Open Access
2018 Cardinality and Acceptable Abstraction
Roy T. Cook, Øystein Linnebo
Notre Dame J. Formal Logic 59(1): 61-74 (2018). DOI: 10.1215/00294527-2017-0012


It is widely thought that the acceptability of an abstraction principle is a feature of the cardinalities at which it is satisfiable. This view is called into question by a recent observation by Richard Heck. We show that a fix proposed by Heck fails but we analyze the interesting idea on which it is based, namely that an acceptable abstraction has to “generate” the objects that it requires. We also correct and complete the classification of proposed criteria for acceptable abstraction.


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Roy T. Cook. Øystein Linnebo. "Cardinality and Acceptable Abstraction." Notre Dame J. Formal Logic 59 (1) 61 - 74, 2018.


Received: 15 July 2014; Accepted: 16 January 2015; Published: 2018
First available in Project Euclid: 16 November 2017

zbMATH: 06848191
MathSciNet: MR3744351
Digital Object Identifier: 10.1215/00294527-2017-0012

Primary: 00A30 , 03A05

Keywords: abstraction , bad company , Hume’s Principle , logicism

Rights: Copyright © 2018 University of Notre Dame

Vol.59 • No. 1 • 2018
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