David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Oxford University Press (1997)
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.
|Categories||categorize this paper)|
|Buy the book||$21.98 used (72% off) $76.37 new (7% off) $82.00 direct from Amazon Amazon page|
|Call number||QA8.4.S533 1997|
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.
Citations of this work BETA
N. Ángel Pinillos (2011). Coreference and Meaning. Philosophical Studies 154 (2):301-324.
Roman Frigg (2010). Models and Fiction. Synthese 172 (2):251 - 268.
Otávio Bueno (2011). An Inferential Conception of the Application of Mathematics. Noûs 45 (2):345 - 374.
Karin Katz & Mikhail Katz (2012). A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography. Foundations of Science 17 (1):51-89.
Steven French (2010). The Interdependence of Structure, Objects and Dependence. Synthese 175 (S1):89 - 109.
Similar books and articles
Stewart Shapiro (2004). Foundations of Mathematics: Metaphysics, Epistemology, Structure. Philosophical Quarterly 54 (214):16 - 37.
Simon Friederich (2010). Structuralism and Meta-Mathematics. Erkenntnis 73 (1):67 - 81.
Stewart Shapiro (2006). Structure and Identity. In Fraser MacBride (ed.), Identity and Modality. Oxford University Press 34--69.
Christopher Pincock (2009). Towards a Philosophy of Applied Mathematics. In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave Macmillan
Stewart Shapiro (1983). Mathematics and Reality. Philosophy of Science 50 (4):523-548.
Stewart Shapiro (2000). Thinking About Mathematics: The Philosophy of Mathematics. Oxford University Press.
Michael D. Resnik (1997). Mathematics as a Science of Patterns. New York ;Oxford University Press.
Stewart Shapiro (2005). Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-Mathematics. Philosophia Mathematica 13 (1):61-77.
Stewart Shapiro (1994). Mathematics and Philosophy of Mathematics. Philosophia Mathematica 2 (2):148-160.
O. Linnebo (2003). Stewart Shapiro. Philosophy of Mathematics: Structure and Ontology. Philosophia Mathematica 11 (1):92-103.
Added to index2009-01-28
Total downloads52 ( #65,834 of 1,726,249 )
Recent downloads (6 months)8 ( #84,767 of 1,726,249 )
How can I increase my downloads?