Philosophy of Mathematics: Structure and Ontology

Philosophy of Mathematics: Structure and Ontology

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.
Country USA
Brand Oxford University Press
Manufacturer Oxford University Press
Binding Paperback
ItemPartNumber 9780195139303
UnitCount 1
EANs 9780195139303
ReleaseDate 0000-00-00

Country	USA
Brand	Oxford University Press
Manufacturer	Oxford University Press
Binding	Paperback
ItemPartNumber	9780195139303
UnitCount	1
EANs	9780195139303
ReleaseDate	0000-00-00

Philosophy of Mathematics: Structure and Ontology

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