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Author: Y. Gauthier
Publisher: Springer Science & Business Media
ISBN: 9781402006890
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer. The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene.
Author: Y. Gauthier
Publisher: Springer Science & Business Media
ISBN: 9781402006890
Category : Mathematics
Languages : en
Pages : 276
Get Book Here
Book Description
Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer. The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene.
Author: Maggie Taylor
Publisher:
ISBN: 9780999532539
Category :
Languages : en
Pages : 176
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Book Description
This is a collection of digitally composited surreal images by artist Maggie Taylor with an essay by Mark Sloan. 117 color plates. The works span the years 2012-2021.
Author: Eugenia Cheng
Publisher: Basic Books
ISBN: 154167250X
Category : Mathematics
Languages : en
Pages : 296
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Book Description
How both logical and emotional reasoning can help us live better in our post-truth world In a world where fake news stories change election outcomes, has rationality become futile? In The Art of Logic in an Illogical World, Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life. Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic -- for example, emotion -- is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.
Author: B. Jacobs
Publisher: Gulf Professional Publishing
ISBN: 9780444508539
Category : Computers
Languages : en
Pages : 784
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Book Description
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.
Author: Yvon Gauthier
Publisher: Birkhäuser
ISBN: 331922087X
Category : Mathematics
Languages : en
Pages : 193
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Book Description
This book offers an original contribution to the foundations of logic and mathematics and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic and combines Fermat’s method of infinite descent with Kronecker’s general arithmetic of homogeneous polynomials. The book also includes a treatment of theories in physics and mathematical physics to underscore the role of arithmetic from a constructivist viewpoint. The scope of the work intertwines historical, mathematical, logical and philosophical dimensions in a unified critical perspective; as such, it will appeal to a broad readership from mathematicians to logicians, to philosophers interested in foundational questions. Researchers and graduate students in the fields of philosophy and mathematics will benefit from the author’s critical approach to the foundations of logic and mathematics.
Author: Francesco Logozzo
Publisher: Springer Science & Business Media
ISBN: 3540781625
Category : Computers
Languages : en
Pages : 333
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Book Description
The book constitutes the refereed proceedings of the 9th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2007, held in San Francisco, USA, in January 2008. The 21 revised full papers presented together with 2 invited lectures and 2 invited tutorials were carefully reviewed and selected from a total of over 60 submissions. The papers feature current research from the communities of verification, program certification, model checking, debugging techniques, abstract interpretation, abstract domains, static analysis, cross-fertilization, and advancement of hybrid methods.
Author: Graham Priest
Publisher: Cambridge University Press
ISBN: 1009089080
Category : Philosophy
Languages : en
Pages : 93
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Book Description
Mathematical pluralism is the view that there is an irreducible plurality of pure mathematical structures, each with their own internal logics; and that qua pure mathematical structures they are all equally legitimate. Mathematical pluralism is a relatively new position on the philosophical landscape. This Element provides an introduction to the position.
Author: United States. Patent and Trademark Office
Publisher:
ISBN:
Category : Patents
Languages : en
Pages : 1398
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Book Description
Author: Alexander Bochman
Publisher: Springer Science & Business Media
ISBN: 3662045605
Category : Computers
Languages : en
Pages : 439
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Book Description
This is the first book that integrates nonmonotonic reasoning and belief change into a single framework from an artificial intelligence logic point-of-view. The approach to both these subjects is based on a powerful notion of an epistemic state that subsumes both existing models for nonmonotonic inference and current models for belief change. Many results and constructions in the book are completely new and have not appeared earlier in the literature.
Author: Yanjie Bian
Publisher: John Wiley & Sons
ISBN: 1509500421
Category : Business & Economics
Languages : en
Pages : 212
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Book Description
How do social relations, or guanxi, matter in China today and how can this distinctive form of personal connection be better understood? In Guanxi: How China Works, Yanjie Bian analyzes the forms, dynamics, and impacts of guanxi relations in reform-era China, and shows them to be a crucial part of the puzzle of how Chinese society operates. Rich in original studies and insightful analyses, this concise book offers a critical synthesis of guanxi research, including its empirical controversies and theoretical debates. Bian skillfully illustrates the growing importance of guanxi in diverse areas such as personal network building, employment and labor markets, informal business relationships, and the broader political sphere, highlighting guanxi’s central value in China's contemporary social structure. A definitive statement on the topic from a top authority on the sociology of guanxi, this book is an excellent classroom introduction for courses on China, a useful reference for guanxi researchers, and ideal reading for anyone interested in Chinese culture and society.
