Mathematical Structuralism
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| Author | : Geoffrey Hellman |
| Publisher | : Cambridge University Press |
| Total Pages | : 167 |
| Release | : 2018-11-29 |
| Genre | : Science |
| ISBN | : 110863074X |
The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the Element considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives.
| Author | : Erich H. Reck |
| Publisher | : Oxford University Press |
| Total Pages | : 469 |
| Release | : 2020 |
| Genre | : Mathematics |
| ISBN | : 0190641223 |
This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.
| Author | : Luca Incurvati |
| Publisher | : Cambridge University Press |
| Total Pages | : 255 |
| Release | : 2020-01-23 |
| Genre | : Science |
| ISBN | : 1108758355 |
Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.
| Author | : Mirja Hartimo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 244 |
| Release | : 2010-03-11 |
| Genre | : Philosophy |
| ISBN | : 9048137292 |
During Edmund Husserl’s lifetime, modern logic and mathematics rapidly developed toward their current outlook and Husserl’s writings can be fruitfully compared and contrasted with both 19th century figures (Boole, Schröder, Weierstrass) as well as the 20th century characters (Heyting, Zermelo, Gödel). Besides the more historical studies, the internal ones on Husserl alone and the external ones attempting to clarify his role in the more general context of the developing mathematics and logic, Husserl’s phenomenology offers also a systematically rich but little researched area of investigation. This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics. It gathers the contributions of the main scholars of this emerging field into one publication for the first time. Combining both historical and systematic studies from various angles, the volume charts answers to the question "What kind of philosophy of mathematics is phenomenology?"
| Author | : Joel David Hamkins |
| Publisher | : MIT Press |
| Total Pages | : 350 |
| Release | : 2021-03-09 |
| Genre | : Mathematics |
| ISBN | : 0262542234 |
An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
| Author | : Alberto Peruzzi |
| Publisher | : Springer Nature |
| Total Pages | : 191 |
| Release | : 2020-09-14 |
| Genre | : Philosophy |
| ISBN | : 3030518213 |
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.
| Author | : Charles S. Chihara |
| Publisher | : Clarendon Press |
| Total Pages | : 298 |
| Release | : 1990-04-12 |
| Genre | : Mathematics |
| ISBN | : 0191520004 |
This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach in an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.
| Author | : Leon Horsten |
| Publisher | : Cambridge University Press |
| Total Pages | : 251 |
| Release | : 2019-06-13 |
| Genre | : History |
| ISBN | : 110703941X |
Develops and defends a new metaphysical and logical theory of arbitrary objects that will reinvigorate the philosophy of mathematics.
| Author | : Oxford University Press |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 27 |
| Release | : 2010-06-01 |
| Genre | : Philosophy |
| ISBN | : 0199808937 |
This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.
| Author | : Matthias Schirn |
| Publisher | : Oxford University Press |
| Total Pages | : 668 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 9780198236542 |
Representing the state of the art in the field of the philosophy of mathematics, this collection of 20 essays deals with fundamental issues, ranging from the nature of mathematical knowledge to sets and natural 'number'.
