Neo-Fregean Foundations for Real Analysis: Some Reflections on Frege's Constraint

now of a number of ways of developing Real Analysis on a basis of abstraction principles and second-order logic. One, outlined by Shapiro in his contribution to this volume, mimics Dedekind in identifying the reals with cuts in the series of rationals under their natural order. The result is an essentially structuralist conception of the reals. An earlier approach, developed by Hale Reals by Abstraction", differs by placing additional emphasis upon what I here term Frege's Constraint, that a satisfactory foundation for any branch of mathematics should somehow so explain its basic concepts that their applications are immediate. This paper is concerned with the meaning of and motivation for this constraint. Structuralism has to represent the application of a mathematical theory as always posterior to the understanding of it, turning upon the appreciation of structural affinities between the structure it concerns and a domain to which it is to be applied. There is therefore a c...

• Type: Journal
• Year: 2000
• Where: NDJFL
• Authors: Crispin Wright
• Keywords: Basic Concepts, Hale Reals, NDJFL 2000, Reals