Chapter

A Problem for Present-Day Mathematics

Steven French and Décio Krause

in Identity in Physics

Published in print June 2006 | ISBN: 9780199278244
Published online September 2006 | e-ISBN: 9780191603952 | DOI: http://dx.doi.org/10.1093/0199278245.003.0006
 A Problem for Present-Day Mathematics

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This chapter explores Manin’s suggestion that formal axioms for indiscernible objects in physics should be given. Collections of such objects cannot be regarded as sets, since such sets are typically taken to be collections of distinguishable objects. The theory of identity in classical logic and set theory is considered to lay the groundwork for the discussion of the corresponding theory for (truly) indiscernible objects in Chapter 7. The usual ways of accommodating such objects in standard logic and mathematics are critically assessed, with emphasis on the concept of indiscernibility in a structure.

Keywords: Identity of Indiscernibles; indiscernibility; structure

Chapter.  15676 words. 

Subjects: Philosophy of Science

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