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    Any consistent fragment of Basic Law V (e.g., New Foundat... — Carmelics
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    Supports→Frege's Basic Law V cannot be true

    Any consistent fragment of Basic Law V (e.g., New Foundations or Hume's Principle) requires abandoning the universality that made Basic Law V philosophically significant to Frege.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Frege's philosophical motivation for BLV was to ground arithmetic in logic via universal abstraction principles applying to all concepts without restriction.
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    • 2.Any consistent fragment (NFU, Hume's Principle) must restrict the domain of concepts or predicates to which the abstraction principle applies.
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    • 3.Restricting abstraction principles abandons the universalist vision that gave BLV its philosophical significance and appeal to Frege.
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    Reasons Against

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    • 1.Hume's Principle achieves Frege's core goal: deriving Peano arithmetic from a single logical abstraction principle without inconsistency.
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    • 2.The philosophical significance of BLV lies in reducing numbers to logical objects, not in the cardinality of the domain—restrictions preserve this core insight.
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    • 3.Restrictions on quantifier domains do not defeat universality if the principle holds uniformly for all concepts within legitimately characterizable domains.
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    Related

    Any consistent fragment (NFU, Hume's Principle) must restrict the domain of conc...Frege's Basic Law V cannot be trueFrege's philosophical motivation for BLV was to ground arithmetic in logic via u...Hume's Principle achieves Frege's core goal: deriving Peano arithmetic from a si...
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    Restricting abstraction principles abandons the universalist vision that gave BL...Restrictions on quantifier domains do not defeat universality if the principle h...The philosophical significance of BLV lies in reducing numbers to logical object...

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