Reals by Abstraction

Philosophia Mathematica 8 (2):100--123 (2000)
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Abstract

On the neo-Fregean approach to the foundations of mathematics, elementary arithmetic is analytic in the sense that the addition of a principle wliich may be held to IMJ explanatory of the concept of cardinal number to a suitable second-order logical basis suffices for the derivation of its basic laws. This principle, now commonly called Hume's principle, is an example of a Fregean abstraction principle. In this paper, I assume the correctness of the neo-Fregean position on elementary aritlunetic and seek to explain one way in which it may be extended to encompass the theory of real numbers, introducing the reals, by means of suitable further abstraction principles, as ratios of quantities.

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Citations of this work

Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.
Neo-Fregeanism: An Embarrassment of Riches.Alan Weir - 2003 - Notre Dame Journal of Formal Logic 44 (1):13-48.
Frege meets dedekind: A neologicist treatment of real analysis.Stewart Shapiro - 2000 - Notre Dame Journal of Formal Logic 41 (4):335--364.
Is Hume's principle analytic?Crispin Wright - 1999 - Notre Dame Journal of Formal Logic 40 (1):307-333.
Is Hume's Principle Analytic?Crispin Wright - 1999 - Notre Dame Journal of Formal Logic 40 (1):6-30.

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References found in this work

Frege's conception of numbers as objects.Crispin Wright - 1983 - [Aberdeen]: Aberdeen University Press.
Frege.Michael Dummett - 1973 - Cambridge, Mass.: Harvard University Press.
Frege’s Conception of Numbers as Objects.Crispin Wright - 1983 - Critical Philosophy 1 (1):97.
The limits of abstraction.Kit Fine - 2002 - New York: Oxford University Press. Edited by Matthias Schirn.
Frege: Philosophy of Mathematics.Michael DUMMETT - 1991 - Philosophy 68 (265):405-411.

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