*Charles S. Chihara*

- Published in print:
- 1991
- Published Online:
- November 2003
- ISBN:
- 9780198239758
- eISBN:
- 9780191597190
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198239750.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

A continuation of the study of mathematical existence begun in Ontology and the Vicious‐Circle Principle (published in 1973); in the present work, Quine's indispensability argument is rebutted by the ...
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A continuation of the study of mathematical existence begun in Ontology and the Vicious‐Circle Principle (published in 1973); in the present work, Quine's indispensability argument is rebutted by the development of a new nominalistic version of mathematics (the Constructibility Theory) that is specified as an axiomatized theory formalized in a many‐sorted first‐order language. What is new in the present work is its abandonment of the predicative restrictions of the earlier work and its much greater attention to the applications of mathematics in science and everyday life. The book also contains detailed discussions of rival views (Mathematical Structuralism, Field's Instrumentalism, Burgess's Moderate Realism, Maddy's Set Theoretical Realism, and Kitcher's Ideal Agent account of mathematics), in which many comparisons with the Constructibility Theory are made.Less

A continuation of the study of mathematical existence begun in *Ontology and the Vicious‐Circle Principle* (published in 1973); in the present work, Quine's indispensability argument is rebutted by the development of a new nominalistic version of mathematics (the Constructibility Theory) that is specified as an axiomatized theory formalized in a many‐sorted first‐order language. What is new in the present work is its abandonment of the predicative restrictions of the earlier work and its much greater attention to the applications of mathematics in science and everyday life. The book also contains detailed discussions of rival views (Mathematical Structuralism, Field's Instrumentalism, Burgess's Moderate Realism, Maddy's Set Theoretical Realism, and Kitcher's Ideal Agent account of mathematics), in which many comparisons with the Constructibility Theory are made.

*Charles S. Chihara*

- Published in print:
- 1991
- Published Online:
- November 2003
- ISBN:
- 9780198239758
- eISBN:
- 9780191597190
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198239750.003.0007
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

The first of six chapters in which rival views are critically evaluated and compared with the Constructibility view described in earlier chapters. The views considered here (forms of ‘Structuralism’) ...
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The first of six chapters in which rival views are critically evaluated and compared with the Constructibility view described in earlier chapters. The views considered here (forms of ‘Structuralism’) are those of Stewart Shapiro and Michael Resnik. A number of difficulties with these two views are detailed and it is explained how the Constructibility Theory is not troubled by the problems that Structuralism was explicitly developed to resolve.Less

The first of six chapters in which rival views are critically evaluated and compared with the Constructibility view described in earlier chapters. The views considered here (forms of ‘Structuralism’) are those of Stewart Shapiro and Michael Resnik. A number of difficulties with these two views are detailed and it is explained how the Constructibility Theory is not troubled by the problems that Structuralism was explicitly developed to resolve.