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.

    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 brings comfort, purpose, and sense of pride. These feelings mean so much to the Christian. But are these feelings justified? Do Christians have good reason to trust the truth of their beliefs? Author J. D. Brucker brings forth a short collection of arguments against Christian beliefs, exposing the falsehoods of the faith so many all around the world cherish.

    This guidebook includes the island's history, culture and all of its significant archaeological sites. It also contains all of the practical information needed for your visit, including island activities and up-to-date restaurant and shopping recommendations. It will also tell you the best times to visit the sites in order to get the optimal light for photography and to avoid the crowds, as well as many other 'local' tips that no other guidebook will tell you. Contains over 100 color photos of Easter Island, as well as color maps of both the island and the one town, Hanga Roa. New, Updated edition (2014).

    No human being who stood on her decks that fateful night was alive to commemorate the event on its 100th anniversary. Their stories are with us, however, and the lessons remain. From the moment the world learned the Titanic had sunk, we wanted to know, who had survived? Those answers didn’t come until the evening of Thursday, April 18, 1912―when the Cunard liner Carpathia finally reached New York with the 706 survivors who had been recovered from Titanic’s lifeboats. Harold Bride, “Titanic’s surviving wireless operator,” relayed the story of the ship’s band. “The way the band kept playing was a noble thing. I heard it first while still we were working wireless when there was a ragtime tune for us. The last I saw of the band, when I was floating out in the sea with my lifebelt on, it was still on deck playing ‘Autumn.’ How they ever did it I cannot imagine.” There were stories of heroism―such as that of Edith Evans, who was waiting to board collapsible Lifeboat D, the last boat to leave Titanic, when she turned to Caroline Brown and said, “You go first. You have children waiting at home.” The sacrifice cost Evans her life, but as Mrs. Brown said later, “It was a heroic sacrifice, and as long as I live I shall hold her memory dear as my preserver, who preferred to die so that I might live.” There was mystery. There was bravery. There was suspense. There was cowardice. Most men who survived found themselves trying to explain how they survived when women and children had died. But mostly, there was loss. On her return to New York after picking up Titanic’s survivors, Carpathia had become known as a ship of widows. Rene Harris, who lost her husband, Broadway producer Henry Harris, in the disaster, later spoke of her loss when she said, “It was not a night to remember. It was a night to forget.” Drawing on a wealth of previously unpublished letters, memoirs, and diaries as well as interviews with survivors and family members, veteran author and writer Alan Rockwell brings to life the colorful voices and the harrowing experiences of many of those who lived to tell their story. More than 100 years after the RMS Titanic met its fatal end, the story of the tragic wreck continues to fascinate people worldwide. Though many survivors and their family members disappeared into obscurity or were hesitant to talk about what they went through, others were willing to share their experiences during the wreck and in its aftermath. This book recounts many of these first-hand accounts in graphic, compelling detail.

    With exceptional clarity, Franz n gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of "Logical Dilemmas: The Life and Work of Kurt G del

    Barrow's Pi in the Sky is a profound -- and profoundly different -- exploration of the world of mathematics: where it comes from, what it is, and where it's going to take us if we follow it to the limit in our search for the ultimate meaning of the universe. Barrow begins by investigating whether math is a purely human invention inspired by our practical needs. Or is it something inherent in nature waiting to be discovered?In answering these questions, Barrow provides a bridge between the usually irreconcilable worlds of mathematics and theology. Along the way, he treats us to a history of counting all over the world, from Egyptian hieroglyphics to logical friction, from number mysticism to Marxist mathematics. And he introduces us to a host of peculiar individuals who have thought some of the deepest and strangest thoughts that human minds have ever thought, from Lao-Tse to Robert Pirsig, Charles Darwin, and Umberto Eco. Barrow thus provides the historical framework and the intellectual tools necessary to an understanding of some of today's weightiest mathematical concepts.

    

    Most books on world history overly emphasize the role of Western nations in the vast saga of mankind - the author of this book rectifies the gaps in books by Western historians by beginning the narration of world history with East Asia, and progresses from there through the rest of Asia to the Middle East.

    Illustrated.

    His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.

    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.

    Discover the events that have shaped your Clan and hear about the people who form part of your Scottish ancestry.

    Where some accounts of human nature and the particularly human good fall short by the reduction of human being to physical or psychical phenomena, Stoicism’s power lies in engaging with the whole range of human experience, addressing rationality, emotion, piety, will, and both inner and outer impressions, each on their own terms, in language that treats each as significant in its own right. Stoicism is an active philosophy. That means that it is not enough to know its doctrines, one must also live them, develop habits that expand on and complete their ideas in practice. Practice, therefore, is also the focus of this book. The development of the reader’s inner and outer life, that they may follow their own path and discover what it means to “live life in accordance with nature.”   This book is a general introduction to Stoicism that pulls no punches when faced with the more complex aspects of Stoic doctrine. Topics addressed include: The history of the ancient Stoics. The nature of good and evil, virtue and vice, and positive and negative externals. The difference between those things in our control and those things not in our control. Stoic Logic and practical reasoning. Stoicism’s role in the development of cognitive behavioral therapy (CBT). Stoic exercises and daily practice. Theology’s role in Stoicism and Stoic cosmology. And much more! Grab your copy of a detailed guide on stoicism philosphy and wisdom!