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Rov T. Cook, The State of the Economy: Neo-logicism and Inflationt, Philosophia Mathematica, Volume 10, Issue 1, February 2002, Pages 43–66, https://doi.org/10.1093/philmat/10.1.43
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Abstract
In this paper I examine the prospects for a successful neo–logicist reconstruction of the real numbers, focusing on Bob Hale's use of a cut-abstraction principle. There is a serious problem plaguing Hale's project. Natural generalizations of this principle imply that there are far more objects than one would expect from a position that stresses its epistemological conservativeness. In other words, the sort of abstraction needed to obtain a theory of the reals is rampantly inflationary. I also indicate briefly why this problem is likely to reappear in any neo–logicist reconstruction of real analysis.