Relativism in Set Theory and Mathematics

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

According to the mathematical relativist, mathematical statements, if true, are relatively true only - that is, they are true relative to (i) the specifi cation of concepts and theories that characterize the relevant mathematical domain, (ii) the mathematical framework in which such mathematical truths are formulated, and (iii) the logic that is employed in the derivation of such truths. This chapter surveys mathematical relativism and its signifi cance. First, it clarifi es what mathematical relativism is not. It then examines a formulation of the view in which conceptual, structural, and logical relativity play a central role, but which still preserves the objectivity of mathematics. The implications of mathematical relativism for the ontology of mathematics are then considered. While some forms of Platonism and nominalism in mathematics are compatible with mathematical relativism, others are not. Finally, some remarks about the signifi cance of mathematical relativism conclude the chapter.

Original languageEnglish (US)
Title of host publicationA Companion to Relativism
PublisherWiley-Blackwell
Pages553-568
Number of pages16
ISBN (Print)9781405190213
DOIs
StatePublished - Apr 20 2011

Fingerprint

Relativism
Set Theory
Mathematics
Signifier
Logic
Platonism
Ontology
Mathematical Truth
Relativity
Objectivity
Nominalism
Relativist

Keywords

  • "the Russell set exists"
  • Conceptual, Structural and Logical Relativity in Mathematics
  • Mathematical Relativism and Mathematical Objectivity
  • Mathematical Relativism and the Ontology of Mathematics: Nominalism
  • Mathematical Relativism and the Ontology of Mathematics: Platonism
  • Mathematical relativism is the view according to which every mathematical
  • Mathematical Relativism: Does Everything Go In Mathematics?
  • Relativism in set theory and mathematics
  • The Significance of Mathematical Relativism
  • Typically, the set theory one considers depends on the underlying

ASJC Scopus subject areas

  • Arts and Humanities(all)

Cite this

Bueno, O. (2011). Relativism in Set Theory and Mathematics. In A Companion to Relativism (pp. 553-568). Wiley-Blackwell. https://doi.org/10.1002/9781444392494.ch28

Relativism in Set Theory and Mathematics. / Bueno, Otavio.

A Companion to Relativism. Wiley-Blackwell, 2011. p. 553-568.

Research output: Chapter in Book/Report/Conference proceedingChapter

Bueno, O 2011, Relativism in Set Theory and Mathematics. in A Companion to Relativism. Wiley-Blackwell, pp. 553-568. https://doi.org/10.1002/9781444392494.ch28
Bueno O. Relativism in Set Theory and Mathematics. In A Companion to Relativism. Wiley-Blackwell. 2011. p. 553-568 https://doi.org/10.1002/9781444392494.ch28
Bueno, Otavio. / Relativism in Set Theory and Mathematics. A Companion to Relativism. Wiley-Blackwell, 2011. pp. 553-568
@inbook{6fd415bd21ed40adb2a55c3aaf59b0fc,
title = "Relativism in Set Theory and Mathematics",
abstract = "According to the mathematical relativist, mathematical statements, if true, are relatively true only - that is, they are true relative to (i) the specifi cation of concepts and theories that characterize the relevant mathematical domain, (ii) the mathematical framework in which such mathematical truths are formulated, and (iii) the logic that is employed in the derivation of such truths. This chapter surveys mathematical relativism and its signifi cance. First, it clarifi es what mathematical relativism is not. It then examines a formulation of the view in which conceptual, structural, and logical relativity play a central role, but which still preserves the objectivity of mathematics. The implications of mathematical relativism for the ontology of mathematics are then considered. While some forms of Platonism and nominalism in mathematics are compatible with mathematical relativism, others are not. Finally, some remarks about the signifi cance of mathematical relativism conclude the chapter.",
keywords = "{"}the Russell set exists{"}, Conceptual, Structural and Logical Relativity in Mathematics, Mathematical Relativism and Mathematical Objectivity, Mathematical Relativism and the Ontology of Mathematics: Nominalism, Mathematical Relativism and the Ontology of Mathematics: Platonism, Mathematical relativism is the view according to which every mathematical, Mathematical Relativism: Does Everything Go In Mathematics?, Relativism in set theory and mathematics, The Significance of Mathematical Relativism, Typically, the set theory one considers depends on the underlying",
author = "Otavio Bueno",
year = "2011",
month = "4",
day = "20",
doi = "10.1002/9781444392494.ch28",
language = "English (US)",
isbn = "9781405190213",
pages = "553--568",
booktitle = "A Companion to Relativism",
publisher = "Wiley-Blackwell",

}

TY - CHAP

T1 - Relativism in Set Theory and Mathematics

AU - Bueno, Otavio

PY - 2011/4/20

Y1 - 2011/4/20

N2 - According to the mathematical relativist, mathematical statements, if true, are relatively true only - that is, they are true relative to (i) the specifi cation of concepts and theories that characterize the relevant mathematical domain, (ii) the mathematical framework in which such mathematical truths are formulated, and (iii) the logic that is employed in the derivation of such truths. This chapter surveys mathematical relativism and its signifi cance. First, it clarifi es what mathematical relativism is not. It then examines a formulation of the view in which conceptual, structural, and logical relativity play a central role, but which still preserves the objectivity of mathematics. The implications of mathematical relativism for the ontology of mathematics are then considered. While some forms of Platonism and nominalism in mathematics are compatible with mathematical relativism, others are not. Finally, some remarks about the signifi cance of mathematical relativism conclude the chapter.

AB - According to the mathematical relativist, mathematical statements, if true, are relatively true only - that is, they are true relative to (i) the specifi cation of concepts and theories that characterize the relevant mathematical domain, (ii) the mathematical framework in which such mathematical truths are formulated, and (iii) the logic that is employed in the derivation of such truths. This chapter surveys mathematical relativism and its signifi cance. First, it clarifi es what mathematical relativism is not. It then examines a formulation of the view in which conceptual, structural, and logical relativity play a central role, but which still preserves the objectivity of mathematics. The implications of mathematical relativism for the ontology of mathematics are then considered. While some forms of Platonism and nominalism in mathematics are compatible with mathematical relativism, others are not. Finally, some remarks about the signifi cance of mathematical relativism conclude the chapter.

KW - "the Russell set exists"

KW - Conceptual, Structural and Logical Relativity in Mathematics

KW - Mathematical Relativism and Mathematical Objectivity

KW - Mathematical Relativism and the Ontology of Mathematics: Nominalism

KW - Mathematical Relativism and the Ontology of Mathematics: Platonism

KW - Mathematical relativism is the view according to which every mathematical

KW - Mathematical Relativism: Does Everything Go In Mathematics?

KW - Relativism in set theory and mathematics

KW - The Significance of Mathematical Relativism

KW - Typically, the set theory one considers depends on the underlying

UR - http://www.scopus.com/inward/record.url?scp=84885719198&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885719198&partnerID=8YFLogxK

U2 - 10.1002/9781444392494.ch28

DO - 10.1002/9781444392494.ch28

M3 - Chapter

SN - 9781405190213

SP - 553

EP - 568

BT - A Companion to Relativism

PB - Wiley-Blackwell

ER -