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Ideas from 'Reals by Abstraction' by Bob Hale [1998], by Theme Structure

[found in 'The Reason's Proper Study' by Hale,B/Wright,C [OUP 2003,978-0-19-926632-6]].

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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10632 The real numbers may be introduced by abstraction as ratios of quantities
                        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.
                        From: report of Bob Hale (Reals by Abstraction [1998]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' 3.3
                        A reaction: This is Hale's neo-logicist attempt to derive the real numbers from Hume's Principle.