Download or read book Categories for the Working Philosopher written by Elaine M. Landry and published by Oxford University Press. This book was released on 2017 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Categories for the Working Philosopher written by Elaine Landry and published by Oxford University Press. This book was released on 2017-11-17 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Categories for the Working Philosopher written by Elaine Landry and published by Oxford University Press, USA. This book was released on 2023-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Diagrammatic Immanence written by Rocco Gangle and published by Edinburgh University Press. This book was released on 2016-08-18 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book From a Geometrical Point of View written by Jean-Pierre Marquis and published by Springer Science & Business Media. This book was released on 2008-11-20 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein’s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane’s work in the early 1940’s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics. From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.
Download or read book Categories Types and Structures written by Andrea Asperti and published by MIT Press (MA). This book was released on 1991 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Categories We Live by written by Ásta and published by Oxford University Press. This book was released on 2018 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Conceptual Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2009-07-30 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.
Download or read book Category Mistakes written by Ofra Magidor and published by Oxford Philosophical Monograph. This book was released on 2013-07-25 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category mistakes are sentences such as "Green ideas sleep furiously", "Saturday is in bed", and "The theory of relativity is eating breakfast". Such sentences strike most speakers as highly infelicitous but it is a challenge to explain precisely why they are so. Ofra Magidor addresses this challenge, while providing a comprehensive discussion of the various treatments of category mistakes in both philosophy of language and linguistics. The phenomenon of category mistakes is particularly interesting to both these fields because a plausible case can be (and has been) made for explaining it in terms of syntax, semantics, and pragmatics - making it a fruitful case for exploring the relations between and nature of these three fundamental realms of language. Category Mistakes follows this division. After an introduction which explains the aims and motivations for the project and provides a brief historical survey of the (modern) treatment of category mistakes in each of philosophy, linguistics, and computer science, Magidor discusses four approaches in turn: first, the syntactic approach, which maintains that category mistakes are syntactically ill-formed; then two semantic approaches, though ones that appeal to different semantic facets: the meaninglessness view, which maintains that category mistakes are meaningless, and the MBT view, according to which category mistakes are meaningful but truth-valueless; and finally the pragmatic approach, according to which category mistakes are syntactically well-formed, meaningful, truth-valued but nevertheless pragmatically inappropriate. Magidor argues that the first three approaches ought to be rejected, and in the final chapter addresses the main challenge by developing and defending a particular version of the pragmatic approach: a presuppositional account of category mistakes.
Download or read book An Introduction to the Language of Category Theory written by Steven Roman and published by Birkhäuser. This book was released on 2017-01-05 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in university-level mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, step-by-step manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. The first chapter of the book introduces the definitions of category and functor and discusses diagrams,duality, initial and terminal objects, special types of morphisms, and some special types of categories,particularly comma categories and hom-set categories. Chapter 2 is devoted to functors and naturaltransformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions – products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts.
Download or read book Making and Breaking Mathematical Sense written by Roi Wagner and published by Princeton University Press. This book was released on 2017-01-10 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Thinking about Mathematics written by Stewart Shapiro and published by OUP Oxford. This book was released on 2000-07-13 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Aristotle s Theory of Bodies written by Christian Pfeiffer and published by Oxford University Press. This book was released on 2018-07-12 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Christian Pfeiffer explores an important, but neglected topic in Aristotle's theoretical philosophy: the theory of bodies. A body is a three-dimensionally extended and continuous magnitude bounded by surfaces. This notion is distinct from the notion of a perceptible or physical substance. Substances have bodies, that is to say, they are extended, their parts are continuous with each other and they have boundaries, which demarcate them from their surroundings. Pfeiffer argues that body, thus understood, has a pivotal role in Aristotle's natural philosophy. A theory of body is a presupposed in, e.g., Aristotle's account of the infinite, place, or action and passion, because their being bodies explains why things have a location or how they can act upon each other. The notion of body can be ranked among the central concepts for natural science which are discussed in Physics III-IV. The book is the first comprehensive and rigorous account of the features substances have in virtue of being bodies. It provides an analysis of the concept of three-dimensional magnitude and related notions like boundary, extension, contact, continuity, often comparing it to modern conceptions of it. Both the structural features and the ontological status of body is discussed. This makes it significant for scholars working on contemporary metaphysics and mereology because the concept of a material object is intimately tied to its spatial or topological properties.
Download or read book Philosophy of Nature written by Paul K. Feyerabend and published by John Wiley & Sons. This book was released on 2016-09-26 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philosopher, physicist, and anarchist Paul Feyerabend was one of the most unconventional scholars of his time. His book Against Method has become a modern classic. Yet it is not well known that Feyerabend spent many years working on a philosophy of nature that was intended to comprise three volumes covering the period from the earliest traces of stone age cave paintings to the atomic physics of the 20th century – a project that, as he conveyed in a letter to Imre Lakatos, almost drove him nuts: “Damn the ,Naturphilosophie.” The book’s manuscript was long believed to have been lost. Recently, however, a typescript constituting the first volume of the project was unexpectedly discovered at the University of Konstanz. In this volume Feyerabend explores the significance of myths for the early period of natural philosophy, as well as the transition from Homer’s “aggregate universe” to Parmenides’ uniform ontology. He focuses on the rise of rationalism in Greek antiquity, which he considers a disastrous development, and the associated separation of man from nature. Thus Feyerabend explores the prehistory of science in his familiar polemical and extraordinarily learned manner. The volume contains numerous pictures and drawings by Feyerabend himself. It also contains hitherto unpublished biographical material that will help to round up our overall image of one of the most influential radical philosophers of the twentieth century.
Download or read book Concepts and Categories written by Isaiah Berlin and published by Random House. This book was released on 2012-08-31 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although Isaiah Berlin liked to say that he left philosophy for the history of ideas after the Second World War, there is a decided continuity between his more purely philosophical writings, most of which are collected in this volume, and the more historical work for which he is better known. Included here are Berlin's early arguments against logical positivism and later essays which more evidently reflect his life-long interest in political theory, intellectual history and the philosophy of history. In two related pieces he gives his view on the philosopher's task, to uncover the various models - the concepts and categories - that we bring to our experience, and that help to form it. In his own words 'The goal of philosophy is always the same, to assist men to understand themselves and thus operate in the open, and not wildly, in the dark.'
Download or read book Introduction to Mathematical Philosophy written by Bertrand Russell and published by . This book was released on 1920 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
