Mathematical Structuralism

Nonfiction, Science & Nature, Science, Other Sciences, Philosophy & Social Aspects
Cover of the book Mathematical Structuralism by Geoffrey Hellman, Stewart Shapiro, Cambridge University Press
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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.

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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.

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