LEADER 03369nam 2200565Ia 450 001 9910777534203321 005 20230421045028.0 010 $a1-280-45096-7 010 $a9786610450961 010 $a0-19-802545-9 010 $a1-4237-6518-4 035 $a(CKB)1000000000460559 035 $a(StDuBDS)AH24085063 035 $a(SSID)ssj0000221045 035 $a(PQKBManifestationID)12059909 035 $a(PQKBTitleCode)TC0000221045 035 $a(PQKBWorkID)10160222 035 $a(PQKB)10330997 035 $a(MiAaPQ)EBC3052385 035 $a(Au-PeEL)EBL3052385 035 $a(CaPaEBR)ebr10212170 035 $a(CaONFJC)MIL45096 035 $a(OCoLC)922953120 035 $a(EXLCZ)991000000000460559 100 $a19960709d1997 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPhilosophy of mathematics$b[electronic resource] $estructure and ontology /$fStewart Shapiro 210 $aOxford $cOxford University Press$d1997 215 $a1 online resource (x, 279 p.) 300 $aOriginally published: 1997. 311 $a0-19-509452-2 320 $aIncludes bibliographical references and index. 330 8 $aThis text argues that both realist and anti-realist accounts of mathematics are problematic. It articulates a structuralist approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers.$bDo 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. 606 $aMathematics$xPhilosophy 606 $aMathematics 615 0$aMathematics$xPhilosophy. 615 0$aMathematics. 676 $a510/.1 700 $aShapiro$b Stewart$f1951-$0447519 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910777534203321 996 $aPhilosophy of mathematics$9105548 997 $aUNINA