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Mechanizing Proof

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Release : 2004-01-30
Genre : Social Science
Kind : eBook
Book Rating : 959/5 ( reviews)

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Book Synopsis Mechanizing Proof by : Donald MacKenzie

Download or read book Mechanizing Proof written by Donald MacKenzie. This book was released on 2004-01-30. Available in PDF, EPUB and Kindle. Book excerpt: Most aspects of our private and social lives—our safety, the integrity of the financial system, the functioning of utilities and other services, and national security—now depend on computing. But how can we know that this computing is trustworthy? In Mechanizing Proof, Donald MacKenzie addresses this key issue by investigating the interrelations of computing, risk, and mathematical proof over the last half century from the perspectives of history and sociology. His discussion draws on the technical literature of computer science and artificial intelligence and on extensive interviews with participants. MacKenzie argues that our culture now contains two ideals of proof: proof as traditionally conducted by human mathematicians, and formal, mechanized proof. He describes the systems constructed by those committed to the latter ideal and the many questions those systems raise about the nature of proof. He looks at the primary social influence on the development of automated proof—the need to predict the behavior of the computer systems upon which human life and security depend—and explores the involvement of powerful organizations such as the National Security Agency. He concludes that in mechanizing proof, and in pursuing dependable computer systems, we do not obviate the need for trust in our collective human judgment.

Mechanizing Proof Theory

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Release : 1990
Genre : Computers
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Mechanizing Proof Theory by : Gianluigi Bellin

Download or read book Mechanizing Proof Theory written by Gianluigi Bellin. This book was released on 1990. Available in PDF, EPUB and Kindle. Book excerpt: In Part II we study Herbrand's Theorem in Linear Logic and the No Counterexample Interpretation in a fragment of Peano Arithmetic (section 10). As an application to Ramsey Theory we give a parametric form of the Ramsey Theorem, that generalizes the Infinite, the Finite and the Ramsey-Paris-Harrington Theorems for a fixed exponent (sections 10-13)."

Reactionary Mathematics

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Release : 2023-05-12
Genre : History
Kind : eBook
Book Rating : 732/5 ( reviews)

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Book Synopsis Reactionary Mathematics by : Massimo Mazzotti

Download or read book Reactionary Mathematics written by Massimo Mazzotti. This book was released on 2023-05-12. Available in PDF, EPUB and Kindle. Book excerpt: A forgotten episode of mathematical resistance reveals the rise of modern mathematics and its cornerstone, mathematical purity, as political phenomena. The nineteenth century opened with a major shift in European mathematics, and in the Kingdom of Naples, this occurred earlier than elsewhere. Between 1790 and 1830 its leading scientific institutions rejected as untrustworthy the “very modern mathematics” of French analysis and in its place consolidated, legitimated, and put to work a different mathematical culture. The Neapolitan mathematical resistance was a complete reorientation of mathematical practice. Over the unrestricted manipulation and application of algebraic algorithms, Neapolitan mathematicians called for a return to Greek-style geometry and the preeminence of pure mathematics. For all their apparent backwardness, Massimo Mazzotti explains, they were arguing for what would become crucial features of modern mathematics: its voluntary restriction through a new kind of rigor and discipline, and the complete disconnection of mathematical truth from the empirical world—in other words, its purity. The Neapolitans, Mazzotti argues, were reacting to the widespread use of mathematical analysis in social and political arguments: theirs was a reactionary mathematics that aimed to technically refute the revolutionary mathematics of the Jacobins. During the Restoration, the expert groups in the service of the modern administrative state reaffirmed the role of pure mathematics as the foundation of a newly rigorous mathematics, which was now conceived as a neutral tool for modernization. What Mazzotti’s penetrating history shows us in vivid detail is that producing mathematical knowledge was equally about producing certain forms of social, political, and economic order.

The Science of Computing

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Release : 2014-12-03
Genre : Computers
Kind : eBook
Book Rating : 708/5 ( reviews)

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Book Synopsis The Science of Computing by : Matti Tedre

Download or read book The Science of Computing written by Matti Tedre. This book was released on 2014-12-03. Available in PDF, EPUB and Kindle. Book excerpt: The identity of computing has been fiercely debated throughout its short history. Why is it still so hard to define computing as an academic discipline? Is computing a scientific, mathematical, or engineering discipline? By describing the mathematical, engineering, and scientific traditions of computing, The Science of Computing: Shaping a Discipli

AI

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Release : 2024-02-23
Genre : Computers
Kind : eBook
Book Rating : 912/5 ( reviews)

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Book Synopsis AI by : Roman V. Yampolskiy

Download or read book AI written by Roman V. Yampolskiy. This book was released on 2024-02-23. Available in PDF, EPUB and Kindle. Book excerpt: Delving into the deeply enigmatic nature of Artificial Intelligence (AI), AI: Unexplainable, Unpredictable, Uncontrollable explores the various reasons why the field is so challenging. Written by one of the founders of the field of AI safety, this book addresses some of the most fascinating questions facing humanity, including the nature of intelligence, consciousness, values and knowledge. Moving from a broad introduction to the core problems, such as the unpredictability of AI outcomes or the difficulty in explaining AI decisions, this book arrives at more complex questions of ownership and control, conducting an in-depth analysis of potential hazards and unintentional consequences. The book then concludes with philosophical and existential considerations, probing into questions of AI personhood, consciousness, and the distinction between human intelligence and artificial general intelligence (AGI). Bridging the gap between technical intricacies and philosophical musings, AI: Unexplainable, Unpredictable, Uncontrollable appeals to both AI experts and enthusiasts looking for a comprehensive understanding of the field, whilst also being written for a general audience with minimal technical jargon.

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