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.

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

    Consciously following the design and presentation of the Bible, in the beauty of its language and its arrangement into short chapters and verses, acclaimed philosopher Anthony Grayling has crafted an epic stimulating narrative that ultimately reveals how life--a good life--should be lived.Inspired by the thinking of Herodotus and Cicero, Confucious and Mencius, Montaigne, Bacon and so many others, Grayling has distilled the work of hundreds of authors and more than one thousand texts using the same techniques of editing, redaction, and adaptation that produced the holy books of the Judeo-Christian and Islamic religions. Their wit and yearnings, love and consolations are shaped into fourteen constituent parts that recall the Bible in structure--Genesis, Wisdom, Parables, Concord, Lamentations, Consolations, Sages, Songs, Histories, Proverbs, The Lawgiver, Acts, Epistles, and The Good. Opening with meditations on the origin and progress of the world and human life within it, Grayling then focuses on the questions of how life should be lived, how we relate to one another, and how vicissitudes are to be faced and joys appreciated.For a secular age in which many find that religion no longer speaks to them, The Good Book is a literary tour de force--a book of life and practice invoking the greatest minds of the past in the perennial challenge of being human.

    The outlook of that earlier world, MacIntyre claims, was definitively articulated in the Ninth Edition of the Encyclopaedia Brittanica, which conceived of moral enquiry as both providing insight into and continuing the rational progress of mankind into ever greater enlightenment. MacIntyre compares that conception of moral enquiry to two rival conceptions also formulated in the late nineteenth century: that of Nietzsche's Zur Genealogie der Moral and that expressed in the encyclical letter of Pope Leo XIII Aeterni Patris. The lectures focus on Aquinas's integration of Augustinian and Aristotelian modes of enquiry, the inability of the encyclopaedists' standpoint to withstand Thomistic or genealogical criticism, and the problems confronting the contemporary post-Nietzschean genealogist. MacIntyre concludes by considering the implications for education in universities and colleges. Alasdair MacIntyre is research professor of philosophy at the University of Notre Dame. He is the author of numerous books, including After Virtue, A Short History of Ethics, and Whose Justice? Which Rationality?, all published by the University of Notre Dame Press.

    Beautifully illustrated, it remains one of those rare works of scholarship which the general reader simply cannot afford to ignore.

    Christopher Hitchens continues to make the case for a splendidly godless universe in this first-ever gathering of the influential voices--past and present--that have shaped his side of the current (and raging) God/no-god debate. With Hitchens as your erudite and witty guide, you'll be led through a wealth of philosophy, literature, and scientific inquiry, including generous portions of the words of Lucretius, Benedict de Spinoza, Charles Darwin, Karl Marx, Mark Twain, George Eliot, Bertrand Russell, Emma Goldman, H. L. Mencken, Albert Einstein, Daniel Dennett, Sam Harris, Richard Dawkins, and many others well-known and lesser known. And they're all set in context and commented upon as only Christopher Hitchens political and literary journalist extraordinaire can.” (Los Angeles Times) Atheist? Believer? Uncertain? No matter: The Portable Atheist will speak to you and engage you every step of the way.

    Now, the new Second Edition offers these highlights.This landmark anthology includes the work of 120 writers over two centuries, from the earliest known work by an African American, Lucy Terry's poem "Bars Fight, " to the fiction of the Nobel Laureate Toni Morrison and the poems of the U.S. Poet Laureate, Rita Dove.

    To understand algebra is to possess the power to grow your skills and knowledge so you can ace your courses and possibly pursue further study in math. Algebra II For Dummies is the fun and easy way to get a handle on this subject and solve even the trickiest algebra problems. This friendly guide shows you how to get up to speed on exponential functions, laws of logarithms, conic sections, matrices, and other advanced algebra concepts. In no time you'll have the tools you need to:Interpret quadratic functions Find the roots of a polynomial Reason with rational functions Expose exponential and logarithmic functions Cut up conic sections Solve linear and non linear systems of equations Equate inequalities Simplifyy complex numbers Make moves with matrices Sort out sequences and sets This straightforward guide offers plenty of multiplication tricks that only math teachers know. It also profiles special types of numbers, making it easy for you to categorize them and solve any problems without breaking a sweat. When it comes to understanding and working out algebraic equations, Algebra II For Dummies is all you need to succeed!

    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.

    This anthology brings together into one volume the most influential and commonly taught works of existentialism. Contributors include Simone de Beauvoir, Albert Camus, Fyodor Dostoevsky, Ralph Ellison, Martin Heidegger, Soren Kierkegaard, Friedrich Nietzsche, Jean-Paul Sartre, and Miguel de Unamuno y Jugo.

    Long celebrated as a pathbreaking achievement in the social history of the ancient world, M.I. Finley's brilliant study remains, as classicist Bernard Knox notes in his introduction to this new edition, "as indispensable to the professional as it is accessible to the general reader"--a fundamental companion for students of Homer and Homeric Greece.

    In this seventh edition, Robert L. Heilbroner provides a new theme that connects thinkers as diverse as Adam Smith and Karl Marx. The theme is the common focus of their highly varied ideas—namely, the search to understand how a capitalist society works. It is a focus never more needed than in this age of confusing economic headlines.In a bold new concluding chapter entitled “The End of the Worldly Philosophy?” Heilbroner reminds us that the word “end” refers to both the purpose and limits of economics. This chapter conveys a concern that today’s increasingly “scientific” economics may overlook fundamental social and political issues that are central to economics. Thus, unlike its predecessors, this new edition provides not just an indispensable illumination of our past but a call to action for our future. (amazon.com)

    Travel back to ancient Greece with Professor Emeritus of Philosophy Donald R. Moor and author Robert M. Pirsig ("Zen and the Art of Motorcycle Maintenance") to meet this legendary thinker. In addition to expanding upon his famous allegory of the cave, Plato talks about learning through dialogue, the primacy of good and the price of wrong doing, democracy, freedom and censorship, women's equality, love, and mathematics, and the search for truth.

    ASIN: 0312295170

    In its scope and itnerest it can be compared with Freud's Totem and Taboo, the subtext Girard refutes with polemic daring, vast erudition, and a persuasiveness that leaves the reader compelled to respond, one way or another.This is the single fullest summation of Girard's ideas to date, the book by which they will stand or fall. In a dialogue with two psychiatrists (Jean-Michel Oughourlian and Guy Lefort), Girard probes an encyclopedic array of topics, ranging across the entire spectrum of anthropology, psychoanalysis, and cultural production.Girard's point of departure is what he calles "mimesis," the conflict that arises when human rivals compete to differentiate themselves from each other, yet succeed only in becoming more and more alike. At certain points in the life of a society, according to Girard, this mimetic conflict erupts into a crisis in which all difference dissolves in indiscriminate violence. In primitive societies, such crises were resolved by the "scapegoating mechanism," in which the community, en masse, turned on an unpremeditated victim. The repression of this collective murder and its repetition in ritual sacrifice then formed the foundations of both religion and the restored social order.How does Christianity, at once the most "sacrificial" of religions and a faith with a non-violent ideology, fit into this scheme? Girard grants Freud's point, in Totem and Taboo, that Christianity is similar to primitive religion, but only to refute Freud—if Christ is sacrificed, Girard argues, it is not becuase God willed it, but because human beings wanted it.The book is not merely, or perhaps not mainly, biblical exegesis, for within its scope fall some of the most vexing problems of social history—the paradox that violence has social efficacy, the function of the scapegoat, the mechanism of anti-semitism.