- 北海道大学哲学会 = The Philosophical Society of Hokkaido University
- 哲学 (ISSN:02872560)
- vol.40, pp.45-63, 2004-07-18
The aim of this paper is to examine Shapiro's structuralism in philosophy of mathematics and to show several difficulties in his structuralism. He adopts ante rem structuralism which is based upon his realism. After delineating his arguments I will point out some advantages of his structuralism, which become apparent when it is compared especially with a traditional type of mathematical Platonism. Then I will show, by using examples taken from mathematics, that there are some ambiguities in his uses of the basic notions, such as structure, system, exemplification and place. Finally I criticize his axiomatic theory of structure mainly because it relies upon too many undefined terms, and show that in his ontological views there is an underlying discrepancy between his ante rem structuralism and his set-theoretic approach to structures.