Notre Dame Journal of Formal Logic

Cardinality and Acceptable Abstraction

Roy T. Cook and Øystein Linnebo

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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.

Article information

Notre Dame J. Formal Logic, Volume 59, Number 1 (2018), 61-74.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30} 00A30: Philosophy of mathematics [See also 03A05]

logicism abstraction bad company Hume’s Principle


Cook, Roy T.; Linnebo, Øystein. Cardinality and Acceptable Abstraction. Notre Dame J. Formal Logic 59 (2018), no. 1, 61--74. doi:10.1215/00294527-2017-0012.

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