Download or read book Bolzano s Logical System written by Ettore Casari and published by Oxford University Press. This book was released on 2016-09-08 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is focused on the first three parts of Bolzano's Theory of Sciene and introduces a more systematic reconsideration of Bolzano's logial thought. In undertaking this task, the book is intended as an exploration, not so much of the more specifically discursive aspects of Bolzano's logial thought - already amply studied - as muh as on identifying the singularly coherent and systematic nature of the logic presented in Bolzano's work. Casari presents this within a formal system and adopts the approach of the predicate calculus with identity and choice operator by using Hilbert's epsilon calculus (the logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics).

Download or read book Essays on Husserl s Logic and Philosophy of Mathematics written by Stefania Centrone and published by Springer. This book was released on 2017-09-07 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Gödel and Hermann Weyl. Most of the papers consider Husserl and another scholar – e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege – and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one.

Download or read book Bolzano s Philosophy of Grounding written by Stefan Roski and published by Oxford University Press. This book was released on 2022-02-24 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the liveliest debates in contemporary philosophy concerns the notions of grounding and metaphysical explanation. Many consider these notions to be of prime importance for metaphysics and the philosophy of explanation, or even for philosophy in general, and lament that they had been neglected for far too long. Although the current debate about grounding is of recent origin, its central ideas have a long and rich history in Western philosophy, going back at least to the works of Plato and Aristotle. Bernard Bolzano's theory of grounding, developed in the first half of the nineteenth century, is a peak in the history of these ideas. On Bolzano's account, grounding lies at the heart of a broad conception of explanation encompassing both causal and non-causal cases. Not only does his theory exceed most earlier theories in scope, depth, and rigour, it also anticipates a range of ideas that take a prominent place in the contemporary debate. But despite the richness and modernity of his theory, it is known only by a comparatively small circle of philosophers predominantly consisting of Bolzano scholars. Bolzano's Philosophy of Grounding is meant to make Bolzano's ideas on grounding accessible to a broader audience. The book gathers translations of Bolzano's most important writings on these issues, including material that has hitherto not been available in English. Additionally, it contains a survey article on Bolzano's conception and nine research papers critically assessing elements of the theory and/or exploring its broad range of applications in Bolzano's philosophy and beyond.

Download or read book Aristotle s Syllogism and the Creation of Modern Logic written by Lukas M. Verburgt and published by Bloomsbury Publishing. This book was released on 2023-01-26 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering a bold new vision on the history of modern logic, Lukas M. Verburgt and Matteo Cosci focus on the lasting impact of Aristotle's syllogism between the 1820s and 1930s. For over two millennia, deductive logic was the syllogism and syllogism was the yardstick of sound human reasoning. During the 19th century, this hegemony fell apart and logicians, including Boole, Frege and Peirce, took deductive logic far beyond its Aristotelian borders. However, contrary to common wisdom, reflections on syllogism were also instrumental to the creation of new logical developments, such as first-order logic and early set theory. This volume presents the period under discussion as one of both tradition and innovation, both continuity and discontinuity. Modern logic broke away from the syllogistic tradition, but without Aristotle's syllogism, modern logic would not have been born. A vital follow up to The Aftermath of Syllogism, this book traces the longue durée history of syllogism from Richard Whately's revival of formal logic in the 1820s through the work of David Hilbert and the Göttingen school up to the 1930s. Bringing together a group of major international experts, it sheds crucial new light on the emergence of modern logic and the roots of analytic philosophy in the 19th and early 20th centuries.

Download or read book The Routledge Handbook of Propositions written by Chris Tillman and published by Taylor & Francis. This book was released on 2022-09-30 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: Propositions are routinely invoked by philosophers, linguists, logicians, and other theorists engaged in the study of meaning, communication, and the mind. To investigate the nature of propositions is to investigate the very nature of our connection to each other, and to the world around us. As one of the only volumes of its kind, The Routledge Handbook of Propositions provides a comprehensive overview of the philosophy of propositions, from both historical and contemporary perspectives. Comprising 33 original chapters by an international team of scholars, the volume addresses both traditional and emerging questions concerning the nature of propositions, and our capacity to engage with them in thought and in communication. The chapters are clearly organized into the following three sections: I. Foundational Issues in the Theory of Propositions II. Historical Theories of Propositions III. Contemporary Theories of Propositions Essential reading for philosophers of language and mind, and for those working in neighboring areas, The Routledge Handbook of Propositions is suitable for upper-level undergraduate study, as well as graduate and professional research.

Download or read book Provability Computability and Reflection written by Lev D. Beklemishev and published by Elsevier. This book was released on 2009-06-15 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection

Download or read book The Routledge Handbook of Metaphysical Grounding written by Michael J. Raven and published by Routledge. This book was released on 2020-05-04 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some of philosophy’s biggest questions, both historically and today, are in-virtue-of questions: In virtue of what is an action right or wrong? In virtue of what am I the same person my mother bore? In virtue of what is an artwork beautiful? Philosophers attempt to answer many of these types of in-virtue-of questions, but philosophers are also increasingly focusing on what an in-virtue-of question is in the first place. Many assume, at least as a working hypothesis, that in-virtue-of questions involve a distinctively metaphysical kind of determinative explanation called “ground.” This Handbook surveys the state of the art on ground as well as its connections and applications to other topics. The central issues of ground are discussed in 37 chapters, all written exclusively for this volume by a wide range of leading experts. The chapters are organized into the following sections: I. History II. Explanation and Determination III. Logic and Structure IV. Connections V. Applications Introductions at the start of each section provide an overview of the section’s contents, and a list of Related Topics at the end of each chapter points readers to other germane areas throughout the volume. The resulting volume is accessible enough for advanced students and informative enough for researchers. It is essential reading for anyone hoping to get clearer on what the biggest questions of philosophy are really asking.

Download or read book The Realism Antirealism Debate in the Age of Alternative Logics written by Shahid Rahman and published by Springer Science & Business Media. This book was released on 2011-09-22 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relation between logic and knowledge has been at the heart of a lively debate since the 1960s. On the one hand, the epistemic approaches based their formal arguments in the mathematics of Brouwer and intuitionistic logic. Following Michael Dummett, they started to call themselves `antirealists'. Others persisted with the formal background of the Frege-Tarski tradition, where Cantorian set theory is linked via model theory to classical logic. Jaakko Hintikka tried to unify both traditions by means of what is now known as `explicit epistemic logic'. Under this view, epistemic contents are introduced into the object language as operators yielding propositions from propositions, rather than as metalogical constraints on the notion of inference. The Realism-Antirealism debate has thus had three players: classical logicians, intuitionists and explicit epistemic logicians. The editors of the present volume believe that in the age of Alternative Logics, where manifold developments in logic happen at a breathtaking pace, this debate should be revisited. Contributors to this volume happily took on this challenge and responded with new approaches to the debate from both the explicit and the implicit epistemic point of view.

Download or read book Husserl s Logical Investigations Reconsidered written by D. Fisette and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twelve original studies collected in this volume examine different aspects of Edmund Husserl's Logical Investigations. They are authored by scholars and specialists internationally recognized for their expertise in the fields of logic, phenomenology, history of philosophy and philosophy of mind. They approach Husserl's groundwork from different angles and perspectives and shed new light on a number of issues such as meaning, intentionality, ontology, logic, etc.

Download or read book Residuated Structures in Algebra and Logic written by George Metcalfe and published by American Mathematical Society. This book was released on 2023-11-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to residuated structures, viewed as a common thread binding together algebra and logic. The framework includes well-studied structures from classical abstract algebra such as lattice-ordered groups and ideals of rings, as well as structures serving as algebraic semantics for substructural and other non-classical logics. Crucially, classes of these structures are studied both algebraically, yielding a rich structure theory along the lines of Conrad's program for lattice-ordered groups, and algorithmically, via analytic sequent or hypersequent calculi. These perspectives are related using a natural notion of equivalence for consequence relations that provides a bridge offering benefits to both sides. Algorithmic methods are used to establish properties like decidability, amalgamation, and generation by subclasses, while new insights into logical systems are obtained by studying associated classes of structures. The book is designed to serve the purposes of novices and experts alike. The first three chapters provide a gentle introduction to the subject, while subsequent chapters provide a state-of-the-art account of recent developments in the field.

Download or read book A M written by Thomas A. Sebeok and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "A - M".

Download or read book Judgement and the Epistemic Foundation of Logic written by Maria van der Schaar and published by Springer Science & Business Media. This book was released on 2012-11-28 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is a settled feature of the landscape. His paper opens the first of four sections that examine, in turn, historical philosophical assessments of judgement and reason; their place in early modern philosophy; the notion of judgement and logical theory in Wolff, Kant and Neo-Kantians like Windelband; their development in the Husserlian phenomenological paradigm; and the work of Bolzano, Russell and Frege. The papers, whose authors include Per Martin-Löf, Göran Sundholm, Michael Della Rocca and Robin Rollinger, represent a finely judged editorial selection highlighting work on philosophers exercised by the question of whether or not an epistemic notion of judgement has a role to play in logic. The volume will be of profound interest to students and academicians for its application of historical developments in philosophy to the solution of vexatious contemporary issues in the foundation of logic. ​

Download or read book Logic from Kant to Russell written by Sandra Lapointe and published by Routledge. This book was released on 2018-12-21 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scope and method of logic as we know it today eminently reflect the ground-breaking developments of set theory and the logical foundations of mathematics at the turn of the 20th century. Unfortunately, little effort has been made to understand the idiosyncrasies of the philosophical context that led to these tremendous innovations in the 19thcentury beyond what is found in the works of mathematicians such as Frege, Hilbert, and Russell. This constitutes a monumental gap in our understanding of the central influences that shaped 19th-century thought, from Kant to Russell, and that helped to create the conditions in which analytic philosophy could emerge. The aim of Logic from Kant to Russell is to document the development of logic in the works of 19th-century philosophers. It contains thirteen original essays written by authors from a broad range of backgrounds—intellectual historians, historians of idealism, philosophers of science, and historians of logic and analytic philosophy. These essays question the standard narratives of analytic philosophy’s past and address concerns that are relevant to the contemporary philosophical study of language, mind, and cognition. The book covers a broad range of influential thinkers in 19th-century philosophy and analytic philosophy, including Kant, Bolzano, Hegel, Herbart, Lotze, the British Algebraists and Idealists, Moore, Russell, the Neo-Kantians, and Frege.

Download or read book Varieties of Logic written by Stewart Shapiro and published by . This book was released on 2014 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. In Varieties of Logic, Stewart Shapiro develops several ways in which one can be a pluralist or relativist about logic. One of these is an extended argument that words and phrases like "valid" and "logical consequence" are polysemous or, perhaps better, are cluster concepts. The notions can be sharpened in various ways. This explains away the "debates" in the literature between inferentialists and advocates of a truth-conditional, model-theoretic approach, and between those who advocate higher-order logic and those who insist that logic is first-order. A significant kind of pluralism flows from an orientation toward mathematics that emerged toward the end of the nineteenth century, and continues to dominate the field today. The theme is that consistency is the only legitimate criterion for a theory. Logical pluralism arises when one considers a number of interesting and important mathematical theories that invoke a non-classical logic, and are rendered inconsistent, and trivial, if classical logic is imposed. So validity is relative to a theory or structure. The perspective raises a host of important questions about meaning. The most significant of these concern the semantic content of logical terminology, words like 'or', 'not', and 'for all', as they occur in rigorous mathematical deduction. Does the intuitionistic 'not', for example, have the same meaning as its classical counterpart? Shapiro examines the major arguments on the issue, on both sides, and finds them all wanting. He then articulates and defends a thesis that the question of meaning-shift is itself context-sensitive and, indeed, interest-relative. He relates the issue to some prominent considerations concerning open texture, vagueness, and verbal disputes. Logic is ubiquitous. Whenever there is deductive reasoning, there is logic. So there are questions about logical pluralism that are analogous to standard questions about global relativism. The most pressing of these concerns foundational studies, wherein one compares theories, sometimes with different logics, and where one figures out what follows from what in a given logic. Shapiro shows that the issues are not problematic, and that is usually easy to keep track of the logic being used and the one mentioned.

Download or read book The Development of Modern Logic written by Leila Haaparanta and published by OUP USA. This book was released on 2009-06-18 with total page 1005 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains newly-commissioned articles covering the development of modern logic from the late medieval period (fourteenth century) through the end of the twentieth-century. It is the first volume to discuss the field with this breadth of coverage and depth. It will appeal to scholars and students of philosophical logic and the philosophy of logic.

Download or read book The History of Philosophical and Formal Logic written by Alex Malpass and published by Bloomsbury Publishing. This book was released on 2017-06-29 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The History of Philosophical and Formal Logic introduces ideas and thinkers central to the development of philosophical and formal logic. From its Aristotelian origins to the present-day arguments, logic is broken down into four main time periods: Antiquity and the Middle Ages (Aristotle and The Stoics) The early modern period (Bolzano, Boole) High modern period (Frege, Peano & Russell and Hilbert) Early 20th century (Godel and Tarski) Each new time frame begins with an introductory overview highlighting themes and points of importance. Chapters discuss the significance and reception of influential works and look at historical arguments in the context of contemporary debates. To support independent study, comprehensive lists of primary and secondary reading are included at the end of chapters, along with exercises and discussion questions. By clearly presenting and explaining the changes to logic across the history of philosophy, The History of Philosophical and Formal Logic constructs an easy-to-follow narrative. This is an ideal starting point for students looking to understand the historical development of logic.

Download or read book The Philosophy of Logical Mechanism written by M.H. Salmon and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is divided into two parts. Part I contains sixteen critical es says by prominent philosophers and computer scientists. Their papers offer insightful, well-argued contemporary views of a broad range of topics that lie at the heart of philosophy in the second half of the twen tieth century: semantics and ontology, induction, the nature of prob ability, the foundations of science, scientific objectivity, the theory of naming, the logic of conditionals, simulation modeling, the relatiOn be tween minds and machines, and the nature of rules that guide be havior. In this volume honoring Arthur W. Burks, the philosophical breadth of his work is thus manifested in the diverse aspects of that work chosen for discussion and development by the contributors to his Festschrift. Part II consists of a book-length essay by Burks in which he lays out his philosophy of logical mechanism while responding to the papers in Part I. In doing so, he provides a unified and coherent context for the range of problems raised in Part I, and he highlights interesting relationships among the topics that might otherwise have gone un noticed. Part II is followed by a bibliography of Burks's published works.