Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the humanist idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos.What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

    We're all looking for new ways of thinking that can bring about real solutions to modern problems, from the pursuit of inner serenity to solving world conflicts. In Do You QuantumThink? author Dianne Collins shares her ingenious discovery that reveals a critical missing link to make sense of our changing times. Her discovery provides us with the understanding and methodology to rise above problems of today by laying the foundation for an entirely new way to think.Part science, part philosophy, part spirituality, Do You QuantumThink? draws on a wide spectrum of sources, from cutting edge innovations in the sciences to the insights of the world's greatest spiritual leaders. This book will make you laugh, free you from limiting ideas, and introduce you to the most advanced principles and practical methods for living. Do You QuantumThink? will rock your world in the best of ways as you experience one revelation after another.

    Widely praised for providing a lucid and historically informed account of Wittgenstein's core philosophical concerns.Demonstrates the continuity between Wittgenstein's early and later writings.Provides a persuasive argument for the unity of Wittgenstein's thought.Kenny also assesses Wittgenstein's influence in the latter part of the twentieth century.Inside:PrefaceAbbreviations in References to Works by WittgensteinBiographical Sketch of Wittgenstein's PhilosophyThe Legacy of Frege & RussellThe Criticism of PrincipiaThe Picture Theory of the PropositionThe Metaphysics of Logical AtomismThe Dismantling of Logical AtomismAnticipation, Intentionality & VerificationUnderstanding, Thinking & MeaningLanguage-GamesPrivate LanguagesOn Scepticism & CertaintyThe Continuity of Wittgenstein's PhilosophySuggestions for Further ReadingIndex

    Includes such gems as:? There are 42 eyes in a deck of cards, and 42 dots on a pair of dice ? In order to fill in a map so that neighboring regions never get the same color, one never needs more than four colors ? Hells Angels use the number 81 in their insignia because the initials H and A are the eighth and first numbers in the alphabet respectively

    He shows that freedom of choice isn't nearly enough. To be free, we must also be able to navigate life. People often need something like a GPS device to help them get where they want to go--whether the issue involves health, money, jobs, children, or relationships.In both rich and poor countries, citizens often have no idea how to get to their desired destination. That is why they are unfree. People also face serious problems of self-control, as many of them make decisions today that can make their lives worse tomorrow. And in some cases, we would be just as happy with other choices, whether a different partner, career, or place to live--which raises the difficult question of which outcome best promotes our well-being.Accessible and lively, and drawing on perspectives from the humanities, religion, and the arts, as well as social science and the law, On Freedom explores a crucial dimension of the human condition that philosophers and economists have long missed--and shows what it would take to make freedom real.

    In this delightful tour of the galaxies, Merlin often recounts his conversations with these historical figures in his responses to popular astronomy questions asked by adults and children alike. Merlin's well-informed answers combine a unique combination of wit and poetry along with serious science explained in refreshingly clear, reader-friendly language.Dear Merlin: Can a person cross our galaxy in a spaceship during one human lifespan?Merlin: In 1905, Merlin's good friend Albert Einstein introduced the "Special Theory of Relativity," which predicts that time will tick slower and slower the faster you travel. Were you to embark on such an adventure you could conceivably age as little as you wish, depending of course, on your exact speed. The problem arises when you return to Earth, which will have moved several hundred thousand years into the future and everyone will have forgotten about you.A skywatcher's book for lovers of the universe by one of its greatest lights.

    The result is nothing less than an archaeology of the sciences that unearths old patterns of meaning and reveals the shocking arbitrariness of our received truths.In the work that established him as the most important French thinker since Sartre, Michel Foucault offers startling evidence that “man”—man as a subject of scientific knowledge—is at best a recent invention, the result of a fundamental mutation in our culture.

    This is the view of Ayn Rand, a view so radically opposed to prevailing attitudes that it constitutes a major philosophic revolution. In this series of essays, she presents her stand on the persecution of big business, the causes of war, the default of conservatism, and the evils of altruism. Here is a challenging new look at modern society by one of the most provocative intellectuals on the American scene.   This edition includes two articles by Ayn Rand that did not appear in the hardcover edition: “The Wreckage of the Consensus,” which presents the Objectivists’ views on Vietnam and the draft; and “Requiem for Man,” an answer to the Papal encyclical Progresso Populorum.

    This work has played a major role in the development of our current understanding of the profound nature of quantum concepts and of the fundamental limitations they impose on the applicability of the classical ideas of space, time and locality. This book contains all of John Bell's published and unpublished papers on the conceptual and philosophical problems of quantum mechanics.

     Lessons From Critical Thinkers provides intellectual power to engage with and participate in effective critical thoughts, arguments, debates, reading, and reflection drawn from methods in the history of philosophical cognitive development. •Learn to think slowly and deliberately before making a decision •Get ready to question opinions and even facts •Learn to gather information before jumping to conclusions •Accept and expect the biased and flawed nature of human cognition Lessons From Critical Thinkers gives you a thorough presentation of the ideas and principles of critical thinking practiced by the greatest minds in history. Learn about the most important critical thinking methods to make better decisions in your personal life, career, and friendships. Equip yourself with the essential methods for clear, analytical, logical thinking and critique in a range of ideas and everyday situations. • Discover critical thinking by familiarizing with concepts from other disciplines, like philosophy, cognitive biases and errors, race and gender from sociology and political science, and symbols from rhetoric. • Apply critical thinking and reasoning skills to your day to day problems • Find the most rewarding options in any opportunity. Lessons From Critical Thinkers is a helpful book for readers of any age and background who want to improve their critical thinking skills by learning from the greatest thinkers of all time. Learn to filter out irrelevant information efficiently and prioritize your resources to get the best results. Enhance your communication skills, reasoning, and logic. Improve your critical, logical, observational, and rational thinking skills with the timeless principles presented in this book.

    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.

    Topics: elimination of metaphysics, function of philosophy, nature of philosophical analysis, the a priori, truth & probability, critique of ethics & theology, self & the common world etc.IntroductionThe elimination of metaphysicsThe function of philosophy The nature of philosophical analysisThe a priori Truth & probabilityCritique of ethics & theologyThe self & the common worldSolutions of outstanding philosophical disputesIndex

    The material is arranged chronologically beginning with archaic origins and covers Egyptian, Mesopotamian, Greek, Chinese, Indian, Arabic and European contributions done to the nineteenth century and present day. There are revised references and bibliographies and revised and expanded chapters on the nineteeth and twentieth centuries.

    Each reading is based on a quotation from one of the world’s great philosophers, poets, saints, and sages. Augustine and Einstein, Emily Dickinson and Jalaladdin Rumi, Biblical verses, Buddhist sutras, Hasidic proverbs, and Hindu Upanishads can all be found here. Each quote is accompanied by a commentary from Easwaran, explaining how the wisdom of the ages can help us here and now. Some days offer gentle reminders to slow down and be mindful. Other days give advice for changing an unwanted habit, mending a relationship, staying strong in hard times, or striving toward the peaks of spirituality described in all religions. This is a book to read in the morning to start the day right, or at night to prepare for peaceful rest. Each day, each year, brings fresh insights and inspiration.

    But it's coming, and when it does, it will change our lives as much as any invention ever has. Imagine being able to program matter itself-to change it, with the click of a cursor, from hard to soft, from paper to stone, from fluorescent to super-reflective to invisible. Supported by organizations ranging from Levi Strauss and IBM to the Defense Department, solid-state physicists in renowned laboratories are working to make it a reality. In this dazzling investigation, Wil McCarthy visits the laboratories and talks with the researchers who are developing this extraordinary technology, describes how they are learning to control it, and tells us where all this will lead. The possibilities are truly astonishing.