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First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.

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Genre: Mathematics
Author: Kurt Gödel
Publisher: Courier Corporation
Release: 2012-05-24
File: 80 Pages
ISBN-13: 9780486158402

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"A valuable collection both for original source material as well as historical formulations of current problems." — The Review of Metaphysics "Much more than a mere collection of papers. A valuable addition to the literature." — Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field , this classic reference is ideally suited as a text for graduate and undergraduate courses in logic, philosophy, and foundations of mathematics. It is also appropriate for self-study. The text opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by Godel, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. Additional papers by Church, Turing, and Post cover unsolvable problems from the theory of abstract computing machines, mathematical logic, and algebra, and material by Kleene and Post includes initiation of the classification theory of unsolvable problems. Supplementary items include corrections, emendations, and added commentaries by Godel, Church, and Kleene for this volume's original publication, along with a helpful commentary by the editor.

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Genre: Mathematics
Author: Martin Davis
Publisher: Courier Corporation
Release: 2004-01-01
File: 413 Pages
ISBN-13: 0486432289

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Genre:
Author: Kurt GOEDEL
Publisher:
Release: 1962
File: 72 Pages
ISBN-13: OCLC:558776891

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A new theory of culture presented with a new method achieved by comparing closely the art and science in 20th century Austria and Hungary. Major achievements that have influenced the world like psychoanalysis, abstract art, quantum physics, Gestalt psychology, formal languages, vision theories, and the game theory etc. originated from these countries, and influence the world still today as a result of exile nurtured in the US. A source book with numerous photographs, images and diagrams, it opens up a nearly infinite horizon of knowledge that helps one to understand what is going on in today’s worlds of art and science.

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Genre: Architecture
Author: Peter Weibel
Publisher: Springer Science & Business Media
Release: 2005-05-17
File: 616 Pages
ISBN-13: 3211245626

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A short e-book with a very long title Fathoming Gödel: an Examination of Kurt Gödel’s 1931 Paper: On Formally Undeciable Propositions of Principia Mathematica and Related Systems 1. The title of my e-book includes the title of Kurt Gödel’s 1931 paper, and the title of his 1931 paper includes the title of Bertrand Russell and Alfred North Whitehead’s monumental work Principia Mathematica, the title of which harkens back to Isaac Newton’s Philosophiae Naturalis Principia Mathematica. I remember in high school someone lent me Ernest Nagel and James R. Newman’s book Gödel’s Proof published in 1958. At the time I was quite impressed and thought that if I kept studying assiduously I would one day understand the complex mathematics present in that text. It seems that Gödel’s proofs have had an aura of mystery around them for quite sometime. In high school I believed that Gödel had discovered something profound about the nature of reality and about the limits of human understanding. Now I think he is a fraud.

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Genre: Science
Author: James Spinosa
Publisher: Lulu Press, Inc
Release: 2017-06-02
File: Pages
ISBN-13: 9781329765740

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A portrait of the eminent twentieth-century mathematician discusses his theorem of incompleteness, relationships with such contemporaries as Albert Einstein, and untimely death as a result of mental instability and self-starvation.

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Genre: Biography & Autobiography
Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
Release: 2006-02-17
File: 296 Pages
ISBN-13: 9780393327601

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Dialectic and narrative reflect the respective inclinations of philosophy and literature as disciplines that fix one another in a Sartrean gaze, admixing envy with suspicion. Ever since Plato and Aristotle distinguished scientific knowledge (episteme) from opinion (doxa) and valued demonstration through formal final causes over emplotment (mythos), the palm has been awarded to dialectic as the proper instrument of rational discourse, the arbiter of coherence, consistency, and ultimately of truth. The matter becomes more complicated when we recognize the various uses of the term "dialectic" in the tradition, some of which complement and even overlap the narrative domain. By confronting these concepts with one another, either de facto or ex professo, the following essays not only raise anew the ancient questions of the identities of philosophy and literature, but do so in the context of recent "postmodern" challenges to their relative autonomy. -- Back cover.

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Genre: Philosophy
Author: Thomas R. Flynn
Publisher: SUNY Press
Release: 1993-01-01
File: 382 Pages
ISBN-13: 9781438402970

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The Shakespearean image of a tempest and its aftermath forms the beginning as well as a major guiding thread of Logic of Imagination. Moving beyond the horizons of his earlier work, Force of Imagination, John Sallis sets out to unsettle the traditional conception of logic, to mark its limits, and, beyond these limits, to launch another, exorbitant logic—a logic of imagination. Drawing on a vast range of sources, including Plato, Aristotle, Kant, Hegel, Nietzsche, and Freud, as well as developments in modern logic and modern mathematics, Sallis shows how a logic of imagination can disclose the most elemental dimensions of nature and of human existence and how, through dialogue with contemporary astrophysics, it can reopen the project of a philosophical cosmology.

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Genre: Philosophy
Author: John Sallis
Publisher: Indiana University Press
Release: 2012
File: 286 Pages
ISBN-13: 9780253005908

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This abridged text of the most famous work ever written on the foundations of mathematics contains material that is most relevant to an introductory study of logic and the philosophy of mathematics.

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Genre: Mathematics
Author: Alfred North Whitehead
Publisher: Cambridge University Press
Release: 1997-09-11
File: 410 Pages
ISBN-13: 9780521626064

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Unifying Themes in Complex Systems is a well-established series of carefully edited conference proceedings that serve to document and archive the progress made regarding cross-fertilization in this field. The International Conference on Complex Systems (ICCS) creates a unique atmosphere for scientists from all fields, engineers, physicians, executives, and a host of other professionals, allowing them to explore common themes and applications of complex systems science. With this new volume, Unifying Themes in Complex Systems continues to establish common ground between the wide-ranging domains of complex systems science.

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Genre: Science
Author: Alfredo J. Morales
Publisher: Springer
Release: 2018-07-23
File: 506 Pages
ISBN-13: 9783319966618

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