Professor Koslow advances a new account of the basic concepts of logic. A central feature of the theory is that it does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of logic in a simple, but insightful way. The study has four parts. In the first two parts the various sources of the general concept of an (...) implication structure and its forms are illustrated and explained. Part 3 defines the various logical operations and systematically explores their properties. A generalized account of extensionality and dual implication is given, and the extensionality of each of the operators, as well as the relation of negation and its dual are given substantial treatment because of the novel results they yield. Part 4 considers modal operators and studies their interaction with logical operators. By obtaining the usual results without the usual assumptions this new approach allows one to give a very simple account of modal logic minus the excess baggage of possible world semantics. (shrink)
Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. To provide a balanced treatment of logic, tableaux are related to deductive proof systems.The logical systems presented are:- Propositional calculus (including binary decision diagrams);- Predicate calculus;- Resolution;- Hoare logic;- Z;- (...) Temporal logic.Answers to exercises (for instructors only) as well as Prolog source code for algorithms may be found via the Springer London web site: http://www.springer.com/978-1-85233-319-5 Mordechai Ben-Ari is an associate professor in the Department of Science Teaching of the Weizmann Institute of Science. He is the author of numerous textbooks on concurrency, programming languages and logic, and has developed software tools for teaching concurrency. In 2004, Ben-Ari received the ACM/SIGCSE Award for Outstanding Contributions to Computer Science Education. (shrink)
Highlights of this volume from the 2004 Annual European Meeting of the Association for Symbolic Logic (ASL) include a tutorial survey of the recent highpoints of universal algebra, written by a leading expert; explorations of foundational questions; a quartet of model theory papers giving an excellent reflection of current work in model theory, from the most abstract aspect "abstract elementary classes" to issues around p-adic integration.
This is a comprehensive study of the English word 'or', and the logical operators variously proposed to present its meaning. Although there are indisputably disjunctive uses of or in English, it is a mistake to suppose that logical disjunction represents its core meaning. 'Or' is descended from the Anglo-Saxon word meaning second, a form which survives in such expressions as "every other day." Its disjunctive uses arise through metalinguistic applications of an intermediate adverbial meaning which is conjunctive rather than disjunctive (...) in character. These conjunctive uses have puzzled philosophers and logicians, and have been discussed extensively under such headings as "free choice permission." This study examines the textbook myths that have clouded our understanding of how or and other "logical" vocabulary comes to have something approaching its logical meaning in natural languages. It considers the various historical conceptions of disjunction and its place in logic from the Stoics to the present day. (shrink)
This is a volume of specially commissioned essays of analytical philosophy, on topics of current interest in ethics and the philosophy of logic and language. Among the topics discussed are the making of wicked promises, G. E. Moore's early ethical views, as well as indexicals, tense, indeterminism, conventionalism in mathematics, and identity and necessity. The essays are all by former students of Casimir Lewy, until recently Reader in Philosophy at the University of Cambridge and an exponent of a particularly thoroughgoing (...) form of philosophical analysis. Together, they represent some of the best work in these areas at present, and express what may be described as a characteristic 'Cambridge' voice. (shrink)
This work is derived from the SERC "Logic for IT" Summer School Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles which form an invaluable introduction to proof theory aimed at both mathematicians and computer scientists.
Free logic is an important field of philosophical logic that first appeared in the 1950s. J. Karel Lambert was one of its founders and coined the term itself. The essays in this collection (written over a period of 40 years) explore the philosophical foundations of free logic and its application to areas as diverse as the philosophy of religion and computer science. Amongst the applications on offer are those to the analysis of existence statements, to definite descriptions and to partial (...) functions. The volume contains a proof that free logics of any kind are non-extensional and then uses that proof to show that Quine's theory of predication and referential transparency must fail. The purpose of this collection is to bring an important body of work to the attention of a new generation of professional philosophers, computer scientists, and mathematicians. (shrink)
Quantum theory is our deepest theory of the nature of matter. It is a theory that, notoriously, produces results which challenge the laws of classical logic and suggests that the physical world is illogical. This book gives a critical review of work on the foundations of quantum mechanics at a level accessible to non-experts. Assuming his readers have some background in mathematics and physics, Peter Gibbins focuses on the questions of whether the results of quantum theory require us to abandon (...) classical logic and whether quantum logic can resolve the paradoxes produced by quantum mechanics. He argues that quantum logic does not dispose of the problems faced by classical logic, that no reasonable interpretation of quantum mechanics in terms of 'hidden variables' can be found, and that after all these years quantum mechanics remains a mystery to us. Particles and Paradoxes provides a much-needed and valuable introduction to the philosophy of quantum mechanics and, at the same time, an example of just what it is to do the philosophy of physics. (shrink)
Medieval Modal Logic & Science uses modal reasoning in a new way to fortify the relationships between science, ethics, and politics. Robert C. Trundle accomplishes this by analyzing the role of modal logic in the work of St. Augustine and St. Thomas Aquinas, then applying these themes to contemporary issues. He incorporates Augustine's ideas involving thought and consciousness, and Aquinas's reasoning to a First Cause. The author also deals with Augustine's ties to Aristotelian modalities of thought regarding science and logic, (...) reassessing the commonly held belief in Augustine's Platonism to not be a mistake as much as a simplistic view of his philosophy. Trundle links contemporary issues in epistemology, morality, theology, and logic, making several useful connections between ancient and medieval studies in modal logic and modern concerns. These applications of modal theory illuminate many puzzles in the works of Heidegger, Wittgenstein, Whitehead, and Kuhn. (shrink)
The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, (...) the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert’s program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights. Key Features - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic -Useful bibliographies in every chapter - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic - Useful bibliographies in every chapter. (shrink)
A-LOGIC is a full-length book (600+ pg). It functions as a system of logic designed to: 1) solve the standard paradoxes and major problems of standard mathematical logic; 2) minimize that logic's anomalies with respect to ordinary language, yet; 3) prove that all theorems in mathematical logic are tautologies. It covers lst order logic the logic of the words "and", "or", "not", "all" and "some". But it also has a non truth functional "if...then" and differs in its definition of validity, (...) its semantics and its theorems. In the book A-logic is contrasted step by step with standard mathematical logic as presented and defended by Quine. All of standard logic's theorems are proven tautologies in A-logic. But some argument-forms called "valid" in standard logic are not valid in A-logic -- notably non-sequiturs like "(P and not-P), therefore Q". In addition A-logic has many tautologies with its non-truthfunctional "if ... then" that standard logic can not derive -- e.g., "Not-(if P&Q then not-P)." A-logic's semantics is based on syntactically defined concepts of logical synonymy and containment of meanings rather than on truth-values and truth-functions. Its "if...then" sentences (called "C-conditionals") are valid if and only if (i) the meaning of the consequent is logically contained in that of the antecedent, and (ii) the antecedent and consequent are jointly consistent. The predicate "valid" holds only of C-conditionals and arguments. No valid C-conditionals are translatable into standard logic though all of them imply tautologies of standard logic. (shrink)
In this book, Yaqub describes a simple conception of truth and shows that it yields a semantical theory that accommodates the whole range of our seemingly conflicting intuitions about truth. This conception takes the Tarskian biconditionals (such as "The sentence 'Johannes loved Clara' is true if and only if Johannes loved Clara") as correctly and completely defining the notion of truth. The semantical theory, which is called the revision theory, that emerges from this conception paints a metaphysical picture of truth (...) as a property whose applicability is given by a revision process rather than by a fixed extension. The main advantage of this revision process is its ability to explain why truth seems in many cases almost redundant, in others substantial, and yet in others paradoxical (as in the famous Liar). Yaub offers a comprehensive defense of the revision theory of truth by developing consistent and adequate formal semantics for languages in which all sorts of problematic sentences (Liar and company) can be constructed. Yaqub concludes by introducing a logic of truth that further demonstrates the adequacy of the revision theory. (shrink)
In this book Yaqub describes a simple conception of truth and shows that it yields a semantical theory that accommodates the whole range of our seemingly conflicting intuitions about truth. This conception takes the Tarskian biconditionals as correctly and completely defining the notion of truth. He offers a comprehensive defense of the semantical theory by developing consistent and adequate formal semantics for languages in which all sorts of problematic sentences can be constructed. Yaqub concludes by introducing a logic of truth (...) that further demonstrates the adequacy of this theory. (shrink)
Meaning and Argument shifts introductory logic from the traditional emphasis on proofs to the symbolization of arguments. Another distinctive feature of this book is that it shows how the need for expressive power and for drawing distinctions forces formal language development. This revised edition includes expanded sections, additional exercises, and an updated bibliography. Updated and revised edition includes extended sections, additional exercises, and an updated bibliography. Distinctive approach in that this text is a philosophical, rather than mathematical introduction to logic. (...) Concentrates on symbolization and does all the technical logic simply with truth tables and no derivations at all. Contains numerous exercises and a corresponding answer key. Extensive appendix which allows the reader to explore subjects that go beyond what is usually covered in an introductory logic course. Features accompanying website at www.meaningargument.com. (shrink)
This book explores an important central thread that unifies Russell's thoughts on logic in two works previously considered at odds with each other, the Principles of Mathematics and the later Principia Mathematica. This thread is Russell's doctrine that logic is an absolutely general science and that any calculus for it must embrace wholly unrestricted variables. The heart of Landini's book is a careful analysis of Russell's largely unpublished "substitutional" theory. On Landini's showing, the substitutional theory reveals the unity of Russell's (...) philosophy of logic and offers new avenues for a genuine solution of the paradoxes plaguing Logicism. (shrink)
Now in its fourth edition, this classic work clearly and concisely introduces the subject of logic and its applications. The first part of the book explains the basic concepts and principles which make up the elements of logic. The author demonstrates that these ideas are found in all branches of mathematics, and that logical laws are constantly applied in mathematical reasoning. The second part of the book shows the applications of logic in mathematical theory building with concrete examples that draw (...) upon the concepts and principles presented in the first section. Numerous exercises and an introduction to the theory of real numbers are also presented. Students, teachers and general readers interested in logic and mathematics will find this book to be an invaluable introduction to the subject. (shrink)
In a world plagued by disagreement and conflict one might expect that the exact sciences of logic and mathematics would provide a safe harbor. In fact these disciplines are rife with internal divisions between different, often incompatible, systems. Do these disagreements admit of resolution? Can such resolution be achieved without disturbing assumptions that the theorems of logic and mathematics state objective truths about the real world? In this original and historically rich book John Woods explores apparently intractable disagreements in logic (...) and the foundations of mathematics and sets out conflict resolution strategies that evade or disarm these stalemates. An important sub-theme of the book is the extent to which pluralism in logic and the philosophy of mathematics undermines realist assumptions. This book makes an important contribution to such areas of philosophy as logic, philosophy of language and argumentation theory. It will also be of interest to mathematicians and computer scientists. (shrink)
The purpose of this book is to develop a framework for analyzing strategic rationality, a notion central to contemporary game theory, which is the formal study of the interaction of rational agents, and which has proved extremely fruitful in economics, political theory, and business management. The author argues that a logical paradox (known since antiquity as "the Liar paradox") lies at the root of a number of persistent puzzles in game theory, in particular those concerning rational agents who seek to (...) establish some kind of reputation. Building on the work of Parsons, Burge, Gaifman, and Barwise and Etchemendy, Robert Koons constructs a context-sensitive solution to the whole family of Liar-like paradoxes, including, for the first time, a detailed account of how the interpretation of paradoxial statements is fixed by context. This analysis provides a new understanding of how the rational agent model can account for the emergence of rules, practices, and institutions. (shrink)
Lewis, D. Semantic analyses for dyadic deontic logic.--Salomaa, A. Some remarks concerning many-valued propositional logics.--Chellas, B. F. Conditional obligation.--Jeffrey, R.C. Remarks on interpersonal utility theory.--Hintikka, J. On the proper treatment of quantifiers in Montague semantics.--Mayoh, B.H. Extracting information from logical proofs.--Åqvist, L. A new approach to the logical theory of actions and causality.--Pörn, I. Some basic concepts of action.--Bouvère, K. de. Some remarks concerning logical and ontological theories.--Hacking, I. Combined evidence.--Äberg, C. Solution to a problem raised by Stig Kanger and (...) a set theoretical statement equivalent to the axiom of choice.--Lindström, P. On characterizing elementary logic.--Scott, D. Rules and derived rules.--Hansson, B. A program for pragmatics.--Hermerén, G. Models.--Fenstad, J.E. Remarks on logic and probability.--Stenlund, S. Analytic and synthetic arithmetical statements. (shrink)
Dependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets - but what is the logic of dependence? This book is the first to carry out a systematic logical study of this important concept, giving on the way a precise mathematical treatment of Hintikka’s independence friendly logic. Dependence logic adds the concept of dependence to first order logic. Here the syntax and semantics of dependence logic are studied, dependence logic is given an alternative game theoretic (...) semantics, and results about its complexity are proven. This is a graduate textbook suitable for a special course in logic in mathematics, philosophy and computer science departments, and contains over 200 exercises, many of which have a full solution at the end of the book. It is also accessible to readers, with a basic knowledge of logic, interested in new phenomena in logic. (shrink)
Demonstrating the practical relevance and import of many historically significant philosophers , Critical Thinking Unleashed presents a practical, non-technical, and comprehensive approach to critical thinking. In contrast to other treatments of practical reasoning, Elliot D. Cohen not only teaches students how to identify and refute irrational premises_he also teaches them how to construct rational antidotes to combat the personal, social, and political obstacles they confront in everyday life.
The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is basically self-contained and special (...) attention has been made to present the material in a convenient manner for the reader. Proofs of results, many of which are not readily available elsewhere, are also included. The book is written at a level appropriate for first-year graduate students in mathematics or computer science. Although some knowledge of elementary logic and universal algebra are necessary, the first chapter includes all the results from universal algebra and logic that the reader needs. For graduate students in mathematics and computer science the book is an excellent textbook. (shrink)
Introduction: Major terms, their classification, and their relation to the book's objective -- The problem of analogous forms -- Natural logic, categories, and the individual -- Shift to individual categories, dynamics, and a psychological look at identity form versus function -- What is the difference between the logic governing a figure of speech and the logic that is immature or unconscious? -- What are the role and function of the self vis-à-vis consciousness? -- Development in the logic from immature to (...) mature modes -- Pathological and defensive logical forms -- The "I," identity, and the part-whole resolutions -- The "I," entropy, and the trope. (shrink)