Mathematical Structuralism
Nonfiction, Science & Nature, Science, Other Sciences, Philosophy & Social Aspects
| Author: | Geoffrey Hellman, Stewart Shapiro | ISBN: | 9781108630740 |
| Publisher: | Cambridge University Press | Publication: | November 29, 2018 |
| Imprint: | Cambridge University Press | Language: | English |
| Author: | Geoffrey Hellman, Stewart Shapiro |
| ISBN: | 9781108630740 |
| Publisher: | Cambridge University Press |
| Publication: | November 29, 2018 |
| Imprint: | Cambridge University Press |
| Language: | English |
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 book 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.
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 book 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.
