Axiomatic Method And Category Theory
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Axiomatic Method And Category Theory
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Author : Andrei Rodin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-14
Axiomatic Method And Category Theory written by Andrei Rodin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-14 with Philosophy categories.
This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.
Intuition And The Axiomatic Method
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Author : Emily Carson
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-02
Intuition And The Axiomatic Method written by Emily Carson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-02 with Philosophy categories.
Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method, dealing with both their strengths and limitations; in short, the volume covers logical and non-logical, historical and systematic issues in both mathematics and physics.
Monoidal Category Theory
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Author : Noson S. Yanofsky
language : en
Publisher: MIT Press
Release Date : 2024-11-05
Monoidal Category Theory written by Noson S. Yanofsky and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Computers categories.
A comprehensive, cutting-edge, and highly readable textbook that makes category theory and monoidal category theory accessible to students across the sciences. Category theory is a powerful framework that began in mathematics but has since expanded to encompass several areas of computing and science, with broad applications in many fields. In this comprehensive text, Noson Yanofsky makes category theory accessible to those without a background in advanced mathematics. Monoidal Category Theorydemonstrates the expansive uses of categories, and in particular monoidal categories, throughout the sciences. The textbook starts from the basics of category theory and progresses to cutting edge research. Each idea is defined in simple terms and then brought alive by many real-world examples before progressing to theorems and uncomplicated proofs. Richly guided exercises ground readers in concrete computation and application. The result is a highly readable and engaging textbook that will open the world of category theory to many. Makes category theory accessible to non-math majors Uses easy-to-understand language and emphasizes diagrams over equations Incremental, iterative approach eases students into advanced concepts A series of embedded mini-courses cover such popular topics as quantum computing, categorical logic, self-referential paradoxes, databases and scheduling, and knot theory Extensive exercises and examples demonstrate the broad range of applications of categorical structures Modular structure allows instructors to fit text to the needs of different courses Instructor resources include slides
Axiomatic Thinking I
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Author : Fernando Ferreira
language : en
Publisher: Springer Nature
Release Date : 2022-10-13
Axiomatic Thinking I written by Fernando Ferreira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-13 with Mathematics categories.
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations. Chapter 8 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Intelligence Science
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Author : Zhongzhi Shi
language : en
Publisher: Elsevier
Release Date : 2021-04-16
Intelligence Science written by Zhongzhi Shi and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-16 with Computers categories.
Intelligence Science: Leading the Age of Intelligence covers the emerging scientific research on the theory and technology of intelligence, bringing together disciplines such as neuroscience, cognitive science, and artificial intelligence to study the nature of intelligence, the functional simulation of intelligent behavior, and the development of new intelligent technologies. The book presents this complex, interdisciplinary area of study in an accessible volume, introducing foundational concepts and methods, and presenting the latest trends and developments. Chapters cover the Foundations of neurophysiology, Neural computing, Mind models, Perceptual intelligence, Language cognition, Learning, Memory, Thought, Intellectual development and cognitive structure, Emotion and affect, and more. This volume synthesizes a very rich and complex area of research, with an aim of stimulating new lines of enquiry. - Presents a complex, interdisciplinary area in an accessible way, including the latest trends and developments - Brings together disciplines such as neuroscience, cognitive science and artificial intelligence - Gives the latest methods and theories in the development of new intelligent technologies - Reflects upon the most important achievements in the study of natural and artificial intelligence - Contextualizes intelligence research within the history and progress of twenty-first century science
Structures M Res Semantics Mathematics And Cognitive Science
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Author : Alberto Peruzzi
language : en
Publisher: Springer Nature
Release Date : 2020-09-14
Structures M Res Semantics Mathematics And Cognitive Science written by Alberto Peruzzi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-14 with Philosophy categories.
This book reports on cutting-edge concepts related to Bourbaki’s notion of structures mères. It merges perspectives from logic, philosophy, linguistics and cognitive science, suggesting how they can be combined with Bourbaki’s mathematical structuralism in order to solve foundational, ontological and epistemological problems using a novel category-theoretic approach. By offering a comprehensive account of Bourbaki’s structuralism and answers to several important questions that have arisen in connection with it, the book provides readers with a unique source of information and inspiration for future research on this topic.
An Historical Introduction To The Philosophy Of Mathematics A Reader
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Author : Russell Marcus
language : en
Publisher: Bloomsbury Publishing
Release Date : 2016-02-11
An Historical Introduction To The Philosophy Of Mathematics A Reader written by Russell Marcus and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-11 with Philosophy categories.
A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.
Danish Yearbook Of Philosophy Vol 45
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Author : Finn Collin
language : en
Publisher: Museum Tusculanum Press
Release Date : 2013-04-15
Danish Yearbook Of Philosophy Vol 45 written by Finn Collin and has been published by Museum Tusculanum Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-15 with Philosophy categories.
Danish Yearbook of Philosophy publishes contributions in English, German and French. Danish Yearbook of Philosophy mainly publishes articles relating to Danish philosophy, or by authors with ties to Danish philosophy.
Human Systems Engineering And Design
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Author : Tareq Ahram
language : en
Publisher: Springer
Release Date : 2018-10-16
Human Systems Engineering And Design written by Tareq Ahram and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-16 with Technology & Engineering categories.
This book focuses on novel design and systems engineering approaches, including theories and best practices, for promoting a better integration of people and engineering systems. It covers a range of hot topics related to: development of activity-centered and user-centered systems; interface design and human-computer interaction; usability and user experience; cooperative, participatory and contextual models; emergent properties of human behavior; innovative materials in manufacturing, and many more. Particular emphasis is placed on applications in sports, healthcare, and medicine. The book, which gathers selected papers presented at the 1st International Conference on Human Systems Engineering and Design: Future Trends and Applications (IHSED 2018), held on October 25-27, 2018, at CHU-Université de Reims Champagne-Ardenne, France, provides researchers, practitioners and program managers with a snapshot of the state-of-the-art and current challenges in the field of human systems engineering and design.
Categories For The Working Philosopher
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Author : Elaine M. Landry
language : en
Publisher: Oxford University Press
Release Date : 2017
Categories For The Working Philosopher written by Elaine M. Landry and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, in an accessible waythat builds on the concepts that are already familiar to philosophers working in these areas.