The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.

    Heath's translation of the thirteen books of Euclid's Elements. In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for notes is allowed between propositions and around diagrams. The all-new index has built into it a glossary of Euclid's Greek terms.Heath's translation has stood the test of time, and, as one done by a renowned scholar of ancient mathematics, it can be relied upon not to have inadvertantly introduced modern concepts or nomenclature. We have excised the voluminous historical and scholarly commentary that swells the Dover edition to three volumes and impedes classroom use of the original text. The single volume is not only more convenient, but less expensive as well.

    Even as a young child, Louisa May was exposed to the leading radical minds of her time, such as Ralph Waldo Emerson and Henry David Thoreau, both of whom became her lifelong friends. Louisa May Alcott had to help support her family from an early age and was both proud of her ability to do so and frustrated by her family’s perpetual poverty.Her most famous novel, Little Women, was a semi-biographical version of her life with her three sisters and how they grew up. While her father, the educator Amos Bronson Alcott, could make her life exasperating, her beloved mother, Abigail, always supported her daughters’ right to chart their own course in life, whether society approved or not.An early feminist, Louisa May Alcott fought for women’s rights throughout her life and became the first woman in Concord, Massachusetts to register to vote.

    Can you believe that physical reality is created by our observation of it? Physicists were forced to this conclusion, the quantum enigma, by what they observed in their laboratories.Trying to understand the atom, physicists built quantum mechanics and found, to their embarrassment, that their theory intimately connects consciousness with the physical world. Quantum Enigma explores what that implies and why some founders of the theory became the foremost objectors to it. Schr�dinger showed that it absurdly allowed a cat to be in a superposition simultaneously dead and alive. Einstein derided the theory's spooky interactions. With Bell's Theorem, we now know Schr�dinger's superpositions and Einstein's spooky interactions indeed exist.Authors Bruce Rosenblum and Fred Kuttner explain all of this in non-technical terms with help from some fanciful stories and bits about the theory's developers. They present the quantum mystery honestly, with an emphasis on what is and what is not speculation.Physics' encounter with consciousness is its skeleton in the closet. Because the authors open the closet and examine the skeleton, theirs is a controversial book. Quantum Enigma's description of the experimental quantum facts, and the quantum theory explaining them, is undisputed. Interpreting what it all means, however, is controversial.Every interpretation of quantum physics encounters consciousness. Rosenblum and Kuttner therefore turn to exploring consciousness itself--and encounter quantum physics. Free will and anthropic principles become crucial issues, and the connection of consciousness with the cosmos suggested by some leading quantum cosmologists is mind-blowing.Readers are brought to a boundary where the particular expertise of physicists is no longer a sure guide. They will find, instead, the facts and hints provided by quantum mechanics and the ability to speculate for themselves.

    But most people who lived during the 10,000 years before the nineteenth century thought just the opposite. Drawing on archaeology, anthropology, biology, and history, Ian Morris explains why. Fundamental long-term changes in values, Morris argues, are driven by the most basic force of all: energy. Humans have found three main ways to get the energy they need--from foraging, farming, and fossil fuels. Each energy source sets strict limits on what kinds of societies can succeed, and each kind of society rewards specific values. But if our fossil-fuel world favors democratic, open societies, the ongoing revolution in energy capture means that our most cherished values are very likely to turn out not to be useful any more. Foragers, Farmers, and Fossil Fuels offers a compelling new argument about the evolution of human values, one that has far-reaching implications for how we understand the past--and for what might happen next. Originating as the Tanner Lectures delivered at Princeton University, the book includes challenging responses by classicist Richard Seaford, historian of China Jonathan Spence, philosopher Christine Korsgaard, and novelist Margaret Atwood.

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide.

    His life coincided with an extraordinary time in history: the first half of the miraculous seventeenth century, replete with genius in the arts and sciences, and wracked by civil and international conflicts across Europe. But at his birth in 1596 the world was still dominated by medieval beliefs in phenomena such as miracles and spontaneous generation. It was Descartes who identified the intellectual tools his peers needed to free themselves from the grip of religious authority and in doing so he founded modern philosophy.In this new biography, A. C. Grayling tells the story of Descartes' life, and places it in his tumultuous times—with the unexpected result that an entirely new aspect of the story comes to light.

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    This invaluable treasure of the Western philosophical canon has eluded us so far because Schopenhauer's argument has been consistently misunderstood and misrepresented, even at the hands of presumed experts. Hoping to change this situation, Decoding Schopenhauer's Metaphysics, offers a conceptual framework, a decoding key for unlocking the sense of Schopenhauer's metaphysical contentions in a way that renders them mutually consistent. With this key in mind, even those who earlier dismissed Schopenhauer's metaphysics should be able to return to it with fresh eyes and at last grasp its meaning. And for those as yet unacquainted with Schopenhauerian thought, this volume offers a succinct and accessible entry path.

    Bronowski was both a distinguished mathematician and a poet, a philosopher of science and a literary critic who wrote a well-known study of William Blake. Dr. Bronowski's very career was founded on the premise of an intimate connection between science and the humanities, disciplines which are still generally thought to be worlds apart.The Common Sense of Science, a book which remains as topical today as it was when it first appeared twenty-five years ago, articulates and develops Bronowski's provocative idea that the sciences and the arts fundamentally share the same imaginative vision.

    

    These lectures are based on their seminar course at Columbia University on Western intellectual history augmented by additional lectures by selected "guest" lecturers. Gives a guided tour through 3,000 years of Western thought.In 7 containers (26 cm.).Lectures by Darren M. Staloff, Louis Markos, Jeremy Adams, Phillip Cary, Dennis G. Dalton, Alan Charles Kors, Jeremy Shearmur, Kathleen M. Higgins, Robert Hilary Kane, Robert C. Solomon, Douglas Kellner, and Mark W. Risjord.42 audiocassettes (approximately 2520 min.) : analog, Dolby processed + 7 course guidebooks (22 cm).Contents:pt. 1. Classical origins --pt. 2. Christian age --pt. 3. From the Renaissance to the Age of Reason --pt. 4. Enlightenment and its critics --pt. 5. Age of ideology --pt. 6. Modernism and the age of analysis --pt. 7. Age of modernity.

    Escher -- goes to some of the strangest spots imaginable. It takes us to a place where the purely intellectual enters our daily world: where our outraged senses, overloaded with grocery bills, the price of gas, and what to eat for lunch, are expected to absorb really bizarre ideas. And no better guide to this weird universe exists than the brilliant thinker Clifford A. Pickover, the 21st century's answer to Buckminster Fuller. Come along as Pickover traces the origins of the Mobius strip from the mid-1800s, when the visionary scientist Dr. August Mobius became the first to describe the properties of one-sided surfaces, to the present, where it is an integral part of mathematics, magic, science, art, engineering, literature, and music. It has become a metaphor for change, strangeness, looping, and rejuvenation. Touching on everything from molecules and metal sculptures to postage stamps, architectural structures, and models of our entire universe, The Mobius Strip is lavishly illustrated and gives readers a glimpse into other worlds and new ways of thinking as Pickover reaches across cultures and dimensions.