Full Idea
The real numbers may be introduced by abstraction as ratios of quantities. ..They are not defined by Dedekind cuts; rather, the cuts constitute a domain with the properties that are a necessary precondition.
Gist of Idea
The real numbers may be introduced by abstraction as ratios of quantities
Source
report of Bob Hale (Reals by Abstraction [1998]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' 3.3
Book Reference
Hale,B/Wright,C: 'The Reason's Proper Study' [OUP 2003], p.27
A Reaction
This is Hale's neo-logicist attempt to derive the real numbers from Hume's Principle.