Landry E. (ed.) Categories for the Working Philosopher

Oxford: Oxford University Press, 2018. — 528 p.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.Notes on Contributors.
The Roles of Set Theories in Mathematics.
Reviving the Philosophy of Geometry.
Homotopy Type Theory: A Synthetic Approach to Higher Equalities.
Structuralism, Invariance, and Univalence.
Category Theory and Foundations.
Canonical Maps.
Categorical Logic and Model Theory.
Unfolding FOLDS: A Foundational Framework for Abstract Mathematical Concepts.
Categories and Modalities.
Proof Theory of the Cut Rule.
Contextuality: At the Borders of Paradox.
Categorical Quantum Mechanics I: Causal Quantum Processes.
Category Theory and the Foundations of Classical Space–Time Theories.
Six-Dimensional Lorentz Category.
Applications of Categories to Biology and Cognition.
Categories as Mathematical Models.
Categories of Scientific Theories.
Structural Realism and Category Mistakes.
Name Index.
Subject Index.Качество: True PDF