03369nam 2200565Ia 450 991077753420332120230421045028.01-280-45096-797866104509610-19-802545-91-4237-6518-4(CKB)1000000000460559(StDuBDS)AH24085063(SSID)ssj0000221045(PQKBManifestationID)12059909(PQKBTitleCode)TC0000221045(PQKBWorkID)10160222(PQKB)10330997(MiAaPQ)EBC3052385(Au-PeEL)EBL3052385(CaPaEBR)ebr10212170(CaONFJC)MIL45096(OCoLC)922953120(EXLCZ)99100000000046055919960709d1997 uy 0engur|||||||||||txtccrPhilosophy of mathematics[electronic resource] structure and ontology /Stewart ShapiroOxford Oxford University Press19971 online resource (x, 279 p.) Originally published: 1997.0-19-509452-2 Includes bibliographical references and index.This text argues that both realist and anti-realist accounts of mathematics are problematic. It articulates a structuralist approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers.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.MathematicsPhilosophyMathematicsMathematicsPhilosophy.Mathematics.510/.1Shapiro Stewart1951-447519MiAaPQMiAaPQMiAaPQBOOK9910777534203321Philosophy of mathematics105548UNINA