Frege, the complex numbers, and the identity of indiscernibles

Logique Et Analyse 53 (209):51-60 (2010)
Download Edit this record How to cite View on PhilPapers
Abstract
There are mathematical structures with elements that cannot be distinguished by the properties they have within that structure. For instance within the field of complex numbers the two square roots of −1, i and −i, have the same algebraic properties in that field. So how do we distinguish between them? Imbedding the complex numbers in a bigger structure, the quaternions, allows us to algebraically tell them apart. But a similar problem appears for this larger structure. There seems to be always a background and a context that we rely upon. Thus mathematicians naturally make use of Kantian intuition and references fixed by names and denotations. I argue that such features cannot be avoided.
PhilPapers/Archive ID
WENFTC
Revision history
Archival date: 2017-01-02
View upload history
References found in this work BETA
Naming and Necessity.Kripke, Saul A.

View all 14 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Added to PP index
2013-12-19

Total views
59 ( #34,367 of 43,916 )

Recent downloads (6 months)
17 ( #32,808 of 43,916 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.