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

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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

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