Philosophia Mathematica 10 (3):304-323 (2002)

Defining the real numbers by abstraction as ratios of quantities gives prominence to then- applications in just the way that Frege thought we should. But if all the reals are to be obtained in this way, it is necessary to presuppose a rich domain of quantities of a land we cannot reasonably assume to be exemplified by any physical or other empirically measurable quantities. In consequence, an explanation of the applications of the reals, defined in this way, must proceed indirectly. This paper explains the main complications involved and answers the main objections advanced in Batitsky's paper in this issue.
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DOI 10.1093/philmat/10.3.304
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References found in this work BETA

Die Grundlagen der Arithmetik.Gottlob Frege - 1988 - Felix Meiner Verlag.
Frege: Philosophy of Mathematics.Michael Dummett - 1991 - Harvard University Press.
Frege: Philosophy of Mathematics. [REVIEW]Charles Parsons - 1996 - Philosophical Review 105 (4):540.

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What is Neologicism?Bernard Linsky & Edward N. Zalta - 2006 - Bulletin of Symbolic Logic 12 (1):60-99.

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