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Categories for the Working Philosopher

Author: Elaine M. Landry

Publisher: Oxford University Press

Published: 2017

Total Pages: 486

ISBN-13: 019874899X

This is the first book on category theory for a broad philosophical readership. There is no other discussion of category theory comparable in its scope. It is designed to show the interest and significant of category theory for philosophers working in a range of areas, including mathematics, proof theory, computer science, ontology, physics, biology, cognition, mathematical modelling, the structure of scientific theories, and the structure of the world. Moreover, it does 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 fields, in a way that builds on the concepts already familiar to philosophers working in these areas. The book is split into two halves. The 'pure' chapters focus on the use of category theory for mathematical, foundational, and logical purposes, while the 'applied' chapters consider the use of category theory for representational purposes, investigating category theory as a framework for theories of physics and biology, for mathematical modelling more generally, and for the structure of scientific theories. Book jacket.

Diagrammatic Immanence

Author: Rocco Gangle

Publisher: Edinburgh University Press

Published: 2016-08-18

Total Pages: 264

ISBN-13: 1474404200

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A renewal of immanent metaphysics through diagrammatic methods and the tools of category theorySpinoza, Peirce and Deleuze are, in different ways, philosophers of immanence. Rocco Gangle addresses the methodological questions raised by a commitment to immanence in terms of how diagrams may be used both as tools and as objects of philosophical investigation. He integrates insights from Spinozist metaphysics, Peircean semiotics and Deleuzes philosophy of difference in conjunction with the formal operations of category theory. Category theory reveals deep structural connections among logic, topology and a variety of different areas of mathematics, and it provides constructive and rigorous concepts for investigating how diagrams work. Gangle introduces the methods of category theory from a philosophical and diagrammatic perspective, allowing philosophers with little or no mathematical training to come to grips with this important field. This coordination of immanent metaphysics, diagrammatic method and category theoretical mathematics opens a new horizon for contemporary thought.

Categories for the Working Mathematician

Author: Saunders Mac Lane

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 320

ISBN-13: 1475747217

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An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

Categories, Types, and Structures

Author: Andrea Asperti

Publisher: MIT Press (MA)

Published: 1991

Total Pages: 330

ISBN-13:

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Category theory is a mathematical subject whose importance in several areas of computer science, most notably the semantics of programming languages and the design of programmes using abstract data types, is widely acknowledged. This book introduces category theory at a level appropriate for computer scientists and provides practical examples in the context of programming language design.

Conceptual Mathematics

Author: F. William Lawvere

Publisher: Cambridge University Press

Published: 2009-07-30

Total Pages: 409

ISBN-13: 0521894859

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This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.

Categories We Live by

Author: Ásta

Publisher: Oxford University Press

Published: 2018

Total Pages: 161

ISBN-13: 0190256796

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We are women, we are men. We are refugees, single mothers, people with disabilities, and queers. We belong to social categories and they frame our actions, self-understanding, and opportunities. But what are social categories? How are they created and sustained? How does one come to belong to them? Ásta approaches these questions through analytic feminist metaphysics. Her theory of social categories centers on an answer to the question: what is it for a feature of an individual to be socially meaningful? In a careful, probing investigation, she reveals how social categories are created and sustained and demonstrates their tendency to oppress through examples from current events. To this end, she offers an account of just what social construction is and how it works in a range of examples that problematize the categories of sex, gender, and race in particular. The main idea is that social categories are conferred upon people. Ásta introduces a 'conferralist' framework in order to articulate a theory of social meaning, social construction, and most importantly, of the construction of sex, gender, race, disability, and other social categories.

The Discipline of Organizing: Professional Edition

Author: Robert J. Glushko

Publisher: "O'Reilly Media, Inc."

Published: 2014-08-25

Total Pages: 743

ISBN-13: 1491911719

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Note about this ebook: This ebook exploits many advanced capabilities with images, hypertext, and interactivity and is optimized for EPUB3-compliant book readers, especially Apple's iBooks and browser plugins. These features may not work on all ebook readers. We organize things. We organize information, information about things, and information about information. Organizing is a fundamental issue in many professional fields, but these fields have only limited agreement in how they approach problems of organizing and in what they seek as their solutions. The Discipline of Organizing synthesizes insights from library science, information science, computer science, cognitive science, systems analysis, business, and other disciplines to create an Organizing System for understanding organizing. This framework is robust and forward-looking, enabling effective sharing of insights and design patterns between disciplines that weren’t possible before. The Professional Edition includes new and revised content about the active resources of the "Internet of Things," and how the field of Information Architecture can be viewed as a subset of the discipline of organizing. You’ll find: 600 tagged endnotes that connect to one or more of the contributing disciplines Nearly 60 new pictures and illustrations Links to cross-references and external citations Interactive study guides to test on key points The Professional Edition is ideal for practitioners and as a primary or supplemental text for graduate courses on information organization, content and knowledge management, and digital collections. FOR INSTRUCTORS: Supplemental materials (lecture notes, assignments, exams, etc.) are available at http://disciplineoforganizing.org. FOR STUDENTS: Make sure this is the edition you want to buy. There's a newer one and maybe your instructor has adopted that one instead.

The Philosopher

Author: Justin E. H. Smith

Publisher: Princeton University Press

Published: 2017-10-31

Total Pages: 286

ISBN-13: 0691178461

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How the role of the philosopher has changed over time and across cultures—and what it reveals about philosophy today What would the global history of philosophy look like if it were told not as a story of ideas but as a series of job descriptions—ones that might have been used to fill the position of philosopher at different times and places over the past 2,500 years? The Philosopher does just that, providing a new way of looking at the history of philosophy by bringing to life six kinds of figures who have occupied the role of philosopher in a wide range of societies around the world over the millennia—the Natural Philosopher, the Sage, the Gadfly, the Ascetic, the Mandarin, and the Courtier. The result is at once an unconventional introduction to the global history of philosophy and an original exploration of what philosophy has been—and perhaps could be again. By uncovering forgotten or neglected philosophical job descriptions, the book reveals that philosophy is a universal activity, much broader—and more gender inclusive—than we normally think today. In doing so, The Philosopher challenges us to reconsider our idea of what philosophers can do and what counts as philosophy.

Aristotle and the Arabic Tradition

Author: Ahmed Alwishah

Publisher: Cambridge University Press

Published: 2015-09-17

Total Pages: 277

ISBN-13: 1107101735

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Examines Aristotle's vast influence upon the medieval Arabic philosophical tradition and includes contributions from every discipline within his corpus.

Thinking about Mathematics

Author: Stewart Shapiro

Publisher: OUP Oxford

Published: 2000-07-13

Total Pages: 323

ISBN-13: 0192893068

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Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.