Originally published in 1941. Professor Ushenko treats of current problems in technical Logic, involving Symbolic Logic to a marked extent. He deprecates the tendency, in influential quarters, to regard Logic as a branch of Mathematics and advances the intuitionalist theory of Logic. This involves criticism of Carnap, Russell,Wittgenstein, Broad and Whitehead, with additional discussions on Kant and Hegel. The author believes that the union of Philosophy and Logic is a natural one, and that an exclusively mathematical treatment cannot give an adequate account of Logic. A fundamental characteristic of Logic is comprehensiveness, which brings out the affinity between logic and philosophy, for to be comprehensive is the aim of philosophical ambition.

This book provides an account of the emergence of norms. Put very crudely, the main thesis of this book is that certain types of norms are possible solutions to problems posed by certain types of social interaction situations. The problems are such that they inhere in the structure (in the game-theoretical sense of structure) of the situations concerned. Three types of paradigmatic situations are dealt with. They are referred to as Prisoners' Dilemma-type situations; co-ordination situations; and inequality (or partiality) situations. Each of them, it is claimed, poses a basic difficulty, to some or all of the individuals involved in them. Three types of norms, respectively, are offered as solutions to these situational problems. It is shown how, and in what sense, the adoption of these norms of social behaviour can indeed resolve the specified problems.

Belief Revision Refutation and systems in Propositional Logic. A Quantifier Scope in Formal Linguistics and Non-deterministic Semantics for Logical Systems.

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.

Philosophical logic has been, and continues to be, a driving force behind much progress and development in philosophy more broadly. This collection by up-and-coming philosophical logicians deals with a broad range of topics, including, for example, proof-theory, probability, context-sensitivity, dialetheism and dynamic semantics.

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.

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.

We do not perceive the present as it is and in totality, nor do we infer the future from the present with any high degree of dependability, nor yet do we accurately know the consequences of our own actions. In addition, there is a fourth source of error to be taken into account, for we do not execute actions in the precise form in which they are imaged and willed. Frank H. Knight [R4.34, p. 202] The "degree" of certainty of confidence felt in the conclusion after it is reached cannot be ignored, for it is of the greatest practical signi- cance. The action which follows upon an opinion depends as much upon the amount of confidence in that opinion as it does upon fav- ableness of the opinion itself. The ultimate logic, or psychology, of these deliberations is obscure, a part of the scientifically unfathomable mystery of life and mind. Frank H. Knight [R4.34, p. 226-227] With some inaccuracy, description of uncertain consequences can be classified into two categories, those which use exclusively the language of probability distributions and those which call for some other principle, either to replace or supplement.

Originally published in 1988. This text gives a lucid account of the most distinctive and influential responses by twentieth century philosophers to the problem of the unity of the proposition. The problem first became central to twentieth-century philosophy as a result of the depsychoiogising of logic brought about by Bradley and Frege who, responding to the 'Psychologism' of Mill and Hume, drew a sharp distinction between the province of psychology and the province of logic. This author argues that while Russell, Ryle and Davidson, each in different ways, attempted a theoretical solution, Frege and Wittgenstein (both in the Tractatus and the Investigations) rightly maintained that no theoretical solution is possible. It is this which explains the importance Wittgenstein attached in his later work to the idea of agreement in judgments. The two final chapters illustrate the way in which a response to the problem affects the way in which we think about the nature of the mind. They contain a discussion of Strawson's concept of a person and provide a striking critique of the philosophical claims made by devotees of artificial intelligence, in particular those made by Daniel Dennett.

Throughout his corpus, Kant repeatedly and resolutely denies that there is a duty to promote one's own happiness, and most present-day Kantians seem to agree with him. In Kant, Ought Implies Can, the Principle of Alternate Possibilities, and Happiness, Samuel Kahn argues that this denial rests on two main ideas: (1) a conception of duty that makes the principle of ought implies can (OIC) and the principle of alternate possibilities (PAP) analytic, and (2) the claim that humans necessarily promote their own happiness. This book defends OIC and PAP but nonetheless attacks the second idea, and it supplements this attack with two additional arguments-an interpersonal one and an intrapersonal one-for the claim that a modern day Kantian ethics should affirm a duty to promote one's own happiness.

This book aims to lay bare the logical foundations of tractable reasoning. It draws on Marvin Minsky's seminal work on frames, which has been highly influential in computer science and, to a lesser extent, in cognitive science. Only very few people have explored ideas about frames in logic, which is why the investigation in this book breaks new ground. The apparent intractability of dynamic, inferential reasoning is an unsolved problem in both cognitive science and logic-oriented artificial intelligence. By means of a logical investigation of frames and frame concepts, Andreas devises a novel logic of tractable reasoning, called frame logic. Moreover, he devises a novel belief revision scheme, which is tractable for frame logic. These tractability results shed new light on our logical and cognitive means to carry out dynamic, inferential reasoning. Modularity remains central for tractability, and so the author sets forth a logical variant of the massive modularity hypothesis in cognitive science. This book conducts a sustained and detailed examination of the structure of tractable and intelligible reasoning in cognitive science and artificial intelligence. Working from the perspective of formal epistemology and cognitive science, Andreas uses structuralist notions from Bourbaki and Sneed to provide new foundational analyses of frames, object-oriented programming, belief revision, and truth maintenance. Andreas then builds on these analyses to construct a novel logic of tractable reasoning he calls frame logic, together with a novel belief revision scheme that is tractable for frame logic. Put together, these logical analyses and tractability results provide new understandings of dynamic and inferential reasoning. Jon Doyle, North Carolina State University

The book offers a reflection on the nature, scope, and limits of knowledge that have been at the focus of the author's work over decades. The essays collected in this volume expound and extend these efforts in exploring the outer fringes of understanding: the outer boundaries of conceivability, the limits of cognition, and the ramifications of ineffability and paradox. They join in exploring the lay of the land at the boundaries of knowledge. The first chapters address basic facts regarding the conceptualization of knowledge. This is followed by a study on how to deal with problems relating to the affirmation and considerations of truth. The final chapters scrutinize the limits of demonstration and the inherent impossibility of realizing an ideal systematization of our knowledge of totalities. The book affords novel perspectives regarding the thought of a widely appreciated philosopher. It is an original work aimed for readers interested in the theory of knowledge and philosophy of cognition.

Originally published in 1990. A common complaint of philosophers, and men in general, has been that women are illogical. On the other hand, rationality, defined as the ability to follow logical argument, is often claimed to be a defining characteristic of man. Andrea Nye undermines assumptions such as: logic is unitary, logic is independent of concrete human relations, logic transcends historical circumstances as well as gender. In a series of studies of the logics of historical figures Parmenides, Plato, Aristotle, Zeno, Abelard, Ockham, and Frege she traces the changing interrelationships between logical innovation and oppressive speech strategies, showing that logic is not transcendent truth but abstract forms of language spoken by men, whether Greek ruling citizens, imperial administrators, church officials, or scientists. She relates logical techniques, such as logical division, syllogisms, and truth functions, to ways in which those with power speak to and about those subject to them. She shows, in the specific historical settings of Ancient and Hellenistic Greece, medieval Europe, and Germany between the World Wars, how logicians reworked language so that dialogue and reciprocity are impossible and one speaker is forced to accept the words of another. In the personal, as well as confrontative style of her readings, Nye points the way to another power in the words of women that might break into and challenge rational discourses that have structured Western thought and practice.

This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: An Introduction to Modal Logic and A Companion to Modal Logic.
A New Introduction to Modal Logic is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works.
The book takes readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic.

This book offers new insights into the nature of human rational capacities by engaging inferentialism with empirical research in the cognitive sciences. Inferentialism advocates that humans' unique kind of intelligence is discursive and rooted in competencies to make, assess and justify claims. This approach provides a rich source of valuable insights into the nature of our rational capacities, but it is underdeveloped in important respects. For example, little attempt has been made to assess inferentialism considering relevant scientific research on human communication, cognition or reasoning. By engaging philosophical and scientific approaches in a productive dialogue, this book shows how we can better understand human rational capacities by comparing their respective strengths and weaknesses. In this vein, the author critically revisits and constructively develops central themes from the work of Robert Brandom and other "language rationalists": the nature of the assertoric practice and its connection to reasoned discourse, the linguistic constitution of the shared space of reasons, the social nature and function of reasoning, the intersubjective roots of social-normative practices and the nature of objective thought. Practices of Reason will be of interest to scholars and advanced students working in philosophy of mind, philosophy of language and philosophy of logic.

Originally published in 1972, Medieval Logic and Metaphysics shows how formal logic can be used in the clarification of philosophical problems. An elementary exposition of Lesniewski's Onotology, an important system of contemporary logic, is followed by studies of central philosophical themes such as Negation and Non-being, Essence and Existence, Meaning and Reference, Part and Whole. Philosophers and theologians discussed include St Anselm, St Thomas Aquinas, Abelard, Ockham, Scotus, Hume and Russell.

This innovative text reinvigorates argumentation studies by exploring the experience of argument across cultures, introducing an anthropological perspective into the domains of rhetoric, communication, and philosophy. The Anthropology of Argument fills an important gap in contemporary argumentation theory by shifting the focus away from the purely propositional element of arguments and onto how they emerge from the experiences of peoples with diverse backgrounds, demonstrating how argumentation can be understood as a means of expression and a gathering place of ideas and styles. Confronting the limitations of the Western tradition of logic and searching out the argumentative roles of place, orality, myth, narrative, and audience, it examines the nature of multi-modal argumentation. Tindale analyzes the impacts of colonialism on the field and addresses both optimistic and cynical assessments of contextual differences. The results have implications for our understanding of contemporary argumentative discourse in areas marked by deep disagreement, like politics, law, and social policy. The book will interest scholars and upper-level students in communication, philosophy, argumentation theory, anthropology, rhetoric, linguistics, and cultural studies.

Arguing that our attachment to Aristotelian modes of discourse makes a revision of their conceptual foundations long overdue, the author proposes the consideration of unacknowledged factors that play a central role in argument itself. These are in particular the subjective imprint and the dynamics of argumentation. Their inclusion in a four-dimensional framework (subjective-objective, structural-procedural) and the focus on thesis validity allow for a more realistic view of our discourse practice. Exhaustive analyses of fascinating historical and contemporary arguments are provided. These range from Columbus s advocacy of the Western Passage to India, over the trial of King Louis XVI during the French Revolution, to today s highly charged controversies surrounding euthanasia and embryo research.

Excavating foundational issues such as the purpose of argument itself (assent of an audience or critical examination of validity claims) and the contested role of argument as a generator of knowledge, the book culminates in a discussion of the relationship between rationality and reasonableness and criticizes the restrictions of rational argument relying on fixed logical, economic or cultural criteria that in reality are mutable. Here, a true, open argument requires the infusion of Paul Lorenzen s principle of transsubjectivity, which recognizes but transcends the partiality of the individual and which can be seen in the pragmatic and expanding consensus that humanity can control itself to safeguard the future of a fragile, damaged world."

This new volume on logic follows a recognizable format that deals in turn with the topics of mathematical logic, moving from concepts, via definitions and inferences, to theories and axioms. However, this fresh work offers a key innovation in its 'pyramidal' graph system for the logical formalization of all these items. The author has developed this new methodology on the basis of original research, traditional logical instruments such as Porphyrian trees, and modern concepts of classification, in which pyramids are the central organizing concept. The pyramidal schema enables both the content of concepts and the relations between the concept positions in the pyramid to be read off from the graph. Logical connectors are analyzed in terms of the direction in which they connect within the pyramid.

Additionally, the author shows that logical connectors are of fundamentally different types: only one sort generates propositions with truth values, while the other yields conceptual expressions or complex concepts. On this basis, strong arguments are developed against adopting the non-discriminating connector definitions implicit in Wittgensteinian truth-value tables. Special consideration is given to mathematical connectors so as to illuminate the formation of concepts in the natural sciences. To show what the pyramidal method can contribute to science, a pyramid of the number concepts prevalent in mathematics is constructed. The book also counters the logical dogma of 'false' contradictory propositions and sheds new light on the logical characteristics of probable propositions, as well as on syllogistic and other inferences.

This book is a companion to logical thought and logical thinking in China with a comparative and interdisciplinary perspective. It introduces the basic ideas and theories of Chinese thought in a comprehensive and analytical way. It covers thoughts in ancient, pre-modern and modern China from a historical point of view. It deals with topics in logical (including logico-philosophical) concepts and theories rooted in China, Indian and Western Logic transplanted to China, and the development of logical studies in contemporary China and other Chinese communities. The term "philosophy of logic" or "logico-philosophical thought" is used in this book to represent "logical thought" in a broad sense which includes thinking on logical concepts, modes of reasoning, and linguistic ideas related to logic and philosophical logic. Unique in its approach, the book uses Western logical theories and philosophy of language, Chinese philology, and history of ideas to deal with the basic ideas and major problems in logical thought and logical thinking in China. In doing so, it advances the understanding of the lost tradition in Chinese philosophical studies.

This book aims to discuss probability and David Hume's inductive scepticism. For the sceptical view which he took of inductive inference, Hume only ever gave one argument. That argument is the sole subject-matter of this book. The book is divided into three parts. Part one presents some remarks on probability. Part two identifies Hume's argument for inductive scepticism. Finally, the third part evaluates Hume's argument for inductive scepticism.

Originally published in 1937. A short account of the traditional logic, intended to provide the student with the fundamentals necessary for the specialized study. Suitable for working through individualy, it will provide sufficient knowledge of the elements of the subject to understand materials on more advanced and specialized topics. This is an interesting historic perspective on this area of philosophy and mathematics.

Originally published in 1962. A clear and simple account of the growth and structure of Mathematical Logic, no earlier knowledge of logic being required. After outlining the four lines of thought that have been its roots - the logic of Aristotle, the idea of all the parts of mathematics as systems to be designed on the same sort of plan as that used by Euclid and his Elements, and the discoveries in algebra and geometry in 1800-1860 - the book goes on to give some of the main ideas and theories of the chief writers on Mathematical Logic: De Morgan, Boole, Jevons, Pierce, Frege, Peano, Whitehead, Russell, Post, Hilbert and Goebel. Written to assist readers who require a general picture of current logic, it will also be a guide for those who will later be going more deeply into the expert details of this field.

Originally published in 1931. This inquiry investigates and develops John Cook Wilson's view of the province of logic. It bases the study on the posthumous collected papers Statement and Inference. The author seeks to answer questions on the nature of logic using Cook Wilson's thought. The chapters introduce and consider topics from metaphysics to grammar and from psychology to knowledge. An early conception of logic in the sciences and presenting the work of an important twentieth century philosopher, this is an engaging work.

Originally published in 1966. Professor Rescher's aim is to develop a "logic of commands" in exactly the same general way which standard logic has already developed a "logic of truth-functional statement compounds" or a "logic of quantifiers". The object is to present a tolerably accurate and precise account of the logically relevant facets of a command, to study the nature of "inference" in reasonings involving commands, and above all to establish a viable concept of validity in command inference, so that the logical relationships among commands can be studied with something of the rigour to which one is accustomed in other branches of logic.