Robert Stern investigates how scepticism can be countered by using transcendental arguments concerning the necessary conditions for the possibility of experience, language, or thought. He shows that the most damaging sceptical questions concern neither the certainty of our beliefs, nor the reliability of our belief-forming methods, but rather how we can justify our beliefs in the light of our doxastic norms.

This book is not a conventional history of mathematics as such, a museum of documents and scientific curiosities. Instead, it identifies this vital science with the thought of those who constructed it and in its relation to the changing cultural context in which it evolved. Particular emphasis is placed on the philosophic and logical systems, from Aristotle onward, that provide the basis for the fusion of mathematics and logic in contemporary thought. Ettore Carruccio covers the evolution of mathematics from the most ancient times to our own day. In simple and non-technical language, he observes the changes that have taken place in the conception of rational theory, until we reach the lively, delicate and often disconcerting problems of modern logical analysis. The book contains an unusual wealth of detail (including specimen demonstrations) on such subjects as the critique of Euclid's fifth postulate, the rise of non-Euclidean geometry, the introduction of theories of infinite sets, the construction of abstract geometry, and-in a notably intelligible discussion-the development of modern symbolic logic and meta-mathematics. Scientific problems in general and mathematical problems in particular show their full meaning only when they are considered in the light of their own history. This book accordingly takes the reader to the heart of mathematical questions, in a way that teacher, student and layman alike will find absorbing and illuminating. The history of mathematics is a field that continues to fascinate people interested in the course of creativity, and logical inference u quite part and in addition to those with direct mathematical interests.

Despite there being deep lines of convergence between the philosophies of Alfred North Whitehead, C. S. Peirce, William James, John Dewey, and other classical American philosophers, it remains an open question whether Whitehead is a pragmatist, and conversation between pragmatists and Whitehead scholars have been limited. Indeed, it is difficult to find an anthology of classical American philosophy that includes Whitehead's writings. These camps began separately, and so they remain. This volume questions the wisdom of that separation, exploring their connections, both historical and in application. The essays in this volume embody original and creative work by leading scholars that not only furthers the understanding of American philosophy, but seeks to advance it by working at the intersection of experience and reality to incite novel and creative thought. This exploration is long overdue. Specific questions that are addressed are: Is Whitehead a pragmatist? What contrasts and affinities exist between American pragmatism and Whitehead's thought? What new questions, strategies, and critiques emerge by juxtaposing their distinct perspectives?

Luciano Floridi presents a book that will set the agenda for the philosophy of information. PI is the philosophical field concerned with (1) the critical investigation of the conceptual nature and basic principles of information, including its dynamics, utilisation, and sciences, and (2) the elaboration and application of information-theoretic and computational methodologies to philosophical problems. This book lays down, for the first time, the conceptual foundations for this new area of research. It does so systematically, by pursuing three goals. Its metatheoretical goal is to describe what the philosophy of information is, its problems, approaches, and methods. Its introductory goal is to help the reader to gain a better grasp of the complex and multifarious nature of the various concepts and phenomena related to information. Its analytic goal is to answer several key theoretical questions of great philosophical interest, arising from the investigation of semantic information.

The notion of logical form and its applications are at the heart of some of the classical problems in philosophical logic and are the focus of Peter Long's investigations in the three essays that comprise this volume. In the first, major, essay the concern is with the notion of logical form as it applies to arguments involving hypotethical statements, for example 'If today is Wednesday then tomorrow is Thursday; today is Wednesday: therefore tomorrow is Thursday.' Whilst such an argument (an argument by modus ponens) is cited by logical textbooks as a paradigm of one that is 'formally valid', it is not hard to show that the conjunction forming a hypothetical statement is not a logical constant, in which case the argument form If p then q; p: therefore q is not a logical form. But, then, how can logic claim to be the science of formal inference? The author resolves this difficulty by drawing a fundamental distinction within the notion of the form under which an argument is valid. With this distinction it becomes possible for the first time to determine the status of any formally valid argument involving hypotheticals, whether as premises or conclusion or both. The second and third essays take up the notion of logical form as it applies to such simple propositions as 'This sheet is white' and 'London is north of Paris.' When we speak of the first as giving expression to the relation of relations's relating to its terms, what is in question is a formal relation and we call it such because the relation is expressed through these propositions having the respective forms Fa and Fab. It is shown that the confusion of formal relations with relations proper explains the assimilation of facts to complexes and is that the root of the theory of universals. Peter Long has taught at the University of Leeds and University College London, and is a past Fellow of Trinity College, Cambridge.

From Concept to Objectivity uncovers the nature and authority of conceptual determination by critically thinking through neglected arguments in Hegel's Science of Logic pivotal for understanding reason and its role in philosophy. Winfield clarifies the logical problems of presuppositionlessness and determinacy that prepare the way for conceiving the concept, examines how universality, particularity, and individuality are determined, investigates how judgment and syllogism are exhaustively differentiated, and, on that basis, explores how objectivity can be categorized without casting thought in irrevocable opposition to reality. Winfield's book will be of interest to readers of Hegel, as well as anyone wondering how thought can be objective.

This book is a study in the methodology of philosophical inquiry. Accordingly, it is a venture in metaphilosophy, perhaps the most controversial of philosophical disciplines.

Philosophy is caught in a dilemma. On one hand, its omission as a legitimate venture in empirical inquiry requires its looking to "the big picture" and striving to counteract the fragmented specialization of other cognitive domains. On the other hand, philosophy does not and cannot avert division of labor. Thus, it remains committed to the quest for unity and coherence in our understanding of the nature of things in a world where our knowledge is exploding in scope and in complexity. "

Philosophical Reasoning" explores this difficult situation and clarifies its implications by expounding and defending the following thesis: that systematization is the proper instrument of philosophical inquiry, and that the effective pursuit of philosophy's mission calls for constructing a doctrinal system that answers our questions in a coherent and comprehensive manner.

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.

The Price of Doubt is an important contribution to the problem of scepticism. It offers a new standard for the appraisal of philosophical arguments. Nicholas Nathan confronts the sceptic. He questions the value of his argument and the knowledge it contains and provides a potential remedy to the frustrations of anti-sceptical epistemology.

Most of the major twentieth-century thinkers develop their thought through critical dialogues with their predecessors. This anthology brings together a selection of these dialogues, offering a fresh approach to modern critical thought from Marx through to the present day.

The essays, lectures and reviews featured in this volume represent thinkers from Lukacs and Heidegger to Judith Butler and Slavoj Zižek. Often at their most accessible introducing their own key influences and predecessors, these writings therefore provide an ideal way into the traditions of modern critical thought and into their own more difficult writings. As the reader proceeds through the book, the pieces build into a series of overlapping conversations and arguments, spanning different generations and crossing boundaries between French, German and English thought. The book offers an invaluable introduction to traditions of Marxist critical theory, phenomenology, psychoanalysis, post-structuralism and post-modern discourse.

The anthology opens with an introductory essay in which the editor introduces key critical terms and maps out the contested terrain of criticism and critique implicit in the choice of particular works. He also introduces each text with contextualizing notes and suggestions for further reading.

The methods of logic are essential to an understanding of philosophy and are crucial in the study of mathematics, computing, linguistics and many other subjects. Introducing the major concepts and techniques involved in the study of logic, this authoritative book explores both formal and philosophical logic, and the ways in which we can achieve good reasoning. Individual chapters include: * Propositions and Arguments * Truth Tables * Trees * Conditionality * Natural Deduction * Predicates, Names and Quantifiers * Definite Descriptions. This exceptionally clear introduction to the subject is ideally suited to students taking introductory courses in logic.

Peter Adamson and Jonardon Ganeri present a lively introduction to one of the world's richest intellectual traditions: the philosophy of classical India. They begin with the earliest extant literature, the Vedas, and the explanatory works that these inspired, known as Upanisads. They also discuss other famous texts of classical Vedic culture, especially the Mahabharata and its most notable section, the Bhagavad-Gita, alongside the rise of Buddhism and Jainism. In this opening section, Adamson and Ganeri emphasize the way that philosophy was practiced as a form of life in search of liberation from suffering. Next, the pair move on to the explosion of philosophical speculation devoted to foundational texts called 'sutras,' discussing such traditions as the logical and epistemological Nyaya school, the monism of Advaita Vedanta, and the spiritual discipline of Yoga. In the final section of the book, they chart further developments within Buddhism, highlighting Nagarjuna's radical critique of 'non-dependent' concepts and the no-self philosophy of mind found in authors like Dignaga, and within Jainism, focusing especially on its 'standpoint' epistemology. Unlike other introductions that cover the main schools and positions in classical Indian philosophy, Adamson and Ganeri's lively guide also pays attention to philosophical themes such as non-violence, political authority, and the status of women, while considering textual traditions typically left out of overviews of Indian thought, like the Carvaka school, Tantra, and aesthetic theory as well. Adamson and Ganeri conclude by focusing on the much-debated question of whether Indian philosophy may have influenced ancient Greek philosophy and, from there, evaluate the impact that this area of philosophy had on later Western thought.

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.

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.

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 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 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 sets out for the first time in English and in the terms of modern logic the semantics of the Port Royal Logic (La Logique ou l'Art de penser, 1662-1685) of Antoine Arnauld and Pierre Nicole, perhaps the most influential logic book in the 17th and 18th centuries. Its goal is to explain how the Logic reworks the foundation of pre-Cartesian logic so as to make it compatible with Descartes' metaphysics. The Logic's authors forged a new theory of reference based on the medieval notion of objective being, which is essentially the modern notion of intentional content. Indeed, the book's central aim is to detail how the Logic reoriented semantics so that it centered on the notion of intentional content. This content, which the Logic calls comprehension, consists of an idea's defining modes. Mechanisms are defined in terms of comprehension that rework earlier explanations of central notions like conceptual inclusion, signification, abstraction, idea restriction, sensation, and most importantly within the Logic's metatheory, the concept of idea-extension, which is a new technical concept coined by the Logic. Although Descartes is famous for rejecting "Aristotelianism," he says virtually nothing about technical concepts in logic. His followers fill the gap. By putting to use the doctrine of objective being, which had been a relatively minor part of medieval logic, they preserve more central semantic doctrines, especially a correspondence theory of truth. A recurring theme of the book is the degree to which the Logic hews to medieval theory. This interpretation is at odds with what has become a standard reading among French scholars according to which this 16th-century work should be understood as rejecting earlier logic along with Aristotelian metaphysics, and as putting in its place structures more like those of 19th-century class theory.

This text provides a truly comprehensive guide to one of the most important and challenging works of modern philosophy. The systematic complexity of Hegel's radical project in the Science of Logic prevents many from understanding and appreciating its value. By independently and critically working through Hegel's argument, this book offers an enlightening aid for study and anchors the Science of Logic at a central position in the philosophical canon.

Were the most serious philosophers of the millennium 200 A.D. to 1200 A.D. just confused mystics? This book shows otherwise. John Martin rehabilitates Neoplatonism, founded by Plotinus and brought into Christianity by St. Augustine. The Neoplatonists devise ranking predicates like good, excellent, perfect to divide the Chain of Being, and use the predicate intensifier hyper so that it becomes a valid logical argument to reason from God is not (merely) good to God is hyper-good. In this way the relational facts underlying reality find expression in Aristotle's subject-predicate statements, and the Platonic tradition proves able to subsume Aristotle's logic while at the same time rejecting his metaphysics. In the Middle Ages when Aristotle's larger philosophy was recovered and joined again to the Neoplatonic tradition which was never lost, Neoplatonic logic lived along side Aristotle's metaphysics in a sometime confusing and unsettled way. Showing Neoplatonism to be significantly richer in its logical and philosophical ideas than it is usually given credit for, this book will be of interest not just to historians of logic, but to philosophers, logicians, linguists, and theologians.

Is it possible to quantify over absolutely all there is? Or must all of our quantifiers range over a less-than-all-inclusive domain? It has commonly been thought that the question of absolute generality is intimately connected with the set-theoretic antinomies. But the topic of absolute generality has enjoyed a surge of interest in recent years. It has become increasingly apparent that its ramifications extend well beyond the foundations of set theory. Connections include semantic indeterminacy, logical consequence, higher-order languages, and metaphysics. Rayo and Uzquiano present for the first time a collection of essays on absolute generality. These newly commissioned articles - written by an impressive array of international scholars - draw the reader into the forefront of contemporary research on the subject. The volume represents a variety of approaches to the problem, with some of the contributions arguing for the possibility of all-inclusive quantification and some of them arguing against it. An introduction by the editors draws a helpful map of the philosophical terrain.

The subject of the book is a reconsideration of the internalistic model of composition of the Platonic type, more radical than traditional, post-Aristotelian externalistic compositionism, and its application in the field of the ontology of quantum theory. At the centre of quantum ontology is nonseparability. Quantum wholes are atemporal wholes governed by internalistic logic and they are primitive, global physical entities, requiring an extreme relativization of the fundamental notions of mechanics. That ensures quantum theory to be fully consistent with the relativistic causal structure, without any spacelike nonlocality and time asymmetry, and makes the quantum blockworld ontology inevitable. It seems that the more internally relativized physics is, the more Platonic it becomes.

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.

This book presents the heritage of the Lvov-Warsaw School from both the historical and the philosophical perspective. The historical view focuses on the beginnings and the dramatic end of the School brought about by the outbreak of World War II. The philosophical view, on the other hand, encompasses a broad spectrum of issues, including logical, epistemological, axiological, and psychological problems, revealing the interdisciplinary nature of studies carried out by Kazimierz Twardowski and his students. With thirteen diverse and original essays this volume is split into three parts: History, Culture and Axiology; Psychology; and Logic and Methodology. Exploring not only the history of philosophy represented by the Lvov-Warsaw school, the book also reflects on the condition of contemporary philosophy from the perspective of concepts developed by its representatives. Furthermore, the studies presented in this book delve into problems of contemporary science and its distinctive interdisciplinary character. This volume is, therefore, not only a collection of analyses of the Lvov-Warsaw School philosophy, but also an investigation into the interdisciplinarity of science and philosophy itself.