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Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
ISBN: 0393327604
Category : Biography & Autobiography
Languages : en
Pages : 299
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Book Description
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
ISBN: 0393327604
Category : Biography & Autobiography
Languages : en
Pages : 299
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Book Description
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
ISBN: 0393242455
Category : Biography & Autobiography
Languages : en
Pages : 299
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Book Description
"A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven Pinker Probing 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.
Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
ISBN: 9780393051698
Category : Biography & Autobiography
Languages : en
Pages : 316
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Book Description
Considered the 20th century's greatest mathematician, Kurt Godel is the subject of this lucid and accessible study, which explains the significance of his theorems and the remarkable vision behind them, while bringing this eccentric, tortured genius and his world to life.
Author: Martin Goldstern
Publisher: CRC Press
ISBN: 1439863539
Category : Mathematics
Languages : en
Pages : 262
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Book Description
This introduction to mathematical logic takes Gödel's incompleteness theorem as a starting point. It goes beyond a standard text book and should interest everyone from mathematicians to philosophers and general readers who wish to understand the foundations and limitations of modern mathematics.
Author: Raymond M. Smullyan
Publisher: Oxford University Press
ISBN: 0195364376
Category : Mathematics
Languages : en
Pages : 156
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Book Description
Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.
Author: B. Nyamnjoh
Publisher: African Books Collective
ISBN: 9956552402
Category : Political Science
Languages : en
Pages : 417
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Book Description
This is a study of how Donald J. Trump, his populist credentials notwithstanding, borrows without acknowledgment and stubbornly refuses to come to terms with his indebtedness. Taken together with mobility and conviviality, the principle of incompleteness enables us to distinguish between inclusionary and exclusionary forms of populism, and when it is fuelled by ambitions of superiority and zero-sum games of conquest.
Author: Peter Smith
Publisher: Cambridge University Press
ISBN: 1139465937
Category : Mathematics
Languages : en
Pages : 376
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Book Description
In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.
Author: Slavoj Žižek
Publisher: Bloomsbury Academic
ISBN: 1350043788
Category : Philosophy
Languages : en
Pages : 497
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Book Description
In the most rigorous articulation of his philosophical system to date, Slavoj Žižek provides nothing short of a new definition of dialectical materialism. In forging this new materialism, Žižek critiques and challenges not only the work of Alain Badiou, Robert Brandom, Joan Copjec, Quentin Meillassoux, and Julia Kristeva (to name but a few), but everything from popular science and quantum mechanics to sexual difference and analytic philosophy. Alongside striking images of the Möbius strip, the cross-cap, and the Klein bottle, Žižek brings alive the Hegelian triad of being-essence-notion. Radical new readings of Hegel, and Kant, sit side by side with characteristically lively commentaries on film, politics, and culture. Here is Žižek at his interrogative best.
Author: Serafim Batzoglou
Publisher: Springer Nature
ISBN: 3031642171
Category :
Languages : en
Pages : 303
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Book Description
Author: Melvin Fitting
Publisher:
ISBN: 9781904987345
Category : Incompleteness theorems
Languages : en
Pages : 0
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Book Description
Russell's paradox arises when we consider those sets that do not belong to themselves. The collection of such sets cannot constitute a set. Step back a bit. Logical formulas define sets (in a standard model). Formulas, being mathematical objects, can be thought of as sets themselves-mathematics reduces to set theory. Consider those formulas that do not belong to the set they define. The collection of such formulas is not definable by a formula, by the same argument that Russell used. This quickly gives Tarski's result on the undefinability of truth. Variations on the same idea yield the famous results of Gödel, Church, Rosser, and Post. This book gives a full presentation of the basic incompleteness and undecidability theorems of mathematical logic in the framework of set theory. Corresponding results for arithmetic follow easily, and are also given. Gödel numbering is generally avoided, except when an explicit connection is made between set theory and arithmetic. The book assumes little technical background from the reader. One needs mathematical ability, a general familiarity with formal logic, and an understanding of the completeness theorem, though not its proof. All else is developed and formally proved, from Tarski's Theorem to Gödel's Second Incompleteness Theorem. Exercises are scattered throughout.
