Advocating a "bottom-up," inductive approach to cognition, the book covers the gamut of topics starting with the axioms of existence, identity, and consciousness, then taking up concept-formation, propositions, logic, and principles. A chapter on free will, treated as the choice to exercise reason, presents the author's interpretation of Rand's view on volition, supplemented by his own analysis.

    It confronts important issues left open in that work -- among them, the semantics of proper names and natural kind terms as they occur in fiction and in myth;negative existential statements; the ontology of fiction and myth (whether it is true that fictional characters like Hamlet, or mythical kinds like bandersnatches, might have existed). In treating these questions, he makes a number of methodological observations that go beyond the framework of hisearlier book -- including the striking claim that fiction cannot provide a test for theories of reference and naming. In addition, these lectures provide a glimpse into the transition to the pragmatics of singular reference that dominated his influential paper, Speaker's Reference and SemanticReference -- a paper that helped reorient linguistic and philosophical semantics. Some of the themes have been worked out in later writings by other philosophers -- many influenced by typescripts of the lectures in circulation -- but none have approached the careful, systematic treatment providedhere. The virtuosity of Naming and Necessity -- the colloquial ease of the tone, the dazzling, on-the-spot formulations, the logical structure of the overall view gradually emerging over the course of the lectures -- is on display here as well.

    C. Schindler shows in this book that only a robust confidence in reason can allow us to remain genuinely open both to God and to the deep mystery of things. Drawing from both contemporary and classical theologians and philosophers, Schindler explores the basic philosophical questions concerning truth, knowledge, and being -- and proposes a new model for thinking about the relationship between faith and reason.The reflections brought together in this book bring forth a dramatic conception of human knowing that both strengthens our trust in reason and opens our mind in faith.

    Each definition is accompanied by commentary that motivates and explains new concepts. Starting with a repetition of the familiar arguments of elementary set theory, the level of abstract thinking gradually rises for a progressive increase in complexity.A historical introduction presents a brief account of the growth of set theory, with special emphasis on problems that led to the development of the various systems of axiomatic set theory. Subsequent chapters explore classes and sets, functions, relations, partially ordered classes, and the axiom of choice. Other subjects include natural and cardinal numbers, finite and infinite sets, the arithmetic of ordinal numbers, transfinite recursion, and selected topics in the theory of ordinals and cardinals. This updated edition features new material by author Charles C. Pinter.

    Doug Erlandson provides a straightforward and easy-to-understand overview of the area of philosophy that deals with the concept of knowledge. Drawing on the thought of philosophers past and present, Erlandson examines and evaluates their views in a lively and engaging manner. The Theory of Knowledge Answers These Questions What is knowledge? Can I really know anything? Where does knowledge come from? What's the relation between the mind and the world? How do I know that other minds exist? ˃˃˃ Suitable as a classroom text and for independent study The Theory of Knowledge is a basic introduction to epistemology and presupposes no prior familiarity with philosophical thought. It is suited for introductory philosophy classes and for independent study. Scroll up and grab a copy today.

    Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all areas of calculus, including functions, gradients, rates of change, differentiation, exponential and logarithmic functions and integration. Everything you will need to know is here in one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.

    Questions for further reflection are included at the end of each chapter as well as helpful diagrams and charts for use in college and graduate-level classrooms.Vern Poythress has undertaken a radical recasting of the study of logic in this revolutionary work from a Christian worldview.

    With two brief exhortations from Piper and eight others from veteran pastors, this short ebook aims to strengthen and challenge Christians in general, and pastors in particular, for the labor of everyday life and ministry. The contributors were asked to express their “heart of hearts” for fellow leaders. You'll find these chapters tap into profound human themes, in both the pastor and his flock, and will be of use, we hope, beyond the North American context of the contributors.

    Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all the key areas of algebra including elementary operations, linear equations, formulae, simultaneous equations, quadratic equations, logarithms, variation, laws and sequences. Everything you will need is here in this one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.

    Paul is seething with righteous indignation over the events at Galatia even as he conveys his hope that the Galatians might be coaxed back to the true Gospel.The Galatians' young faith was grappling with issues that would prove to be a watershed. Do gentile Christians need to adopt Moses’ Law and be circumcised as Jews in order to worship the God of the Jewish Savior? Or does Baptism incorporate every manner of person—without distinction—into Christ? Does faith alone suffice for salvation? Across the divide of two thousand years of time and cultural space, the letter to the Galatians is an authoritative witness to the catholic Gospel of salvation by grace alone, for all people alike.

    It presents the ideas behind the theoretical concepts.

    Reading and memorization are not enough; students must be able to verbalize their understanding and defend it under the pressure of fierce cross-examination. This book, based on the author's successful undergraduate course in the subject, trains readers to develop the analytical skills used in Tibetan-style debate. Making use of sample debate exchanges and definitions and classification systems drawn from Tibetan Buddhist debate manuals, the book shows how to challenge and defend assertions made in the course of debate.

    The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.

    It shows how his secular spiritual exercises expand our horizons, enabling us to be in a fuller, more authentic way. Comprehensive treatment of a neglected theme: philosophy's practical relevance in our lives Interdisciplinary analysis reflects the wide influence of Hadot's thought Explores the links between Hadot's ideas and those of a wealth of ancient and modern thinkers, including the French postmodernists Offers a practical 'third way' in philosophy beyond the dichotomy of Continental and analytical traditions

    Plural logic deals with plural terms ('Whitehead and Russell', 'Henry VIII's wives', 'the real numbers', 'the square root of -1', 'they'), plural predicates ('surrounded the fort', 'are prime', 'are consistent', 'imply'), and plural quantification ('some things', 'any things'). Current logic is singularist: its terms stand for at most one thing. By contrast, the foundational thesis of this book is that a particular term may legitimately stand for several things at once; inother words, there is such a thing as genuinely plural denotation. The authors argue that plural phenomena need to be taken seriously and that the only viable response is to adopt a plural logic, a logic based on plural denotation. They expound a framework of ideas that includes the distinctionbetween distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is presented in three stages, before being applied to Cantorian set theory as an illustration.Technicalities have been kept to a minimum, and anyone who is familiar with the classical predicate calculus should be able to follow it. The authors' approach is an attractive blend of no-nonsense argumentative directness and open-minded liberalism, and they convey the exciting and unexpectedrichness of their subject. Mathematicians and linguists, as well as logicians and philosophers, will find surprises in this book.

    The best way to learn it is to try it out on real instances of arguments found in everyday conversational exchanges and legal argumentation. The introductory chapter of this book gives a clear general idea of what the methods of argumentation are and how they work as tools that can be used to analyze arguments. Each subsequent chapter then applies these methods to a leading problem of argumentation. Today the field of computing has embraced argumentation as a paradigm for research in artificial intelligence and multi-agent systems. Another purpose of this book is to present and refine tools and techniques from computing as components of the methods that can be handily used by scholars in other fields.

    By looking carefully at what mathematicians really do when they are doing mathematics, Reuben Hersh offers an escape from this trap. This book of selected articles and essays provides an honest, coherent, and clearly understandable account of mathematicians' proof as it really is, and of the existence and reality of mathematical entities. It follows in the footsteps of Poincare, Hadamard, and Polya. The pragmatism of John Dewey is a better fit for mathematical practice than the dominant analytic philosophy. Dialogue, satire, and fantasy enliven the philosophical and methodological analysis. Reuben Hersh has written extensively on mathematics, often from the point of view of a philosopher of science. His book with Philip Davis, The Mathematical Experience, won the National Book Award in science.

    Although building on decades of previous work in the field, it is the first collection to take into account the significant changes in the landscape of deontic logic that have occurred in the past twenty years. These changes have resulted largely, though not entirely, from the interaction of deontic logic with a variety of other fields, including computer science, legal theory, organizational theory, economics, and linguistics. This first volume of the Handbook is divided into three parts, containing nine chapters in all, each written by leading experts in the field. The first part concentrates on historical foundations. The second examines topics of central interest in contemporary deontic logic. The third presents some new logical frameworks that have now become part of the mainstream literature. A second volume of the Handbook is currently in preparation, and there may be a third after that.

    Gennaro Chierchia looks at the way syntactic and inferential processes interact in determining polarity sensitive and free choice phenomena. He analyses these as a form of grammaticized scalar implicature and seeks to identify the common core of the polarity system by examining many of its manifestations as well as the choices that determine its diversity. To do so he reassesses the relations between syntax, semantics, and pragmatics and in the process makes startling insights into the relation of syntax to logic. Rudolf Carnap's classic, The Logical Syntax of Language, defines syntax as a lexicon and a set of formation rules and logic as a set of inference rules. Modern generative linguistics maintains a similar modular approach: a combinatorial apparatus is said to generate structures over which semantic and pragmatic relations, such as presupposition and implicature, are defined. This book argues by contrast that many structures typically perceived as syntactically deviant owe their status to their logical properties, in other words to whether they are contradictory or analytically true in specific ways. This alters the Carnapian view. The characterization of grammatical structure requires a more direct role of logical inferences: the functional lexicon of grammar comes, Professor Chierchia shows, with a set of inference rules that crucially and directly determine grammaticality patterns. Logic in Grammar presents the results of the author's decade-long work on pragmatics and scalar implicatures and extends his long-term project on how humans reason and categorize the world. It is a book that will interest linguists, philosophers, and cognitive scientists alike.

    This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding. Some chapters focus on the pioneering work by Turing, Godel, and Church, including the Church-Turing thesis and Godel's response to Church's and Turing's proposals. Other chapters cover more recent technical developments, including computability over the reals, Godel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics.Contributors: Scott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani "