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.

    His conception of the universe pervades Christian theology. Knowledge of his thought is necessary to understand Bacon, Galileo, and the modern scientific view of nature, as well as Dante and many passages from Chaucer, Shakespeare, and Milton. Many phrases such as liberal education and theory contrasted with practice originated with this student of Plato and tutor of Alexander the Great.Writing to inform the beginner and stimulate the expert, eminent scholar A. E. Taylor presents a searching analysis of Aristotle's thought, including classification of the sciences; formal logic; theory of knowledge; matter and form; the four causes; God; physics; biology; sensation; ethics; theory of the state; and the fine arts. He also considers Aristotle's provincialism, errors regarding the nervous system and astronomy, and defense of slavery.The Giants of Philosophy is a series of dramatic presentations, in understandable language, of the concerns, questions, interests, and overall world view of history's greatest philosophers. Special emphasis on clear and relevant explanations gives you a new arsenal of insights toward living a better life.

    Whether you're a student, parent, or teacher, this book is your key to unlocking the aha! moments that make math truly click -- and make learning enjoyable.The book intentionally avoids mindless definitions and focuses on building a deep, natural intuition so you can integrate the ideas into your everyday thinking. Its explanations on the natural logarithm, imaginary numbers, exponents and the Pythagorean Theorem are among the most-visited in the world.The topics in Math, Better Explained include:1. Developing Math Intuition2. The Pythagorean Theorem3. Pythagorean Distance4. Radians and Degrees5. Imaginary Numbers6. Complex Arithmetic7. Exponential Functions & e8. The Natural Logarithm (ln)9. Interest Rates10. Understanding Exponents11. Euler’s Formula12. Introduction To CalculusThe book is written as the author wishes math was taught: with a friendly attitude, vivid illustrations and a focus on true understanding. Learn right, not rote!

    Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.

    For almost 500 years, the masses have been thoroughly deceived by a cosmic fairy-tale of astronomical proportions. We have been taught a falsehood so gigantic and diabolical that it has blinded us from our own experience and common sense, from seeing the world and the universe as they truly are. Through pseudo-science books and programs, mass media and public education, universities and government propaganda, the world has been systematically brain-washed, slowly indoctrinated over centuries into the unquestioning belief of the greatest lie of all time. A multi-generational conspiracy has succeeded, in the minds of the masses, to pick up the fixed Earth, shape it into a ball, spin it in circles, and throw it around the Sun! The greatest cover-up of all time, NASA and Freemasonry's biggest secret, is that we are living on a plane, not a planet, that Earth is the flat, stationary center of the universe.

    Marcelo Gleiser explores the shared quest of ancient prophets and today's astronomers to explain the strange phenomena of our skies--from the apocalypse foretold in Revelations to modern science's ongoing identification of multiple cataclysmic threats, including the impact of comets and asteroids on earthly life, the likelihood of future collisions, the meaning of solar eclipses and the death of stars, the implications of black holes for time travel, and the ultimate fate of the universe and time. Presenting insights to cosmological science and apocalyptic philosophy in an "easily accessible" (Library Journal) style, Gleiser is "a rare astrophysicist as comfortable quoting Scripture as explaining formulas" (Booklist). K. C. Cole praises his ability to "[work] the entwined threads of science and religion into a vision of the end' that is strangely comforting and inspiring.

    From the rising and setting of the sun to the cycles of nature, the thought processes in our brains, and the biorhythms in our day, nothing so pervades our existence and yet is so difficult to explain. Time seems to be woven into the very fabric of the universe. But why? Consider these contrasting views of time: A movie of a person diving into a pool has an obvious arrow of time. When the movie is played backward, everyone recognizes that it shows an event that would never occur in the real world. But zoom in on any part of this scene at the atomic scale and the movie can be run backward or forward and be indistinguishable. Either way, the particle interactions are consistent with the laws of physics. Why does one movie have an arrow of time moving in only one direction and the other does not? Surprisingly, the search for an answer leads through some of the most pioneering fields of physics, including thermodynamics, relativity, quantum theory, and cosmology. The key concept is called "entropy," which is related to the second law of thermodynamics, considered by many scientists to be the most secure law in all of physics. But that's only the beginning, since the quest for the ultimate theory of time draws on such exciting ideas as black holes, cosmic inflation, and dark energy, before closing in on a momentous question that until recently was considered unanswerable: What happened before the big bang? In 24 riveting half-hour lectures, Mysteries of Modern Physics: Time takes you on a mind-expanding journey through the past, present, and future, guided by Professor Sean Carroll, noted author and Senior Research Associate in Physics at the California Institute of Technology.

    A brilliantly clear and penetrating exposition of developments in physical science and mathematics brought about by the advent of non-Euclidean geometries, including in-depth coverage of the foundations of geometry, the theory of time, Einstein's theory of relativity and its consequences, other key topics.

    Korsgaard presents an account of the foundation of practical reason and moral obligation. Moral philosophy aspires to understand the fact that human actions, unlike the actions of the other animals, can be morally good or bad, right or wrong. Few moral philosophers, however, haveexploited the idea that actions might be morally good or bad in virtue of being good or bad of their kind - good or bad as actions. Just as we need to know that it is the function of the heart to pump blood to know that a good heart is one that pumps blood successfully, so we need to know what thefunction of an action is in order to know what counts as a good or bad action. Drawing on the work of Plato, Aristotle, and Kant, Korsgaard proposes that the function of an action is to constitute the agency and therefore the identity of the person who does it. As rational beings, we are aware of, and therefore in control of, the principles that govern our actions. A good action is one that constitutes its agent as the autonomous and efficacious cause of her own movements. These properties correspond, respectively, to Kant's two imperatives of practical reason. Conformity to the categoricalimperative renders us autonomous, and conformity to the hypothetical imperative renders us efficacious. And in determining what effects we will have in the world, we are at the same time determining our own identities. Korsgaard develops a theory of action and of interaction, and of the forminteraction must take if we are to have the integrity that, she argues, is essential for agency. On the basis of that theory, she argues that only morally good action can serve the function of action, which is self-constitution.

    It covered jazz, of course, but it also included Davis’s ruminations on race, politics and culture. Fascinated, Hef sent the writer—future Pulitzer-Prize-winning author Alex Haley, an unknown at the time—back to glean even more opinion and insight from Davis. The resulting exchange, published in the September 1962 issue, became the first official Playboy Interview and kicked off a remarkable run of public inquisition that continues today—and that has featured just about every cultural titan of the last half century.To celebrate the Interview’s 50th anniversary, the editors of Playboy have culled 50 of its most (in)famous Interviews and will publish them over the course of 50 weekdays (from September 4, 2012 to November 12, 2012) via Amazon’s Kindle Direct platform. Here is the interview with the novelist and philosopher Ayn Rand from the March 1964 issue.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.

    From the observations of Ptolemy and Kepler to the Harmony of the Spheres and the hidden structure of the solar system, John Martineau reveals the exquisite orbital patterns of the planets and the mathematical relationships that govern them. A table shows the relative measurements of each planet in eighteen categories, and three pages show the beautiful dance patterns of thirty six pairs of planets and moons.

    Defying sacrosanct platitudes (and risking the wrath of the rationalist, the enmity of the empiricist, the malice of the modalist, and the antipathy of the absolutist), Goodman argues that some true statements and some right versions conflict with one another and that therefore there must be 'many worlds if any'. Included are detailed studies of aspects or examples of worldmaking found in the psychological laboratory, in literary criticism, in scientific theories, and in works of art—all contributing to the central themes that facts are fabricated and that knowing or understanding is no more a matter of finding than of making.

    Each chapter opens with a surprising insight—not a mathematic formula, but a common observation. From there, the authors leapfrog over math and anecdote toward profound ideas about nature, art, and music. Coincidences is a book for lovers of puzzles and posers of outlandish questions, lapsed math aficionados and the formula-phobic alike.