A timeless introduction to the field and a landmark in symbolic logic, showing that classical logic can be treated algebraically.

    Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.

    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

    Hand argues that extraordinarily rare events are anything but. In fact, they’re commonplace. Not only that, we should all expect to experience a miracle roughly once every month.     But Hand is no believer in superstitions, prophecies, or the paranormal. His definition of “miracle” is thoroughly rational. No mystical or supernatural explanation is necessary to understand why someone is lucky enough to win the lottery twice, or is destined to be hit by lightning three times and still survive. All we need, Hand argues, is a firm grounding in a powerful set of laws: the laws of inevitability, of truly large numbers, of selection, of the probability lever, and of near enough.     Together, these constitute Hand’s groundbreaking Improbability Principle. And together, they explain why we should not be so surprised to bump into a friend in a foreign country, or to come across the same unfamiliar word four times in one day. Hand wrestles with seemingly less explicable questions as well: what the Bible and Shakespeare have in common, why financial crashes are par for the course, and why lightning does strike the same place (and the same person) twice. Along the way, he teaches us how to use the Improbability Principle in our own lives—including how to cash in at a casino and how to recognize when a medicine is truly effective.     An irresistible adventure into the laws behind “chance” moments and a trusty guide for understanding the world and universe we live in, The Improbability Principle will transform how you think about serendipity and luck, whether it’s in the world of business and finance or you’re merely sitting in your backyard, tossing a ball into the air and wondering where it will land.

    In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Godel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

    Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    Can a computer think? Why is your consciousness like Bitcoin? Will there be an artificial intelligence apocalypse?

    The Computer Revolution may be even more life-changing than the Industrial Revolution. We can do things with computers that could never be done before, and computers can do things for us that could never be done before.But our love of computers should not cloud our thinking about their limitations.We are told that computers are smarter than humans and that data mining can identify previously unknown truths, or make discoveries that will revolutionize our lives. Our lives may well be changed, but not necessarily for the better. Computers are very good at discovering patterns, but are uselessin judging whether the unearthed patterns are sensible because computers do not think the way humans think.We fear that super-intelligent machines will decide to protect themselves by enslaving or eliminating humans. But the real danger is not that computers are smarter than us, but that we think computers are smarter than us and, so, trust computers to make important decisions for us.The AI Delusion explains why we should not be intimidated into thinking that computers are infallible, that data-mining is knowledge discovery, and that black boxes should be trusted.

    Life-saving canaries, empire-rescuing geese, dogs who can sniff out disease, ships' cats and even a ship's pig.All these animals are heroes to me - whether they risked their lives to pull people out of the ruins of a bombed building, won a race against impossible odds, danced their way to an Olympic gold medal or have been so incredibly badly behaved that they have managed to inspire something good (Stoffel, the honey badger, I'm thinking of you).Writing this book has brought home to me that there is no such thing as an ordinary animal.Every one has a heroic story to tell.

    This exciting new book, from a leading expert in working with expectant dads, doesn’t sideline or speak down to men. Instead it provides an array of targeted information to fully prepare men for their new roles – as both birth partners and fathers.The Expectant Dad’s Handbook is a one-stop guide for men on their path to fatherhood. It provides practical answers to all the questions on the mind of a dad-to-be – from what to expect at each stage of pregnancy to how to cope with any worries and fears about becoming a dad. It also reveals unique insights into a dad’s role during labour, showing key strategies for improving the birth.Both practical and accessible, this guide will provide all the information and advice fathers need for the journey ahead.

    And, should you ever get to hold one, you will find the human heart to be rubbery and shockingly light.'What Could Possibly Go Wrong? is a report from the front line of emergency medicine, the first ever account of what it is like to work as an air ambulance doctor. Whether describing cutting through a patient's breastbone to plug a stab wound or barrel rolling a light aircraft at 5,000 feet, Tony Bleetman captures the sheer adrenaline of racing through the sky to save lives. You will learn how to land a helicopter on the side of a mountain, what it means to encounter death every day, and how to perform a tracheotomy in real life (clue: it doesn’t involve a ball-point pen).Funny, shocking and moving, What Could Possibly Go Wrong? is a glimpse at a world where the wrong decision can mean the difference between life and death.Originally published as You Can't Park There: The Highs and Lows of an Air Ambulance Doctor.

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    It contains many puzzles and their solutions and aims to attract many readers in an age where computer science, logic, and mathematics are becoming increasingly important and popular.