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 language | English (US) |
|---|---|
| Title of host publication | A Companion to Relativism |
| Publisher | Wiley-Blackwell |
| Pages | 553-568 |
| Number of pages | 16 |
| ISBN (Print) | 9781405190213 |
| DOIs | |
| State | Published - Apr 20 2011 |
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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
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 proceeding › Chapter
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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
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BT - A Companion to Relativism
PB - Wiley-Blackwell
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