Originally published in 1967. The common aim of all logical enquiry is to discover and analyse correctly the forms of valid argument. In this book concise expositions of traditional, Aristotelian logic and of modern systems of propositional and predicative logic show how far that aim has been achieved.

Originally published in 1985. This study concerns the problem of treating identity as a relation between an object and itself. It addresses the Russellian and Fregean solutions and goes on to present in the first part a surfacist account of belief-context ambiguity requiring neither differences in relative scope nor distinctions between sense and reference. The second part offers an account of negative existentials, necessity and identity-statements which resolves problems unlike the Russell-Frege analyses. This is a detailed work in linguistics and philosophy.

This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman's work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman's work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Goedel's incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as "What is logic?" and proposed particular positions regarding the foundations of mathematics including, for example, his "conceptual structuralism." The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman's work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman's distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.

This collection addresses metaphysical issues at the intersection between philosophy and science. A unique feature is the way in which it is guided both by history of philosophy, by interaction between philosophy and science, and by methodological awareness. In asking how metaphysics is possible in an age of science, the contributors draw on philosophical tools provided by three great thinkers who were fully conversant with and actively engaged with the sciences of their day: Kant, Husserl, and Frege. Part I sets out frameworks for scientifically informed metaphysics in accordance with the meta-metaphysics outlined by these three self-reflective philosophers. Part II explores the domain for co-existent metaphysics and science. Constraints on ambitious critical metaphysics are laid down in close consideration of logic, meta-theory, and specific conditions for science. Part III exemplifies the role of language and science in contemporary metaphysics. Quine's pursuit of truth is analysed; Cantor's absolute infinitude is reconstrued in modal terms; and sense is made of Weyl's take on the relationship between mathematics and empirical aspects of physics. With chapters by leading scholars, Metametaphysics and the Sciences is an in-depth resource for researchers and advanced students working within metaphysics, philosophy of science, and the history of philosophy.

Originally published in 1987, this volume reflects the diversity in Hegelianism and every branch of philosophy which he contributed to. It includes essays on his contribution to contemporary social philosophy, logic and the philosophy of religion. His work is examined in relation to Marx, Wittgenstein and his social philosophy discussed from a feminist standpoint.

This book on proof theory centers around the legacy of Kurt Schutte and its current impact on the subject. Schutte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schutte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound 0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Schutte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts close to his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Schutte himself that have never been published before.

William Tait is one of the most distinguished philosophers of mathematics of the last fifty years. This volume collects his most important published philosophical papers from the 1980's to the present. The articles cover a wide range of issues in the foundations and philosophy of mathematics, including some on historical figures ranging from Plato to Godel.
Tait's main contributions were initially in proof theory and constructive mathematics, later moving on to more philosophical subjects including finitism and skepticism about mathematics. This collection, presented as a whole, reveals the underlying unity of Tait's work. The volume includes an introduction in which Tait reflects more generally on the evolution of his point of view, as well as an appendix and added endnotes in which he gives some interesting background to the original essays. This is an important collection of the work of one of the most eminent philosophers of mathematics in this generation.

This volume tells the story of the legacy and impact of the great German polymath Gottfried Wilhelm Leibniz (1646-1716). Leibniz made significant contributions to many areas, including philosophy, mathematics, political and social theory, theology, and various sciences. The essays in this volume explores the effects of Leibniz's profound insights on subsequent generations of thinkers by tracing the ways in which his ideas have been defended and developed in the three centuries since his death. Each of the 11 essays is concerned with Leibniz's legacy and impact in a particular area, and between them they show not just the depth of Leibniz's talents but also the extent to which he shaped the various domains to which he contributed, and in some cases continues to shape them today. With essays written by experts such as Nicholas Jolley, Pauline Phemister, and Philip Beeley, this volume is essential reading not just for students of Leibniz but also for those who wish to understand the game-changing impact made by one of history's true universal geniuses.

If there is one utterly inescapable problem for the metaphysician, it is this: is metaphysics itself a theoretically legitimate discipline? Is it, in other words, capable of a systematic and well-confirmed set of theoretical results? And if not, why not? From its inception, metaphysics has found itself exercised by the nagging worry that its own inquiries might reveal it to be a subject without an object, or a mode of inquiry without a method. Such concerns were voiced as early as Plato's discussion of the battle between the Gods and Giants. Since then, no era of its history has spared metaphysics some rehearsal of this question. In Empiricism and the Problem of Metaphysics, Paul Studtmann defends an empiricist critique of metaphysical theorizing. At the heart of the critique is an empiricist view of a priori knowledge, according to which all a priori knowledge is empirical knowledge of the results of effective procedures. Such a view of a priori knowledge places severe limits on the scope a priori speculation and indeed places beyond our ken the types of claims that metaphysicians as well as traditional epistemologists and ethicists have typically wanted to make.

The International Congresses of Logic, Methodology and Philosophy of Science, which are held every fourth year, give a cross-section of ongoing research in logic and philosophy of science. Both the invited lectures and the many contributed papers are conductive to this end. At the 9th Congress held in Uppsala in 1991 there were 54 invited lectures and around 650 contributed papers divided into 15 different sections. Some of the speakers who presented contributed papers that attracted special interest were invited to submit their papers for publication, and the result is the present volume. A few papers appear here more or less as they were presented at the Congress whereas others are expansions or elaborations of the talks given at the Congress. A selection of this kind, containing 38 papers drawn from the 650 contributed papers presented at the Uppsala Congress, cannot do justice to all facets of the field as it appeared at the Congress. But it should allow the reader to get a representative survey of contemporary research in large areas of philosophical logic and philosophy of science. About half of the papers of the volume appear in sections listed at the Congress under the heading Philosophical and Foundational Problems about the Sciences. The section Foundations of Logic, Mathematics and Computer Science is represented by three papers, Foundations of Physical Sciences by six papers, Foundations of Biological Sciences by three papers, Foundations of Cognitive Science and AI by one paper, and Foundations of Linguistics by three papers.

Originally published in 1994, The Incommensurability Thesis is a critical study of the Incommensurability Thesis of Thomas Kuhn and Paul Feyerabend. The book examines the theory that different scientific theories may be incommensurable because of conceptual variance. The book presents a critique of the thesis and examines and discusses the arguments for the theory, acknowledging and debating the opposing views of other theorists. The book provides a comprehensive and detailed discussion of the incommensurability thesis.

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.

Archaeology of Play: The Re-Discovery of Platonic-Aristotelian Tripartivism in Interdisciplinary Discourses proposes that play's antithesis is not seriousness but rather one-dimensionality. This book argues that the rediscovery of Platonic-Aristotelian tripartivism lends to a more expansive appreciation of play in terms of three rhetorical registers-namely, skhole, agon, and paidia. Scholastic play resides in leisure and contemplation. Agonistics is realmed in competition, contests, and power-play, while paidiatics is expressed in lowly ruses, trickeries, recreation, and amusement of the low-bred and the subaltern. By subjecting play to the tripartite lens, Archaeology of Play highlights vital surpluses and lacunae in the treatment of the subject matter and therefore yields a refreshing, re-politicized understanding of play dynamics in the different fields of human endeavor. Furthermore, Bourdieu's and Ranciere's lusory discourses redeem play from the pitfalls of triadic over-schematization by thinking beyond tripartivism. The lively interlocution with other play theorists-Pieper, Kant, Schiller, Marcuse, Gadamer, Veblen, Arendt, Lyotard, Derrida, Foucault, Bakhtin, de Certeau, among others-adds substance to the mix where play becomes a critical resource for politics, aesthetics, and the democratic reordering of sociality.

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

In the first half of the 20th century, many Polish philosophers focused on defining scientific concepts that could lead to the development of a philosophical synthesis of reality. Benedykt Bornstein elaborated an algebraic logic and developed novum organum philosophiae in the form of geometrical logic, a mathematical system of universal science. It can also be stated that Bornstein was unquestionably the forerunner of philosophers who started research into spatial logic in the second half of the 20th century. The aim of this study on Bornstein's Geometrical Logic is to draw readers' attention not only to the algebraic and geometrical tools used in philosophical research, but also to demonstrate its importance for contemporary philosophical discussions which use mathematical tools in topology and category theory.

This volume represents an advanced, comprehensive state-of-the-art survey of the field of rational agency as it stands today. It covers the philosophical foundations of rational agency, logical and decision-theoretic approaches to rational agency, multi-agent aspects of rational agency and a number of approaches to programming rational agents. It will be of interest to researchers in logic, mainstream computer science, the philosophy of rational action and agency, and economics.

How do organizations become created? Entrepreneurship scholars have debated this question for decades, but only recently have they been able to gain insights into the non-linear dynamics that lead to organizational emergence, through the use of the complexity sciences. Written for social science researchers, Generative Emergence summarizes these literatures, including the first comprehensive review of each of the 15 complexity science disciplines. In doing so, the book makes a bold proposal for a discipline of Emergence, and explores one of its proposed fields, namely Generative Emergence. The book begins with a detailed summary of its underlying science, dissipative structures theory, and rigorously maps the processes of order creation discovered by that science to identify a 5-phase model of order creation in entrepreneurial ventures. The second half of the book presents the findings from an experimental study that tested the model in four fast-growth ventures through a year-long, week-by-week longitudinal analysis of their processes, based on over 750 interviews and 1000 hours of on-site observation. These data, combined with reports from over a dozen other studies, confirm the dynamics of the 5-phase model in multiple contexts. By way of conclusion, the book explores how the model of Generative Emergence could be applied to enact emergence within and across organizations.

Ideas gain legitimacy as they are put to some practical use. A study of Charles Sanders Peirce (1839-1914) supports this pragmatism as a way of thinking about truth and meaning. Architecture has a strong pragmatic strand, not least as we think of building users, architecture as a practice, the practical demands of building, and utility. After all, Vitruvius placed firmness and delight in the company of utilitas amongst his demands on architecture. Peirce (pronounced 'purse') was a logician, and so many of his ideas are couched in terms of formal propositions and their limitations. His work appeals therefore to many architects grappling with the digital age, and references to his work cropped up in the Design Methods Movement that developed and grew from the 1950s. That movement sought to systematise the design process, contributing to the idea of the RIBA Plan of Work, computer-aided design, and various controversies about rendering the design process transparent and open to scrutiny. Peirce's commitment to logic led him to investigate the basic elements of logical statements, notably the element of the sign. His best-known contribution to design revolves around his intricate theory of semiotics, the science of signs. The study of semiotics divided around the 1980s between advocates of Peirce's semiotics, and the broader, more politically charged field of structuralism. The latter has held sway in architectural discourse since the 1980s. Why this happened and what we gain by reviving a Peircean semiotics is the task of this book.

The book presents results from research conducted by Zygmunt Zawirski on the theory of knowledge, quantum mechanics, logic, ontology and metaphysics. The works undertaken in the field of logic, methodology and philosophy of science, and in particular the philosophy of nature and natural science testify to a solid preparation for the fundamental task of developing contemporary scientific philosophy. The emerging mathematical natural science did not have those possibilities which emerged in the 20th Century and which Zygmunt Zawirski (1882-1948) used. In the development of scientific metaphysics, he took into account both the achievements of modern logic, mathematics and physics. Zawirski builds scientific metaphysics by referring to empiricism, broadly understood experience. Modern metaphysics should meet high standards of precision and uniqueness, which is why Zawirski attempts to apply the axiomatic method to both the analysis of the theory of physics and the scientific metaphysics.

Winner of the 2020 Symposium Book Award by the Canadian Society for Continental Philosophy Stella Gaon provides the first fully philosophical account of the critical nature of deconstruction, and she does so by turning in an original way to psychoanalysis. Drawing on close readings of Freud and Laplanche, Gaon argues that Derridean deconstruction is driven by a normative investment in reason's psychological force. Indeed, deconstruction is more faithful to the principle of reason than the various forms of critical theory prevalent today. For if one pursues the classical demand for rational grounds vigilantly, one finds that claims to ethical or political legitimacy cannot be rationally justified, because they are undone by logical undecidability. Gaon's argument is borne out in the cases of Kantian deontology, Deweyan pragmatism, progressive pedagogy, Habermasian moral theory, Levinasian ethics and others. What emerges is the groundbreaking demonstration that deconstruction is impelled by a quasi-ethical critical drive, and that to read deconstructively is to radicalize the emancipatory practice of reason as self-critique. This important volume will be of great value to critical theorists as well as to Derrida scholars and researchers in social and political thought.

This book brings together an influential sequence of papers that argue for a radical re-conceptualisation of the psychology of inference, and of cognitive science more generally. The papers demonstrate that the thesis that logic provides the basis of human inference is central to much cognitive science, although the commitment to this view is often implicit. They then note that almost all human inference is uncertain, whereas logic is the calculus of certain inference. This mismatch means that logic is not the appropriate model for human thought. Oaksford and Chater's argument draws on research in computer science, artificial intelligence and philosophy of science, in addition to experimental psychology. The authors propose that probability theory, the calculus of uncertain inference, provides a more appropriate model for human thought. They show how a probabilistic account can provide detailed explanations of experimental data on Wason's selection task, which many have viewed as providing a paradigmatic demonstration of human irrationality. Oaksford and Chater show that people's behaviour appears irrational only from a logical point of view, whereas it is entirely rational from a probabilistic perspective. The shift to a probabilistic framework for human inference has significant implications for the psychology of reasoning, cognitive science more generally, and forour picture of ourselves as rational agents.

Timothy Williamson is one of the most influential living philosophers working in the areas of logic and metaphysics. His work in these areas has been particularly influential in shaping debates about metaphysical modality, which is the topic of his recent provocative and closely-argued book Modal Logic as Metaphysics (2013). This book comprises ten essays by metaphysicians and logicians responding to Williamson's work on metaphysical modality, as well as replies by Williamson to each essay. In addition, it contains an original essay by Williamson, 'Modal science,' concerning the role of modal claims in natural science. This book was originally published as a special issue of the Canadian Journal of Philosophy.

Reading Wittgenstein's Philosophical Investigations: A Beginners Guide is written for anyone who faces the challenge of reading Philosophical Investigations. John J. Ross guides the reader slowly through each relevant section of text, explaining and elaborating key ideas, and providing the philosophical and biographical background that illuminates the problems Wittgenstein is addressing. Reading Wittgenstein's Philosophical Investigations is designed to be used in the examination of the Investigations as a whole or in part; the reader can focus solely on Mathematics or Psychology, if needed. While Ross does address some of the philosophical controversies surrounding Wittgenstein's ideas, the discussions are appropriate for an undergraduate, so the book can be used fruitfully by anyone with that level of education who has an interest in Wittgenstein's seminal work.

The Quantum of Explanation advances a bold new theory of how explanation ought to be understood in philosophical and cosmological inquiries. Using a complete interpretation of Alfred North Whitehead's philosophical and mathematical writings and an interpretive structure that is essentially new, Auxier and Herstein argue that Whitehead has never been properly understood, nor has the depth and breadth of his contribution to the human search for knowledge been assimilated by his successors. This important book effectively applies Whitehead's philosophy to problems in the interpretation of science, empirical knowledge, and nature. It develops a new account of philosophical naturalism that will contribute to the current naturalism debate in both Analytic and Continental philosophy. Auxier and Herstein also draw attention to some of the most important differences between the process theology tradition and Whitehead's thought, arguing in favor of a Whiteheadian naturalism that is more or less independent of theological concerns. This book offers a clear and comprehensive introduction to Whitehead's philosophy and is an essential resource for students and scholars interested in American philosophy, the philosophy of mathematics and physics, and issues associated with naturalism, explanation and radical empiricism.

This book presents an interpretation of Kant's Critique of Pure Reason as a priori psychologism. It groups Kant's philosophy together with those of the British empiricists-Locke, Berkeley, and Hume-in a single line of psychologistic succession and offers a clear explanation of how Kant's psychologism differs from psychology and idealism. The book reconciles Kant's philosophy with subsequent developments in science and mathematics, including post-Fregean mathematical logic, non-Euclidean geometry, and both relativity and quantum theory. It also relates Kant's psychologism to Wittgenstein's later conception of language. Finally, the author reveals the ways in which Kant's philosophy dovetails with contemporary scientific theorizing about the natural phenomenon of consciousness and its place in nature. This book will be of interest to Kant scholars and historians of philosophy working on the British empiricists.