Reissue from the classic Muirhead Library of Philosophy series (originally published between 1890s - 1970s).

Vagueness, volume XX, contains twenty-seven essays, with issues covered including: nihilism, phenomenal sorites, degrees of truth, epistemicism, higher-order vagueness, contextualism, and intuitionism. Written by leading contemporary philosophers, these essays will be of interest to researchers in philosophy of language, philosophical logic, metaphysics and epistemology; as well as those in natural language semantics, artificial intelligence and cognitive science more generally. A substantial introduction written by the editors provides a guide to the topic and to the essays in the volume.

This volume collects 22 essays on the history of logic written by outstanding specialists in the field. The book was originally prompted by the 2018-2019 celebrations in honor of Massimo Mugnai, a world-renowned historian of logic, whose contributions on Medieval and Modern logic, and to the understanding of the logical writings of Leibniz in particular, have shaped the field in the last four decades. Given the large number of recent contributions in the history of logic that have some connections or debts with Mugnai's work, the editors have attempted to produce a volume showing the vastness of the development of logic throughout the centuries. We hope that such a volume may help both the specialist and the student to realize the complexity of the history of logic, the large array of problems that were touched by the discipline, and the manifold relations that logic entertained with other subjects in the course of the centuries. The contributions of the volume, in fact, span from Antiquity to the Modern Age, from semantics to linguistics and proof theory, from the discussion of technical problems to deep metaphysical questions, and in it the history of logic is kept in dialogue with the history of mathematics, economics, and the moral sciences at large.

Contents:
Introduction
1. Plural Quantifications
1. Singular Versus Plural Quantifications
2. Implication
3. Paraphrase
2. The Logic of Plurals
1. Language
2. Logic
Appx: Partial Axiomatization of the Logic of Plurals
3. Is Two a Property?
1. Why Property Two?
2. A Theory of Plural Properties
3. Two As an Intrinsic Plural Property
4. Concluding Remarks
4. What Numbers Should Be
1. Are Numbers Objects?
2. Plural Properties As Components of Numerical Facts
3. Analysis of Numerical Facts
4. Numbers Are Properties
5. How Sets Are Determined by Their Members
1. The Hierarchy of Sets and the Determination of Sets by Their Members
2. Reference to Set-like Objects
Plural Reference to Mundane Objects
3. Exclusive Reference to Mundane Objects
4. Concluding Remarks
References
Index

Knocking on Heaven's Door is the oldest human dream that seems unrealized still. Religious discourse does show the road, but it requires a blind faith in return. In this book logicians try to hear Heaven's Call and to analyze religious discourse. As a result, the notion of religious logic as a part of philosophical logic is introduced. Its tasks are (1) to construct consistent logical systems formalizing religious reasoning that at first sight seems inconsistent (this research is fulfilled within the limits of modal logic, paraconsistent logic and many-valued logic), (2) to carry out an illocutionary analysis of religious discourse (this research is fulfilled in frames of illocutionary logics), and (3) to formalize Ancient and Medieval logical theories used in the theology of an appropriate religion (they could be studied within the limits of unconventional logics, such as non-monotonic logics, non-well-founded logics, etc.).

First published in 1998, Taking on Wittgensteinianism themes, but also using, or relying on several mathematical results, Slater in this book explores the idea of realism and further argues how in a philosophical viewpoint is incorrect. Slater also surveys various philosophers in the field of logic to argue against the idea of realism.

Morton Schoolman explores what makes humankind capable of genocide in this fascinating interpretation of Horkheimer and Adorno. He recasts their views on diversity and individuality before and after the Holocaust, as well as re-examining Nietzsche and even Whitman and Tocqueville. He argues that the sensibility the critical theorists argued for is actually nurtured in a democracy, and concludes that to avoid the possibility of genocide people must also change the way they feel, and cultivate an aesthetic sensibility.

Morton Schoolman explores what makes humankind capable of genocide in this fascinating interpretation of Horkheimer and Adorno. He recasts their views on diversity and individuality before and after the Holocaust, as well as re-examining Nietzsche and even Whitman and Tocqueville. He argues that the sensibility the critical theorists argued for is actually nurtured in a democracy, and concludes that to avoid the possibility of genocide people must also change the way they feel, and cultivate an aesthetic sensibility.

Originally published in 1964. This book is concerned with general arguments, by which is meant broadly arguments that rely for their force on the ideas expressed by all, every, any, some, none and other kindred words or phrases. A main object of quantificational logic is to provide methods for evaluating general arguments. To evaluate a general argument by these methods we must first express it in a standard form. Quantificational form is dealt with in chapter one and in part of chapter three; in the remainder of the book an account is given of methods by which arguments when formulated quantificationally may be tested for validity or invalidity. Some attention is also paid to the logic of identity and of definite descriptions. Throughout the book an attempt has been made to give a clear explanation of the concepts involved and the symbols used; in particular a step-by-step and partly mechanical method is developed for translating complicated statements of ordinary discourse into the appropriate quantificational formulae. Some elementary knowledge of truth-functional logic is presupposed.

Originally published in 1962. This book gives an account of the concepts and methods of a basic part of logic. In chapter I elementary ideas, including those of truth-functional argument and truth-functional validity, are explained. Chapter II begins with a more comprehensive account of truth-functionality; the leading characteristics of the most important monadic and dyadic truth-functions are described, and the different notations in use are set forth. The main part of the book describes and explains three different methods of testing truth-functional aguments and agument forms for validity: the truthtable method, the deductive method and the method of normal forms; for the benefit mainly of readers who have not acquired in one way or another a general facility in the manipulation of symbols some of the procedures have been described in rather more detail than is common in texts of this kind. In the final chapter the author discusses and rejects the view, based largely on the so called paradoxes of material implication, that truth-functional logic is not applicable in any really important way to arguments of ordinary discourse.

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 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.

Originally published in 1934. This fourth edition originally published 1954., revised by C. W. K. Mundle. "It must be the desire of every reasonable person to know how to justify a contention which is of sufficient importance to be seriously questioned. The explicit formulation of the principles of sound reasoning is the concern of Logic". This book discusses the habit of sound reasoning which is acquired by consciously attending to the logical principles of sound reasoning, in order to apply them to test the soundness of arguments. It isn't an introduction to logic but it encourages the practice of logic, of deciding whether reasons in argument are sound or unsound. Stress is laid upon the importance of considering language, which is a key instrument of our thinking and is imperfect.

Originally published in 1973. This book is directed to the student of philosophy whose background in mathematics is very limited. The author strikes a balance between material of a philosophical and a formal kind, and does this in a way that will bring out the intricate connections between the two. On the formal side, he gives particular care to provide the basic tools from set theory and arithmetic that are needed to study systems of logic, setting out completeness results for two, three, and four valued logic, explaining concepts such as freedom and bondage in quantificational logic, describing the intuitionistic conception of the logical operators, and setting out Zermelo's axiom system for set theory. On the philosophical side, he gives particular attention to such topics as the problem of entailment, the import of the Loewenheim-Skolem theorem, the expressive powers of quantificational logic, the ideas underlying intuitionistic logic, the nature of set theory, and the relationship between logic and set theory. There are exercises within the text, set out alongside the theoretical ideas that they involve.

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.

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 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.

The articles in this volume are all landmarks in the evolution of modern studies in Indian logic. The book traces the development of modern studies in Indian logic from their beginnings right up to 1998. Each of the articles has very specific reasons for its inclusion.

The articles in this volume are all landmarks in the evolution of modern studies in Indian logic. The book traces the development of modern studies in Indian logic from their beginnings right up to the latest work.

Contents:
Hamblin, C L, The Indian Tradition, Fallacies [London: Methuen, 1970]
Randle, H H, A Note on the Indian Syllogism, Mind, 33 [1924]
Staal, Frits, The Concept of Paksa in Indian Logic, Journal of Indian Philosophy 2 [1973]
Staal, J F, Negation and the Law of Contradiction in Indian Thought, Bulletin of the School of Oriental and African Studies 25 [1962]
Gillon, Brendan S and Martha Lile Love, Indian Logic Revisited: Nyayapravesa Reviewed, Journal of Indian Philosophy 8 [1980]
Bhattacharyya, Sibajiban, Some Features of the Technical Language of Navya-Nyaya, Philosophy East and West 40 [1990]
Shaw, J L, The Nyaya on Double Negation, Notre Dame Journal of Formal Logic 29 [1988]
Bhattacharyya, Sibajiban, The Middle Term, Notre Dame Journal of Formal Logic 9 [1968]
Mohanty, J N, Psychologism in Indian Logic, In B K Matilal and J L Shaw eds., Analytical Philosophy in Comparitive Perspective [Dordrecht: Reidel, 1985]
David, Lawrence, Tarka in the Nyaya Theory of Inference, Journal of Indian Philosophy 9 [1981]
Matilal, B K Anenkanta: Both Yes and No? Journal of the Indian Council of Philosophical Research 8 [1991]
Staal, J F, Sanskrit Philosophy of Language, In Thomas A Seboek ed., Current Trends in Linguistics: Vol 5, Linguistics in South Asia [The Hague: Mouton, 1969]
Brough, John, Some Indian Theories of Meaning, Transactions of the Philological Society [1953]
Matilal, B K, Reference and Existence in Nyaya and Buddhist Logic, Journal of Indian Philosophy 1 [1970]
Matilal, B K, and P K Sen, The Context Principle and Some Indian Controversies Over Meaning, Mind 97 [1988]
Siderits, Mark, The Sense-Reference Distinction in Indian Philosophy of Language, Synthese 69 [1986]
Herzberger, Hans, and Radhika Hersberger, Bhartrhari's Paradox, Journal of Indian Philosophy 9 [1981]

W.V. Quine (1908-) has played a crucial role in philosophy during the second half of the twentieth century. These five volumes contain the most essential of the more than 2000 articles written about Quine's work. Chosen for their clarity and brevity, they cover both basic ideas as well as objections to Quine's work. These articles are a valuable resource for students and scholars; many have been previously available only in hard-to-find sources, and in addition, some have been written or translated expressly for this collection. Available individually or by volume

Russell's "On Denoting" and Frege's "On Sense and Reference" are now widely held to be two of the founding papers of 20th-century philosophy and form the heart of the famous "linguistic turn". They have generated a wealth of secondary literature and remain at the forefront of contemporary discussion in philosophy of language, thought and logic. This book challenges the accepted understanding of these two seminal papers. It forces us to reconsider contemporary approaches to the semantics of proper names and definite descriptions through a historically sensitive interpretation of Russell's and Frege's work on meaning. Gideon Makin compares the work Russell did shortly before his famous essay "On Denoting" with the essay itself and argues that this comparison shows that the traditional view of the problem Russell was trying to solve is untenable. Makin then examines Frege's classic essay and argues that some of the less well-known views that Frege held have radical implications for our understanding of this essay.

Philosophy in the medieval Latin West before 1200 is often thought to have been dominated by Platonism. The articles in this volume question this view, by cataloguing, describing and investigating the tradition of Aristotelian logic during this period, examining its influence on authors usually placed within the Aristotelian tradition (Eriugena, Anselm, Gilbert of Poitiers), and also looking at some of the characteristics of early medieval Platonism. Abelard, the most brilliant logician of the age, is the main subject of three articles, and the book concludes with two more general discussions about how and why medieval philosophy should be studied.

Originally published in 1991, this volume examines Hegel's political philosophy from the perspective of his argument for constitutional monarchy. It offers an interpretation of Hegelian theory that is relevant for the understanding of modern republican constitutions. Modern republican theories are assessed together with those of Plato, Kant and Marx in order to put Hegel's model to the most rigorous test. The arguments are based on fresh analysis of Hegel's system and on new translations of key passages in Hegel's text.