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  1. Frege's Cardinals and Neo-Logicism.Roy T. Cook - 2016 - Philosophia Mathematica 24 (1):60-90.
    Gottlob Frege defined cardinal numbers in terms of value-ranges governed by the inconsistent Basic Law V. Neo-logicists have revived something like Frege's original project by introducing cardinal numbers as primitive objects, governed by Hume's Principle. A neo-logicist foundation for set theory, however, requires a consistent theory of value-ranges of some sort. Thus, it is natural to ask whether we can reconstruct the cardinal numbers by retaining Frege's definition and adopting an alternative consistent principle governing value-ranges. Given some natural assumptions regarding (...)
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  • Paolo Mancosu.*Abstraction and Infinity. [REVIEW]Roy T. Cook & Michael Calasso - 2019 - Philosophia Mathematica 27 (1):125-152.
    MancosuPaolo.* *ion and Infinity. Oxford University Press, 2016. ISBN: 978-0-19-872462-9. Pp. viii + 222.
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