However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

    It adopts the fairly traditional conception of metaphysics as a subject that deals with the deepest questions that can be raised concerning the fundamental structure ofreality as a whole. The book is divided into six main sections that address the following themes: identity and change, necessity and essence, causation, agency and events, space and time, and universals and particulars. It focuses on contemporary views and issues throughout, rather than on thehistory of metaphysics.

    Mathematics: The Loss of Certainty refutes that myth.

    In Mind and World, based on the 1991 John Locke Lectures, one of the most distinguished philosophers writing today offers his diagnosis of this difficulty and points to a cure. In doing so, he delivers the most complete and ambitious statement to date of his own views, a statement that no one concerned with the future of philosophy can afford to ignore.John McDowell amply illustrates a major problem of modern philosophy--the insidious persistence of dualism--in his discussion of empirical thought. Much as we would like to conceive empirical thought as rationally grounded in experience, pitfalls await anyone who tries to articulate this position, and McDowell exposes these traps by exploiting the work of contemporary philosophers from Wilfrid Sellars to Donald Davidson. These difficulties, he contends, reflect an understandable--but surmountable--failure to see how we might integrate what Sellars calls the logical space of reasons" into the natural world. What underlies this impasse is a conception of nature that has certain attractions for the modern age, a conception that McDowell proposes to put aside, thus circumventing these philosophical difficulties. By returning to a pre-modern conception of nature but retaining the intellectual advance of modernity that has mistakenly been viewed as dislodging it, he makes room for a fully satisfying conception of experience as a rational openness to independent reality. This approach also overcomes other obstacles that impede a generally satisfying understanding of how we are placed in the world.

    Strasser and published in the first volume of Husserliana: Cartesianische Meditationen und Pariser Vortrage, ISBN 90-247-0214-3. Most of Husserl's emendations, as given in the Appendix to that volume, have been treated as if they were part of the text. The others have been translated in footnotes. Secondary consideration has been given to a typescript (cited as "Typescript C") on which Husserl wrote in 1933: "Cartes. Meditationen / Original text 1929 / E. Husserl / fur Dorion Cairns." Its use of emphasis and quotation marks conforms more closely to Husserl's practice, as exemplified in works published during his lifetime. In this respect the translation usually follows Typescript C. Moreover, some of the variant readings n this typescript are preferable and have been used as the basis for the translation. Where that is the case, the published text is given or translated in a footnote. The published text and Typescript C have been compared with the French translation by Gabrielle Pfeiffer and Emmanuel Levinas (Paris, Armand Collin, 1931). The use of emphasis and quotation marks in the French translation corresponds more closely to that in Typescript C than to that in the published text. Often, where the wording of the published text and that of Typescript C differ, the French translation indicates that it was based on a text that corresponded more closely to one or the other - usually to Typescript C. In such cases the French translation has been quoted or cited in a foornote."

    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.

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    At eighteen, fate would take his remaining family, sending him on the road with three hundred dollars and into the life of a Depression Era migrant worker, but his appetite for knowledge--history, science, mankind--remained and became the basis for his insights on human nature. Filled with timeless aphorisms and entertaining stories, Truth Imagined tracks Hoffer's years on the road, which served as the breeding ground for his most fertile thoughts.

    "An excellent book presenting many of the major issues of ordinary language philosophy--very readable."--Mark Hamilton, Ashland University"The clarity, the wit, and the patience of the writing are liable to deceive the reader on only one point, namely the amount of hard work that lies behind these thoughts....This book is the one to put into the hands of those who have been over-impressed by Austin's critics....[Warnock's] brilliant editing puts everybody who is concerned with philosophical problems in his debt."--The Guardian

    In this book van Fraassen develops an alternative to scientific realism by constructing and evaluating three mutually reinforcing theories.

    Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

    Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that mathematics is logic (logicism), the view that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV brings the reader up-to-date with a look at contemporary developments within the discipline.This sweeping introductory guide to the philosophy of mathematics makes these fascinating concepts accessible to those with little background in either mathematics or philosophy.

    A modern classic by an accomplished mathematician and best-selling author has been updated to encompass and explain the recent headline-making advances in the field in non-technical terms.

    It remains the one of the most widely read books about science to come out of the twentieth century.(Note: the book was first published in 1934, in German, with the title Logik der Forschung. It was "reformulated" into English in 1959. See Wikipedia for details.)

     Now Roy Sorensen offers the first narrative history of paradoxes, a fascinating and eye-opening account that extends from the ancient Greeks, through the Middle Ages, the Enlightenment, and into the twentieth century. When Augustine asked what God was doing before He made the world, he wastold: Preparing hell for people who ask questions like that. A Brief History of the Paradox takes a close look at questions like that and the philosophers who have asked them, beginning with the folk riddles that inspired Anaximander to erect the first metaphysical system and ending with suchthinkers as Lewis Carroll, Ludwig Wittgenstein, and W.V. Quine. Organized chronologically, the book is divided into twenty-four chapters, each of which pairs a philosopher with a major paradox, allowing for extended consideration and putting a human face on the strategies that have been taken towardthese puzzles. Readers get to follow the minds of Zeno, Socrates, Aquinas, Ockham, Pascal, Kant, Hegel, and many other major philosophers deep inside the tangles of paradox, looking for, and sometimes finding, a way out. Filled with illuminating anecdotes and vividly written, A Brief History of the Paradox will appeal to anyone who finds trying to answer unanswerable questions a paradoxically pleasant endeavor.