This book provides an exceptionally clear introduction to classical logic, with a unique approach that emphasizes both the hows and whys of logic. Here Nicholas Smith thoroughly covers the formal tools and techniques of logic while also imparting a deeper understanding of their underlying rationales and broader philosophical significance. In addition, this is the only introduction to logic available today that presents all the major forms of proof--trees, natural deduction in all its major variants, axiomatic proofs, and sequent calculus. The book also features numerous exercises, with solutions available on an accompanying website.Logic is the ideal textbook for undergraduates and graduate students seeking a comprehensive and accessible introduction to the subject.Provides an essential introduction to classical logicEmphasizes the how and why of logicCovers both formal and philosophical issuesPresents all the major forms of proof--from trees to sequent calculusFeatures numerous exercises, with solutions available at http: //njjsmith.com/philosophy/lawsoftruth/The ideal textbook for undergraduates and graduate students

    

    Kalantzis not only provides the reader with many new translations of pre-Constantinian texts, he also tells the story of the struggle of the earliest Church, the communities of Christ at the margins of power and society, to bear witness to the nations that enveloped them as they transformed the dominant narratives of citizenship, loyalty, freedom, power, and control. Although Kalantzis examines writings on war and military service in the first three centuries of the Christian Church in an organized manner, the ways earliest Christians thought of themselves and the state are not presented here through the lens of antiquarian curiosity. With theological sensitivity and historical acumen this companion leads the reader into the world in which Christianity arose and asks questions of the past that help us understand the early character of the Christian faith with the hope that such an enterprise will also help us evaluate its expression in our own time. Endorsement: "Kalantzis's skills as a historian shine in this remarkable, illuminating history. But his narration is much more than a fine historical survey; it is also a profound engagement with the theological and ethical reasons on why this history matters. Historians, theologians, ethicists, and anyone interested in discovering the witness of the early church are in his debt for such careful work. Any future discussion on the early church's response to war, and the Constantinian shift that occurred, must now pass through Caesar and the Lamb, or be ignored as incomplete." --D. Stephen Long, Professor of Systematic Theology, Marquette University "Caesar and the Lamb is a wonderful collection of pertinent voices from the early church on war and military service that will be of interest to laity, students, and scholars. But it is also much more than this. Kalantzis brings new insight to these texts with his brilliant introduction, placing the conversation in its proper context of identities, worldviews, and ways of life. The result is a collection with surprising and refreshing relevance today." --Daniel M. Bell, Jr., Professor of Theology and Ethics, Lutheran Theological Southern Seminary "Caesar and the Lamb offers a valuable deepening of our understanding, not only of early Christian teachings and practices related to violence, but also the social-cultural-religious practices of the Roman Empire and the Roman military. This book contains both a helpful collection of the primary Christian texts and a substantial interpretive discussion. A significant addition to a growing Christian library of resources on this critical issue." --David P. Gushee, Professor of Christian Ethics, Mercer University Author Biography: George Kalantzis is Associate Professor of Theology at Wheaton College where he also directs The Wheaton Center for Early Christian Studies. He specializes in fourth- and fifth-century historical theology, and has written extensively on Theodore of Mopsuestia, Cyril, and the Nestorian controversy. His has recently co-edited The Sovereignty of God Debate (Cascade 2009), Life in the Spirit: Spiritual Formation in Theological Perspective (2010), and Evangelicals and the Early Church: Recovery, Reform, Renewal (Cascade 2011).

    Geared toward undergraduates taking a first course in graph theory, its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.

    The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and mathematics.

    Notions like denumerability, modal scope distinction, Bayesian conditionalization, and logical completeness are usually only elucidated deep within difficultspecialist texts. By offering simple explanations that by-pass much irrelevant and boring detail, Philosophical Devices is able to cover a wealth of material that is normally only available to specialists.The book contains four sections, each of three chapters. The first section is about sets and numbers, starting with the membership relation and ending with the generalized continuum hypothesis. The second is about analyticity, a prioricity, and necessity. The third is about probability, outliningthe difference between objective and subjective probability and exploring aspects of conditionalization and correlation. The fourth deals with metalogic, focusing on the contrast between syntax and semantics, and finishing with a sketch of Godel's theorem.Philosophical Devices will be useful for university students who have got past the foothills of philosophy and are starting to read more widely, but it does not assume any prior expertise. All the issues discussed are intrinsically interesting, and often downright fascinating. It can be read withpleasure and profit by anybody who is curious about the technical infrastructure of contemporary philosophy.

    He is believed to be the author of several New Thought books which, in part, work to introduce Western readers to Eastern ideas about the topic spirituality. During the course of his writing career, Atkinson wrote under several pen names including “Yogi Ramacharaka,” "Swami Bhakta Vishita" and “Swami Panchadasi.”This Kindle collection of Atkinson's writings include:Thought VibrationDynamic ThoughtHow to Read Human Nature: Its Inner States and Outer FormsThought Force in Business and Everyday LifePractical Mental InfluenceMind PowerThe Secret of SuccessReincarnation and the Law of KarmaMemory CulturePractical Mind-ReadingThe Law of New ThoughtNuggets of the New ThoughtGenuine Mediumship or the Invisible PowersThe Human Aura: Astral Colors and Thought FormsClairvoyance and Occult PowersThe Inner ConsciousnessThe Science of Psychic HealingMemory: How to Develop, Train and Use ItPractical Water CureThe Hindu-Yogi Science of BreathHatha YogaFourteen Lessons in Yogi Philosophy and Oriental OccultismAdvanced Course in Yogi Philosophy and Oriental OccultismA Series of Lesson on Raja YogaA Series of Lessons in Gnani YogaThe KybalionThe Life Beyond DeathMystic ChristianityThe Inner Teachings of the Philosophies and Religions of IndiaThe Bhagavad Gita or the Message of the MasterThe Spirit of the UpanishadsEach book has an active link table of contents.

    Jensen challenges the confidence with which we define the commonplace. Sharing historical knowledge and unexpected insights, this manifesto for nominological consistency illuminates the lunch counter with surprising rigor and alacrity. Think you know what a sandwich is? Prepare to be challenged!

    Offering a unique combination of two approaches--the historical and the technical--he presents logic as both a fascinating, evolving story and a body of essential technical information with applications to every area of human thought.Perfectly suited for use in any introductory logic course, Introduction to Logic is also tailored to the online logic course Philosophy 106, available as part of the Open Course Library at www.opencourselibrary.org. Jointly sponsored by the Washington State Board for Community and Technical Colleges and the Bill & Melinda Gates Foundation, the Open Course Library offers instructors complete, expertly developed online courses in eighty essential college subjects--including the logic class developed by Paul Herrick and his colleague Mark Storey--all available to faculty at no charge.SUPPLEMENTS: * An Instructor's Resource CD (978-0-19-989052-1) contains brief chapter summaries, answers to all of the questions in the text, additional questions and exercises to use on quizzes and exams, and a PowerPoint presentation that covers the entire book.* A Companion Website at www.oup.com/us/herrick provides extra resources for teachers and students, including a Teacher's Manual, Student Manual, and practice quizzes with answers on all key topics.* An additional online resource at www.manyworldsoflogic.com offers additional practice quizzes, material for extra-credit assignments, and further information on the nature and history of logic.

    Some of the greatest logicians in the world--including Alonzo Church, Kurt Godel, John von Neumann, and Stephen Kleene--were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton.A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal--a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine.Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science."

    It will be of central interest to linguists and philosophers of language of all theoretical persuasions.

    Do you want to reach America’s largest mission field? Look in your home or Sunday School classroom: Young People! And with this new book they can learn to defend the Christian worldview. A fresh and simple way for your kids and youth to learn how to prove Christian truth.Research demonstrates that our child’s moral development is largely set before the age of thirteen. Find out the simple ways to nurture the intellectual and theological aspects of your child through biblical and philosophical truth. Help raise the next generation of apologists. Excellent for all kids 7-16 years old--or even adults. Your youth can know that God must exist.

    Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use (and the uses of formalisms more generally elsewhere) actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put these tools to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science.

    The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers.

    The essays are divided into four sections: Biblical studies, historical studies, doctrinal studies and practical studies. This updated edition adds six additional essays, three which are from women offering a female voice on the subject of the role of women in the Church.

    The book provides a background in U.S. copyright law, as well as international treaties. It offers an in depth discussion of the provisions of the Copyright Act most important to librarians: fair use (section 107), the library exemption (section 108), and the public performance exemption (section 110). The author discusses copyright issues regarding the use of print, digital, and audiovisual works, including court decisions that interpret the 1976 Copyright Act and its amendments.

    But because of the disaster of Russell's Paradox, which undermined Frege's proofs, the moremathematical parts of the book have rarely been read. Richard G. Heck, Jr., aims to change that, and establish it as a neglected masterpiece that must be placed at the center of Frege's philosophy.Part I of Reading Frege's Grundgesetze develops an interpretation of the philosophy of logic that informs Grundgesetze, paying especially close attention to the difficult sections of Frege's book in which he discusses his notorious 'Basic Law V' and attempts to secure its status as a law of logic.Part II examines the mathematical basis of Frege's logicism, explaining and exploring Frege's formal arguments. Heck argues that Frege himself knew that his proofs could be reconstructed so as to avoid Russell's Paradox, and presents Frege's arguments in a way that makes them available to a wideaudience. He shows, by example, that careful attention to the structure of Frege's arguments, to what he proved, to how he proved it, and even to what he tried to prove but could not, has much to teach us about Frege's philosophy.

    The philosopher is trying to learn things. He defines, after investigating reality, in an attempt to describe reality clearly and to sum up some aspect of his understanding of reality. Hence, we find our scholastic philosophers adopting as a main feature of their method this insistence on defining, on precise and detailed explanation of their definitions, and on proving that their definitions do correctly express what a nature or activity is.This dictionary of the language of scholastic philosophy has been fitted to the needs of beginners and undergraduate students of the subject and has not been previously available in English.This is a reprint of the 1956 edition.

    The systematic complexity of Hegel's radical project in the Science of Logic prevents many from understanding and appreciating its value. By independently and critically working through Hegel's argument, this book offers an enlightening aid for study and anchors the Science of Logic at a central position in the philosophical canon.

    Formerly seen as too complicated and amorphous to be included in early textbooks on the science of cognition, the study of thinking and reasoning has since taken off, brancing off in a distinct direction from the field from which it originated.The Oxford Handbook of Thinking and Reasoning is a comprehensive and authoritative handbook covering all the core topics of the field of thinking and reasoning. Written by the foremost experts from cognitive psychology, cognitive science, and cognitive neuroscience, individual chapters summarize basic concepts and findings for a major topic, sketch its history, and give a sense of the directions in which research is currently heading. Chapters include introductions to foundational issues and methods of study in the field, as well as treatment of specific types of thinking and reasoning and their application in a broad range of fields including business, education, law, medicine, music, and science. The volume will be of interest to scholars and students working in developmental, social and clinical psychology, philosophy, economics, artificial intelligence, education, and linguistics.