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.

    

    The author suggests that, like the black holes of outer space, from which nothing, not even light, can escape, our contemporary cultural landscape contains numerous intellectual black-holes—belief systems constructed in such a way that unwary passers-by can similarly find themselves drawn in. While such self-sealing bubbles of belief will most easily trap the gullible or poorly educated, even the most intelligent and educated of us are potentially vulnerable. Some of the world’s greatest thinkers have fallen in, never to escape. This witty, insightful critique will help immunize readers against the wiles of cultists, religious and political zealots, conspiracy theorists, promoters of flaky alternative medicines, and various other nutcases by clearly setting out the tricks of the trade by which such insidious belief systems are created and maintained.

    The arguement is developed by means of the notion of possible worlds and ranges over key problems including the nature of essence, trans-world identity, negative existential propositions, and the existence of unactual objects in other possible worlds. In the final chapters Professor Plantinga applies his logical theories to the elucidation of two problems in the philosophy of religion: the Problem of Evil and the Ontological Arguement. The first of these, the problem of reconciling the moral perfection and omnipotence of God with the existence of evil, can, he concludes, be resolved, and the second given a sound formulation. The book ends with an appendix on Quine's objection to quantified modal logic.

    Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be "computable," creating the field of computability theory in the process, a foundation of present-day computer programming.The book expands Turing's original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing's statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others.Interwoven into the narrative are the highlights of Turing's own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.

    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.

    It aims to reach students who have already done an introductory philosophy course.Topics covered include perception and reflection as grounds of knowledge, and the nature, structure, and varieties of knowledge. The character and scope of knowledge in the crucial realms of ethics, science and religion are also considered.Unique features of Epistemology: * Provides a comprehensive survey of basic concepts and major theories* Gives an up-to-date account of important developments in the field* Contains many lucid examples to support ideas* Cites key literature in an annotated bibliography.

    In 1967, they said the USSR would have one of the fastest-growing economies in the year 2000; in 2000, the USSR did not exist. In 1911, it was pronounced that there would be no more wars in Europe; we all know how that turned out. Face it, experts are about as accurate as dart-throwing monkeys. And yet every day we ask them to predict the future — everything from the weather to the likelihood of a catastrophic terrorist attack. Future Babble is the first book to examine this phenomenon, showing why our brains yearn for certainty about the future, why we are attracted to those who predict it confidently, and why it’s so easy for us to ignore the trail of outrageously wrong forecasts.In this fast-paced, example-packed, sometimes darkly hilarious book, journalist Dan Gardner shows how seminal research by UC Berkeley professor Philip Tetlock proved that pundits who are more famous are less accurate — and the average expert is no more accurate than a flipped coin. Gardner also draws on current research in cognitive psychology, political science, and behavioral economics to discover something quite reassuring: The future is always uncertain, but the end is not always near.

    Some people, especially those who are not religious, are not sure how to substantiate this view. Whatever Happened to Good and Evil? provides a basis for exploring these doubts and ultimately defends the objectivity of ethics. Engaging and accessible, it is the first introduction to meta-ethics written especially for students and general readers with no philosophical background. Focusing on the issues at the foundation of morality, it poses such questions as: How can we know what is right and wrong? Does ethical objectivity require God? Why should I be moral? Where do moral standards come from? What is a moral value, and how can it exist in a scientific world? Do cultural diversity and persistent moral disagreement support moral skepticism? Writing in a clear and lively style and employing many examples to illustrate theoretical arguments, Russ Shafer-Landau identifies the many weaknesses in contemporary moral skepticism and devotes considerable attention to presenting, and critiquing, the most difficult objections to his view. Also included in the book are a helpful summary of all the major arguments covered, as well as a glossary of key philosophical terms. Whatever Happened to Good and Evil? is ideal for a variety of philosophy courses and compelling reading for anyone interested in ethics.

    Unlike party puzzles or brain teasers, many paradoxes are serious in that they raise serious philosophical problems, and are associated with crises of thought and revolutionary advances. To grapple with them is not merely to engage in an intellectual game, but to come to grips with issues of real import. The second, revised edition of this intriguing book expands and updates the text to take account of new work on the subject. It provides a valuable and accessible introduction to a range of paradoxes and their possible solutions, with questions designed to engage the reader with the arguments and full bibliographical references to both classic and current literature on the topic.

    Now Blackburn offers a tour de force exploration of what he calls the most exciting and engaging issue in the whole of philosophy--the age-old war over truth.The front lines of this war are well defined. On one side are those who believe in plain, unvarnished facts, rock-solid truths that can be found through reason and objectivity--that science leads to truth, for instance. Their opponents mock this idea. They see the dark forces of language, culture, power, gender, class, ideology and desire--all subverting our perceptions of the world, and clouding our judgement with false notions of absolute truth. Beginning with an early skirmish in the war--when Socrates confronted the sophists in ancient Athens--Blackburn offers a penetrating look at the longstanding battle these two groups have waged, examining the philosophical battles fought by Plato, Protagoras, William James, David Hume, Hans-Georg Gadamer, Jacques Derrida, Michel Foucault, Richard Rorty, and many others, with a particularly fascinating look at Nietzsche. Among the questions Blackburn considers are: is science mere opinion, can historians understand another historical period, and indeed can one culture ever truly understand another.Blackburn concludes that both sides have merit, and that neither has exclusive ownership of truth. What is important is that, whichever side we embrace, we should know where we stand and what is to be said for our opponents.

    Composed of such luminaries as Kurt Gödel and Rudolf Carnap, and stimulated by the works of Ludwig Wittgenstein and Karl Popper, the Vienna Circle left an indelible mark on science.Exact Thinking in Demented Times tells the often outrageous, sometimes tragic, and never boring stories of the men who transformed scientific thought. A revealing work of history, this landmark book pays tribute to those who dared to reinvent knowledge from the ground up.

    

    Following on the success of Quadrivium and Sciencia, Trivium gathers six Wooden Books titles together into a beautiful six-color package that presents ancient wisdom in an accessible way. Trivium includes the books Euphonics, Grammar, Logic, Rhetoric,, Poetic Meter and Form, and Ethics.

    Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added, as well as commentary to the exercises explaining how they relate to the preceding section, and how they foreshadow later topics.