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Mathematical structuralism / Geoffrey Hellman, Stewart Shapiro.

By: Contributor(s): Material type: TextTextSeries: Elements in the philosophy of mathematics | Cambridge elementsPublisher: Cambridge : Cambridge University Press, 2019Description: 1 online resource (92 pages) : digital, PDF file(s)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781108582933 (ebook)
Subject(s): Additional physical formats: Print version: : No titleDDC classification:
  • 510.1 23
LOC classification:
  • QA8.4 .H45 2019
Online resources: 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, 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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Title from publisher's bibliographic system (viewed on 11 Dec 2018).

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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