ISBN: 9780195139303

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 attr… More...

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. New Textbooks>Trade Paperback>Science>Mathematics>Mathematics, Oxford University Press Core >1 >T<

ISBN: 9780195139303

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 attr… More...

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. New Textbooks>Trade Paperback>Science>Mathematics>Mathematics, Oxford University Press Core >1 >T<

1997, ISBN: 9780195139303

Oxford University Press USA, Taschenbuch, 296 Seiten, Publiziert: 1997-01-01T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: 9780195139303, 0.46 kg, Verkaufsrang: 1530897, Logik, Philosop… More...

Oxford University Press USA, Taschenbuch, 296 Seiten, Publiziert: 1997-01-01T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: 9780195139303, 0.46 kg, Verkaufsrang: 1530897, Logik, Philosophie, Sozialwissenschaft, Kategorien, Bücher, Ingenieurwissenschaft & Technik, Naturwissenschaften & Technik, Mathematik, Verschiedenes, Taschenbücher, Fremdsprachige Bücher, Featured Categories, Englische Bücher, 7c9a6c79-19ea-4dea-90da-d7d47042d341_2301, 7c9a6c79-19ea-4dea-90da-d7d47042d341_0, Arborist Merchandising Root, Oxford University Press USA, 1997<

2000, ISBN: 9780195139303

[ED: Kartoniert / Broschiert], [PU: OXFORD UNIV PR], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. A structuralist approach to mathemati… More...

[ED: Kartoniert / Broschiert], [PU: OXFORD UNIV PR], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. A structuralist approach to mathematical theory in which Shapiro argues that both realist and anti-realist accounts of mathematics are problematic . He claims t, DE, [SC: 0.00], Neuware, gewerbliches Angebot, Softcover, 296, [GW: 431g], Banküberweisung, PayPal, [CT: Naturwissenschaft/Mathematik / Sonstiges - Naturwissenschaften]<