The philosophical thought of Ludwig Wittgenstein continues to have a profound influence that transcends barriers between philosophical disciplines and reaches beyond philosophy itself. Less than one hundred years after their publication, his early masterpiece 'Tractatus Logico-Philosophicus' and the posthumously published 'Philosophical Investigations' have emerged as two classic philosophical texts, each of which has elicited widely divergent readings and spawned contesting schools of interpretation. This collection of original essays by leading experts offers deep insights into the forces that shaped and influenced Wittgenstein's thought on a broad variety of topics. It also contains the text - in both the original German and an English translation by Juliet Floyd and Burton Dreben - of letters and cards sent to Wittgenstein by the philosopher and logician Gottlob Frege, which shed light on their interaction during the crucial period when Wittgenstein completed work on the 'Tractatus'. This important record of a philosophical friendship is complemented by a scholarly apparatus and an introduction. Other essays featured in this volume document and discuss Wittgenstein's thinking on music and religion as well as issues that take center stage in the 'Investigations' such as Wittgenstein's account of rule-following. The volume provides an invaluable research tool not only for students of the history of philosophy and for scholars of both Wittgenstein and Frege but also for anyone interested in the intellectual history of the first half of the twentieth century.

Kawalec's monograph is a novel defence of the programme of inductive logic, developed initially by Rudolf Carnap in the 1950s and Jaakko Hintikka in the 1960s. It revives inductive logic by bringing out the underlying epistemology. The main strength of the work is its link between inductive logic and contemporary discussions of epistemology. Through this perspective the author succeeds to shed new light on the significance of inductive logic. The resulting structural reliabilist theory propounds the view that justification supervenes on syntactic and semantic properties of sentences as justification-bearers. The claim is made that this sets up a genuine alternative to the prevailing theories of justification. Kawalec substantiates this claim by confronting structural reliabilism with a number of epistemological problems. Therefore, the book is interesting for philosophers of science dealing with problems of induction, but it will also appeal to readers working in the theory of knowledge. Kawalec writes in a clear manner, makes his theses and arguments explicit, and gives ample bibliographical references. The book will be a valuable companion to graduate and postgraduate courses on inductive logic.

Cognition is a paradoxical process, from the moment of the formation of human subjectivity, through its relationship with the Other (or more precisely: l'autre) and with the world, to the ontological status of the world as such. This is what this book has at stake. The book deals with selected aspects of poststructural thought which are introduced into the language of contemporary science, prose, and poetry. Such an enterprise is possible by treating philosophy, science, and poetry as languages which can try to enter into a dialogue through metaphors. This is the ground on which the project is implemented.

Are there such things as merely possible people, who would have lived if our ancestors had acted differently? Are there future people, who have not yet been conceived? Questions like those raise deep issues about both the nature of being and its logical relations with contingency and change. In Modal Logic as Metaphysics, Timothy Williamson argues for positive answers to those questions on the basis of an integrated approach to the issues, applying the technical resources of modal logic to provide structural cores for metaphysical theories. He rejects the search for a metaphysically neutral logic as futile. The book contains detailed historical discussion of how the metaphysical issues emerged in the twentieth century development of quantified modal logic, through the work of such figures as Rudolf Carnap, Ruth Barcan Marcus, Arthur Prior, and Saul Kripke. It proposes higher-order modal logic as a new setting in which to resolve such metaphysical questions scientifically, by the construction of systematic logical theories embodying rival answers and their comparison by normal scientific standards. Williamson provides both a rigorous introduction to the technical background needed to understand metaphysical questions in quantified modal logic and an extended argument for controversial, provocative answers to them. He gives original, precise treatments of topics including the relation between logic and metaphysics, the methodology of theory choice in philosophy, the nature of possible worlds and their role in semantics, plural quantification compared to quantification into predicate position, communication across metaphysical disagreement, and problems for truthmaker theory.

This book presents a mechanist philosophy of mind. I hold that the human mind is a system of computational or recursive rules that are embodied in the nervous system; that the material presence of these rules accounts for perception, conception, speech, belief, desire, intentional acts, and other forms of intelligence. In this edition I have retained the whole of the fIrst edition except for discussion of issues which no longer are relevant in philosophy of mind and cognitive psychology. Earlier reference to disputes of the 1960's and 70's between hard-line empiricists and neorationalists over the psychological status of grammars and language acquisition, for instance, has simply been dropped. In place of such material I have entered some timely or new topics and a few changes. There are brief references to the question of computer versus distributed processing (connectionist) theories. Many of these questions dissolve if one distinguishes as I now do in Chapter II between free and embodied algorithms. I have also added to my comments on artifIcal in telligence some reflections. on Searle's Chinese Translator. The irreducibility of machine functionalist psychology in my version or any other has been exaggerated. Input, output, and state entities are token identical to physical or biological things of some sort, while a machine system as a collection of recursive rules is type identical to representatives of equivalence classes. This nuld technicality emerges in Chapter XI. It entails that so-called "anomalous monism" is right in one sense and wrong in another."

This book focuses on the problem of responsibility voids: these are cases where responsibility for a morally undesirable outcome cannot be attributed to any of the involved agents. Responsibility voids are thought to occur in collective decision-making and in the context of artificial intelligent systems. In these cases, philosophers worry that there is a shortfall of moral responsibility. In particular, such voids are often assumed to justify a notion of collective responsibility that cannot be reduced to individual responsibility. One of the aims of the book is to study how collective responsibility and joint action relate to individual responsibility and individual actions. The book offers a unifying framework for modelling moral responsibility by drawing from modal logic and game theory. The book investigates the possibility and scope of the problem of responsibility voids. One of its characteristics is its pluralistic perspective on moral responsibility: in contrast to giving a unique and all-encompassing definition of it, the book makes progress by spelling out and modelling several conceptions of moral responsibility. One of the appealing features of the book is that a relatively small range of models is used to investigate a variety of conceptions of moral responsibility. The unifying framework can thus be used to characterize the conditions under which responsibility voids are ruled out.

This book is dedicated to V.A. Yankov's seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov's results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics. The book also contains an exposition of Yankov's revolutionary approach to constructive proof theory. The editors also include Yankov's contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics.

This book presents an English translation of a classic Russian text on duality theory for Heyting algebras. Written by Georgian mathematician Leo Esakia, the text proved popular among Russian-speaking logicians. This translation helps make the ideas accessible to a wider audience and pays tribute to an influential mind in mathematical logic. The book discusses the theory of Heyting algebras and closure algebras, as well as the corresponding intuitionistic and modal logics. The author introduces the key notion of a hybrid that "crossbreeds" topology (Stone spaces) and order (Kripke frames), resulting in the structures now known as Esakia spaces. The main theorems include a duality between the categories of closure algebras and of hybrids, and a duality between the categories of Heyting algebras and of so-called strict hybrids. Esakia's book was originally published in 1985. It was the first of a planned two-volume monograph on Heyting algebras. But after the collapse of the Soviet Union, the publishing house closed and the project died with it. Fortunately, this important work now lives on in this accessible translation. The Appendix of the book discusses the planned contents of the lost second volume.

There is a tradition of interpreting Heidegger's remarks on logic as an attempt to flout, revise, or eliminate logic, and of thus characterizing Heidegger as an irrationalist. Heidegger and Logic looks closely at Heidegger's writings on logic in the Being and Time era and argues that Heidegger does not seek to discredit logic, but to determine its scope and explain its foundations. Through a close examination of the relevant texts, Greg Shirley shows that this tradition of interpretation rests on mischaracterizations and false assumptions. What emerges from Heidegger's remarks on logic is an account of intelligibility that is both novel and relevant to issues in contemporary philosophy of logic. Heidegger's views on logic form a coherent whole that is an important part of his larger philosophical project and helps us understand it better, and that constitutes a unique contribution to the philosophy of logic

An introductory textbook, Logic for Justice covers, in full detail, the language and semantics of both propositional logic and first-order logic. It motivates the study of those logical systems by drawing on social and political issues. Basically, Logic for Justice frames propositional logic and first-order logic as two theories of the distinction between good arguments and bad arguments. And the book explains why, for the purposes of social justice and political reform, we need theories of that distinction. In addition, Logic for Justice is extremely lucid, thorough, and clear. It explains, and motivates, many different features of the formalism of propositional logic and first-order logic, always connecting those features back to real-world issues. Key Features Connects the study of logic to real-world social and political issues, drawing in students who might not otherwise be attracted to the subject. Offers extremely clear and thorough presentations of technical material, allowing students to learn directly from the book without having to rely on instructor explanations. Carefully explains the value of arguing well throughout one’s life, with several discussions about how to argue and how arguments – when done with care – can be helpful personally. Includes examples that appear throughout the entire book, allowing students to see how the ideas presented in the book build on each other. Provides a large and diverse set of problems for each chapter. Teaches logic by connecting formal languages to natural languages with which students are already familiar, making it much easier for students to learn how logic works.

An introductory textbook, Logic for Justice covers, in full detail, the language and semantics of both propositional logic and first-order logic. It motivates the study of those logical systems by drawing on social and political issues. Basically, Logic for Justice frames propositional logic and first-order logic as two theories of the distinction between good arguments and bad arguments. And the book explains why, for the purposes of social justice and political reform, we need theories of that distinction. In addition, Logic for Justice is extremely lucid, thorough, and clear. It explains, and motivates, many different features of the formalism of propositional logic and first-order logic, always connecting those features back to real-world issues. Key Features Connects the study of logic to real-world social and political issues, drawing in students who might not otherwise be attracted to the subject. Offers extremely clear and thorough presentations of technical material, allowing students to learn directly from the book without having to rely on instructor explanations. Carefully explains the value of arguing well throughout one’s life, with several discussions about how to argue and how arguments – when done with care – can be helpful personally. Includes examples that appear throughout the entire book, allowing students to see how the ideas presented in the book build on each other. Provides a large and diverse set of problems for each chapter. Teaches logic by connecting formal languages to natural languages with which students are already familiar, making it much easier for students to learn how logic works.

How does Russell's realist conception of the proposition and its constituents inform the techniques for analysis which he adopted in mathematics? Jolen Galaugher's book sheds light on this perplexing issue. In this book, Galaugher provides a detailed treatment of Russell's early conception of analysis in the light of the philosophical doctrines to which it answered, and the demands imposed by existing mathematics on his early logicist program. She ties together the philosophical commitments which occasioned Russell's break with idealism and the problems which guided his selection of technical apparatus in his embrace of logicism. The result is a detailed synthesis of the primary materials from the emergence of Russell's realism in 1898 to his landmark theory of descriptions in 1905. Galaugher's broad thesis is that although Russell adopted increasingly refined techniques by which to carry out his logical analyses and avoid the Contradiction, the most crucial aspects of his philosophical conception of logical analysis were retained.

The book contains a collection of chapters written by experts from the fields of philosophy, law, logic, computer science and artificial intelligence who pay tribute to Professor Risto Hilpinen's impressive work on the logic of induction, on deontic logic and epistemology, and on philosophy of science. In addition to an introduction by the editors, a section on Professor Hilpinen's positions, professional services and honors, as well as a complete bibliography of his writings, the editors, McNamara, Jones and Brown, have compiled a multidisciplinary global cross-section of academic contemporaries that provides insights and perspectives on Hilpinen's influence and legacy. The essays reflect central aspects of Risto Hilpinen's research interests, and offer further contributions to some of the philosophical fields for which he is best known: applied modal logic, including deontic logic (from the ancient Greek deon, pertaining to the concepts of duty and obligation), the semantics of normative language, the logic of action, and the theory of practical reasoning; the analysis of the concept of artifact; and the theory of semiotics in the tradition of Charles Peirce. The presence in the collection of several papers relating to deontic logic underlines Hilpinen's importance in that area, in which his publications have long been recognized as standard works. The book is an essential collection of ideas for all those who feel at home in a variety of formal disciplines, from propositional logic to the logic of artificial intelligence.

This book offers the first-ever English translation of Oskar Becker's Zur Logik der Modalitaten. This essay, published in 1930, is a pioneering yet often neglected contribution in the context of prewar modal logic research in Europe. Becker's text is complemented by an extended commentary that explains, analyzes and highlights Becker's accomplishments and the philosophical background of his investigations. The commentary provides an in-depth analysis of all of Becker's important contributions, both from a philosophical and logical perspective, making it a very useful book for scholars in both philosophy and logic.

This book argues that languages are composed of sets of 'signs', rather than 'strings'. This notion, first posited by de Saussure in the early 20th century, has for decades been neglected by linguists, particularly following Chomsky's heavy critiques of the 1950s. Yet since the emergence of formal semantics in the 1970s, the issue of compositionality has gained traction in the theoretical debate, becoming a selling point for linguistic theories.

Yet the concept of 'compositionality' itself remains ill-defined, an issue this book addresses. Positioning compositionality as a cornerstone in linguistic theory, it argues that, contrary to widely held beliefs, there exist non-compositional languages, which shows that the concept of compositionality has empirical content. The author asserts that the existence of syntactic structure can flow from the fact that a compositional grammar cannot be delivered without prior agreement on the syntactic structure of the constituents.

This volume brings together those papers of mine which may be of interest not only to various specialists but also to philosophers. Many of my writings in mathematics were motivated by epistemological considerations; some papers originated in the critique of certain views that at one time dominated the discussions of the Vienna Cirele; others grew out of problems in teaching fundamental ideas of mathematics; sti II others were occasioned by personal relations with economists. Hence a wide range of subjects will be discussed: epistemology, logic, basic concepts of pure and applied mathematics, philosophical ideas resulting from geometric studies, mathematical didactics and, finally, economics. The papers also span a period of more than fifty years. What unifies the various parts of the book is the spirit of searching for the elarification of basic concepts and methods and of articulating hidden ideas and tacit procedures. Part 1 ineludes papers published about 1930 which expound an idea that Carnap, after a short period of opposition in the Cirele, fully adopted ; and, under the name "Princip/e of To/erance", he eloquently formulated it in great generality in his book, Logica/ Syntax of Language (1934), through which it was widely disseminated. "The New Logic" in Chapter 1 furthermore ineludes the first report (I932) to a larger public of Godel's epochal discovery presented among the great logic results of ali time. Chapter 2 is a translation of an often quoted 1930 paper presenting a detailed exposition and critique of intuitionism.

Stig Kanger (1924-1988) made important contributions to logic and formal philosophy. Kanger's most original achievements were in the areas of general proof theory, the semantics of modal and deontic logic, and the logical analysis of the concept of rights. But he contributed significantly to action theory, preference logic and the theory of measurement as well. This is the second of two volumes dedicated to the work of Stig Kanger. The first volume is a complete collection of Kanger's philosophical papers. The present volume contains critical essays on the various aspects of Kanger's work as well as some biographical sketches. Lennart A...qvist, Jan Berg, Brian Chellas, Anatoli Degtyarev, Lars Gustafsson, SAren HalldA(c)n, Kaj BA, rge Hansen, Sven Ove Hansson, Risto Hilpinen, Jaakko Hintikka, Ghita HolmstrAm-Hintikka, Lars Lindahl, Sten LindstrAm, Ingmar PArn, Dag Prawitz, Wlodek Rabinowicz, Krister Segerberg, Amartya Sen, SAren Stenlund, GAran Sundholm, and Andrei Voronkov have contributed to this volume.

1. 1. The Principle of Universalizability-an informal explication This work is concerned with the so-called Principle of Universalizability. As we shall understand it, this principle represents a claim that moral properties of things (persons, actions, state of affairs, situations) are essentially independent of their purely 'individual' or-as one often says -'numerical' aspects. l Thus, if a thing, x, is better than another thing, y, then this fact is not dependent on x's being x nor on y's being y. If a certain person, a, has a duty to help another person, b, then this duty does not arise as a consequence of their being a and b, respectively. And if in a certain situation, W, it ought to be the case that certain goods are transferred from one person to another, then this moral obligation does not depend on the individual identities of the persons involved. The Universalizability Principle may also be expressed in terms of similarities. Instead of saying that the moral properties of x are essentially independent of the individual aspects of x, we may say that any object which is exactly similar to x, which is precisely like x in all non-individual, 'qualitative' respects, must exhibit exactly similar moral properties. Thus, if two persons are exactly similar to each other, (if they are placed in exactly similar circumstances, have exactly similar information, preferences, character, etc. ), then they will have exactly similar rights and duties.

This volume collects selected papers presented at the Second Chinese Conference on Logic and Argumentation in 2018 held in Hangzhou, China. The papers presented reflect recent advances in logic and argumentation, as well as the connections between the two, and also include invited papers contributed by leading experts in these fields. The book covers a wide variety of topics related to dynamics, uncertainty and reasoning. It continues discussions on the interplay between logic and argumentation which has a long history from Aristotle's ancient logic to very recent formal argumentation in AI.

Stanislaw Lesniewski (1886-1939) was one of the leading Polish logicians and founders of the Warsaw School of Logic whose membership included, beside himself, Jan Lukasiewicz, Tadeusz Kotarbinski, Alfred Tarski, and many others. In his lifetime LeSniewski published only a few hundred pages. He produced many important results in many areas of mathematics; these stood in various relations to each other, and to materials produced by others, and, in time, created more and more editorial problems. Very many were left unpublished at the time of his death. Then in 1944 in the fire of Warsaw the whole of this material was burned and lost -a considerable loss since a great deal of what is important could have been reconstructed from these notes. The present publication aims at presenting unique Lesniewski's materials from alternative sources comprising lecture notes taken during some of Lesniewski's lectures and seminars delivered at the University of Warsaw be tween the two world wars. The editors are aware of the limitations of student notes which cannot compensate for the loss of the original materials. However, they are unique in reflecting Lesniewski's ideas as he himself presented them. Already at the time of his death it was realized that these notes would provide a unique access to Lesniewski's own thought as well as a valuable record of some of the activities of the Warsaw School of Logic."

Jaakko Hintikka is one of the most creative figures in contemporary philosophy. He has made significant contributions to virtually all areas of the discipline, from epistemology and the philosophy of logic to the history of philosophy and the philosophy of science. Part of the fruitfulness of Hintikka 's work is due to its opening important new lines of investigation and new approaches to traditional philosophical problems. This volume gathers together essays from some of Hintikka 's colleagues and former students exploring his influence on their work and pursuing some of the insights that we have found in his work. This book includes a comprehensive overview of Hintikka 's philosophy by Dan Kolak and John Symons and an annotated bibliography of Hintikka 's work.

This book examines the birth of the scientific understanding of motion. It investigates which logical tools and methodological principles had to be in place to give a consistent account of motion, and which mathematical notions were introduced to gain control over conceptual problems of motion. It shows how the idea of motion raised two fundamental problems in the 5th and 4th century BCE: bringing together being and non-being, and bringing together time and space. The first problem leads to the exclusion of motion from the realm of rational investigation in Parmenides, the second to Zeno's paradoxes of motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitly in the atomists, and explicitly in Plato who also employs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline of the fundamental framework with which we conceptualise motion today.

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of (basic) truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice (a lattice of truth values with two ordering relations) constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, a trilattice of truth values - a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi.

This book provides a comprehensive overview of the nature of explanations as given in both natural and social sciences. It discusses models of explanation adopted in natural and social sciences. The author also elaborates upon naturalistic and anti-naturalistic views and other types of explanations such as functional, purposive, etc in social science. The volume elaborates upon themes like bridge principle; functional explanation; purposive explanation; teleological explanation; prediction; methodological individualism; methodological collectivism; illocutionary redescription; principle of action; and dispositional explanations, to understand whether the explanations given in the realm of social sciences are the same or different from the explanations that are given in the field of natural sciences. This introductory book is a must read for students and scholars of philosophy of science, logic, science and technology studies, social sciences, and philosophy in general.