Philosophy of Mathematics: Structure and Ontology

Oxford University Press (1997)
Abstract
Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.
Keywords Mathematics Philosophy
Categories (categorize this paper)
Reprint years 2000
Buy the book $34.89 used (58% off)   $82.00 direct from Amazon   $149.85 new    Amazon page
Call number QA8.4.S533 1997
ISBN(s) 0195094522   9780195094527     9780195139303
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 27,208
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Models and Fiction.Roman Frigg - 2009 - Synthese 172 (2):251-268.
Contingentism in Metaphysics.Kristie Miller - 2010 - Philosophy Compass 5 (11):965-977.

View all 101 citations / Add more citations

Similar books and articles
Mathematics and Philosophy of Mathematics.Stewart Shapiro - 1994 - Philosophia Mathematica 2 (2):148-160.
Mathematics as a Science of Patterns.D. Resnik Michael - 1997 - New York ;Oxford University Press.
Mathematics and Reality.Stewart Shapiro - 1983 - Philosophy of Science 50 (4):523-548.
Towards a Philosophy of Applied Mathematics.Christopher Pincock - 2009 - In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan.
Structure and Identity.Stewart Shapiro - 2006 - In Fraser MacBride (ed.), Identity and Modality. Oxford University Press. pp. 34--69.
Structuralism and Meta-Mathematics.Simon Friederich - 2010 - Erkenntnis 73 (1):67 - 81.

Monthly downloads

Added to index

2009-01-28

Total downloads

89 ( #57,861 of 2,164,550 )

Recent downloads (6 months)

10 ( #33,392 of 2,164,550 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums