Chapter

On a Question of Frege's About Right‐Ordered Groups*

Michael Dummett, S. A. Adeleke and P. M. Neumann

in Frege and Other Philosophers

Published in print January 1996 | ISBN: 9780198236283
Published online November 2003 | e-ISBN: 9780191597343 | DOI: http://dx.doi.org/10.1093/019823628X.003.0003
On a Question of Frege's About Right‐Ordered Groups*

More Like This

Show all results sharing this subject:

  • History of Western Philosophy

GO

Show Summary Details

Preview

Concerns a problem posed, but not solved, by Frege in part III of his Grundgesetze. As a preliminary to defining ‘real number’, Frege attempts to analyse the notion of a quantitative domain (e.g. that of distances or of masses). He was unaware of the previous attempt of Otto Holder to do this; it is remarked how much weaker Frege's assumptions were in deriving theorems than Holder's. Frege deals with groups on which there is a right‐invariant semilinear ordering, although he does not use this terminology. He is uncertain whether it can be deduced that the ordering is also left‐invariant, and proves as much as possible without invoking the assumption that it is. The independence proof, due to Dr Peter Neumann, establishes that it could not be deduced.

Keywords: Archimedean; complete; Frege; group; Grundgesetze; Holder; left‐invariant; linear; Peter Neumann; right‐invariant; semilinear order

Chapter.  5285 words.  Illustrated.

Subjects: History of Western Philosophy

Full text: subscription required

How to subscribe Recommend to my Librarian

Buy this work at Oxford University Press »

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.