Frege's Theory of Real Numbers

History and Philosophy of Logic 8 (1):25--44 (1987)

Authors
Peter Simons
Trinity College, Dublin
Abstract
Frege's theory of real numbers has undeservedly received almost no attention, in part because what we have is only a fragment. Yet his theory is interesting for the light it throws on logicism, and it is quite different from standard modern approaches. Frege polemicizes vigorously against his contemporaries, sketches the main features of his own radical alternative, and begins the formal development. This paper summarizes and expounds what he has to say, and goes on to reconstruct the most important steps which he is likely to have subsequently taken. The various difficulties facing his theory in this reconstruction are outlined, and some surprising consequences drawn about the nature of his logicism
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DOI 10.1080/01445348708837106
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Reals by Abstraction.Bob Hale - 2000 - Philosophia Mathematica 8 (2):100--123.
The State of the Economy: Neo-Logicism and Inflationt.Roy T. Cook - 2002 - Philosophia Mathematica 10 (1):43-66.
Frege's Approach to the Foundations of Analysis (1874–1903).Matthias Schirn - 2013 - History and Philosophy of Logic 34 (3):266-292.

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