How can we advance knowledge? Which methods do we need in order to make new discoveries? How can we rationally evaluate, reconstruct and offer discoveries as a means of improving the 'method' of discovery itself? And how can we use findings about scientific discovery to boost funding policies, thus fostering a deeper impact of scientific discovery itself? The respective chapters in this book provide readers with answers to these questions. They focus on a set of issues that are essential to the development of types of reasoning for advancing knowledge, such as models for both revolutionary findings and paradigm shifts; ways of rationally addressing scientific disagreement, e.g. when a revolutionary discovery sparks considerable disagreement inside the scientific community; frameworks for both discovery and inference methods; and heuristics for economics and the social sciences.

This meticulous critical assessment of the ground-breaking work of philosopher Stanislaw Lesniewski focuses exclusively on primary texts and explores the full range of output by one of the master logicians of the Lvov-Warsaw school. The author's nuanced survey eschews secondary commentary, analyzing Lesniewski's core philosophical views and evaluating the formulations that were to have such a profound influence on the evolution of mathematical logic. One of the undisputed leaders of the cohort of brilliant logicians that congregated in Poland in the early twentieth century, Lesniewski was a guide and mentor to a generation of celebrated analytical philosophers (Alfred Tarski was his PhD student). His primary achievement was a system of foundational mathematical logic intended as an alternative to the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. Its three strands-'protothetic', 'ontology', and 'mereology', are detailed in discrete sections of this volume, alongside a wealth other chapters grouped to provide the fullest possible coverage of Lesniewski's academic output. With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy's great pioneers.

This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tubingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.

After Plato's Forms, and Aristotle's substances, the Stoics posited the fundamental reality of lekta - the meanings of sentences, distinct from the sentences themselves. This is the first time in the tradition of Western philosophy that what is signified is properly distinguished from signs and signifiers. The Stoics on Lekta offers a synoptic treatment of the many implications of this distinction, which grants an existential autonomy to lekta: language can only ever express meanings, but what happens to meanings which are there, ready to be said, but which are never actually expressed? It analyses the deep shift in ontological paradigm required by the presence of lekta in reality, and reveals a truly unique, complex, and consistent cosmic view in which lekta are the keystones of the structure of reality. According to this view, we cannot not speak or think in terms of lekta, and for this reason, they are in fact all there is to say. The Stoics' position ignited many fiery debates in antiquity and continues to do so in the modern era: they were the first to be concerned with questions about language and grammar, and the first to put the relation of language to reality at the heart of the enquiry into human understanding and the place of man in the cosmos. Such questions remain central to life and philosophy to this day, and by explicitly comparing and contrasting the themes and topics discussed to twentieth-century treatments of the status of the proposition, propositional structure, speech act theory, and the relation of attribution of the predicate to a subject-term, this volume seeks to demonstrate the enduring value of a direct Stoic contribution to the contemporary debate.

This text offers an extension to the traditional Kripke semantics for non-classical logics by adding the notion of reactivity. Reactive Kripke models change their accessibility relation as we progress in the evaluation process of formulas in the model. This feature makes the reactive Kripke semantics strictly stronger and more applicable than the traditional one. Here we investigate the properties and axiomatisations of this new and most effective semantics, and we offer a wide landscape of applications of the idea of reactivity. Applied topics include reactive automata, reactive grammars, reactive products, reactive deontic logic and reactive preferential structures. Reactive Kripke semantics is the next step in the evolution of possible world semantics for non-classical logics, and this book, written by one of the leading authorities in the field, is essential reading for graduate students and researchers in applied logic, and it offers many research opportunities for PhD students.

In this volume, the author investigates and argues for, a particular answer to the question: What is the right way to logically analyze modalities from natural language within formal languages? The answer is: by formalizing modal expressions in terms of predicates. But, as in the case of truth, the most intuitive modal principles lead to paradox once the modal notions are conceived as predicates. The book discusses the philosophical interpretation of these modal paradoxes and argues that any satisfactory approach to modality will have to face the paradoxes independently of the grammatical category of the modal notion. By systematizing modal principles with respect to their joint consistency and inconsistency, Stern provides an overview of the options and limitations of the predicate approach to modality that may serve as a useful starting point for future work on predicate approaches to modality. Stern also develops a general strategy for constructing philosophically attractive theories of modal notions conceived as predicates. The idea is to characterize the modal predicate by appeal to its interaction with the truth predicate. This strategy is put to use by developing the modal theories Modal Friedman-Sheard and Modal Kripke-Feferman.

This book presents the current state of the art regarding the application of logical tools to the problems of theory and practice of lawmaking. It shows how contemporary logic may be useful in the analysis of legislation, legislative drafting and legal reasoning concerning different contexts of law making. Elaborations of the process of law making have variously emphasised its political, social or economic aspects. Yet despite strong interest in logical analyses of law, questions remains about the role of logical tools in law making. This volume attempts to bridge that gap, or at least to narrow it, drawing together some important research problems-and some possible solutions-as seen through the work of leading contemporary academics. The volume encompasses 20 chapters written by authors from 16 countries and it presents diversified views on the understanding of logic (from strict mathematical approaches to the informal, argumentative ones) and differentiated choices concerning the aspects of law making taken into account. The book presents a broad set of perspectives, insights and results into the emerging field of research devoted to the logical analysis of the area of creation of law. How does logic inform lawmaking? Are legal systems consistent and complete? How can legal rules be represented by means of formal calculi and visualization techniques? Does the structure of statutes or of legal systems resemble the structure of deductive systems? What are the logical relations between the basic concepts of jurisprudence that constitute the system of law? How are theories of legal interpretation relevant to the process of legislation? How might the statutory text be analysed by means of contemporary computer programs? These and other questions, ranging from the theoretical to the immediately practical, are addressed in this definitive collection.

Ricoeur lectured and wrote for over twenty years on negation ('Do I understand something better if I know what it is not, and what is not-ness?') and never published his extensive writings on this subject. Ricoeur concluded that there are multiple forms of negation; it can, for example, be the other person (Plato), the not knowable nature of our world (Kant), the included opposite (Hegel), apophatic spirituality (Plotinus on not being able to know God) and existential nothingness (Sartre). Ricoeur, working on Kant, Hegel and Sartre, decided that all these forms of negation are incompatible and also fatally flawed because they fail to resolve false binaries of negative: positive. Alison Scott-Baumann demonstrates how Ricoeur subsequently incorporated negation into his linguistic turn, using dialectics, metaphor, narrative, parable and translation in order to show how negation is in us, not outside us: language both creates and clarifies false binaries. He bestows upon negation a strong and central role in the human condition, and its inevitability is reflected in his writings, if we look carefully. Ricoeur and the Negation of Happiness draws on Ricoeur's published works, previously unavailable archival material and many other sources. Alison Scott-Baumann argues that thinking positively is necessary but not sufficient for aspiring to happiness - what is also required is affirmation of negative impulses: we know we are split by contradictions and still try to overcome them. She also demonstrates the urgency of analysing current socio-cultural debates about wellbeing, education and equality, which rest insecurely upon our loose use of the negative as a category mistake.

This book aims to familiarize readers in a very simple and easy manner the rules and proper procedures of rational debate. It will help reduce the frustration that many experience when engaging in debates. The proper conduct of debate is both fun and mentally stimulating, and we trust that implementing the rules of debate outlined in this book will help you and your friends increase your ability to learn, improve and engage in rational and intellectual debates.

This collection of essays explores the philosophy of human knowledge from a multitude of perspectives, with a particular emphasis upon the justification component of the classical analysis of knowledge and with an excursion along the way to explore the role of knowledge in Texas Hold 'Em poker. An important theme of the collection is the role of knowledge in religion, including a detailed argument for agnosticism. A number of the essays touch upon issues in philosophical logic, among them a fascinating new counter-example to Modus Ponens. The collection is rounded out with essays on causality and the philosophy of mind. The author's perspective on the philosophy of human knowledge is fresh and challenging, as evidenced by essays entitled "On Epistemic Preferability;" "On Being Unjustified;" "The Logic of 'Unless'" and "Is 'This sentence is true.' True?" An interesting feature of The Logic of Philosophy: Pesky Essays is the inclusion of responses to several of its key essays, contributed by such prominent contemporary philosophers as Roderick Chisholm, Ted Sider and Tomas Kapitan.

This book presents diverse topics in mathematical logic such as proof theory, meta-mathematics, and applications of logic to mathematical structures. The collection spans the first 100 years of modern logic and is dedicated to the memory of Irving Anellis, founder of the journal 'Modern Logic', whose academic work was essential in promoting the algebraic tradition of logic, as represented by Charles Sanders Peirce. Anellis's association with the Russian logic community introduced their school of logic to a wider audience in the USA, Canada and Western Europe. In addition, the collection takes a historical perspective on proof theory and the development of logic and mathematics in Eastern Logic, the Soviet Union and Russia. The book will be of interest to historians and philosophers in logic and mathematics, and the more specialized papers will also appeal to mathematicians and logicians.

A Logical Introduction to Probability and Induction is a textbook on the mathematics of the probability calculus and its applications in philosophy. On the mathematical side, the textbook introduces these parts of logic and set theory that are needed for a precise formulation of the probability calculus. On the philosophical side, the main focus is on the problem of induction and its reception in epistemology and the philosophy of science. Particular emphasis is placed on the means-end approach to the justification of inductive inference rules. In addition, the book discusses the major interpretations of probability. These are philosophical accounts of the nature of probability that interpret the mathematical structure of the probability calculus. Besides the classical and logical interpretation, they include the interpretation of probability as chance, degree of belief, and relative frequency. The Bayesian interpretation of probability as degree of belief locates probability in a subject's mind. It raises the question why her degrees of belief ought to obey the probability calculus. In contrast to this, chance and relative frequency belong to the external world. While chance is postulated by theory, relative frequencies can be observed empirically. A Logical Introduction to Probability and Induction aims to equip students with the ability to successfully carry out arguments. It begins with elementary deductive logic and uses it as basis for the material on probability and induction. Throughout the textbook results are carefully proved using the inference rules introduced at the beginning, and students are asked to solve problems in the form of 50 exercises. An instructor's manual contains the solutions to these exercises as well as suggested exam questions. The book does not presuppose any background in mathematics, although sections 10.3-10.9 on statistics are technically sophisticated and optional. The textbook is suitable for lower level undergraduate courses in philosophy and logic.

This volume, "The Brazilian Studies in the Philosophy and History of Science, "is the first attempt to present to a general audience, works from Brazil on this subject. The included papers are original, covering a remarkable number of relevant topics of philosophy of science, logic and on the history of science. The Brazilian community has increased in the last years in quantity and in quality of the works, most of them being published in respectable international journals on the subject. The chapters of this volume are forwarded by a general introduction, which aims to sketch not only the contents of the chapters, but it is conceived as a historical and conceptual guide to the development of the field in Brazil. The introduction intends to be useful to the reader, and not only to the specialist, helping them to evaluate the increase in production of this country within the international context.

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The papers in this volume address fundamental, and interrelated, philosophical issues concerning modality and identity, issues that have not only been pivotal to the development of analytic philosophy in the twentieth century, but remain a key focus of metaphysical debate in the twenty-first. How are we to understand the concepts of necessity and possibility? Is chance a basic ingredient of reality? How are we to make sense of claims about personal identity? Do numbers require distinctive identity criteria? Does the capacity to identify an object presuppose an ability to bring it under a sortal concept? Rather than presenting a single, partisan perspective, Identity and Modality enriches our understanding of identity and modality by bringing together papers written by leading researchers working in metaphysics, the philosophy of mind, the philosophy of science, and the philosophy of mathematics. The resulting variety of perspectives correspondingly reflects both the breadth and depth of contemporary theorizing about identity and modality, each paper addressing a particular issue and advancing our knowledge of the area. This volume will provide essential reading for graduate students in the subject and professional philosophers.

This is the second of two volumes of essays in commemoration of Alan Turing, celebrating his intellectual legacy within the philosophy of mind and cognitive science. It focuses on the relationship between a scientific, computational image of the mind and a common-sense picture of the mind as an inner arena populated by concepts, beliefs, intentions, and qualia. Topics covered include the causal potency of folk-psychological states, the connectionist reconception of learning and concept formation, the understanding of the notion of computation itself, and the relation between philosophical and psychological theories of concepts.

This book demonstrates how analytical thinking and intuition can be systematically connected and trained. It is illustrated by figures and photographs and includes creative and stimulating exercises. We are living in a world of increasing complexity, in which perceiving reality accurately is increasingly important and difficult. Society's need to address "global grand challenges" requires that the scientific community initiates inter-disciplinary research programmes. These are often far removed from current programmes, which are usually based on intra-disciplinary science. Improving our understanding of complex problems and communicating this understanding to a large group of people from different backgrounds represents an important educational challenge. Connecting Analytical Thinking and Intuition stimulates students and scientists to improve their skills in thinking, communicating and learning more about being humans. A guide to connecting analytical thinking and intuition is presented using the "dream group" method developed by Montague Ullman, in which a group of 6-8 people systematically and carefully helps the dreamer to appreciate dreams. The importance of good memory, which can be trained through recalling the dreams, is also discussed in relation to science and literature.

Philosophers have warned of the perils of a life spent without reflection, but what constitutes reflective inquiry - and why it's necessary in our lives - can be an elusive concept. Synthesizing ideas from minds as diverse as John Dewey and Paulo Freire, theHandbook of Reflection and Reflective Inquiry presents reflective thought in its most vital aspects, not as a fanciful or nostalgic exercise, but as a powerful means of seeing familiar events anew, encouraging critical thinking and crucial insight, teaching and learning. In its opening pages, two seasoned educators, Maxine Greene and Lee Shulman, discuss reflective inquiry as a form of active attention (Thoreau's "wide-awakeness"), an act of consciousness, and a process by which people can understand themselves, their work (particularly in the form of life projects), and others. Building on this foundation, the Handbook analyzes through the work of 40 internationally oriented authors: - Definitional issues concerning reflection, what it is and is not; - Worldwide social and moral conditions contributing to the growing interest in reflective inquiry in professional education; - Reflection as promoted across professional educational domains, including K-12 education, teacher education, occupational therapy, and the law; - Methods of facilitating and scaffolding reflective engagement; - Current pedagogical and research practices in reflection; - Approaches to assessing reflective inquiry. Educators across the professions as well as adult educators, counselors and psychologists, and curriculum developers concerned with adult learning will find the Handbook of Reflection and Reflective Inquiry an invaluable teaching tool for challenging times.

This second edition of the Handbook of Philosophical Logic reflects great changes in the landscape of philosophical logic since the first edition. It gives readers an idea of that landscape and its relation to computer science and formal language and artificial intelligence. It shows how the increased demand for philosophical logic from computer science and artificial intelligence and computational linguistics accelerated the development of the subject directly and indirectly. This development in turn, directly pushed research forward, stimulated by the needs of applications. New logic areas became established and old areas were enriched and expanded. At the same time, it socially provided employment for generations of logicians residing in computer science, linguistics and electrical engineering departments which of course helped keep the logic community to thrive. The many contributors to this Handbook are active in these application areas and are among the most famous leading figures of applied philosophical logic of our times.

A group of 100 prisoners, all together in the prison dining area, are told that they will be all put in isolation cells and then will be interrogated one by one in a room containing a light with an on/off switch. The prisoners may communicate with one another by toggling the light switch (and that is the only way in which they can communicate). The light is initially switched off. There is no fixed order of interrogation, or interval between interrogations, and the same prisoner may be interrogated again at any stage. When interrogated, a prisoner can either do nothing, or toggle the light switch, or announce that all prisoners have been interrogated. If that announcement is true, the prisoners will (all) be set free, but if it is false, they will all be executed. While still in the dining room, and before the prisoners go to their isolation cells (forever), can the prisoners agree on a protocol that will set them free? At first glance, this riddle may seem impossible to solve: how can all of the necessary information be transmitted by the prisoners using only a single light bulb? There is indeed a solution, however, and it can be found by reasoning about knowledge. This book provides a guided tour through eleven classic logic puzzles that are engaging and challenging and often surprising in their solutions. These riddles revolve around the characters' declarations of knowledge, ignorance, and the appearance that they are contradicting themselves in some way. Each chapter focuses on one puzzle, which the authors break down in order to guide the reader toward the solution. For general readers and students with little technical knowledge of mathematics, One Hundred Prisoners and a Light Bulb will be an accessible and fun introduction to epistemic logic. Additionally, more advanced students and their teachers will find it to be a valuable reference text for introductory course work and further study.

This second volume of a collection of papers offers new perspectives and challenges in the study of logic. It is presented in honor of the fiftieth birthday of Jean-Yves Beziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions (identity, rule, quantification) and history of logic (Leibniz, Peirce, Hilbert). The volume gathers personal recollections about Jean-Yves Beziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Nemeti, Henri Prade. These essays will be of interest to all students and researchers interested in the nature and future of logic.

Over a million students have learned to be more discerning at constructing and evaluating arguments with the help of A CONCISE INTRODUCTION TO LOGIC, 13th Edition. The text's clear, friendly, thorough presentation has made it the most widely used logic text in North America. The book shows you how the content connects to real-life problems and gives you everything you need to do well in your logic course. Doing well in logic improves your skills in ways that translate to other courses you take, your everyday life, and your future career. The accompanying technological resources offered through MindTap, a highly robust online platform, include self-grading interactive exercises, a new digital activity that allows you to apply the skills you learn to a real-world problem, and videos to reinforce what you learn in the book and hear in class.

For courses in Introduction to Logic or Critical Thinking. Fundamental, Fresh, Focused. Rendered from Copi/Cohen's Introduction to Logic, the most respected introductory logic text on the market, this concise version explains all concepts and techniques clearly, accurately, and thoroughly, bringing them to life using a wealth of contemporary examples. Essentials of Logic was created in response to a need in the market for a book that effectively covered the fundamental issues in logic. The first edition of Essentials of Logic was abridged from Copi and Cohen's Introduction, 11th edition, with an eye to including all and only those elements that most logic teachers would consider essential. In the second edition, new topics have been added based on readers' suggestions. For example, indirect and conditional proof techniques have been added and many examples have been thoroughly revised and rewritten. The result is a book that closely reflects what users deem essential and does so in a way that is sensitive to the needs of today's students.

Provides clear distinctions between the subjective and objective dimensions of architecture and the arts Arguments are reinforced by the analysis of seminal architectural examples Bullet points at the end of each chapter summarise the arguments and provide further guidance to the reader

The Critical Thinking Toolkit is a comprehensive compendium that equips readers with the essential knowledge and methods for clear, analytical, logical thinking and critique in a range of scholarly contexts and everyday situations. * Takes an expansive approach to critical thinking by exploring concepts from other disciplines, including evidence and justification from philosophy, cognitive biases and errors from psychology, race and gender from sociology and political science, and tropes and symbols from rhetoric * Follows the proven format of The Philosopher s Toolkit and The Ethics Toolkit with concise, easily digestible entries, see also recommendations that connect topics, and recommended reading lists * Allows readers to apply new critical thinking and reasoning skills with exercises and real life examples at the end of each chapter * Written in an accessible way, it leads readers through terrain too often cluttered with jargon * Ideal for beginning to advanced students, as well as general readers, looking for a sophisticated yet accessible introduction to critical thinking

An exploration of quantum entanglement and the ways in which it contradicts our everyday assumptions about the ultimate nature of reality. Quantum physics is notable for its brazen defiance of common sense. (Think of Schroedinger's Cat, famously both dead and alive.) An especially rigorous form of quantum contradiction occurs in experiments with entangled particles. Our common assumption is that objects have properties whether or not anyone is observing them, and the measurement of one can't affect the other. Quantum entanglement-called by Einstein "spooky action at a distance"-rejects this assumption, offering impeccable reasoning and irrefutable evidence of the opposite. Is quantum entanglement mystical, or just mystifying? In this volume in the MIT Press Essential Knowledge series, Jed Brody equips readers to decide for themselves. He explains how our commonsense assumptions impose constraints-from which entangled particles break free. Brody explores such concepts as local realism, Bell's inequality, polarization, time dilation, and special relativity. He introduces readers to imaginary physicists Alice and Bob and their photon analyses; points out that it's easier to reject falsehood than establish the truth; and reports that some physicists explain entanglement by arguing that we live in a cross-section of a higher-dimensional reality. He examines a variety of viewpoints held by physicists, including quantum decoherence, Niels Bohr's Copenhagen interpretation, genuine fortuitousness, and QBism. This relatively recent interpretation, an abbreviation of "quantum Bayesianism," holds that there's no such thing as an absolutely accurate, objective probability "out there," that quantum mechanical probabilities are subjective judgments, and there's no "action at a distance," spooky or otherwise.