This volume presents the state of the art in the algebraic investigation into substructural logics. It features papers from the workshop AsubL (Algebra & Substructural Logics - Take 6). Held at the University of Cagliari, Italy, this event is part of the framework of the Horizon 2020 Project SYSMICS: SYntax meets Semantics: Methods, Interactions, and Connections in Substructural logics. Substructural logics are usually formulated as Gentzen systems that lack one or more structural rules. They have been intensively studied over the past two decades by logicians of various persuasions. These researchers include mathematicians, philosophers, linguists, and computer scientists. Substructural logics are applicable to the mathematical investigation of such processes as resource-conscious reasoning, approximate reasoning, type-theoretical grammar, and other focal notions in computer science. They also apply to epistemology, economics, and linguistics. The recourse to algebraic methods -- or, better, the fecund interplay of algebra and proof theory -- has proved useful in providing a unifying framework for these investigations. The AsubL series of conferences, in particular, has played an important role in these developments. This collection will appeal to students and researchers with an interest in substructural logics, abstract algebraic logic, residuated lattices, proof theory, universal algebra, and logical semantics.

Truth, etc. is a wide-ranging study of ancient logic based upon the John Locke lectures given by the eminent philosopher Jonathan Barnes in Oxford. Its six chapters discuss, first, certain ancient ideas about truth; secondly, the Aristotelian conception of predication; thirdly, various ideas about connectors which were developed by the ancient logicians and grammarians; fourthly, the notion of logical form, insofar as it may be discovered in the ancient texts; fifthly, the question of the 'justification of deduction'; and sixthly, the attitude which has been called logical utilitarianism and which restricts the scope of logic to those forms of inference which are or might be useful for scientific proofs. In principle, the book presupposes no knowledge of logic and no skill in ancient languages: all ancient texts are cited in English translation; and logical symbols and logical jargon are avoided so far as possible. There is no scholarly apparatus of footnotes, and no bibliography. It can be read in an armchair. Anyone interested in ancient philosophy, or in logic and its history, will find it interesting.

Sortal concepts are at the center of certain logical discussions and have played a significant role in solutions to particular problems in philosophy. Apart from logic and philosophy, the study of sortal concepts has found its place in specific fields of psychology, such as the theory of infant cognitive development and the theory of human perception. In this monograph, different formal logics for sortal concepts and sortal-related logical notions (such as sortal identity and first-order sortal quantification) are characterized. Most of these logics are intensional in nature and possess, in addition, a bidimensional character. That is, they simultaneously represent two different logical dimensions. In most cases, the dimensions are those of time and natural necessity, and, in other cases, those of time and epistemic necessity. Another feature of the logics in question concerns second-order quantification over sortal concepts, a logical notion that is also represented in the logics. Some of the logics adopt a constant domain interpretation, others a varying domain interpretation of such quantification. Two of the above bidimensional logics are philosophically grounded on predication sortalism, that is, on the philosophical view that predication necessarily requires sortal concepts. Another bidimensional logic constitutes a logic for complex sortal predicates. These three sorts of logics are among the important novelties of this work since logics with similar features have not been developed up to now, and they might be instrumental for the solution of philosophically significant problems regarding sortal predicates. The book assumes a modern variant of conceptualism as a philosophical background. For this reason, the approach to sortal predicates is in terms of sortal concepts. Concepts, in general, are here understood as intersubjective realizable cognitive capacities. The proper features of sortal concepts are determined by an analysis of the main features of sortal predicates. Posterior to this analysis, the sortal-related logical notions represented in the above logics are discussed. There is also a discussion on the extent to which the set-theoretic formal semantic systems of the book capture different aspects of the conceptualist approach to sortals. These different semantic frameworks are also related to realist and nominalist approaches to sortal predicates, and possible modifications to them are considered that might represent those alternative approaches.

This is a guide to the thought and ideas of Gottlob Frege, one of the most important but also perplexing figures in the history of analytic philosophy. Gottlob Frege is regarded as one of the founders of modern logic and analytic philosophy, indeed as the greatest innovator in logic since Aristotle. His groundbreaking work identified many of the basic conceptions and distinctions that later came to dominate analytic philosophy. The literature on him is legion and ever-growing in complexity, representing a considerable challenge to the non-expert. The details of his logic, which have come into focus in recent research, are particularly difficult to grasp, although they are crucial to the development of his grand project, the reduction of arithmetic to logic, and the associated philosophical innovations. This book offers a lucid and accessible introduction to Frege's logic, taking the reader directly to the core of his philosophy, and ultimately to some of the most pertinent issues in contemporary philosophy of language, logic, mathematics, and the mind. "Continuum's Guides for the Perplexed" are clear, concise and accessible introductions to thinkers, writers and subjects that students and readers can find especially challenging - or indeed downright bewildering. Concentrating specifically on what it is that makes the subject difficult to grasp, these books explain and explore key themes and ideas, guiding the reader towards a thorough understanding of demanding material.

Reference is a central topic in philosophy of language, and has been the main focus of discussion about how language relates to the world. R. M. Sainsbury sets out a new approach to the concept, which promises to bring to an end some long-standing debates in semantic theory. There is a single category of referring expressions, all of which deserve essentially the same kind of semantic treatment. Included in this category are both singular and plural referring expressions ('Aristotle', 'The Pleiades'), complex and non-complex referring expressions ('The President of the USA in 1970', 'Nixon'), and empty and non-empty referring expressions ('Vulcan', 'Neptune'). Referring expressions are to be described semantically by a reference condition, rather than by being associated with a referent. In arguing for these theses, Sainsbury's book promises to end the fruitless oscillation between Millian and descriptivist views. Millian views insist that every name has a referent, and find it hard to give a good account of names which appear not to have referents, or at least are not known to do so, like ones introduced through error ('Vulcan'), ones where it is disputed whether they have a bearer ('Patanjali') and ones used in fiction. Descriptivist theories require that each name be associated with some body of information. These theories fly in the face of the fact names are useful precisely because there is often no overlap of information among speakers and hearers. The alternative position for which the book argues is firmly non-descriptivist, though it also does not require a referent. A much broader view can be taken of which expressions are referring expressions: not just names and pronouns used demonstratively, but also some complex expressions and some anaphoric uses of pronouns. Sainsbury's approach brings reference into line with truth: no one would think that a semantic theory should associate a sentence with a truth value, but it is commonly held that a semantic theory should associate a sentence with a truth condition, a condition which an arbitrary state of the world would have to satisfy in order to make the sentence true. The right analogy is that a semantic theory should associate a referring expression with a reference condition, a condition which an arbitrary object would have to satisfy in order to be the expression's referent. Lucid and accessible, and written with a minimum of technicality, Sainsbury's book also includes a useful historical survey. It will be of interest to those working in logic, mind, and metaphysics as well as essential reading for philosophers of language.

This book offers insight into the nature of meaningful discourse. It presents an argument of great intellectual scope written by an author with more than four decades of experience. Readers will gain a deeper understanding into three theories of the logos: analytic, dialectical, and oceanic. The author first introduces and contrasts these three theories. He then assesses them with respect to their basic parameters: necessity, truth, negation, infinity, as well as their use in mathematics. Analytic Aristotelian logic has traditionally claimed uniqueness, most recently in its Fregean and post-Fregean variants. Dialectical logic was first proposed by Hegel. The account presented here cuts through the dense, often incomprehensible Hegelian text. Oceanic logic was never identified as such, but the author gives numerous examples of its use from the history of philosophy. The final chapter addresses the plurality of the three theories and of how we should deal with it. The author first worked in analytic logic in the 1970s and 1980s, first researched dialectical logic in the 1990s, and discovered oceanic logic in the 2000s. This book represents the culmination of reflections that have lasted an entire scholarly career.

This book collects a renowned scholar's essays from the past five decades and reflects two main concerns: an approach to logic that stresses argumentation, reasoning, and critical thinking and that is informal, empirical, naturalistic, practical, applied, concrete, and historical; and an interest in Galileo's life and thought-his scientific achievements, Inquisition trial, and methodological lessons in light of his iconic status as "father of modern science." These republished essays include many hard to find articles, out of print works, and chapters which are not available online. The collection provides an excellent resource of the author's lifelong dedication to the subject. Thus, the book contains critical analyses of some key Galilean arguments about the laws of falling bodies and the Copernican hypothesis of the earth's motion. There is also a group of chapters in which Galileo's argumentation is compared and contrasted with that of other figures such as Socrates, Karl Marx, Giordano Bruno, and his musicologist father Vincenzo Galilei. The chapters on Galileo's trial illustrate an approach to the science-vs-religion issue which Finocchiaro labels "para-clerical" and conceptualizes in terms of a judicious consideration of arguments for and against Galileo and the Church. Other essays examine argumentation about Galileo's life and thought by the major Galilean scholars of recent decades. The book will be of interest to scholars in philosophy, logic, philosophy of science, history of science, history of religion, philosophy of religion, argumentation, rhetoric, and communication studies.

Now in a new edition --the classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of G del's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics."

This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna's logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.

This book is a tribute to Professor Ewa Orlowska, a Polish logician who was celebrating the 60th year of her scientific career in 2017. It offers a collection of contributed papers by different authors and covers the most important areas of her research. Prof. Orlowska made significant contributions to many fields of logic, such as proof theory, algebraic methods in logic and knowledge representation, and her work has been published in 3 monographs and over 100 articles in internationally acclaimed journals and conference proceedings. The book also includes Prof. Orlowska's autobiography, bibliography and a trialogue between her and the editors of the volume, as well as contributors' biographical notes, and is suitable for scholars and students of logic who are interested in understanding more about Prof. Orlowska's work.

Contents: Introduction; I. ONTOLOGY; 1. Existence (1987); 2. Nonexistence (1998); 3. Mythical Objects (2002); II. NECESSITY; 4. Modal Logic Kalish-and-Montague Style (1994); 5. Impossible Worlds (1984); 6. An Empire of Thin Air (1988); 7. The Logic of What Might Have Been (1989); III. IDENTITY; 8. The fact that x=y (1987); 9. This Side of Paradox (1993); 10. Identity Facts (2003); 11. Personal Identity: What's the Problem? (1995); IV. PHILOSOPHY OF MATHEMATICS; 12. Wholes, Parts, and Numbers (1997); 13. The Limits of Human Mathematics (2001); V. THEORY OF MEANING AND REFERENCE; 14. On Content (1992); 15. On Designating (1997); 16. A Problem in the Frege-Church Theory of Sense and Denotation (1993); 17. The Very Possibility of Language (2001); 18. Tense and Intension (2003); 19. Pronouns as Variables (2005)

This volume is the first extensive study of the historical and philosophical connections between technology and mathematics. Coverage includes the use of mathematics in ancient as well as modern technology, devices and machines for computation, cryptology, mathematics in technological education, the epistemology of computer-mediated proofs, and the relationship between technological and mathematical computability. The book also examines the work of such historical figures as Gottfried Wilhelm Leibniz, Charles Babbage, Ada Lovelace, and Alan Turing.

This volume comprises a selection of contributions to the theorizing about argumentation that have been presented at the 9th conference of the International Society for the Study of Argumentation (ISSA), held in Amsterdam in July 2018. The chapters included provide a general theoretical perspective on central topics in argumentation theory, such as argument schemes and the fallacies. Some contributions concentrate on the treatment of the concept of conductive argument. Other contributions are dedicated to specific issues such as the justification of questions, the occurrence of mining relations, the role of exclamatives, argumentative abduction, eudaimonistic argumentation and a typology of logical ways to counter an argument. In a number of cases the theoretical problems addressed are related to a specific type of context, such as the burden of proof in philosophical argumentation, the charge of committing a genetic fallacy in strategic manoeuvring in philosophy, the necessity of community argument, and connection adequacy for arguments with institutional warrants. The volume offers a great deal of diversity in its breadth of coverage of argumentation theory and wide geographic representation from North and South America to Europe and China.

This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest's research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism-the thesis that there exist true but inconsistent sentences-and paraconsistency-an account of deduction in which contradictory premises do not entail the truth of arbitrary sentences. Priest's work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth. This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest's work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, and applications of Priest's work and attest to its continued relevance and topicality. The book also includes Priest's responses to the contributors, providing a further layer to the development of these themes .

Strong reasoning skills are an important aspect to cultivate in life, as they directly impact decision making on a daily basis. By examining the different ways the world views logic and order, new methods and techniques can be employed to help expand on this skill further in the future. Philosophical Perceptions on Logic and Order is a pivotal scholarly resource that discusses the evolution of logical reasoning and future applications for these types of processes. Highlighting relevant topics including logic patterns, deductive logic, and inductive logic, this publication is an ideal reference source for academicians, students, and researchers that would like to expand their understanding of how society currently employs the use of logical reasoning techniques.

This volume examines the entire logical and philosophical production of Nicolai A. Vasil'ev, studying his life and activities as a historian and man of letters. Readers will gain a comprehensive understanding of this influential Russian logician, philosopher, psychologist, and poet. The author frames Vasil'ev's work within its historical and cultural context. He takes into consideration both the situation of logic in Russia and the state of logic in Western Europe, from the end of the 19th century to the beginning of the 20th. Following this, the book considers the attempts to develop non-Aristotelian logics or ideas that present affinities with imaginary logic. It then looks at the contribution of traditional logic in elaborating non-classical ideas. This logic allows the author to deal with incomplete objects just as imaginary logic does with contradictory ones. Both logics are objects of interesting analysis by modern researchers. This volume will appeal to graduate students and scholars interested not only in Vasil'ev's work, but also in the history of non-classical logics.

Many systems of logic diagrams have been offered both historically and more recently. Each of them has clear limitations. An original alternative system is offered here. It is simpler, more natural, and more expressively and inferentially powerful. It can be used to analyze not only syllogisms but arguments involving relational terms and unanalyzed statement terms.

Friedrich Ueberweg (1826-71) is best remembered for both his compendious "History of Philosophy" and his "System of Logic", both of which went through several editions in the original German. It was the latter's remarkable popularity as a textbook in Germany that led Lindsay to translate it to fill a gap in the English market. As well as incorporating the most up-to-date revisions and additons to the German edition he inserted the opinions of the more important English logicians. As such this is a valuable textbook for the understanding of logic systems as taught in England and Germany before symbolic logic was a formal and distinct discipline.

Published in honor of Sergio Galvan, this collection concentrates on the application of logical and mathematical methods for the study of central issues in formal philosophy. The volume is subdivided into four sections, dedicated to logic and philosophy of logic, philosophy of mathematics, philosophy of science, metaphysics and philosophy of religion. The contributions adress, from a logical point of view, some of the main topics in these areas. The first two sections include formal treatments of: truth and paradoxes; definitions by abstraction; the status of abstract objects, such as mathematical objects and universal concepts; and the structure of explicit knowledge. The last two sections include papers on classical problems in philosophy of science, such as the status of subjective probability, the notion of verisimilitude, the notion of approximation, and the theory of mind and mental causation, and specific issues in metaphysics and philosophy of religion, such as the ontology of species, actions, and intelligible worlds, and the logic of religious belonging.

This book is dedicated to Dov Gabbay, one of the most outstanding and most productive researchers in the area of logic, language and reasoning. He has exerted a profound influence in the major fields of logic, linguistics and computer science. Most of the chapters included, therefore, build on his work and present results or summarize areas where Dov has made major contributions. In particular his work on Labelled Deductive Systems is addressed in most of the contributions. The chapters on computational linguistics address logical and deductive aspects of linguistic problems. The papers by van Benthem Lambek and Moortgat investigate categorial considerations and the use of labels within the "parsing as deduction" approach. Analyses of particular linguistic problems are given in the remaining papers by Kamp, Kempson, Moravcsik, Konig and Reyle. They address the logic of generalized quantifiers, the treatment of cross-over phenomena and temporal/aspectual interpretation, as well as applicability of underspecified deduction in linguistic formalisms. The more logic-oriented chapters address philosophical and proof-theoretic problems and give algorithmic solutions for most of them. The spectrum ranges from K. Segerberg's contribution which brings together the two traditions of epistemic and doxastic logics of belief, to M. Finger and M. Reynold's chapter on two-dimensional executable logics with applications to temporal databases. The book demonstrates that a relatively small number of basic techniques and ideas, in particular the idea of labelled deductive systems, can be successfully applied in many different areas.

Ordinal Computability discusses models of computation obtained by generalizing classical models, such as Turing machines or register machines, to transfinite working time and space. In particular, recognizability, randomness, and applications to other areas of mathematics are covered.