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.|
|Categories||categorize this paper)|
|Buy the book||$50.00 used (33% off) $63.12 new (15% off) $70.30 direct from Amazon (5% off) Amazon page|
|Call number||QA8.4.S533 1997|
|Through your library||Configure|
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.
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.
Added to index2009-01-28
Total downloads32 ( #43,378 of 722,745 )
Recent downloads (6 months)1 ( #60,247 of 722,745 )
How can I increase my downloads?