The limit of language is one of the most pervasive notions found in Wittgenstein's work, both in his early Tractatus Logico-Philosophicus and his later writings. Moreover, the idea of a limit of language is intimately related to important scholarly debates on Wittgenstein's philosophy, such as the debate between the so-called traditional and resolute interpretations, Wittgenstein's stance on transcendental idealism, and the philosophical import of Wittgenstein's latest work On Certainty. This collection includes thirteen original essays that provide a comprehensive overview of the various ways in which Wittgenstein appeals to the limit of language at different stages of his philosophical development. The essays connect the idea of a limit of language to the most important themes discussed by Wittgenstein-his conception of logic and grammar, the method of philosophy, the nature of the subject, and the foundations of knowledge-as well as his views on ethics, aesthetics, and religion. The essays also relate Wittgenstein's thought to his contemporaries, including Carnap, Frege, Heidegger, Levinas, and Moore.

Originally published in 1973. This book presents a valid mode of reasoning that is different to mathematical probability. This inductive logic is investigated in terms of scientific investigation. The author presents his criteria of adequacy for analysing inductive support for hypotheses and discusses each of these criteria in depth. The chapters cover philosophical problems and paradoxes about experimental support, probability and justifiability, ending with a system of logical syntax of induction. Each section begins with a summary of its contents and there is a glossary of technical terms to aid the reader.

This book addresses the argument in the history of the philosophy of science between the positivists and the anti-positivists. The author starts from a point of firm conviction that all science and philosophy must start with the given... But that the range of the given is not definite. He begins with an examination of science from the outside and then the inside, explaining his position on metaphysics and attempts to formulate the character of operational acts before a general theory of symbolism is explored. The last five chapters constitute a treatise to show that the development from one stage of symbolismto the next is inevitable, consequently that explanatory science represents the culmination of knowledge.

Originally published in 1965. This is a textbook of modern deductive logic, designed for beginners but leading further into the heart of the subject than most other books of the kind. The fields covered are the Propositional Calculus, the more elementary parts of the Predicate Calculus, and Syllogistic Logic treated from a modern point of view. In each of the systems discussed the main emphases are on Decision Procedures and Axiomatisation, and the material is presented with as much formal rigour as is compatible with clarity of exposition. The techniques used are not only described but given a theoretical justification. Proofs of Consistency, Completeness and Independence are set out in detail. The fundamental characteristics of the various systems studies, and their relations to each other are established by meta-logical proofs, which are used freely in all sections of the book. Exercises are appended to most of the chapters, and answers are provided.

Originally published in 1967. The common aim of all logical enquiry is to discover and analyse correctly the forms of valid argument. In this book concise expositions of traditional, Aristotelian logic and of modern systems of propositional and predicative logic show how far that aim has been achieved.

This collection addresses metaphysical issues at the intersection between philosophy and science. A unique feature is the way in which it is guided both by history of philosophy, by interaction between philosophy and science, and by methodological awareness. In asking how metaphysics is possible in an age of science, the contributors draw on philosophical tools provided by three great thinkers who were fully conversant with and actively engaged with the sciences of their day: Kant, Husserl, and Frege. Part I sets out frameworks for scientifically informed metaphysics in accordance with the meta-metaphysics outlined by these three self-reflective philosophers. Part II explores the domain for co-existent metaphysics and science. Constraints on ambitious critical metaphysics are laid down in close consideration of logic, meta-theory, and specific conditions for science. Part III exemplifies the role of language and science in contemporary metaphysics. Quine's pursuit of truth is analysed; Cantor's absolute infinitude is reconstrued in modal terms; and sense is made of Weyl's take on the relationship between mathematics and empirical aspects of physics. With chapters by leading scholars, Metametaphysics and the Sciences is an in-depth resource for researchers and advanced students working within metaphysics, philosophy of science, and the history of philosophy.

Used in a variety of courses in various disciplines, Asking the Right Questions helps students bridge the gap between simply memorizing or blindly accepting information, and the greater challenge of critical analysis and synthesis. Specifically, this concise text teaches students to think critically by exploring the components of arguments--issues, conclusions, reasons, evidence, assumptions, language--and on how to spot fallacies and manipulations and obstacles to critical thinking in both written and visual communication. It teaches them to respond to alternative points of view and develop a solid foundation for making personal choices about what to accept and what to reject.

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.

The primary objective of An Inquiry into the Nature of Aesthetic Theory in Its Relation to Theory of Knowledge in Kant's Critical Philosophy is to investigate Kant's aesthetic theory and its problematic relation to theory of knowledge in his transcendental philosophy. In the Critique of Judgment, Kant constructs his aesthetic theory by arguing that the aesthetic experience is based on a certain type of feeling, namely, the feeling of pleasure, rather than a concept. He grounds such a feeling on the aesthetic judgment of reflection. In spite of its nonconceptual and subjective characteristic, an aesthetic reflective judgment still has a claim to be universally valid. Here, the feeling of pleasure in beautiful is produced by the free harmonious relation between the imagination and the understanding. Judgment, in its reflective employment, does not determine its object but determines the feeling of pleasure in the judging subject. On the other hand, the categories, as pure concepts of the understanding, carry nearly all the weight in his theory of knowledge presented in the Critique of Pure Reason. The imagination, in this case, is strictly bound up by the rules that are imposed by the concepts of the understanding. By this way, judgment, as a cognitive faculty, determines its object and gains its objective validity. In this context, this book discusses the nature of Kant's aesthetic theory and the components that constitute a pure aesthetic judgment of reflection and attempts to clarify its proper place in critical philosophy regarding his theory of knowledge.

Originally published in 1966 On the Syllogism and Other Logical Writings assembles for the first time the five celebrated memoirs of Augustus De Morgan on the syllogism. These are collected together with the more condensed accounts of his researches given in his Syllabus of a Proposed System of Logic an article on Logic contributed to the English Cyclopaedia. De Morgan was among the most distinguished of nineteenth century British mathematicians but is chiefly remembered today as one of the founders of modern mathematical logic. His writings on this subject have been little read, however since apart from his Formal Logic, they lie buried for the most part in inaccessible periodicals. De Morgan's own later amendments are inserted in the text and the editorial introduction gives a summary of the whole and traces in some detail the course of the once-famous feud with Sir William Hamilton of Edinburgh.

This book provides an accessible and thorough analysis of "The Doctrine of Being," the first part of Hegel's Science of Logic. Though it received much scholarly attention in the past, interpreters of this text have generally refrained from examining it in a sufficiently detailed manner. Through a rigorous and critical reading of Hegel's speculative arguments, Mehmet Tabak illustrates that Hegel meant his logic to be both a presuppositionless analysis and development of the basic categories of thought, on the one hand, and a post-Kantian ontology on the other. However, the analysis of the text demonstrates that Hegel fails to deliver such logic. This volume promises to be an indispensable guide to those who wish to understand the first book of Science of Logic.

Lacan and the Formulae of Sexuation provides the first critical reading of Lacan's formulae of sexuation, examining both their logical consistency and clinical consequences. Are there two different entities named Man and Woman, separated by the gulf of sexual difference? Or is it better to conceive of this difference as something purely relative, each human being situated on a sort of continuum from more or less 'man' to more or less 'woman'? Sigmund Freud established the strange way through which sexuality determines being human: his concept of drive was no longer the heteronormative sexual instinct used by the psychiatrists of his time. With his provocative formula according to which 'there is no sexual relationship', Lacan has reinforced this perspective, combining logic and sexuality through the invention of a new operator, the concept 'not all', which points to a form of incompleteness at stake in his 'formulae of sexuation'. This book examines how these formulae have been constructed, and how we should read them in connection with, on one hand, their own logical consistency (a logical square different from Aristotelian tradition) and, on the other hand, a 'part object' in a very different sense to Melanie Klein's. The book also investigates the underlying logic of clinical vignettes, so much in favour in psychoanalytical literature today. The book represents essential reading for Lacanian psychoanalysts, as well as researchers at the cross-section of psychoanalysis, philosophy, and gender studies.

This volume contains twenty-four essays by the British/Australian analytic metaphysician, Brian Garrett. These essays are followed by four short dialogues that emphasize and summarize some of the main points of the essays and discuss new perspectives that have emerged since their original publication. The volume covers topics on the metaphysics of time, the nature of identity, and the nature and importance of persons and human beings. The chapters constitute the fruits of almost four decades of philosophical research, from Brian's two award-winning essays, published in Analysis in 1983 and The Philosophical Quarterly in 1992, to his latest ideas about Fatalism and the Grandfather Paradox. This book will be of interest to students and professional philosophers in the field of analytic philosophy.

This book offers a comprehensive account of logic that addresses fundamental issues concerning the nature and foundations of the discipline. The authors claim that these foundations can not only be established without the need for strong metaphysical assumptions, but also without hypostasizing logical forms as specific entities. They present a systematic argument that the primary subject matter of logic is our linguistic interaction rather than our private reasoning and it is thus misleading to see logic as revealing "the laws of thought". In this sense, fundamental logical laws are implicit to our "language games" and are thus more similar to social norms than to the laws of nature. Peregrin and Svoboda also show that logical theories, despite the fact that they rely on rules implicit to our actual linguistic practice, firm up these rules and make them explicit. By carefully scrutinizing the project of logical analysis, the authors demonstrate that logical rules can be best seen as products of the so called reflective equilibrium. They suggest that we can profit from viewing languages as "inferential landscapes" and logicians as "geographers" who map them and try to pave safe routes through them. This book is an essential resource for scholars and researchers engaged with the foundations of logical theories and the philosophy of language.

This book on proof theory centers around the legacy of Kurt Schutte and its current impact on the subject. Schutte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schutte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound 0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Schutte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts close to his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Schutte himself that have never been published before.

Originally published in 1966. This is a self-instructional course intended for first-year university students who have not had previous acquaintance with Logic. The book deals with "propositional" logic by the truth-table method, briefly introducing axiomatic procedures, and proceeds to the theory of the syllogism, the logic of one-place predicates, and elementary parts of the logic of many-place predicates. Revision material is provided covering the main parts of the course. The course represents from eight to twenty hours work. depending on the student's speed of work and on whether optional chapters are taken.

Originally published in 1981. This is a book for the final year undergraduate or first year graduate who intends to proceed with serious research in philosophical logic. It will be welcomed by both lecturers and students for its careful consideration of main themes ranging from Gricean accounts of meaning to two dimensional modal logic. The first part of the book is concerned with the nature of the semantic theorist's project, and particularly with the crucial concepts of meaning, truth, and semantic structure. The second and third parts deal with various constructions that are found in natural languages: names, quantifiers, definite descriptions, and modal operators. Throughout, while assuming some familiarity with philosophical logic and elementary formal logic, the text provides a clear exposition. It brings together related ideas, and in some places refines and improves upon existing accounts.

Originally published in 1968. This is a critical study of the concept of 'rule' featuring in law, ethics and much philosophical analysis which the author uses to investigate the concept of 'rationality'. The author indicates in what manner the modes of reasoning involved in reliance upon rules are unique and in what fashion they provide an alternative both to the modes of logico-mathematical reasoning and to the modes of scientific reasoning. This prepares the groundwork for a methodology meeting the requirements of the fields using rules such as law and ethics which could be significant for communications theory and the use of computers in normative fields. Other substantive issues related to the mainstream of legal philosophy are discussed - theories of interpretation, the notion of purpose and the requirements of principled decision-making. The book utilizes examples drawn from English and American legal decisions to suggest how the positions of legal positivism and of natural law are equally artificial and misleading.

The aim of this monograph is to present some of the basic ideas and results in pure combinatory logic and their applications to some topics in proof theory, and also to present some work of my own. Some of the material in chapter 1 and 3 has already appeared in my notes Introduction to Combinatory Logic. It appears here in revised form since the presen tation in my notes is inaccurate in several respects. I would like to express my gratitude to Stig Kanger for his invalu able advice and encouragement and also for his assistance in a wide variety of matters concerned with my study in Uppsala. I am also in debted to Per Martin-USf for many valuable and instructive conversa tions. As will be seen in chapter 4 and 5, I also owe much to the work of Dag Prawitz and W. W. Tait. My thanks also to Craig McKay who read the manuscript and made valuable suggestions. I want, however, to emphasize that the shortcomings that no doubt can be found, are my sole responsibility. Uppsala, February 1972."

What is the true worth of Wittgenstein's contribution to philosophy? Answers to this question are strongly divided. However, most assessments rest on certain popular misreadings of his purpose. This book challenges both "theoretical" and "therapeutic" interpretations. In their place, it seeks to establish that, from beginning to end, Wittgenstein regarded clarification as the true end of philosophy. It argues that, properly understood, his approach exemplifies rather than betrays critical philosophy and provides a viable alternative to other contemporary offerings.

This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz's work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science.

The range of contributions includes material on the extension of natural deduction with higher-order rules, as opposed to higher-order connectives, and a paper discussing the application of natural deduction rules to dealing with equality in predicate calculus. The volume continues with a key chapter summarizing work on the extension of the Curry-Howard isomorphism (itself a by-product of the work on natural deduction), via methods of category theory that have been successfully applied to linear logic, as well as many other contributions from highly regarded authorities. With an illustrious group of contributors addressing a wealth of topics and applications, this volume is a valuable addition to the libraries of academics in the multiple disciplines whose development has been given added scope by the methodologies supplied by natural deduction. The volume is representative of the rich and varied directions that Prawitz work has inspired in the area of natural deduction.
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Peirce's Speculative Grammar: Logic as Semiotics offers a comprehensive, philologically accurate, and exegetically ambitious developmental account of Peirce's theory of speculative grammar. The book traces the evolution of Peirce's grammatical writings from his early research on the classification of arguments in the 1860s up to the complex semiotic taxonomies elaborated in the first decade of the twentieth century. It will be of interest to academic specialists working on Peirce, the history of American philosophy and pragmatism, the philosophy of language, the history of logic, and semiotics.

This book addresses the hasty development of modern logic, especially its introducing and embracing various kinds of artificial languages and moving from the study of natural languages to that of artificial ones. This shift seemed extremely helpful and managed to elevate logic to a new level of rigor and clarity. However, the change that logic underwent in this way was in no way insignificant, and it is also far from an insignificant matter to determine to what extent the "new logic" only engaged new and more powerful instruments to answer the questions posed by the "old" one, and to what extent it replaced these questions with new ones. Hence, this movement has generated brand new kinds of philosophical problems that have still not been dealt with systematically. Philosophy of Logical Systems addresses these new kinds of philosophical problems that are intertwined with the development of modern logic. Jaroslav Peregrin analyzes the rationale behind the introduction of the artificial languages of logic; classifies the various tools which were adopted to build such languages; gives an overview of the various kinds of languages introduced in the course of modern logic and the motifs of their employment; discusses what can actually be achieved by relocating the problems of logic from natural language into them; and reaches certain conclusions with respect to the possibilities and limitations of this "formal turn" of logic. This book is both an important scholarly contribution to the philosophy of logic and a systematic survey of the standard (and not so standard) logical systems that were established during the short history of modern logic.

"Exploring Hegels philosophical psychology to uncover viable remedies to the chief dilemmas plaguing contemporary philosophy of mind, Hegel and Mind exposes why mind cannot be an epistemological foundation nor reduced to discursive consciousness not modelled after computing machines"--Provided by publisher.