Originally published in 1965. This is a textbook of modern deductive logic, designed for beginners but leading further into the heart of the subject than most other books of the kind. The fields covered are the Propositional Calculus, the more elementary parts of the Predicate Calculus, and Syllogistic Logic treated from a modern point of view. In each of the systems discussed the main emphases are on Decision Procedures and Axiomatisation, and the material is presented with as much formal rigour as is compatible with clarity of exposition. The techniques used are not only described but given a theoretical justification. Proofs of Consistency, Completeness and Independence are set out in detail. The fundamental characteristics of the various systems studies, and their relations to each other are established by meta-logical proofs, which are used freely in all sections of the book. Exercises are appended to most of the chapters, and answers are provided.

This book presents Goedel's incompleteness theorems and the other limitative results which are most significant for the philosophy of mathematics. Results are stated in the form most relevant for use in the philosophy of mathematics. An appendix considers their implications for Hilbert's Program for the foundations of mathematics. The text is self-contained, all notions being explained in full detail, but of course previous exposure to the very first rudiments of mathematical logic will help.

Over the past few years, the tree model of time has been widely employed to deal with issues concerning the semantics of tensed discourse. The thought that has motivated its adoption is that the most plausible way to make sense of indeterminism is to conceive of future possibilities as branches that depart from a common trunk, constituted by the past and the present. However, the thought still needs to be further articulated and defended, and several important questions remain open, such as the question of how actuality can be understood and formally represented in a branching framework. The present volume is intended to be a 360 degree reflection on the tree model. The contributions is gathers concern the model and its alternatives, both from a semantic and from a metaphysical point of view. "

This book argues that there is a common cognitive mechanism underlying all indexical thoughts, in spite of their seeming diversity. Indexical thoughts are mental representations, such as beliefs and desires. They represent items from a thinker's point of view or her cognitive perspective. We typically express them by means of sentences containing linguistic expressions such as 'this (F)' or 'that (F)', adverbs like 'here', 'now', and 'today', and the personal pronoun 'I'. While generally agreeing that representing the world from a thinker's cognitive perspective is a key feature of indexical thoughts, philosophers disagree as to whether a thinker's cognitive perspective can be captured and rationalized by semantic content and, if so, what kind of content this is. This book surveys competing views and then advances its own positive account. Ultimately, it argues that a thinker's cognitive perspective - or her indexical point of view - is to be explained in terms of the content that is believed and asserted as the only kind of content that there is which thereby serves as the bearer of cognitive significance. The Indexical Point of View will be of interest to philosophers of mind and language, linguists, and cognitive scientists.

This innovative text reinvigorates argumentation studies by exploring the experience of argument across cultures, introducing an anthropological perspective into the domains of rhetoric, communication, and philosophy. The Anthropology of Argument fills an important gap in contemporary argumentation theory by shifting the focus away from the purely propositional element of arguments and onto how they emerge from the experiences of peoples with diverse backgrounds, demonstrating how argumentation can be understood as a means of expression and a gathering place of ideas and styles. Confronting the limitations of the Western tradition of logic and searching out the argumentative roles of place, orality, myth, narrative, and audience, it examines the nature of multi-modal argumentation. Tindale analyzes the impacts of colonialism on the field and addresses both optimistic and cynical assessments of contextual differences. The results have implications for our understanding of contemporary argumentative discourse in areas marked by deep disagreement, like politics, law, and social policy. The book will interest scholars and upper-level students in communication, philosophy, argumentation theory, anthropology, rhetoric, linguistics, and cultural studies.

Originally published in 1990. This study was first written in 1965 when interest in Leibniz was intensifying. The book looks in detail at the doctrine of necessity - that necessary truths are those derivable from the principle of identity by the substitution of definitions. It first considers views of philosophic predecessors, relating Leibniz' doctrine to Aristotle and Hobbes among others. The second section examines the conflict between his reductionistic and formalistic views and the opposing intuitionism and anti-reductionism of Descartes and Locke. The author critically examines the theory of necessity, including Leibniz's arguments against the views of Hobbes and Locke, concluding with distinctions between necessary and contingent truths.

This book introduces the principles of place and time by discussing the main roles they play in argumentation, unpacking the multifarious meanings of spatiality and temporality. Definitions of kairos are explored to yield suggestions as to how this concept, and that of 'place', can operate in argumentation. The chapters explore various related concepts such as the role of different arguments in different places, and how some places are not intended for argument; argumentation, time and temporality; visual argumentation; the effect of the passage of time on argument evaluation; and the image as a site of discursive production. This collection is of interest to students and researchers in argumentation studies, rhetoric, reasoning, and philosophy. Previously published in Argumentation Volume 34, issue 1, March 2020

How do we think? What does a faithful use of logic look like? Without even pausing to think about it, we exercise our capacity for rational thought. But how exactly does logic work? What makes some arguments valid and others not? In this Questions in Christian Philosophy volume, philosopher Forrest Baird offers an introduction to logic. He considers the basic building blocks of human reason, including types of arguments, fallacies, syllogisms, symbols, and proofs, all of which are demonstrated with exercises for students throughout. In addition, he reflects on the relationship between the use of reason and the Christian faith. With this academic but accessible primer, readers will be introduced to the basics of logic-and encouraged to reason better. The Questions in Christian Philosophy Series features introductory textbooks that offer students a Christian perspective on the various branches of philosophy, enabling them as they seek to understand all facets of life including existence, knowledge, ethics, art, and more.

At the turn of the century, Gottlob Frege and Edmund Husserl both participated in the discussion concerning the foundations of logic and mathematics. Since the 1960s, comparisons have been made between Frege's semantic views and Husserl's theory of intentional acts. In quite recent years, new approaches to the two philosophers' views have appeared. This collection of articles opens with the first English translation of Dagfinn Follesdal's early classic on Husserl and Frege of 1958. The book brings together a number of new contributions by well-known authors and gives a survey of recent developments in the field. It shows that Husserl's thought is coming to occupy a central role in the philosophy of logic and mathematics, as well as in the philosophy of mind and cognitive science. The work is primarily meant for philosophers, especially for those working on the problems of language, logic, mathematics, and mind. It can also be used as a textbook in advanced courses in philosophy. "

Introductory logic is generally taught as a straightforward technical discipline. In this book, John MacFarlane helps the reader think about the limitations of, presuppositions of, and alternatives to classical first-order predicate logic, making this an ideal introduction to philosophical logic for any student who already has completed an introductory logic course. The book explores the following questions. Are there quantificational idioms that cannot be expressed with the familiar universal and existential quantifiers? How can logic be extended to capture modal notions like necessity and obligation? Does the material conditional adequately capture the meaning of 'if'-and if not, what are the alternatives? Should logical consequence be understood in terms of models or in terms of proofs? Can one intelligibly question the validity of basic logical principles like Modus Ponens or Double Negation Elimination? Is the fact that classical logic validates the inference from a contradiction to anything a flaw, and if so, how can logic be modified to repair it? How, exactly, is logic related to reasoning? Must classical logic be revised in order to be applied to vague language, and if so how? Each chapter is organized around suggested readings and includes exercises designed to deepen the reader's understanding. Key Features: An integrated treatment of the technical and philosophical issues comprising philosophical logic Designed to serve students taking only one course in logic beyond the introductory level Provides tools and concepts necessary to understand work in many areas of analytic philosophy Includes exercises, suggested readings, and suggestions for further exploration in each chapter

Introductory logic is generally taught as a straightforward technical discipline. In this book, John MacFarlane helps the reader think about the limitations of, presuppositions of, and alternatives to classical first-order predicate logic, making this an ideal introduction to philosophical logic for any student who already has completed an introductory logic course. The book explores the following questions. Are there quantificational idioms that cannot be expressed with the familiar universal and existential quantifiers? How can logic be extended to capture modal notions like necessity and obligation? Does the material conditional adequately capture the meaning of 'if'-and if not, what are the alternatives? Should logical consequence be understood in terms of models or in terms of proofs? Can one intelligibly question the validity of basic logical principles like Modus Ponens or Double Negation Elimination? Is the fact that classical logic validates the inference from a contradiction to anything a flaw, and if so, how can logic be modified to repair it? How, exactly, is logic related to reasoning? Must classical logic be revised in order to be applied to vague language, and if so how? Each chapter is organized around suggested readings and includes exercises designed to deepen the reader's understanding. Key Features: An integrated treatment of the technical and philosophical issues comprising philosophical logic Designed to serve students taking only one course in logic beyond the introductory level Provides tools and concepts necessary to understand work in many areas of analytic philosophy Includes exercises, suggested readings, and suggestions for further exploration in each chapter

Originally published in 1973. This final collection of thought by founder of the New School for Social Research in New York, Horace M. Kallen, touches on topics from language to death and from freedom to value. The author's treatise explores his understanding of logic and existence.

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.

Originally published in 1934. This fourth edition originally published 1954., revised by C. W. K. Mundle. "It must be the desire of every reasonable person to know how to justify a contention which is of sufficient importance to be seriously questioned. The explicit formulation of the principles of sound reasoning is the concern of Logic". This book discusses the habit of sound reasoning which is acquired by consciously attending to the logical principles of sound reasoning, in order to apply them to test the soundness of arguments. It isn't an introduction to logic but it encourages the practice of logic, of deciding whether reasons in argument are sound or unsound. Stress is laid upon the importance of considering language, which is a key instrument of our thinking and is imperfect.

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 1966. This is a self-instructional course intended for first-year university students who have not had previous acquaintance with Logic. The book deals with "propositional" logic by the truth-table method, briefly introducing axiomatic procedures, and proceeds to the theory of the syllogism, the logic of one-place predicates, and elementary parts of the logic of many-place predicates. Revision material is provided covering the main parts of the course. The course represents from eight to twenty hours work. depending on the student's speed of work and on whether optional chapters are taken.

The book aims to formalise tableau methods for the logics of propositions and names. The methods described are based on Set Theory. The tableau rule was reduced to an ordered n-tuple of sets of expressions where the first element is a set of premises, and the following elements are its supersets.

This book provides a fresh reading of Aquinas' metaphysics in the light of insights from the works of Frege. In particular, Ventimiglia argues that Aquinas' doctrine of being can be better understood through Frege's distinction between the 'there is' sense and the 'present actuality' sense of being, as interpreted by Peter Geach and Anthony Kenny. Aquinas' notion of essence becomes clearer in the light of Frege's distinction between objects and concepts and his account of concepts as functions. Aquinas' doctrine of trancendentals is clarified with the help of Frege's accounts of assertion and negation. Aquinas after Frege provides us with a new Aquinas, which pays attention to his texts and their historical context. Ventimiglia's development of 'British Thomism' furnishes us with a lucid and exciting re-reading of Aquinas' metaphysics.

This Handbook offers students and more advanced readers a valuable resource for understanding linguistic reference; the relation between an expression (word, phrase, sentence) and what that expression is about. The volume's forty-one original chapters, written by many of today's leading philosophers of language, are organized into ten parts: I Early Descriptive Theories II Causal Theories of Reference III Causal Theories and Cognitive Significance IV Alternate Theories V Two-Dimensional Semantics VI Natural Kind Terms and Rigidity VII The Empty Case VIII Singular (De Re) Thoughts IX Indexicals X Epistemology of Reference Contributions consider what kinds of expressions actually refer (names, general terms, indexicals, empty terms, sentences), what referring expressions refer to, what makes an expression refer to whatever it does, connections between meaning and reference, and how we know facts about reference. Many contributions also develop connections between linguistic reference and issues in metaphysics, epistemology, philosophy of mind, and philosophy of science.

This open access book is a timely contribution in presenting recent issues, approaches, and results that are not only central to the highly interdisciplinary field of concept research but also particularly important to newly emergent paradigms and challenges. The contributors present a unique, holistic picture for the understanding and use of concepts from a wide range of fields including cognitive science, linguistics, philosophy, psychology, artificial intelligence, and computer science. The chapters focus on three distinct points of view that lie at the core of concept research: representation, learning, and application. The contributions present a combination of theoretical, experimental, computational, and applied methods that appeal to students and researchers working in these fields.

This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato's dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers' willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.

Real Essentialism presents a comprehensive defence of neo-Aristotelian essentialism. Do objects have essences? Must they be the kinds of things they are in spite of the changes they undergo? Can we know what things are really like - can we define and classify reality? Many, if not most, philosophers doubt this, influenced by centuries of empiricism, and by the anti-essentialism of Wittgenstein, Quine, Popper, and other thinkers. Real Essentialism reinvigorates the tradition of realist, essentialist metaphysics, defending the reality and knowability of essence, the possibility of objective, immutable definition, and its relevance to contemporary scientific and metaphysical issues such as whether essence transcends physics and chemistry, the essence of life, the nature of biological species, and the nature of the person.

The primary purpose of this book has not been to recount all that past scholars have said about the science, but rather to record the first appearances of those ideas which seem most important in the logic of our own day.

Philosophical questions regarding the nature and methodology of philosophical inquiry have garnered much attention in recent years. Perhaps nowhere are these discussions more developed than in relation to the field of metaphysics. The Routledge Handbook of Metametaphysics is an outstanding reference source to this growing subject. It comprises thirty-eight chapters written by leading international contributors, and is arranged around five themes: * The history of metametaphysics * Neo-Quineanism (and its objectors) * Alternative conceptions of metaphysics * The epistemology of metaphysics * Science and metaphysics. Essential reading for students and researchers in metaphysics, philosophical methodology, and ontology, The Routledge Handbook of Metametaphysics will also be of interest to those in closely related subjects such as philosophy of language, logic, and philosophy of science.