The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    Forensic Faith will help readers:understand why they have a duty to defend the truthdevelop a training strategy to master the evidence for Christianitylearn how to employ the techniques of a detective to discover new insights from God’s Wordbecome better communicators by learning the skills of professional case makersWith real-life detective stories, fascinating strategies, and biblical insights, Wallace teaches readers cold-case investigative disciplines they can apply to their Christian faith. Forensic Faith is an engaging, fresh look at what it means to be a Christian.

    The perfect introductory textbook, this simplified study of logic prepares readers to reason thoughtfully and to spot illogic in an argument.

    Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life.Stephen Budiansky’s Journey to the Edge of Reason is the first biography to fully draw upon Gödel’s voluminous letters and writings—including a never-before-transcribed shorthand diary of his most intimate thoughts—to explore Gödel’s profound intellectual friendships, his moving relationship with his mother, his troubled yet devoted marriage, and the debilitating bouts of paranoia that ultimately took his life. It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna, a haunting account of Gödel’s and Jewish intellectuals’ flight from Austria and Germany at the start of the Second World War, and a vivid re-creation of the early days of Princeton’s Institute for Advanced Study, where Gödel and Einstein both worked.Eloquent and insightful, Journey to the Edge of Reason is a fully realized portrait of the odd, brilliant, and tormented man who has been called the greatest logician since Aristotle, and illuminates the far-reaching implications of Gödel’s revolutionary ideas for philosophy, mathematics, artificial intelligence, and man’s place in the cosmos.

    Most of the major schools of contemporary philosophy, from Marxism to Existentialism, are reactions to Hegelianism and all, if they are to be understood, require some understanding of Hegel's Science of Logic.

    Pinker is the high priest of rationalism' Sunday Times'If you've ever considered taking drugs to make yourself smarter, read Rationality instead. It's cheaper, more entertaining, and more effective' Jonathan Haidt, author of The Righteous MindIn the twenty-first century, humanity is reaching new heights of scientific understanding - and at the same time appears to be losing its mind. How can a species that discovered vaccines for Covid-19 in less than a year produce so much fake news, quack cures and conspiracy theorizing?In Rationality, Pinker rejects the cynical cliché that humans are simply an irrational species - cavemen out of time fatally cursed with biases, fallacies and illusions. After all, we discovered the laws of nature, lengthened and enriched our lives and set the benchmarks for rationality itself. Instead, he explains, we think in ways that suit the low-tech contexts in which we spend most of our lives, but fail to take advantage of the powerful tools of reasoning we have built up over millennia: logic, critical thinking, probability, causal inference, and decision-making under uncertainty. These tools are not a standard part of our educational curricula, and have never been presented clearly and entertainingly in a single book - until now.Rationality matters. It leads to better choices in our lives and in the public sphere, and is the ultimate driver of social justice and moral progress. Brimming with insight and humour, Rationality will enlighten, inspire and empower.'A terrific book, much-needed for our time' Peter Singer

    With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. Constitution contained a terrible contradiction--and whether the universe truly has a future.

    Fierce warfare. Superior pleasure. Our hearts were designed to enjoy a full and forever happiness, not the pitiful temporary pleasures for which we’re too prone to settle. Pride, envy, anger, sloth, greed, gluttony, and lust are woefully inadequate substitutes for the wonder, beauty, and affection of God. They will rob you, not ravish you. They will numb you, not heal you. They will slaughter you, not save you. Killjoys was written to lead you deeper in love with our God and further into war against your sin. The truths, warnings, and promises in these pages are meant to chart a life-giving path to greater holiness and greater joy.

    He brings new perspectives to age-old conundrums while also tackling modern-day dilemmas -- some for the first time. Begin your warm up by contemplating whether a pickled sheep can truly be considered art, or dive right in and tackle the existence of God. In this radically new way of looking at philosophy, Stephen Law illustrates the problem with a story, then lets the argument battle it out in clear, easily digestible and intelligent prose. This perfect little mental health club is sure to give each reader's mind a great workout.

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

     The time-tested secrets this book discloses include Cicero’s three-step strategy for moving an audience to action—as well as Honest Abe’s Shameless Trick of lowering an audience’s expectations by pretending to be unpolished. But it’s also replete with contemporary techniques such as politicians’ use of “code” language to appeal to specific groups and an eye-opening assortment of popular-culture dodges—including The Yoda Technique, The Belushi Paradigm, and The Eddie Haskell Ploy. Whether you’re an inveterate lover of language books or just want to win a lot more anger-free arguments on the page, at the podium, or over a beer, Thank You for Arguing is for you. Written by one of today’s most popular language mavens, it’s warm, witty, erudite, and truly enlightening. It not only teaches you how to recognize a paralipsis and a chiasmus when you hear them, but also how to wield such handy and persuasive weapons the next time you really, really want to get your own way.

    Since then, Sylvia Nasar's celebrated biography A Beautiful Mind, the basis of a new major motion picture, has revealed the man. The Essential John Nash reveals his work--in his own words. This book presents, for the first time, the full range of Nash's diverse contributions not only to game theory, for which he received the Nobel, but to pure mathematics--from Riemannian geometry and partial differential equations--in which he commands even greater acclaim among academics. Included are nine of Nash's most influential papers, most of them written over the decade beginning in 1949.From 1959 until his astonishing remission three decades later, the man behind the concepts "Nash equilibrium" and "Nash bargaining"--concepts that today pervade not only economics but nuclear strategy and contract talks in major league sports--had lived in the shadow of a condition diagnosed as paranoid schizophrenia. In the introduction to this book, Nasar recounts how Nash had, by the age of thirty, gone from being a wunderkind at Princeton and a rising mathematical star at MIT to the depths of mental illness.In his preface, Harold Kuhn offers personal insights on his longtime friend and colleague; and in introductions to several of Nash's papers, he provides scholarly context. In an afterword, Nash describes his current work, and he discusses an error in one of his papers. A photo essay chronicles Nash's career from his student days in Princeton to the present. Also included are Nash's Nobel citation and autobiography.The Essential John Nash makes it plain why one of Nash's colleagues termed his style of intellectual inquiry as "like lightning striking." All those inspired by Nash's dazzling ideas will welcome this unprecedented opportunity to trace these ideas back to the exceptional mind they came from.

    What is less clear is how to think critically about such attempts and how to distinguish those that are sound arguments. Critical Thinking: A Concise Guide is a much needed guide to argument analysis and a clear introduction to thinking clearly and rationally for oneself. Accessibly written, this book equips students with the essential skills required to tell a good argument from a bad one.Key features of the book include: * clear, jargon-free discussion of key concepts in argumentation* how to avoid common confusions surrounding words such as 'truth', 'knowledge' and 'opinion'* how to identify and evaluate the most common types of argument* how to spot fallacies and tell good reasoning from bad* chapter summaries, exercises, examples and a glossary. The second edition has been updated to include topical new examples from politics, sport, medicine and music, as well as new exercises throughout.

    Feed Your Brain   Tastier than a twizzler yet more protein-packed than a spinach smoothie, Brain Candy is guaranteed to entertain your brain—even as it reveals hundreds of secrets behind what’s driving that electric noodle inside your skull.    These delicious and nutritious pages are packed with bits of bite-sized goodness swiped from the bleeding edge of brain science (including the reason why reading these words is changing your hippocampus at this very moment!) Shelved alongside these succulent neurological nuggets are challenging puzzles and paradoxes, eye-opening perception tests and hacks, fiendish personality quizzes and genius testers, and a grab bag of recurring treats including Eye Hacks, Algebraic Eight Ball, iDread, Wild Kingdom, and Logic of Illogic.     Should you look between these covers and inhale the deliciously cherry-flavored scents of knowledge within, you will grow your grey matter while discovering:  • Why you should be writing bad poetry• The simple keys to brain training• What trust smells like  • The origins of human morality• Why expensive wine always tastes better• The truth about brain sweat • How your diet might be making you dumb• The secrets of game theory• Why economists hate psychology • The mental benefits of coffee and cigarettes • How to really spot a liar• Why you can’t make me eat pie• The benefits of daydreaming • Four simple secrets to persuasion• Why your barin’s fzzuy ligoc alowls you to raed this• How to brainwash friends and family• The science of body language• What pigeons know about art   …And much, much more.

    He has gone down in history as one of the greatest philosophers of all time. Cicero, the Roman statesman and philosopher, once called his writing style "a river of gold;" and his scope of thought and subsequent influence on the study of science, logic, philosophical discourse, and theology has led many to dub him "The Philosopher."Contents:Part 1: Logic (Organon)Categories, translated by E. M. EdghillOn Interpretation, translated by E. M. EdghillPrior Analytics (2 Books), translated by A. J. JenkinsonPosterior Analytics (2 Books), translated by G. R. G. MureTopics (8 Books), translated by W. A. Pickard-CambridgeSophistical Refutations, translated by W. A. Pickard-CambridgePart 2: Universal PhysicsPhysics (8 Books), translated by R. P. Hardie and R. K. GayeOn the Heavens (4 Books), translated by J. L. StocksOn Gerneration and Corruption (2 Books), translated by H. H. JoachimMeteorology (4 Books), translated by E. W. WebsterPart 3: Human PhysicsOn the Soul (3 Books), translated by J. A. SmithOn Sense and the Sensible, translated by J. I. BeareOn Memory and Reminiscence, translated by J. I. BeareOn Sleep and Sleeplessness, translated by J. I. BeareOn Dreams, translated by J. I. BeareOn Prophesying by Dreams, translated by J. I. BeareOn Longevity and Shortness of Life, translated by G. R. T. RossOn Youth, Old Age, Life and Death, and Respiration, translated by G. R. T. RossPart 4: Animal PhysicsThe History of Animals (9 Books), translated by D'Arcy Wentworth ThompsonOn the Parts of Animals (4 Books), translated by William OgleOn the Motion of Animals, translated by A. S. L. FarquharsonOn the Gait of Animals, translated by A. S. L. FarquharsonOn the Generation of Animals (5 Books), translated by Arthur PlattPart 5: Metaphysics(15 Books), translated by W. D. RossPart 6: Ethics and PoliticsNicomachean Ethics (10 Books), translated by W. D. RossPolitics (8 Books), translated by Benjamin JowettThe Athenian Constitution, translated by Sir Frederic G. KenyonPart 7: Aesthetic WritingsRhetoric (3 Books), translated by W. Rhys RobertsPoetics, translated by S. H. Butcher