been pushed to the sidelines by the dominance of the geometric model of philosophical argument. Descartes's dream of attaining a `certitude equal to the demonstrations of Arithmetic and Geometry' reinforced the assumption that rationality must be assessed in terms of logical structure. Against this, Pascal invoked the notion of `finesse', and Warner extends Pascal's usage in this book to specify a related set of informal but legitimate styles of argument.

This book argues that there is a common cognitive mechanism underlying all indexical thoughts, in spite of their seeming diversity. Indexical thoughts are mental representations, such as beliefs and desires. They represent items from a thinker's point of view or her cognitive perspective. We typically express them by means of sentences containing linguistic expressions such as 'this (F)' or 'that (F)', adverbs like 'here', 'now', and 'today', and the personal pronoun 'I'. While generally agreeing that representing the world from a thinker's cognitive perspective is a key feature of indexical thoughts, philosophers disagree as to whether a thinker's cognitive perspective can be captured and rationalized by semantic content and, if so, what kind of content this is. This book surveys competing views and then advances its own positive account. Ultimately, it argues that a thinker's cognitive perspective - or her indexical point of view - is to be explained in terms of the content that is believed and asserted as the only kind of content that there is which thereby serves as the bearer of cognitive significance. The Indexical Point of View will be of interest to philosophers of mind and language, linguists, and cognitive scientists.