How can today's computers perform such a bewildering variety of tasks if computing is just glorified arithmetic? The answer, as Martin Davis lucidly illustrates, lies in the fact that computers are essentially engines of logic. Their hardware and software embody concepts developed over centuries by logicians such as Leibniz, Boole, and Godel, culminating in the amazing insights of Alan Turing. The Universal Computer traces the development of these concepts by exploring with captivating detail the lives and work of the geniuses who first formulated them. Readers will come away with a revelatory understanding of how and why computers work and how the algorithms within them came to be.

    Featuring challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory from numerous mathematical competitions and journals, this title is suitable for advanced high school and beginning college students, as well as instructors and Olympiad coaches.

    Drawn from a survey of nearly 200 women who have experienced rape or incest pregnancies, Victims and Victors reveals a seldom-heard truth: that most women who become pregnant through sexual assault do not want abortions! Victims and Victors leaps past the rhetoric that typically dominates the abortion issue to give women a chance to tell their stories. These are the real "experts" on this complex issue: the women who have been there. Just listen to what they have to say: "After my daughter was born, it was love at first sight . . . I know I made the right decision in having her." —Nancy "Cole" "Often I cry. Cry because I could not stop the attacks. Cry because my daughter is dead. And I cry because it still hurts." —Edith Young "I think that rape victims with pregnancies are discriminated against because people seem to think you're nuts to have a baby by a man who raped you. We are looked upon as being liars, or stupid." —Sharon "Bailey" "They say abortion is the easy way out, the best thing for everyone, but they are wrong. It has been over 15 years, and I still suffer." —"Rebecca Morris" "I thank God for the strength He gave me to go through the bad times and for all of the joy in the good times. I will never regret that I chose to give life to my daughter." —Mary Murray "Abortion does not help or solve a problem—it only compounds and creates another trauma for the already grieving victim by taking away the one thing that can bring joy." —Helene Evans "The effects of the abortion are much more far-reaching than the effects of the rape in my life." —"Patricia Ryan" "I, having lived through rape, and having raised a child `conceived in rape,' feel personally assaulted and insulted every time I hear that abortion should be legal for rape and incest. I feel that we're being used to further the abortion issue, even though we've not been asked to tell our side of the story." —Kathleen DeZeeuw In Victims and Victors, 20 women like the ones quoted above share what it is like to face a pregnancy resulting from rape or incest. They speak bravely and candidly of the pain of sexual assault, of the sadness and trauma of abortion, and of the joy and healing of giving birth. Victims and Victors answers these important questions—questions every pro-lifer should be asking: What do women really need when facing a pregnancy resulting from sexual assault, and how can we best meet those needs? How can pro-lifers hold on to their principles while providing compassionate and understanding support for pregnant sexual assault victims at the same time? How can legislators best convey a pro-woman, pro-life philosophy when faced with questions regarding sexual assault and abortion? Why are rape and incest pregnancies the "cornerstone" for abortion on demand, and what can pro-lifers do to counteract this? How can women who have experienced sexual assault pregnancies share the truth about their experiences in a way that will truly make a difference? You will find the answers to these questions in Victims and Victors. It lays out a clear argument against abortion in cases of sexual assault and gives pro-lifers the tools they need to combat the argument that abortion is helpful—or even necessary—for women facing a sexual assault pregnancy. This book is a "must read" for everyone involved in the pro-life movement. Order your copy of Victims and Victors today!

    Table Of Contents: PrefaceviiPart 1Language and Logic1Disputes: Verbal and Otherwise3A few examplesThe analysis of disputes2The Meaning of "Meaning"16Semantics and logicSigns and symbolsCommunicationThe arbitrariness of meaningsEtymologiesGrowth and change in languageSome errors of symbolism3Ambiguity45The meaning of ambiguityThe analysis of ambiguityThe types of ambiguityThe fallacies of ambiguity4The Uses of Language66Neutral, emotive, and directive wordsThe three purposes of discourseAppropriate and inappropriate languageThe logical and non-logical uses of language5The Definition of "Definition"88The importance of definitionTwo basic distinctionsThe types of definitionsThe criteria of an adequate analytical definitionPlato and the rules of definitionTruth and falsity in definitionsThe construction of definitionsPart 2Deductive Logic6Logic and Argument127Argument and assertionThe law of rationality and evasions thereof7Syllogisms, Propositions, and Terms154Introduction to the syllogismThe categorical proposition and its partsThe class-analysis of subject-predicate propositionsAffirmative and negative propositionsUniversal and particular propositionsThe four types of categorical propositionsThe distribution of terms8The Analysis of Categorical Syllogisms176The definition of the syllogismBasic words in the analysis of categorical syllogismsPreliminary analysis of categorical syllogismsThe rules of the categorical syllogismThe diagramming of syllogismsThe corollaries, figures, and moodsA note on deductive systems9Semantics and the Syllogism205The need for semantical analysisSentences in irregular formsEquivalent propositions10The Syllogism and Everyday Discourse226Syllogisms and ordinary discourseA syllogism has three and only three termsThe analysis of syllogisms in everyday discourseThe enthymemeThe soritesThe relations between terms generalized11The Relations Among Propositions245Relations with respect to truth and falsityThe seven relationsThe square of opposit

    Becoming a Critical Thinker: A Guide for the New Millennium provides a clear and useful set of tools for evaluating the probability of claims presented to students in their daily lives. In this new millennium, as the power and influence of the mass media continues to grow, students need to develop both fundamental critical thinking skills as well as specific skills that focus on the issues and obstacles particular to our times. Thus, much of this text aims at honing skills useful for separating the probable from the improbable in the daily barrage of claims hurled at students from newspapers, magazines, television, movies, radios, CDs, and the Internet.

    MIND BENDERS BOOK B1 GR 6 AND UP

    

    The writings in this volume reveal Peirce's powerful mind probing into diverse issues, looking for an underlying unity, but, perhaps, also looking for direction.

    By the end of this course, students will have learned all five noun declensions, some model principal parts for the four verb conjugations, three tenses, and the use of the nominative and accusative cases. The teacher manual has detailed grammar lessons and many helpful teaching hints. Latina Christiana II contains five short "readings," three Scripture passages for translation, passages for memorization, including the Gloria, the Sanctus, and the Doxology, two hymns, Veni, Veni Emmanuel and Veni Creator Spiritus, and the famous medieval school song, Gaudeamus Igitur.

    Starting from scratch, it quickly reaches the essentials, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. It also introduces logic via the study of the models of arithmetic, and it gives complete but accessible exposition of stability theory.

    Mathematicians have made their reputations by solving some of them like Fermat's last theorem, but several remain unsolved including the Riemann Hypotheses, which has eluded all the great minds of this century. A hundred years later, this book takes a fresh look at the problems, the man who set them, and the reasons for their lasting impact on the mathematics of the twentieth century. In this fascinating book, the authors consider what makes this the pre-eminent collection of problems in mathematics, what they tell us about what drives mathematicians, and the nature of reputation, influence and power in the world of modern mathematics. It is written in a clear and entertaining style and will appeal to anyone with interest in mathematics or those mathematicians willing to try their hand at these problems.

    Wolfgang-Rainer Mann argues that the treatise, in fact, presents a revolutionary metaphysical picture, one Aristotle arrives at by (implicitly) criticizing Plato and Plato's strange counterparts, the "Late-Learners" of the Sophist. As Mann shows, the Categories reflects Aristotle's discovery that ordinary items are things (objects with properties). Put most starkly, Mann contends that there were no things before Aristotle.The author's argument consists of two main elements. First, a careful investigation of Plato which aims to make sense of the odd-sounding suggestion that things do not show up as things in his ontology. Secondly, an exposition of the theoretical apparatus Aristotle introduces in the Categories--an exposition which shows how Plato's and the Late-Learners' metaphysical pictures cannot help but seem inadequate in light of that apparatus. In doing so, Mann reveals that Aristotle's conception of things--now so engrained in Western thought as to seem a natural expression of common sense--was really a hard-won philosophical achievement.Clear, subtle, and rigorously argued, The Discovery of Things will reshape our understanding of some of Aristotle's--and Plato's--most basic ideas.

    This 32-page book includes answers. Instructions and Detailed Solutions covers all books in the

    Yet Colin McGinn believes that orthodox views of these topics are misguided in important ways. Philosophers and logicians have often distorted the nature of these concepts in an attempt to define them according to preconceived ideas. Logical Properties aims to respect the ordinary ways we talk and think when we employ these concepts, while at the same time showing that they are far more interesting and peculiar than some have assumed; these notions correspond to real properties--logical properties--that challenge naturalistic metaphysical views. Written with a minimum of formal terminology, this book deals with logico-linguistic issues as well as ontological ones. The focus is on trying to get to the essence of the concept concerned, not merely finding some established notation for providing formal interpretations.

    This important new resource examines a set of semiotic methods for information systems development. Kecheng Liu offers well balanced coverage of recent theoretical investigations and practical applications. He introduces the MEASUR approach for requirements elicitation, analysis, and representation and illustrates the methods in three major case studies. In these cases he demonstrates how information systems can be developed to meet business requirements and to support business objectives.

    Assuming that metaphor cannot be explained by or within semantics, they claim that metaphor has little, if anything, to teach us about semantic theory. In this book Josef Stern challenges these assumptions. He is concerned primarily with the question: Given the received conception of the form and goals of semantic theory, does metaphorical interpretation, in whole or part, fall within its scope? Specifically, he asks, what (if anything) does a speaker-hearer know as part of her semantic competence when she knows the interpretation of a metaphor?According to Stern, the answer to these questions lies in the systematic context-dependence of metaphorical interpretation. Drawing on a deep analogy between demonstratives, indexicals, and metaphors, Stern develops a formal theory of metaphorical meaning that underlies a speaker's ability to interpret a metaphor. With his semantics, he also addresses a variety of philosophical and linguistic issues raised by metaphor. These include the interpretive structure of complex extended metaphors, the cognitive significance of metaphors and their literal paraphrasability, the pictorial character of metaphors, the role of similarity and exemplification in metaphorical interpretation, metaphor-networks, dead metaphors, the relation of metaphors to other figures, and the dependence of metaphors on literal meanings. Unlike most metaphor theorists, however, who take these problems to be "sui generis" to metaphor, Stern subsumes them under the same rubric as other semantic facts that hold for nonmetaphorical language.

    This 32-page book includes answers. Instructions and Detailed Solutions covers all books in the

    The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties).

    Orbiting with Logic problems are easy to incorporate into lesson plans and are formatted to enhance the fullest spectrum of curriculum areas while sharpening thinking skills. Challenging and instructional, these thought-provoking books present sequential exercises in logical reasoning that include relationships, analogies, syllogisms, sequences, deductive reasoning, inference, truth-values, and logical notation. Simple grids coupled with intriguing problems evoke enthusiasm and inspire students to higher and higher levels of thinking. Each book in this series builds on concepts presented previously in the series to offer a comprehensive logic adventure for young thinkers.The skills students build by using this book are applicable to several areas of the curriculum. Academic skills used in reading, math, writing, and science all depend on the ability to perceive and define relationships, sequence events, and form inferences. But, beyond the academic world students will find logical thinking an integral part of everyday life.

    Prepares students for testing! Description & Features Mind Benders®, our bestselling deductive thinking puzzles, develop the logic, reading comprehension, and mental organization skills vital to achieving high grades and top test scores in all subjects. They're also great for developing real-life problem-solving skills. Methods Students carefully analyze each Mind Benders® story and its clues, identifying logical associations between people, places, and things. The key is to start with the most obvious associations, then deduce less obvious associations until everything finally fits together. Teaching Support Includes step-by-step instructions and detailed answers. Levels spiral in difficulty within grade range (B1, B2, B3, B4).

    

    Routledge is an imprint of Taylor & Francis, an informa company.