Categories For The Working Philosopher
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Categories For The Working Philosopher
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Author : Elaine Landry
language : en
Publisher: Oxford University Press
Release Date : 2017-11-17
Categories For The Working Philosopher written by Elaine 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 2017-11-17 with Philosophy categories.
Often people have wondered why there is no introductory text on category theory aimed at philosophers working in related areas. The answer is simple: what makes categories interesting and significant is their specific use for specific purposes. These uses and purposes, however, vary over many areas, both "pure", e.g., mathematical, foundational and logical, and "applied", e.g., applied to physics, biology and the nature and structure of mathematical models. Borrowing from the title of Saunders Mac Lane's seminal work "Categories for the Working Mathematician", this book aims to bring the concepts of category theory to philosophers working in areas ranging from mathematics to proof theory to computer science to ontology, from to physics to biology to cognition, from mathematical modeling to the structure of scientific theories to the structure of the world. Moreover, it aims to do this in a way that is accessible to non-specialists. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, and in a way that builds on the concepts that are already familiar to philosophers working in these areas.
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.
Category Theory In Physics Mathematics And Philosophy
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Author : Marek Kuś
language : en
Publisher: Springer Nature
Release Date : 2019-11-11
Category Theory In Physics Mathematics And Philosophy written by Marek Kuś and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Science categories.
The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes. The book approaches formal ontology in the original sense put forward by the philosopher Edmund Husserl, namely as a science that deals with entities that can be exemplified in all spheres and domains of reality. It is a dynamic, processual, and non-substantial ontology in which all entities can be treated as transformations, and in which objects are merely the sources and aims of these transformations. Thus, in a rather surprising way, when employed as a formal ontology, category theory can unite seemingly disparate disciplines in contemporary science and the humanities, such as physics, mathematics and philosophy, but also computer and complex systems science.
Methods In The Philosophy Of Science
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Author : Sophie J Veigl
language : en
Publisher: MIT Press
Release Date : 2025-07-15
Methods In The Philosophy Of Science written by Sophie J Veigl and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-15 with Science categories.
A guidebook to methods and methodology, encouraging deeper engagement across the philosophy of science and beyond. The last twenty years have seen multiple methodological revolutions in the philosophy of science: There has been increased diversity concerning the questions asked, who asks those questions, who the relevant audiences are, and what the techniques and tools involved are. In Methods in the Philosophy of Science: A User’s Guide, Sophie Veigl and Adrian Currie introduce this range of methods through both practical advice and philosophical reflection. Each chapter introduces the reader to a method or set of methods in the philosophy of science, discusses its advantages and limitations, and provides practical guidance on how to learn skills relevant to applying the method. The volume fulfills several critical roles. First, by introducing and discussing methods in the philosophy of science, the collection increases philosophers' awareness of methodological options—of particular importance for younger scholars who are often not exposed to the diversity of practice. Second, the collection's practical focus will aid established philosophers in diversifying their own methodological toolkits. Third, collecting this diversity serves as a ground for philosophical reflection on what we, as philosophers, take ourselves to be capable of. Fourth, the collection hopes to increase interdisciplinary links between philosophy and other fields by laying clear the methodological continuity and complement between them.
Philosophical Approaches To The Foundations Of Logic And Mathematics
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Author : Marcin Trepczyński
language : en
Publisher: BRILL
Release Date : 2021-01-25
Philosophical Approaches To The Foundations Of Logic And Mathematics written by Marcin Trepczyński and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-25 with Philosophy categories.
Eleven papers collected in the volume Philosophical Approaches to the Foundations of Logic and Mathematics address various aspects of the “roots”, basic concepts and the nature of logic and mathematics. Taken together, these papers reveal how many serious philosophical problems lie at the foundations of logic and mathematics. The topics discussed in this volume include: transcending anti-foundationalism and two concurrent trends of "anthropological" and "practical" understanding of the foundations of mathematics, new approaches to mathematical realism, the “roots” of logic in a genetic perspective, the primacy of truth or satisfaction, and the “effectiveness” of mathematics in terms of categorical semantics.
Mathematical Modelling By Help Of Category Theory
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Author : Dmitrii Legatiuk
language : en
Publisher: Springer Nature
Release Date : 2025-03-19
Mathematical Modelling By Help Of Category Theory written by Dmitrii Legatiuk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-19 with Mathematics categories.
This monograph offers a novel structural perspective on the modelling of engineering problems, utilizing abstract mathematics in the form of category theory. Specifically, the book aims to enhance the understanding of mathematical modelling by developing a category theory-based framework. Category theory is employed to establish clear relationships between mathematical models and their complexities. The theory is then extended to encompass coupled mathematical models, incorporating more advanced categorical structures. To bridge theory and practice, the book presents engineering applications of the abstract categorical framework, providing various modelling examples from real-world engineering scenarios. Additionally, it introduces initial concepts for automatic model generation and error detection in modelling. The theory developed here demonstrates the practical utility of category theory, making this book a valuable resource for researchers in applied mathematics and engineering, particularly those focused on theoretical foundations of modelling.
Beyond Spacetime
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Author : Nick Huggett
language : en
Publisher: Cambridge University Press
Release Date : 2020-05-14
Beyond Spacetime written by Nick Huggett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-14 with Philosophy categories.
A collection of essays discussing the philosophy and foundations of quantum gravity. Written by leading philosophers and physicists in the field, chapters cover the important conceptual questions in the search for a quantum theory of gravity, and the current state of understanding among philosophers and physicists.
The Logic In Philosophy Of Science
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Author : Hans Halvorson
language : en
Publisher: Cambridge University Press
Release Date : 2019-07-11
The Logic In Philosophy Of Science written by Hans Halvorson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-11 with Philosophy categories.
Reconsiders the role of formal logic in the analytic approach to philosophy, using cutting-edge mathematical techniques to elucidate twentieth-century debates.
Philosophy Beyond Spacetime
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Author : Christian Wüthrich
language : en
Publisher: Oxford University Press
Release Date : 2021
Philosophy Beyond Spacetime written by Christian Wüthrich 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 2021 with Philosophy categories.
Philosophy Beyond Spacetime assesses the state of play in the philosophy of quantum gravity. Research in this field aims at a unified theory in which quantum matter is related dynamically to relativistic spacetime. This volume highlights the conceptual questions involved, showing how physics and metaphysics can illuminate each other.
Modal Homotopy Type Theory
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Author : David Corfield
language : en
Publisher: Oxford University Press
Release Date : 2020-02-06
Modal Homotopy Type Theory written by David Corfield 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 2020-02-06 with Philosophy categories.
"The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics. The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.