Stewart Shapiro’s Philosophy of Mathematics [Book Review]

Philosophy and Phenomenological Research 65 (2):467–475 (2002)
  Copy   BIBTEX

Abstract

Two slogans define structuralism: contemporary mathematics studies structures; mathematical objects are places in those structures. Shapiro’s version of structuralism posits abstract objects of three sorts. A system is “a collection of objects with certain relations” between these objects. “An extended family is a system of people with blood and marital relationships.” A baseball defense, e.g., the Yankee’s defense in the first game of the 1999 World Series, is a also a system, “a collection of people with on-field spatial and ‘defensive-role’ relations”. “A structure is the abstract form of a system” ; it consists of “a collection of places [sometimes called positions or offices] and a finite collection of functions and relations on these places”.

Author's Profile

Harold Hodes
Cornell University

Analytics

Added to PP
2009-01-28

Downloads
155 (#71,343)

6 months
75 (#51,100)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?