Frege's cardinals and neo-logicism

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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 what an acceptable neo-logicistic theory of valueranges might look like, successfully implementing this alternative approach is impossible.

Original languageEnglish (US)
Article numbernkv029
Pages (from-to)60-90
Number of pages31
JournalPhilosophia Mathematica
Issue number1
StatePublished - Feb 1 2016

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