Synthese

, Volume 143, Issue 3, pp 291–307 | Cite as

Individuation of objects – a problem for structuralism?

Article

Abstract.

This paper identifies two aspects of the structuralist position of S. Shapiro which are in conflict with the actual practice of mathematics. The first problem follows from Shapiro’s identification of isomorphic structures. Here I consider the so called K-group, as defined by A. Grothendieck in algebraic geometry, and a group which is isomorphic to the K-group, and I argue that these are not equal. The second problem concerns Shapiro’s claim that it is not possible to identify objects in a structure except through the relations and functions that are defined on the structure in which the object has a place. I argue that, in the case of the definition of the so called direct image of a function, it is possible to individuate objects in structures.

Keywords

Algebraic Geometry Actual Practice Direct Image Structuralist Position Problem Concern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Dept. of Curriculum ResearchDanish University of EducationDenmark

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