Philosophy of Mathematics: Structure and Ontology

Oxford, England: Oxford University Press USA (1997)
  Copy   BIBTEX

Abstract

Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

Categories

Keywords

Reprint years

2000

Call number

QA8.4.S533 1997

ISBN(s)

9780195094527   0195094522   0195139305   9780195139303   9780199833658
View all bargains

Buy this book

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,202

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Chapters

Mathematics and Its Philosophy

This chapter deals with the relationship between the practice of mathematics and the philosophy of mathematics. The philosopher of mathematics is, or should be, concerned with mathematics as it is practiced, and so I demur from “philosophy first”, the view that philosophical considerations... see more

Epistemology and Reference

This chapter deals with matters of epistemology and reference, resolving the well‐known problems with realism or platonism due to Paul Benacerraf. A series of speculative epistemic strategies is presented, to cover the various mathematical structures. Small, finite structures are apprehend... see more

Similar books and articles

Philosophy of Mathematics.Stewart Shapiro - 2003 - In Peter Clark & Katherine Hawley (eds.), Philosophy of Science Today. Oxford University Press UK.
Philosophy of mathematics: structure and ontology.Stewart Shapiro - 1997 - New York: Oxford University Press.
Stewart Shapiro. Introduction—intensional mathematics and constructive mathematics. Intensional mathematics, edited by Stewart Shapiro, Studies in logic and the foundations of mathematics, vol. 113, North-Holland, Amsterdam, New York, and Oxford, 1985, pp. 1–10. - Stewart Shapiro. Epistemic and intuitionistic arithmetic. Intensional mathematics, edited by Stewart Shapiro, Studies in logic and the foundations of mathematics, pp. 11–46. - John Myhill. Intensional set theory. Intensional mathematics, edited by Stewart Shapiro, Studies in logic and the foundations of mathematics, pp. 47–61. - Nicolas D. Goodman. A genuinely intensional set theory. Intensional mathematics, edited by Stewart Shapiro, Studies in logic and the foundations of mathematics, pp. 63–79. - Andrej Ščedrov. Extending Godel's modal interpretation to type theory and set theory. Intensional mathematics, edited by Stewart Shapiro, Studies in logic and the foundations of mathematics, pp. 81–119. - Robert C. Flagg. Church's. [REVIEW]Craig A. Smorynski - 1991 - Journal of Symbolic Logic 56 (4):1496-1499.
Towards a Philosophy of Applied Mathematics.Christopher Pincock - 2009 - In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan.
Curves in Gödel-Space: Towards a Structuralist Ontology of Mathematical Signs.Martin Pleitz - 2010 - Studia Logica 96 (2):193-218.
Anti-Realist Classical Logic and Realist Mathematics.Greg Restall - unknown
Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-mathematics.Stewart Shapiro - 2005 - Philosophia Mathematica 13 (1):61-77.
Mathematics and reality.Stewart Shapiro - 1983 - Philosophy of Science 50 (4):523-548.
Life on the Ship of Neurath: Mathematics in the Philosophy of Mathematics.Stewart Shapiro - 2012 - Croatian Journal of Philosophy 26 (2):11--27.
Mathematics as a science of patterns.Michael David Resnik - 1997 - New York ;: Oxford University Press.
Structuralism and Meta-Mathematics.Simon Friederich - 2010 - Erkenntnis 73 (1):67 - 81.
Thinking about mathematics: the philosophy of mathematics.Stewart Shapiro - 2000 - New York: Oxford University Press.
Poincaré's conception of the objectivity of mathematics.Janet Folina - 1994 - Philosophia Mathematica 2 (3):202-227.
Foundations of Mathematics: Metaphysics, Epistemology, Structure.Stewart Shapiro - 2004 - Philosophical Quarterly 54 (214):16 - 37.
Structure and identity.Stewart Shapiro - 2006 - In Fraser MacBride (ed.), Identity and Modality. Oxford University Press. pp. 34--69.

Analytics

Added to PP
2019-05-26

Downloads
13 (#973,701)

6 months
8 (#283,518)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Stewart Shapiro
Ohio State University

Citations of this work

What is a (social) structural explanation?Sally Haslanger - 2016 - Philosophical Studies 173 (1):113-130.
Models and fiction.Roman Frigg - 2010 - Synthese 172 (2):251-268.
Grounding-mechanical explanation.Kelly Trogdon - 2018 - Philosophical Studies 175 (6):1289-1309.

View all 149 citations / Add more citations

References found in this work

No references found.

Add more references