Cardinality and Acceptable Abstraction

Roy T. Cook, Øystein Linnebo

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)61-74
Number of pages14
JournalNotre Dame Journal of Formal Logic
Issue number1
StatePublished - 2018

Bibliographical note

Publisher Copyright:
© 2018 by University of Notre Dame.


  • Abstraction
  • Bad company
  • Hume’s Principle
  • Logicism


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