Mathematical structuralism
by Hellman, Geoffrey Paul, philosophe des mathématiques)
"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 they encounter, Geoffrey Hellman and Steward Shapiro consider three further perspectives formulated by logicians and philosophers of mathem…
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- Full title :Mathematical structuralism / Geoffrey Hellman, Stewart Shapiro.
Summary
"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 they encounter, Geoffrey Hellman and Steward Shapiro consider 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"--Back cover.
Read More ↓Edition Statements
- Publication Date:copyright 2019
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:copyright 2019
The Physical Object
- Description:1 vol. (92 p.) : : couv. ill. en coul. ; : 23 cm.
Edition Identifiers
- ISBN:9781108456432 (broché), 110845643X, 9781108697286, 1108697283
- oclc:on1237564891
- LC Classification:QA8.4
- Dewey Decimal:510.1
Table of Contents
Introduction -- Historical background -- Set-theoretic structuralism -- Category theory as a framework for mathematical structuralism -- Structures as Sui Generis structuralism -- The modal-structural perspective -- Modal set-theoretic structuralism
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